On the origins of generalized fractional calculus

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia

2015-11-01

In Fractional Calculus (FC), as in the (classical) Calculus, the notions of derivatives and integrals (of first, second, etc. or arbitrary, incl. non-integer order) are basic and co-related. One of the most frequent approach in FC is to define first the Riemann-Liouville (R-L) integral of fractional order, and then by means of suitable integer-order differentiation operation applied over it (or under its sign) a fractional derivative is defined - in the R-L sense (or in Caputo sense). The first mentioned (R-L type) is closer to the theoretical studies in analysis, but has some shortages - from the point of view of interpretation of the initial conditions for Cauchy problems for fractional differential equations (stated also by means of fractional order derivatives/ integrals), and also for the analysts' confusion that such a derivative of a constant is not zero in general. The Caputo (C-) derivative, arising first in geophysical studies, helps to overcome these problems and to describe models of applied problems with physically consistent initial conditions. The operators of the Generalized Fractional Calculus - GFC (integrals and derivatives) are based on commuting m-tuple (m = 1, 2, 3, …) compositions of operators of the classical FC with power weights (the so-called Erdélyi-Kober operators), but represented in compact and explicit form by means of integral, integro-differential (R-L type) or differential-integral (C-type) operators, where the kernels are special functions of most general hypergeometric kind. The foundations of this theory are given in Kiryakova 18. In this survey we present the genesis of the definitions of the GFC - the generalized fractional integrals and derivatives (of fractional multi-order) of R-L type and Caputo type, analyze their properties and applications. Their special cases are all the known operators of classical FC, their generalizations introduced by other authors, the hyper-Bessel differential operators of higher integer order m as a multi-order (1, 1,…, 1), the Gelfond-Leontiev generalized differentiation operators, many other integral and differential operators in Calculus that have been used in various topics, some of them not related to FC at all, others involved in differential and integral equations for treating fractional order models.

Fractional calculus in hydrologic modeling: A numerical perspective

PubMed Central

Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

2013-01-01

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

An ellipsoidal calculus based on propagation and fusion.

PubMed

Ros, L; Sabater, A; Thomas, F

2002-01-01

Presents an ellipsoidal calculus based solely on two basic operations: propagation and fusion. Propagation refers to the problem of obtaining an ellipsoid that must satisfy an affine relation with another ellipsoid, and fusion to that of computing the ellipsoid that tightly bounds the intersection of two given ellipsoids. These two operations supersede the Minkowski sum and difference, affine transformation and intersection tight bounding of ellipsoids on which other ellipsoidal calculi are based. Actually, a Minkowski operation can be seen as a fusion followed by a propagation and an affine transformation as a particular case of propagation. Moreover, the presented formulation is numerically stable in the sense that it is immune to degeneracies of the involved ellipsoids and/or affine relations. Examples arising when manipulating uncertain geometric information in the context of the spatial interpretation of line drawings are extensively used as a testbed for the presented calculus.

Operating the production calculus: ordering a production system in the print industry.

PubMed

Button, Graham; Sharrock, Wes

2002-06-01

The topic of shop-floor work has been extensively examined within sociology. However, the organizational structures within which this work takes place have, in the most part, been taken as unexamined givens. Yet, their operation is also the shop-floor work of some people. This paper examines the way in which the stable organizational structures within which shop-floor work takes place are achieved. It is based upon a fieldwork investigation of a large commercial printer and focuses upon the collaborative work of those who are involved in scheduling the production of a job and their use of 'the production calculus' in planning the work of the site. The print industry is undergoing considerable technological change and scheduling technologies have been developed to automate this work. However, there has been little take up of these technologies and the paper also considers how the characteristics of operating the production calculus in practice may account for this.

Varieties of operator manipulation. [for solving differential equations and calculating finite differences

NASA Technical Reports Server (NTRS)

Doohovskoy, A.

1977-01-01

A change in MACSYMA syntax is proposed to accommodate the operator manipulators necessary to implement direct and indirect methods for the solution of differential equations, calculus of finite differences, and the fractional calculus, as well as their modern counterparts. To illustrate the benefits and convenience of this syntax extension, an example is given to show how MACSYMA's pattern-matching capability can be used to implement a particular set of operator identities which can then be used to obtain exact solutions to nonlinear differential equations.

Fractional calculus in bioengineering, part 3.

PubMed

Magin, Richard L

2004-01-01

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub-threshold nerve propagation. By expanding the range of mathematical operations to include fractional calculus, we can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner. In Part 2 of this review (Crit Rev Biomed Eng 2004; 32(1):105-193), fractional calculus was applied to problems in nerve stimulation, dielectric relaxation, and viscoelastic materials by extending the governing differential equations to include fractional order terms. In this third and final installment, we consider distributed systems that represent shear stress in fluids, heat transfer in uniform one-dimensional media, and subthreshold nerve depolarization. Classic electrochemical analysis and impedance spectroscopy are also reviewed from the perspective of fractional calculus, and selected examples from recent studies in neuroscience, bioelectricity, and tissue biomechanics are analyzed to illustrate the vitality of the field.

Miniature endoscopic optical coherence tomography for calculus detection.

PubMed

Kao, Meng-Chun; Lin, Chun-Li; Kung, Che-Yen; Huang, Yi-Fung; Kuo, Wen-Chuan

2015-08-20

The effective treatment of periodontitis involves the detection and removal of subgingival dental calculus. However, subgingival calculus is more difficult to detect than supragingival calculus because it is firmly attached to root surfaces within periodontal pockets. To achieve a smooth root surface, clinicians often remove excessive amounts of root structure because of decreased visibility. In addition, enamel pearl, a rare type of ectopic enamel formation on the root surface, can easily be confused with dental calculus in the subgingival environment. In this study, we developed a fiber-probe swept-source optical coherence tomography (SSOCT) technique and combined it with the quantitative measurement of an optical parameter [standard deviation (SD) of the optical coherence tomography (OCT) intensity] to differentiate subgingival calculus from sound enamel, including enamel pearl. Two-dimensional circumferential images were constructed by rotating the miniprobe (0.9 mm diameter) while acquiring image lines, and the adjacent lines in each rotation were stacked to generate a three-dimensional volume. In OCT images, compared to sound enamel and enamel pearls, dental calculus showed significant differences (P<0.001) in SD values. Finally, the receiver operating characteristic curve had a high capacity (area under the curve=0.934) for discriminating between healthy regions (including enamel pearl) and dental calculus.

A Lesson in Vectors "Plain" and Simple

ERIC Educational Resources Information Center

Bradshaw, David M.

2004-01-01

The United States Military Academy (USMA) has a four course core mathematics curriculum that is studied by all students. The third course is MA205, Calculus II; a multivariate calculus course filled with practical applications. During a Problem Solving Lab (PSL), students participated in a hands-on exercise with multiple vector operations,…

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

2016-02-01

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

Critical Analysis of the Mathematical Formalism of Theoretical Physics. II. Foundations of Vector Calculus

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2014-03-01

A critical analysis of the foundations of standard vector calculus is proposed. The methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is proved that the vector calculus is incorrect theory because: (a) it is not based on a correct methodological basis - the unity of formal logic and of rational dialectics; (b) it does not contain the correct definitions of ``movement,'' ``direction'' and ``vector'' (c) it does not take into consideration the dimensions of physical quantities (i.e., number names, denominate numbers, concrete numbers), characterizing the concept of ''physical vector,'' and, therefore, it has no natural-scientific meaning; (d) operations on ``physical vectors'' and the vector calculus propositions relating to the ''physical vectors'' are contrary to formal logic.

Consistency of the single calculus chain for climatological studies using long-term measurements from thessaloniki lidar station

NASA Astrophysics Data System (ADS)

Siomos, Nikolaos; Voudouri, Kalliopi A.; Filioglou, Maria; Giannakaki, Eleni; Amiridis, Vasilis; D'Amico, Giuseppe; Balis, Dimitris S.

2018-04-01

The long term analysis of 15 years of lidar data derived from a Raman lidar at Thessaloniki is presented here. All measurements have been processed with the latest version 4 of the EARLINET Single Calculus Chain algorithm and are compared with the results from the current operational retrieval algorithm. In this paper we investigate the consistency between the EARLINET database and SCC for the case of Thessaloniki and we identify the issues to be considered when switching from current operations to SCC.

General McChrystal’s Strategic Assessment: Evaluating the Operating Environment in Afghanistan in the Summer of 2009

DTIC Science & Technology

2011-07-01

relationship we had. I think that was part of their calculus .2 Previously, General Rodriguez spent more than a year as the US Operation Enduring Freedom (OEF...recently arrived coinci- dental to the change in USFOR-A leadership had key roles in the assessment. Marine Corps colonel James McGrath, ISAF’s CJ5...mine—Minister Wardak’s as- sessment was part of my calculus . While the situation is serious, success is still achievable. This starts with redefining

Geometry and physics of pseudodifferential operators on manifolds

NASA Astrophysics Data System (ADS)

Esposito, Giampiero; Napolitano, George M.

2016-09-01

A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: existence theorem for the function that generalizes the phase; analogue of Taylor's theorem; torsion and curvature terms in the symbolic calculus; the two kinds of derivative acting on smooth sections of the cotangent bundle of the Riemannian manifold; the concept of symbol as an equivalence class. Physical motivations and applications are then outlined, with emphasis on Green functions of quantum field theory and Parker's evaluation of Hawking radiation.

Two-parameter asymptotics in magnetic Weyl calculus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lein, Max

2010-12-15

This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter {epsilon}, the case of small coupling {lambda} to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols aremore » proven as (i) {epsilon}<< 1 and {lambda}<< 1, (ii) {epsilon}<< 1 and {lambda}= 1, as well as (iii) {epsilon}= 1 and {lambda}<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.« less

a Speculative Study on Negative-Dimensional Potential and Wave Problems by Implicit Calculus Modeling Approach

NASA Astrophysics Data System (ADS)

Chen, Wen; Wang, Fajie

Based on the implicit calculus equation modeling approach, this paper proposes a speculative concept of the potential and wave operators on negative dimensionality. Unlike the standard partial differential equation (PDE) modeling, the implicit calculus modeling approach does not require the explicit expression of the PDE governing equation. Instead the fundamental solution of physical problem is used to implicitly define the differential operator and to implement simulation in conjunction with the appropriate boundary conditions. In this study, we conjecture an extension of the fundamental solution of the standard Laplace and Helmholtz equations to negative dimensionality. And then by using the singular boundary method, a recent boundary discretization technique, we investigate the potential and wave problems using the fundamental solution on negative dimensionality. Numerical experiments reveal that the physics behaviors on negative dimensionality may differ on positive dimensionality. This speculative study might open an unexplored territory in research.

[Factors affecting residual stones after percutaneous nephrolithotomy in patients with renal calculus].

PubMed

Qiao, Mingzhou; Zhang, Haifang; Zhou, Chenlong

2015-11-24

To explore the factors affecting the residual stones after percutaneous nephrolithotomy (PCNL) in patients with renal calculus. A retrospective analysis was performed for 1 200 patients who were affected by renal calculus and treated with PCNL between Jan 2008 and May 2014 in People's Hospital of Anyang City. Among those patients, 16 were diagnosed as bilateral renal stone and had two successive operations. The size, location and number of stones, previous history of surgery, the degree of hydronephrosis, urinary infection were included in the univariate analysis. Significant factors in univariate analysis were included in the multivariate analysis to determine factors affecting stone residual. A total of 385 cases developed stone residual after surgery. The overall residual rate was 31.7%. In univariate analysis, renal pelvis combined with caliceal calculus (P=0.006), stone size larger than 4 cm (P=0.005), stone number more than 4 (P=0.002), the amount of bleeding more than 200 ml (P=0.025), operation time longer than 120 minutes (P=0.028) were associated with an increased rate of stone residual. When subjected to the Cox multivariate analysis, the independent risk factors for residual stones were renal pelvis combined with caliceal calculus (P=0.049), stone size larger than 4 cm (P=0.038) and stone number more than 4 (P=0.018). Factors affecting the incidence of residual stones after PCNL are the size, location and number of stones. Larger size stone and the presence of renal pelvis combined with caliceal calculus are significantly associated with residual stones. Nevertheless, stone number less than 4 indicates an increased stone clearance rate.

CYBER DETERRENCE

DTIC Science & Technology

2016-02-11

directed.36 Protected systems operating on secure networks will weigh into the adversaries calculus of risk and cost of their actions versus this... calculus deterring them from attack. Our extended defense with forts and lookouts searching outside the perimeter providing current intelligence of any...Last accessed 30 January 2016). 51 Phil Stewart , U.S. Defense Chief says pre-emptive action possible over cyber threat, Oct 11, 2012, http

The theory of pseudo-differential operators on the noncommutative n-torus

NASA Astrophysics Data System (ADS)

Tao, J.

2018-02-01

The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct analogy with the theory of pseudo-differential operators on finite-dimensional real vector spaces, one may derive a similar pseudo-differential calculus on noncommutative n-tori, and with the development of this calculus came many results concerning the local differential geometry of noncommutative tori for n=2,4, as shown in the groundbreaking paper in which the Gauss-Bonnet theorem on the noncommutative two-torus is proved and later papers. Certain details of the proofs in the original derivation of the calculus were omitted, such as the evaluation of oscillatory integrals, so we make it the objective of this paper to fill in all the details. After reproving in more detail the formula for the symbol of the adjoint of a pseudo-differential operator and the formula for the symbol of a product of two pseudo-differential operators, we extend these results to finitely generated projective right modules over the noncommutative n-torus. Then we define the corresponding analog of Sobolev spaces and prove equivalents of the Sobolev and Rellich lemmas.

Anisotropic fractal media by vector calculus in non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

Abdominal fat distribution on computed tomography predicts ureteric calculus fragmentation by shock wave lithotripsy.

PubMed

Juan, Hsu-Cheng; Lin, Hung-Yu; Chou, Yii-Her; Yang, Yi-Hsin; Shih, Paul Ming-Chen; Chuang, Shu-Mien; Shen, Jung-Tsung; Juan, Yung-Shun

2012-08-01

To assess the effects of abdominal fat on shock wave lithotripsy (SWL). We used pre-SWL unenhanced computed tomography (CT) to evaluate the impact of abdominal fat distribution and calculus characteristics on the outcome of SWL. One hundred and eighty-five patients with a solitary ureteric calculus treated with SWL were retrospectively reviewed. Each patient underwent unenhanced CT within 1 month before SWL treatment. Treatment outcomes were evaluated 1 month later. Unenhanced CT parameters, including calculus surface area, Hounsfield unit (HU) density, abdominal fat area and skin to calculus distance (SSD) were analysed. One hundred and twenty-eight of the 185 patients were found to be calculus-free following treatment. HU density, total fat area, visceral fat area and SSD were identified as significant variables on multivariate logistic regression analysis. The receiver-operating characteristic analyses showed that total fat area, para/perirenal fat area and visceral fat area were sensitive predictors of SWL outcomes. This study revealed that higher quantities of abdominal fat, especially visceral fat, are associated with a lower calculus-free rate following SWL treatment. Unenhanced CT is a convenient technique for diagnosing the presence of a calculus, assessing the intra-abdominal fat distribution and thereby helping to predict the outcome of SWL. • Unenhanced CT is now widely used to assess ureteric calculi. • The same CT protocol can provide measurements of abdominal fat distribution. • Ureteric calculi are usually treated by shock wave lithotripsy (SWL). • Greater intra-abdominal fat stores are generally associated with poorer SWL results.

Bayesian Inference for Source Reconstruction: A Real-World Application

DTIC Science & Technology

2014-09-25

deliberately or acci- dentally . Two examples of operational monitoring sensor networks are the deployment of biological sensor arrays by the Department of...remarkable paper, Cox [16] demonstrated that proba- bility theory, when interpreted as logic, is the only calculus that conforms to a consistent theory...of inference. This demonstration provides the firm logical basis for asserting that probability calculus is the unique quantitative theory of

Calculation of spontaneous emission from a V-type three-level atom in photonic crystals using fractional calculus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Chih-Hsien; Hsieh, Wen-Feng; Institute of Electro-Optical Science and Engineering, National Cheng Kung University, 1 Dahsueh Rd., Tainan 701, Taiwan

2011-07-15

Fractional time derivative, an abstract mathematical operator of fractional calculus, is used to describe the real optical system of a V-type three-level atom embedded in a photonic crystal. A fractional kinetic equation governing the dynamics of the spontaneous emission from this optical system is obtained as a fractional Langevin equation. Solving this fractional kinetic equation by fractional calculus leads to the analytical solutions expressed in terms of fractional exponential functions. The accuracy of the obtained solutions is verified through reducing the system into the special cases whose results are consistent with the experimental observation. With accurate physical results and avoidingmore » the complex integration for solving this optical system, we propose fractional calculus with fractional time derivative as a better mathematical method to study spontaneous emission dynamics from the optical system with non-Markovian dynamics.« less

Relativistic differential-difference momentum operators and noncommutative differential calculus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mir-Kasimov, R. M., E-mail: mirkr@theor.jinr.ru

2013-09-15

The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics (QM) in the Relativistic Configuration Space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated as the independent term of the total Hamiltonian. This relativistic kinetic energy term is not distinguishing in form from its nonrelativistic counterpart. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generating function for the matrix elements of the unitary irrepsmore » of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS.« less

PREFACE: Fractional Differentiation and its Applications (FDA08) Fractional Differentiation and its Applications (FDA08)

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Tenreiro Machado, J. A.

2009-10-01

The international workshop, Fractional Differentiation and its Applications (FDA08), held at Cankaya University, Ankara, Turkey on 5-7 November 2008, was the third in an ongoing series of conferences dedicated to exploring applications of fractional calculus in science, engineering, economics and finance. Fractional calculus, which deals with derivatives and integrals of any order, is now recognized as playing an important role in modeling multi-scale problems that span a wide range of time or length scales. Fractional calculus provides a natural link to the intermediate-order dynamics that often reflects the complexity of micro- and nanostructures through fractional-order differential equations. Unlike the more established techniques of mathematical physics, the methods of fractional differentiation are still under development; while it is true that the ideas of fractional calculus are as old as the classical integer-order differential operators, modern work is proceeding by both expanding the capabilities of this mathematical tool and by widening its range of applications. Hence, the interested reader will find papers here that focus on the underlying mathematics of fractional calculus, that extend fractional-order operators into new domains, and that apply well established methods to experimental and theoretical problems. The organizing committee invited presentations from experts representing the international community of scholars in fractional calculus and welcomed contributions from the growing number of researchers who are applying fractional differentiation to complex technical problems. The selection of papers in this topical issue of Physica Scripta reflects the success of the FDA08 workshop, with the emergence of a variety of novel areas of application. With these ideas in mind, the guest editors would like to honor the many distinguished scientists that have promoted the development of fractional calculus and, in particular, Professor George M Zaslavsky who supported this special issue but passed away recently. The organizing committee wishes to thank the sponsors and supporters of FDA08, namely Cankaya University represented by the President of the Board of Trustees Sitki Alp and Rector Professor Ziya B Güvenc, The Scientfic and Technological Research Council of Turkey (TUBITAK) and the IFAC for providing the resources needed to hold the workshop, the invited speakers for sharing their expertise and knowledge of fractional calculus, and the participants for their enthusiastic contributions to the discussions and debates.

Boolean integral calculus

NASA Technical Reports Server (NTRS)

Tucker, Jerry H.; Tapia, Moiez A.; Bennett, A. Wayne

1988-01-01

The concept of Boolean integration is developed, and different Boolean integral operators are introduced. Given the changes in a desired function in terms of the changes in its arguments, the ways of 'integrating' (i.e. realizing) such a function, if it exists, are presented. The necessary and sufficient conditions for integrating, in different senses, the expression specifying the changes are obtained. Boolean calculus has applications in the design of logic circuits and in fault analysis.

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

NASA Astrophysics Data System (ADS)

Hâkansson, P.; Mella, M.; Bressanini, Dario; Morosi, Gabriele; Patrone, Marta

2006-11-01

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with Itô calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Itô calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.

Computational approach to Thornley's problem by bivariate operational calculus

NASA Astrophysics Data System (ADS)

Bazhlekova, E.; Dimovski, I.

2012-10-01

Thornley's problem is an initial-boundary value problem with a nonlocal boundary condition for linear onedimensional reaction-diffusion equation, used as a mathematical model of spiral phyllotaxis in botany. Applying a bivariate operational calculus we find explicit representation of the solution, containing two convolution products of special solutions and the arbitrary initial and boundary functions. We use a non-classical convolution with respect to the space variable, extending in this way the classical Duhamel principle. The special solutions involved are represented in the form of fast convergent series. Numerical examples are considered to show the application of the present technique and to analyze the character of the solution.

Anisotropic fractal media by vector calculus in non-integer dimensional space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2014-08-15

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensionalmore » space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.« less

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

An Analysis of Naval Officer Student Academic Performance in the Operations Analysis Curriculum in Relationship to Academic Profile Codes and other Factors.

DTIC Science & Technology

1985-09-01

Code 0 Physics (Calculus-Based) or Physical Science niscioline 0----------------------------------------- lR averaqe...opportunity for fficers with inadequate math- ematical and physical science backgrounds to establish a good math foundation to be able to gualify for a...technical curricu2um [Ref. 5: page 36]. There is also a six week refresher available that is designed to rapidly cover the calculus and physics

Quantum stochastic calculus associated with quadratic quantum noises

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr; Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in

2016-02-15

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculusmore » extends the Hudson-Parthasarathy quantum stochastic calculus.« less

Numerical operator calculus in higher dimensions.

PubMed

Beylkin, Gregory; Mohlenkamp, Martin J

2002-08-06

When an algorithm in dimension one is extended to dimension d, in nearly every case its computational cost is taken to the power d. This fundamental difficulty is the single greatest impediment to solving many important problems and has been dubbed the curse of dimensionality. For numerical analysis in dimension d, we propose to use a representation for vectors and matrices that generalizes separation of variables while allowing controlled accuracy. Basic linear algebra operations can be performed in this representation using one-dimensional operations, thus bypassing the exponential scaling with respect to the dimension. Although not all operators and algorithms may be compatible with this representation, we believe that many of the most important ones are. We prove that the multiparticle Schrödinger operator, as well as the inverse Laplacian, can be represented very efficiently in this form. We give numerical evidence to support the conjecture that eigenfunctions inherit this property by computing the ground-state eigenfunction for a simplified Schrödinger operator with 30 particles. We conjecture and provide numerical evidence that functions of operators inherit this property, in which case numerical operator calculus in higher dimensions becomes feasible.

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

NASA Astrophysics Data System (ADS)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

About Schrödinger Equation on Fractals Curves Imbedding in R 3

NASA Astrophysics Data System (ADS)

Golmankhaneh, Alireza Khalili; Golmankhaneh, Ali Khalili; Baleanu, Dumitru

2015-04-01

In this paper we introduced the quantum mechanics on fractal time-space. In a suggested formalism the time and space vary on Cantor-set and Von-Koch curve, respectively. Using Feynman path method in quantum mechanics and F α -calculus we find Schrëdinger equation on on fractal time-space. The Hamiltonian and momentum fractal operator has been indicated. More, the continuity equation and the probability density is given in view of F α -calculus.

A formalism for the calculus of variations with spinors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bäckdahl, Thomas, E-mail: thobac@chalmers.se; Valiente Kroon, Juan A., E-mail: j.a.valiente-kroon@qmul.ac.uk

2016-02-15

We develop a frame and dyad gauge-independent formalism for the calculus of variations of functionals involving spinorial objects. As a part of this formalism, we define a modified variation operator which absorbs frame and spin dyad gauge terms. This formalism is applicable to both the standard spacetime (i.e., SL(2, ℂ)) 2-spinors as well as to space (i.e., SU(2, ℂ)) 2-spinors. We compute expressions for the variations of the connection and the curvature spinors.

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Frequency-doubled Alexandrite laser for use in periodontology: a scanning electron microscopic investigation

NASA Astrophysics Data System (ADS)

Rechmann, Peter; Hennig, Thomas

1996-12-01

During prior studies it could be demonstrated that engaging a frequency double Alexandrite-laser allows a fast and strictly selective ablation of supra- and subgingival calculus. Furthermore, the removal of unstained microbial plaque was observed. First conclusions were drawn following light microscopic investigations on undecalcified sections of irradiated teeth. In the present study the cementum surface after irradiation with a frequency doubled Alexandrite-laser was observed by means of a scanning electron microscope. After irradiation sections of teeth were dried in alcohol and sputtered with gold. In comparison irradiated cementum surfaces of unerupted operatively removed wisdom teeth and tooth surfaces after the selective removal of calculus were investigated. A complete removal of calculus was observed as well as a remaining smooth surface of irradiated cementum.

Dependence of calculus retropulsion dynamics on fiber size and radiant exposure during Ho:YAG lithotripsy.

PubMed

Lee, Ho; Ryan, Robert T; Kim, Jeehyun; Choi, Bernard; Arakeri, Navanit V; Teichman, Joel M H; Welch, A J

2004-08-01

During pulsed laser lithotripsy, the calculus is subject to a strong recoil momentum which moves the calculus away from laser delivery and prolongs the operation. This study was designed to quantify the recoil momentum during Ho:YAG laser lithotripsy. The correlation among crater shape, debris trajectory, laser-induced bubble and recoil momentum was investigated. Calculus phantoms made from plaster of Paris were ablated with free running Ho:YAG lasers. The dynamics of recoil action of a calculus phantom was monitored by a high-speed video camera and the laser ablation craters were examined with Optical Coherent Tomography (OCT). Higher radiant exposure resulted in larger ablation volume (mass) which increased the recoil momentum. Smaller fibers produced narrow craters with a steep contoured geometry and decreased recoil momentum compared to larger fibers. In the presence of water, recoil motion of the phantom deviated from that of phantom in air. Under certain conditions, we observed the phantom rocking towards the fiber after the laser pulse. The shape of the crater is one of the major contributing factors to the diminished recoil momentum of smaller fibers. The re-entrance flow of water induced by the bubble collapse is considered to be the cause of the rocking of the phantom.

Urethral calculi with a urethral fistula: a case report and review of the literature.

PubMed

Zeng, Mingqiang; Zeng, Fanchang; Wang, Zhao; Xue, Ruizhi; Huang, Liang; Xiang, Xuyu; Chen, Zhi; Tang, Zhengyan

2017-09-06

To explore and summarize the reasons why urethral calculi cause a urethral fistula. We retrospectively studied 1 patient in Xiangya hospital and all relevant literature published in English between 1989 and 2015. The patients (including those reported in the literature) were characterized by age, origin, location of calculus, size of calculus, fistulous track, and etiological factors. Most of urethral calculi associated with a urethral fistula were native generated. Urethral calculi can be formed in various locations of the urethra, and the size of the calculus ranged from small (multiple) calculi to giant stones. The fistula external orifice located at the root of the penis was relatively common, and there were various etiological factors, such as urethral strictures, urethral trauma induced by long-term catheterization, lumbar fractures, and congenital anomaly factors. They were managed by the excision of the fistulous tract, retrieval of the urethral stones, and/or debridement and pus drainage operations. Some elements, such as trauma, recurrent urinary tract infections, abscess formation induced by long-term catheterization, and urethral calculus, may be the risk factors for a urethral fistula.

A Hodge-de Rham Dirac operator on the quantum SU(2)

NASA Astrophysics Data System (ADS)

di Cosmo, Fabio; Marmo, Giuseppe; Pérez-Pardo, Juan Manuel; Zampini, Alessandro

We describe how it is possible to define a Hodge-de Rham Dirac operator associated to a suitable Cartan-Killing metric form upon the exterior algebra over the quantum spheres SUq(2) equipped with a three-dimensional left covariant calculus.

Impacted anterior urethral calculus complicated by a stone-containing diverticulum in an elderly man: outcome of transurethral lithotripsy without resection of the diverticulum.

PubMed

Zhou, Tie; Chen, Guanghua; Zhang, Wei; Peng, Yonghan; Xiao, Liang; Xu, Chuangliang; Sun, Yinghao

2013-01-01

The prevalence of lower urinary tract symptoms (LUTS) is about 20% in men aged 40 or above. Other than benign prostatic hyperplasia (BPH), urethral diverticulum or calculus is not uncommon for LUTS in men. Surgical treatment is often recommended for urethral diverticulum or calculus, but treatment for an impacted urethral calculus complicated by a stone-containing diverticulum is challenging. An 82-year-old man had the persistence of LUTS despite having undergone transurethral resection of prostate for BPH. Regardless of treatment with broad spectrum antibiotics and an α-blocker, LUTS and post-void residual urine volume (100 mL) did not improve although repeated urinalysis showed reduction of WBCs from 100 to 10 per high power field. Further radiology revealed multiple urethral calculi and the stone configuration suggested the existence of a diverticulum. He was successfully treated without resecting the urethral diverticulum; and a new generation of ultrasound lithotripsy (EMS, Nyon, Switzerland) through a 22F offset rigid Storz nephroscope (Karl Storz, Tuttingen, Germany) was used to fragment the stones. The operative time was 30 minutes and the stones were cleanly removed. The patient was discharged after 48 hours with no immediate complications and free of LUTS during a 2 years follow-up. When the diverticulum is the result of a dilatation behind a calculus, removal of the calculus is all that is necessary. Compared with open surgery, ultrasound lithotripsy is less invasive with little harm to urethral mucosa; and more efficient as it absorbs stone fragments while crushing stones.

Tensor calculus: unlearning vector calculus

NASA Astrophysics Data System (ADS)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-02-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can serve as a bridge for vector calculus into tensor calculus.

A Generalized Quantum Theory

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2014-09-01

In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space quantum mechanics, but it is not. The same triple role occurs for the elements of a certain ordered Banach space in a much more general theory based upon quantum logics and a conditional probability calculus (which is a quantum logical model of the Lueders-von Neumann measurement process). It is shown how positive groups, automorphism groups, Lie algebras and statistical operators emerge from one major postulate - the non-existence of third-order interference (third-order interference and its impossibility in quantum mechanics were discovered by R. Sorkin in 1994). This again underlines the power of the combination of the conditional probability calculus with the postulate that there is no third-order interference. In two earlier papers, its impact on contextuality and nonlocality had already been revealed.

Curve Fitting via the Criterion of Least Squares. Applications of Algebra and Elementary Calculus to Curve Fitting. [and] Linear Programming in Two Dimensions: I. Applications of High School Algebra to Operations Research. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 321, 453.

ERIC Educational Resources Information Center

Alexander, John W., Jr.; Rosenberg, Nancy S.

This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to…

Numerical operator calculus in higher dimensions

PubMed Central

Beylkin, Gregory; Mohlenkamp, Martin J.

2002-01-01

When an algorithm in dimension one is extended to dimension d, in nearly every case its computational cost is taken to the power d. This fundamental difficulty is the single greatest impediment to solving many important problems and has been dubbed the curse of dimensionality. For numerical analysis in dimension d, we propose to use a representation for vectors and matrices that generalizes separation of variables while allowing controlled accuracy. Basic linear algebra operations can be performed in this representation using one-dimensional operations, thus bypassing the exponential scaling with respect to the dimension. Although not all operators and algorithms may be compatible with this representation, we believe that many of the most important ones are. We prove that the multiparticle Schrödinger operator, as well as the inverse Laplacian, can be represented very efficiently in this form. We give numerical evidence to support the conjecture that eigenfunctions inherit this property by computing the ground-state eigenfunction for a simplified Schrödinger operator with 30 particles. We conjecture and provide numerical evidence that functions of operators inherit this property, in which case numerical operator calculus in higher dimensions becomes feasible. PMID:12140360

Application of ureterorenoscope and flexible ureterorenoscope lithotripsy in removing calculus from extracorporeal living donor renal graft: a single-center experience.

PubMed

Lin, Chun-Hua; Zhang, Zuo-Fu; Wang, Jiahui; Yu, Lu-Xin; Wang, Wen-Ting; Shi, Lei; Lin, Xiang-Nan

2017-11-01

Here, we reported our clinical application of ureterorenoscope (URS) and flexible URS lithotripsy in stone removal on 10 cases of excised living donor kidney graft. After the extraction of donor kidney by retroperitoneal laparoscopy, the donor graft was perfused with 4 °C HCA solution. Calculus between 2-4 mm were removed intact with lithotomy forceps under direct vision of URS. Larger calculi of >4 mm were fractured with flexible URS combining holmium laser lithotripsy. Fragments of the calculus were extracted with basket extractor and lithotomy forceps. All operations were successful. The operation time was 14-31 min (average 21.2 ± 6.3 min). The kidneys were then transplanted to the recipients using routine procedure. The transplanted kidneys functioned well after transplantation. Gross hematuria resolved 1-4 d after operation (average 2.6 ± 0.9 d). The transplanted kidneys functioned well without early complications such as functional recovery delay and acute graft rejection. The donors and recipients were followed for 12 months. The size of the transplanted kidneys was normal and new stones or urinary obstruction was not seen upon urinary color Doppler ultrasound examination. In conclusion, we believe it is feasible, safe and effective to use URS or flexible URS combining holmium laser lithotripsy on extracorporeal living donor kidney.

"The Age of Newton": An Intensive Physics and Mathematics Course

ERIC Educational Resources Information Center

Calvert, J. B.; And Others

1976-01-01

Describes an intensive course in mathematics (calculus), mechanics, optics, and astronomy directed mainly toward nonscience students. Course format, operation, and student evaluation appear. (Author/CP)

Some subclasses of multivalent functions involving a certain linear operator

NASA Astrophysics Data System (ADS)

Srivastava, H. M.; Patel, J.

2005-10-01

The authors investigate various inclusion and other properties of several subclasses of the class of normalized p-valent analytic functions in the open unit disk, which are defined here by means of a certain linear operator. Problems involving generalized neighborhoods of analytic functions in the class are investigated. Finally, some applications of fractional calculus operators are considered.

Tensor Calculus: Unlearning Vector Calculus

ERIC Educational Resources Information Center

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

SEM investigations of the cementum surface after irradiation with a frequency-doubled Alexandrite laser

NASA Astrophysics Data System (ADS)

Rechmann, Peter; Hennig, Thomas

1996-04-01

During prior studies it could be demonstrated while engaging a frequency doubled Alexandrite-laser (wavelength 380 nm, pulse duration 100 ns, fluence 1 J/cm2, pulse repetition rate 110 Hz) a fast and strictly selective ablation of supra- and subgingival calculus is possible. Even the removal of unstained microbial plaque was observed. First conclusions were drawn after light microscopical investigations on undecalcified sections of irradiated teeth. In the present study the cementum surface after irradiation with a frequency doubled Alexandrite-laser was observed by means of a Scanning Electron Microscope. After irradiation sections of teeth were dried in alcohol and sputtered with gold. In comparison irradiated cementum surfaces of unerupted operatively removed wisdom teeth and tooth surfaces after the selective removal of calculus were investigated. A complete removal of calculus was observed as well as a remaining smooth surface of irradiated cementum.

Toward lattice fractional vector calculus

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

[Endoscopy-assisted sialolithectomy for the calculus of the Stensen's duct].

PubMed

Ye, Xin; Xie, Xiaoyan; Liu, Denggao; Zhang, Lei; Zhang, Zuyan; Yu, Guangyan

2014-11-01

To investigate the clinical effects of endoscopy-assisted sialolithectomy for the calculus in the Stensen's duct. From August 2005 to July 2013, 67 consecutive patients with calculus (or foreign bodies) in the Stensen's duct underwent explorative and interventional endoscopy in our hospital. The stones (or foreign bodies) were removed by endoscopy-assisted technique. After operation, the patients were followed-up periodically, and treatment effects were analyzed. Among the 67 patients, the stones (or foreign bodies) were completely removed in 58 cases, and almost completely removed in 3 cases, with a success rate of 87% (58/67). Among the 61 stone-removed cases, treatment options included direct removal with aid of basket or forceps (24 cases), basket entrapment and opening-up of the ostium (21 cases), basket entrapment and mucosal incision near the ostium (8 cases), open removal via buccal incision (2 cases) and open removal via pre-auricular flap (6 cases). During the 6-90 months' follow-up of the 61 cases, 48 cases were asymptomatic, 7 had mild symptoms, 3 developed ductal obturation, 1 had numbness in the parotid region, and the remaining 2 were missed. Endoscopy-assisted sialolithectomy is a safe and effective gland-preservation technique for the patients with parotid gland calculus.

Conormal distributions in the Shubin calculus of pseudodifferential operators

NASA Astrophysics Data System (ADS)

Cappiello, Marco; Schulz, René; Wahlberg, Patrik

2018-02-01

We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of a Fourier-Bros-Iagolnitzer transform. Based on this, we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We study their transformation behavior, normal forms, and microlocal properties.

Reconstructing Operational Theory: A Framework for Emerging Threats in a Complex Environment

DTIC Science & Technology

2007-01-01

General Shimon Naveh. While the composition and construction of the urban environment traditionally influence targeting calculus , this is not the same as... Anton . "The Relevance of Chaos Theory to Operations." Australian Defense Force Journal. No. 162. Sep/Oct 2003, 4-18. Lind, William

Existence results for degenerate p(x)-Laplace equations with Leray-Lions type operators

NASA Astrophysics Data System (ADS)

Ho, Ky; Sim, Inbo

2017-01-01

We show the various existence results for degenerate $p(x)$-Laplace equations with Leray-Lions type operators. A suitable condition on degeneracy is discussed and proofs are mainly based on direct methods and critical point theories in Calculus of Variations. In particular, we investigate the various situations of the growth rates between principal operators and nonlinearities.

The impact of taking a college pre-calculus course on students' college calculus performance

NASA Astrophysics Data System (ADS)

Sonnert, Gerhard; Sadler, Philip M.

2014-11-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.

Water content contribution in calculus phantom ablation during Q-switched Tm:YAG laser lithotripsy.

PubMed

Zhang, Jian J; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Wang, Hui; Chia, Ray W J; Hasenberg, Tom; Kang, Hyun Wook

2015-01-01

Q-switched (QS) Tm:YAG laser ablation mechanisms on urinary calculi are still unclear to researchers. Here, dependence of water content in calculus phantom on calculus ablation performance was investigated. White gypsum cement was used as a calculus phantom model. The calculus phantoms were ablated by a total 3-J laser pulse exposure (20 mJ, 100 Hz, 1.5 s) and contact mode with N=15 sample size. Ablation volume was obtained on average 0.079, 0.122, and 0.391  mm3 in dry calculus in air, wet calculus in air, and wet calculus in-water groups, respectively. There were three proposed ablation mechanisms that could explain the effect of water content in calculus phantom on calculus ablation performance, including shock wave due to laser pulse injection and bubble collapse, spallation, and microexplosion. Increased absorption coefficient of wet calculus can cause stronger spallation process compared with that caused by dry calculus; as a result, higher calculus ablation was observed in both wet calculus in air and wet calculus in water. The test result also indicates that the shock waves generated by short laser pulse under the in-water condition have great impact on the ablation volume by Tm:YAG QS laser.

Generalized Differential Calculus and Applications to Optimization

NASA Astrophysics Data System (ADS)

Rector, Robert Blake Hayden

This thesis contains contributions in three areas: the theory of generalized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geometric approach is used to advance the theory and tools used for studying generalized notions of derivatives for nonsmooth functions. These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions. A strong understanding of the subdifferential is essential for numerical optimization algorithms, which are developed and applied to nonsmooth problems in operations research, including non-convex problems. Finally, an optimization framework is applied to solve a problem in electric power systems involving a smart solar inverter and battery storage system providing energy and ancillary services to the grid.

A Loomis-Sikorski theorem and functional calculus for a generalized Hermitian algebra

NASA Astrophysics Data System (ADS)

Foulis, David J.; Jenčová, Anna; Pulmannová, Sylvia

2017-10-01

A generalized Hermitian (GH-) algebra is a generalization of the partially ordered Jordan algebra of all Hermitian operators on a Hilbert space. We introduce the notion of a gh-tribe, which is a commutative GH-algebra of functions on a nonempty set X with pointwise partial order and operations, and we prove that every commutative GH-algebra is the image of a gh-tribe under a surjective GH-morphism. Using this result, we prove that each element a of a GH-algebra A corresponds to a real observable ξa on the σ-orthomodular lattice of projections in A and that ξa determines the spectral resolution of a. Also, if f is a continuous function defined on the spectrum of a, we formulate a definition of f (a), thus obtaining a continuous functional calculus for A.

Study on bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis.

PubMed

Wan, Tien-Chun; Cheng, Fu-Yuan; Liu, Yu-Tse; Lin, Liang-Chuan; Sakata, Ryoichi

2009-12-01

The purpose of the study was to investigate bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis obtained as valuable by-products from animals used for meat production. The results showed that the components of natural Calculus Bovis were rich in bilirubin and biliverdin and had higher content of essential amino acids. The major amino acids of in vitro cultured Calculus Suis were identified as glycine, alanine, glutamic acid and aspartic acid, and those for natural Calculus Bovis were found to be glutamic acid, aspartic acid, proline, and arginine. The methionine and cysteine contents of precursors for glutathione in natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The mineral contents of zinc, iron and manganese of natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The major bile acids in both products were cholic acid and dehydrocholic acid, respectively. The chenodeoxycholic and ursodeoxycholic acid content of in vitro cultured Calculus Suis was significantly higher than that of natural Calculus Bovis.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order. Throughout the survey, we illustrate the parallels in the relationships: Laplace type integral transforms - special functions as kernels - operators of generalized integration and differentiation generated by special functions - special functions as solutions of related differential equations. The role of the so-called Special Functions of Fractional Calculus is emphasized.

DNA algorithms of implementing biomolecular databases on a biological computer.

PubMed

Chang, Weng-Long; Vasilakos, Athanasios V

2015-01-01

In this paper, DNA algorithms are proposed to perform eight operations of relational algebra (calculus), which include Cartesian product, union, set difference, selection, projection, intersection, join, and division, on biomolecular relational databases.

If Gravity is Geometry, is Dark Energy just Arithmetic?

NASA Astrophysics Data System (ADS)

Czachor, Marek

2017-04-01

Arithmetic operations (addition, subtraction, multiplication, division), as well as the calculus they imply, are non-unique. The examples of four-dimensional spaces, R+4 and (- L/2, L/2)4, are considered where different types of arithmetic and calculus coexist simultaneously. In all the examples there exists a non-Diophantine arithmetic that makes the space globally Minkowskian, and thus the laws of physics are formulated in terms of the corresponding calculus. However, when one switches to the `natural' Diophantine arithmetic and calculus, the Minkowskian character of the space is lost and what one effectively obtains is a Lorentzian manifold. I discuss in more detail the problem of electromagnetic fields produced by a pointlike charge. The solution has the standard form when expressed in terms of the non-Diophantine formalism. When the `natural' formalsm is used, the same solution looks as if the fields were created by a charge located in an expanding universe, with nontrivially accelerating expansion. The effect is clearly visible also in solutions of the Friedman equation with vanishing cosmological constant. All of this suggests that phenomena attributed to dark energy may be a manifestation of a miss-match between the arithmetic employed in mathematical modeling, and the one occurring at the level of natural laws. Arithmetic is as physical as geometry.

Deducing the form factors for shear used in the calculus of the displacements based on strain energy methods. Mathematical approach for currently used shapes

NASA Astrophysics Data System (ADS)

Constantinescu, E.; Oanta, E.; Panait, C.

2017-08-01

The paper presents an initial study concerning the form factors for shear, for a rectangular and for a circular cross section, being used an analytical method and a numerical study. The numerical study considers a division of the cross section in small areas and uses the power of the definitions in order to compute the according integrals. The accurate values of the form factors are increasing the accuracy of the displacements computed by the use of the strain energy methods. The knowledge resulted from this study will be used for several directions of development: calculus of the form factors for a ring-type cross section of variable ratio of the inner and outer diameters, calculus of the geometrical characteristics of an inclined circular segment and, using a Bool algebra that operates with geometrical shapes, for an inclined circular ring segment. These shapes may be used to analytically define the geometrical model of a complex composite section, i.e. a ship hull cross section. The according calculus relations are also useful for the development of customized design commands in CAD commercial applications. The paper is a result of the long run development of original computer based instruments in engineering of the authors.

Factors Associated with Success in College Calculus II

ERIC Educational Resources Information Center

Rosasco, Margaret E.

2013-01-01

Students are entering college having earned credit for college Calculus 1 based on their scores on the College Board's Advanced Placement (AP) Calculus AB exam. Despite being granted credit for college Calculus 1, it is unclear whether these students are adequately prepared for college Calculus 2. College calculus classes are often taught from a…

Retroperitoneal laparoendoscopic single-site ureterolithotomy and ureteroureterostomy for retrocaval ureter with ureteral calculus: first case report.

PubMed

Chen, Zhi; Chen, Xiang; Luo, Yan-Cheng; He, Yao; Li, Nan-Nan; Xie, Chao-Qun; Lai, Chen; Fang, Xiao-Long

2012-12-01

A 53-year-old man presented with a 6-month history of intermittent right flank pain. Radiological imaging confirmed the diagnosis of retrocaval ureter (RCU) and ureteral calculus. Retroperitoneal laparoendoscopic single-site surgery (LESS) ureterolithotomy and ureteroureterostomy was successfully performed. The operative time was 185 min and the blood loss was approximately 20 ml. The patient's postoperative course was uneventful. Postoperative analgesia was not needed. The patient was discharged on the third postoperative day. The drain and double-J stent were respectively removed at 1 and 8 weeks postoperatively. At the 3-month follow-up, nuclear scan showed no evidence of obstruction of the right kidney and the patient also remained symptom free. It may be concluded that retroperitoneal LESS repair for RCU is a feasible and safe procedure, which can be considered as a option for the management of RCU even if it is complicated by the presence of a ureteral calculus.

Management of calculus anuria using ureteroscopic lithotripsy as a first line treatment: its efficacy and safety.

PubMed

Savić, Slaviša; Vukotić, Vinka; Lazić, Miodrag; Savić, Nataša

2014-05-06

To present our experience with emergency ureteroscopic lithotripsy (URSL) for ureteral calculi associated with acute kidney injury (AKI). We retrospectively evaluated the 61 patients consisted of 90 ureteral units (UU), who underwent URSL. The cause of anuria was bilateral calculus obstructions in 29 cases, and unilateral calculus obstruction with, absent, nephrectomized contralateral kidney in 32 cases. In the case of bilateral synchronous ureteric calculi same-session bilateral ureteroscopy (SBBU) was done. The duration of anuria varied between 12 to 72 hours. At the end of the procedure, ureteral stent was systematically left in place in all patients. Surgery was performed 6-12 hours after admission to hospital. Patients were followed at least 1 month postoperatively. The stone free rates (SFR) were determined as baseline, on the first post-operative day, and as overall on the 30 days after procedure. The greatest success was achieved in the distal localization of stones up to 10 mm (93%). Renal function returned in 51 (83.6%) patients within 7 days. In 18 (29.5%) patients [18 (20%) UU] we performed second procedure as extracorporeal shockwave lithotripsy in 16.7% and open surgery in 2.2%. In 43 (70.5%) patients URSL was a successful therapeutic approach in dealing with pain, obstruction and calculus. Calculus anuria is a medical emergency that requires rapid diagnosis and prompt treatment for the purpose of decompression. URSL is the proper method of choice for selected patients and can be performed safely and has high success rates with minimal morbidity.

[Calculus formation in the prostatic cavity after transurethral resection of the prostate: causes, treatment and prevention].

PubMed

Wei, Zhi-Feng; Xu, Xiao-Feng; Cheng, Wen; Zhou, Wen-Quan; Ge, Jing-Ping; Zhang, Zheng-Yu; Gao, Jian-Ping

2012-05-01

To study the causes, clinical manifestations, treatment and prevention of calculus that develops in the prostatic cavity after transurethral resection of the prostate. We reported 11 cases of calculus that developed in the prostatic cavity after transurethral resection or transurethral plasmakinetic resection of prostate. The patients complained of repeated symptoms of frequent micturition, urgent micturition and urodynia after operation, accompanied with urinary tract infection and some with urinary obstruction, which failed to respond to anti-infective therapies. Cystoscopy revealed calculi in the prostatic cavity, with eschar, sphacelus, uneven wound surface and small diverticula in some cases. After diagnosis, 1 case was treated by holmium laser lithotripsy and a second transurethral resection of the prostate, while the other 10 had the calculi removed under the cystoscope, followed by 1 -2 weeks of anti-infective therapy. After treatment, all the 11 cases showed normal results of routine urinalysis, and no more symptoms of frequent micturition, urgent micturition and urodynia. Three- to six-month follow-up found no bladder irritation symptoms and urinary tract infection. Repeated symptoms of frequent micturition, urgent micturition, urodynia and urinary tract infection after transurethral resection of the prostate should be considered as the indicators of calculus in the prostatic cavity, which can be confirmed by cystoscopy. It can be treated by lithotripsy or removal of the calculus under the cystoscope, or even a second transurethral resection of the prostate. For its prevention, excessive electric coagulation and uneven wound surface should be avoided and anti-infection treatment is needed.

A Verification System for Distributed Objects with Asynchronous Method Calls

NASA Astrophysics Data System (ADS)

Ahrendt, Wolfgang; Dylla, Maximilian

We present a verification system for Creol, an object-oriented modeling language for concurrent distributed applications. The system is an instance of KeY, a framework for object-oriented software verification, which has so far been applied foremost to sequential Java. Building on KeY characteristic concepts, like dynamic logic, sequent calculus, explicit substitutions, and the taclet rule language, the system presented in this paper addresses functional correctness of Creol models featuring local cooperative thread parallelism and global communication via asynchronous method calls. The calculus heavily operates on communication histories which describe the interfaces of Creol units. Two example scenarios demonstrate the usage of the system.

Impact of Calculus Reform in a Liberal Arts Calculus Course.

ERIC Educational Resources Information Center

Brosnan, Patricia A.; Ralley, Thomas G.

This report describes the changes in a freshman-level calculus course that occurred as a consequence of adopting the Harvard Consortium Calculus text. The perspective is that of the lecturer. The course is intended as an introduction to calculus for liberal arts students, that is, students who will not be expected to use calculus as a mathematical…

Computer Algebra Systems in Undergraduate Instruction.

ERIC Educational Resources Information Center

Small, Don; And Others

1986-01-01

Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)

The Impact of Taking a College Pre-Calculus Course on Students' College Calculus Performance

ERIC Educational Resources Information Center

Sonnert, Gerhard; Sadler, Philip M.

2014-01-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and…

Geometric interpretation of vertex operator algebras.

PubMed Central

Huang, Y Z

1991-01-01

In this paper, Vafa's approach to the formulation of conformal field theories is combined with the formal calculus developed in Frenkel, Lepowsky, and Meurman's work on the vertex operator construction of the Monster to give a geometric definition of vertex operator algebras. The main result announced is the equivalence between this definition and the algebraic one in the sense that the categories determined by these definitions are isomorphic. PMID:11607240

Motivation and Study Habits of College Calculus Students: Does Studying Calculus in High School Make a Difference?

ERIC Educational Resources Information Center

Gibson, Megan

2013-01-01

Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the…

Surmounting the Cartesian Cut Through Philosophy, Physics, Logic, Cybernetics, and Geometry: Self-reference, Torsion, the Klein Bottle, the Time Operator, Multivalued Logics and Quantum Mechanics

NASA Astrophysics Data System (ADS)

Rapoport, Diego L.

2011-01-01

In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown's primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard's gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the matrix logic which supersedes the classical logic of connectives and which has for particular subtheories fuzzy and quantum logics. Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succinctly described above.

Computer-Oriented Calculus Courses Using Finite Differences.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been…

Complexity and the Fractional Calculus

DTIC Science & Technology

2013-01-01

these trajectories over the entire Lotka - Volterra cycle thereby generating the mistaken impression that the resulting average trajectory reaches...interpreted as a form of phase decor- relation process rather than one with friction. The fractional version of the popular Lotka - Volterra ecological...trajectory is an ordinary Lotka - Volterra cycle in the operational time . Transitioning from the operational time to the chronological time spreads

Explanation Capabilities for Behavior-Based Robot Control

NASA Technical Reports Server (NTRS)

Huntsberger, Terrance L.

2012-01-01

A recent study that evaluated issues associated with remote interaction with an autonomous vehicle within the framework of grounding found that missing contextual information led to uncertainty in the interpretation of collected data, and so introduced errors into the command logic of the vehicle. As the vehicles became more autonomous through the activation of additional capabilities, more errors were made. This is an inefficient use of the platform, since the behavior of remotely located autonomous vehicles didn't coincide with the "mental models" of human operators. One of the conclusions of the study was that there should be a way for the autonomous vehicles to describe what action they choose and why. Robotic agents with enough self-awareness to dynamically adjust the information conveyed back to the Operations Center based on a detail level component analysis of requests could provide this description capability. One way to accomplish this is to map the behavior base of the robot into a formal mathematical framework called a cost-calculus. A cost-calculus uses composition operators to build up sequences of behaviors that can then be compared to what is observed using well-known inference mechanisms.

Percutaneous nephrolithotomy of bilateral staghorn renal calculi in pediatric patients: 12 years experience in a tertiary care centre.

PubMed

Purkait, Bimalesh; Kumar, Manoj; Sokhal, Ashok Kumar; Bansal, Ankur; Sankhwar, Satya Narayan; Gupta, Ashok Kumar

2017-08-01

To assess the outcomes of percutaneous nephrolithotomy (PCNL) in bilateral staghorn calculi in pediatric patients, we have performed a retrospective analysis. Staghorn calculus is defined as stone that fills a greater part of the pelvic-caliceal system. Still, in developing countries, patients may present with staghorn calculus. PCNL is the preferred treatment modality for staghorn calculus both in adult and children. Our study included fifty-one pediatric patients (<15 years) of bilateral staghorn calculi from 2004 to 2015. Staged PCNL was done after 2-3 days if needed and opposite side PCNL was performed after 10-14 days. Fifty-one patients with bilateral staghorn renal calculi underwent PCNL. The mean age of the study group was 10.25 ± 2.13 (range 3-15). Mean stone burden was 778.3 + 613.4 (range 231-3850 mm 2 ). Forty-five patients underwent single puncture, twenty-two patients underwent double punctures whereas six patients underwent triple punctures during first session PCNL procedure. Most common puncture location was through the superior calyx (58.82 %). The mean operating time was 77.25 + 30.21 (range 58-145). After the first session PCNL, the success rate was 76.47 %. Thirteen patients (17 renal units) underwent relook PCNL and seven patients underwent ESWL. Overall complication noted in twenty-four (47.05 %) cases. Most of the complications were minor grade. Percutaneous nephrolithotomy for staghorn calculus in children needs expertise. PCNL in B/L staghorn renal calculus in children is safe and effective. B/L staghorn renal calculi with compromised renal function have higher chance of complications including bleeding.

A randomised study to compare salivary pH, calcium, phosphate and calculus formation after using anticavity dentifrices containing Recaldent(®) and functionalized tri-calcium phosphate.

PubMed

Sharma, Ena; Vishwanathamurthy, Ramesh Alampalli; Nadella, Manjari; Savitha, A N; Gundannavar, Gayatri; Hussain, M Ahad

2012-10-01

The aim of this study was to estimate the pH of saliva, concentration of calcium and inorganic phosphate, and calculus formation before and after usage of Recaldent(®) (GC Tooth Mousse Plus™), Functionalized Tricalcium Phosphate (3M ESPE ClinPro™ Tooth Crème) and standard dentifrice (Colgate dental cream). Randomized double-blind study. A total of 50 subjects were recruited, the subjects were assessed at their first visit, on the 21(st) day and on the 42(nd) day. At the first visit, scaling was carried out and oral hygiene instructions were given. After 21 days, the subjects were given coded dentifrices where the operator and the subjects both were unaware of the type of dentifrice. Clinical parameters assessed were Plaque index, Gingival index, and Calculus index. Salivary samples were obtained to measure calcium, phosphate levels, and pH at 21(st) day and 42(nd) day. ANOVA test, t-test, Mann-Whitney test, Kruskal-Wallis test. The mean salivary calcium level and mean salivary phosphate level were higher in Group III (functionalized tricalcium phosphate (3M ESPE ClinPro™ Tooth Creme) as compared to Group II (Recaldent(®) GC Tooth Mousse Plus™) and Group I (Colgate dental cream) on the 42(nd) day after using dentifrices, which was statistically significant. This showed that the usage of remineralizing dentifrices led to an increase in the salivary calcium, phosphate, and pH but it did not reach the level of super saturation of the ions caused by elevated pH which could lead to calculus formation. Thought here was a statistically significant increase in salivary calcium and phosphate level in all three groups from baseline to 42(nd) day, there was no calculus formation.

Patients with dental calculus have increased saliva and gingival crevicular fluid fetuin-A levels but no association with fetuin-A polymorphisms.

PubMed

Doğan, Gülnihal Emrem; Demir, Turgut; Laloğlu, Esra; Sağlam, Ebru; Aksoy, Hülya; Yildirim, Abdulkadir; Akçay, Fatih

2016-12-22

Fetuin-A is a potent inhibitor of calcium-phosphate precipitation and of the calcification process, therefore it can also be related with dental calculus. Thus, we aimed to investigate a possible relationship between fetuin-A gene polymorphism and the presence of dental calculus. A possible relationship between serum, saliva and gingival crevicular fluid (GCF) levels of fetuin-A was also investigated. Fetuin-A c.742C > T and c.766C > G polymorphisms were investigated in 103 patients with or without dental calculus. Additionally, serum, saliva and GCF fetuin-A levels of patients were compared according to dental calculus presence. A significant difference was not observed in the distribution of the fetuin-A c.742C > T and c.766C > G polymorphisms between patients with or without dental calculus. Saliva and GCF fetuin-A concentrations of patients with dental calculus were statistically higher than those without dental calculus (P=0.001, P=0.036 respectively). According to our results, fetuin-A c.742C > T and c.766C > G polymorphisms were not associated with presence of dental calculus. However, higher GCF and saliva fetuin-A levels were detected in patients with dental calculus than in patients without dental calculus, which may result from an adaptive mechanism to inhibit mineral precipitation and eventually calculus formation.

Oliver Heaviside's "Dinner"

NASA Astrophysics Data System (ADS)

Giorello, Giulio; Sinigaglia, Corrado

In the following pages we begin, in the first chapter, with a reappraisal of some ideas of Edouard Le Roy about mathematical experience, mainly in relation with the history of complex numbers. In the second chapter we discuss in some detail the i-story, and we draw a comparison between "Imaginary Quantity" and Operational Calculus from the perspective of Heaviside's conceptions of the growth of mathematics. In the third chapter we reconstruct the δ-story, i.e. the Heaviside calculus leading to the constitution of a new mathematical object, the so-called Dirac's δ-function. Finally, in the last chapter, we bring together methodological and historical considerations in order to support Lakatos' idea of quasi-empiricism in mathematics.

Line integral on engineering mathematics

NASA Astrophysics Data System (ADS)

Wiryanto, L. H.

2018-01-01

Definite integral is a basic material in studying mathematics. At the level of calculus, calculating of definite integral is based on fundamental theorem of calculus, related to anti-derivative, as the inverse operation of derivative. At the higher level such as engineering mathematics, the definite integral is used as one of the calculating tools of line integral. the purpose of this is to identify if there is a question related to line integral, we can use definite integral as one of the calculating experience. The conclusion of this research says that the teaching experience in introducing the relation between both integrals through the engineer way of thinking can motivate and improve students in understanding the material.

A Simple Acronym for Doing Calculus: CAL

ERIC Educational Resources Information Center

Hathaway, Richard J.

2008-01-01

An acronym is presented that provides students a potentially useful, unifying view of the major topics covered in an elementary calculus sequence. The acronym (CAL) is based on viewing the calculus procedure for solving a calculus problem P* in three steps: (1) recognizing that the problem cannot be solved using simple (non-calculus) techniques;…

Giant calculus: review and report of a case.

PubMed

Woodmansey, Karl; Severine, Anthony; Lembariti, Bakari S

2013-01-01

Dental calculus is a common oral finding. The term giant calculus is used to describe unusually large deposits of dental calculus. Several extreme cases have been reported in the dental literature. The specific etiology of these cases remains uncertain. This paper reviews previously reported cases, and presents another extreme example of giant calculus.

Calculus: The Dynamics of Change. MAA Notes Number 39.

ERIC Educational Resources Information Center

Roberts, A. Wayne, Ed.

This book discusses the calculus reform effort. The first essay captures the basic themes that should characterize a calculus course that is modern in its vision as well as its pedagogy and content. The next section contains essays on the vision of calculus reform: "Visions of Calculus" (Sharon Cutler Ross); "Nonalgebraic Approaches…

Renal vein thrombosis mimicking urinary calculus: a dilemma of diagnosis.

PubMed

Wang, Yimin; Chen, Shanwen; Wang, Wei; Liu, Jianyong; Jin, Baiye

2015-07-02

Renal vein thrombosis (RVT) with flank pain, and hematuria, is often mistaken with renal colic originating from ureteric or renal calculus. Especially in young and otherwise healthy patients, clinicians are easily misled by clinical presentation and calcified RVT. A 38-year-old woman presented with flank pain and hematuria suggestive of renal calculus on ultrasound. She underwent extracorporeal shock wave lithotripsy that failed, leading to the recommendation that percutaneous lithotomy was necessary to remove the renal calculus. In preoperative view of the unusual shape of the calculus without hydronephrosis, noncontrast computed tomography was taken and demonstrated left ureteric calculus. However computed tomography angiography revealed, to our surprise, a calcified RVT that was initially thought to be a urinary calculus. This case shows that a calcified RVT might mimic a urinary calculus on conventional ultrasonography and ureteric calculus on noncontrast computed tomography. Subsequent computed tomography angiography disclosed that a calcified RVT caused the imaging findings, thus creating a potentially dangerous clinical pitfall. Hence, it is suggested that the possibility of a RVT needs to be considered in the differential diagnosis whenever one detects an uncommon shape for a urinary calculus.

Noninvasive control of dental calculus removal: qualification of two fluorescence methods

NASA Astrophysics Data System (ADS)

Gonchukov, S.; Sukhinina, A.; Bakhmutov, D.; Biryukova, T.

2013-02-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.

Reliability of recordings of subgingival calculus detected using an ultrasonic device.

PubMed

Corraini, Priscila; López, Rodrigo

2015-04-01

To assess the intra-examiner reliability of recordings of subgingival calculus detected using an ultrasonic device, and to investigate the influence of subject-, tooth- and site-level factors on the reliability of these subgingival calculus recordings. On two occasions, within a 1-week interval, 147 adult periodontitis patients received a full-mouth clinical periodontal examination by a single trained examiner. Duplicate subgingival calculus recordings, in six sites per tooth, were obtained using an ultrasonic device for calculus detection and removal. Agreement was observed in 65 % of the 22,584 duplicate subgingival calculus recordings, ranging 45 % to 83 % according to subject. Using hierarchical modeling, disagreements in the subgingival calculus duplicate recordings were more likely in all other sites than the mid-buccal, and in sites harboring supragingival calculus. Disagreements were less likely in sites with PD ≥  4 mm and with furcation involvement  ≥  degree 2. Bleeding on probing or suppuration did not influence the reliability of subgingival calculus. At the subject-level, disagreements were less likely in patients presenting with the highest and lowest extent categories of the covariate subgingival calculus. The reliability of subgingival calculus recordings using the ultrasound technology is reasonable. The results of the present study suggest that the reliability of subgingival calculus recordings is not influenced by the presence of inflammation. Moreover, subgingival calculus can be more reliably detected using the ultrasound device at sites with higher need for periodontal therapy, i.e., sites presenting with deep pockets and premolars and molars with furcation involvement.

Using Dynamic Software to Address Common College Calculus Stumbling Blocks

ERIC Educational Resources Information Center

Seneres, Alice W.; Kerrigan, John A.

2014-01-01

There are specific topics in college calculus that can be major stumbling blocks for students. Having taught college calculus for four years to over a thousand students, we observed that even the students who have already taken pre-calculus or calculus during their high school careers had common misunderstandings. Students may remember a technique…

Leveraging Prior Calculus Study with Embedded Review

ERIC Educational Resources Information Center

Nikolov, Margaret C.; Withers, Wm. Douglas

2016-01-01

We propose a new course structure to address the needs of college students with previous calculus study but no course validations as an alternative to repeating the first year of calculus. Students are introduced directly to topics from Calculus III unpreceded by a formal review of topics from Calculus I or II, but with additional syllabus time…

The Effects of Two Semesters of Secondary School Calculus on Students' First and Second Quarter Calculus Grades at the University of Utah

ERIC Educational Resources Information Center

Robinson, William Baker

1970-01-01

The predicted and actual achievement in college calculus is compared for students who had studied two semesters of calculus in high school. The regression equation used for prediction was calculated from the performance data of similar students who had not had high school calculus. (CT)

[Fluorescence control of dental calculus removal].

PubMed

Bakhmutov, D N; Gonchukov, S A; Lonkina, T V; Sukhinina, A V

2012-01-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In the frames of this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise detection of tooth-calculus interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing (as ultrasonic or laser devices).

Differintegration: The One Branch of Calculus

ERIC Educational Resources Information Center

Berry, Andrew J.

2007-01-01

How might one define a functional operator D[superscript I]f(x), say for f(x) = 1 + x[superscript 2] + sin x, such that D[superscript +1](1 + x[superscript 2] + sin x) = 2x + cos x and D[superscript -1](1 + x[superscript 2] + sin x) = x + x[superscript 3]/3 - cos x? Our task in this article is to describe such an operator using a single formula…

The Development of Newtonian Calculus in Britain, 1700-1800

NASA Astrophysics Data System (ADS)

Guicciardini, Niccoló

2003-11-01

Introduction; Overture: Newton's published work on the calculus of fluxions; Part I. The Early Period: 1. The diffusion of the calculus (1700-1730); 2. Developments in the calculus of fluxions (1714-1733); 3. The controversy on the foundations of the calculus (1734-1742); Part II. The Middle Period: 4. The textbooks on fluxions (1736-1758); 5. Some applications of the calculus (1740-1743); 6. The analytic art (1755-1785); Part III. The Reform: 7. Scotland (1785-1809); 8. The Military Schools (1773-1819); 9. Cambridge and Dublin (1790-1820); 10. Tables; Endnotes; Bibliography; Index.

The impacts of gingivitis and calculus on Thai children's quality of life.

PubMed

Krisdapong, Sudaduang; Prasertsom, Piyada; Rattanarangsima, Khanit; Sheiham, Aubrey; Tsakos, Georgios

2012-09-01

To assess associations of socio-demographic, behavioural and the extent of gingivitis and calculus with oral health-related quality of life (OHRQoL) in nationally representative samples of 12- and 15-year-old Thai children. In the Thailand National Oral Health Survey, 1,063 twelve-year olds and 811 fifteen-year olds were clinically examined and interviewed for OHRQoL using the Child-OIDP and OIDP indices, respectively, and completed a behavioural questionnaire. We assessed associations of condition-specific impacts (CS-impacts) with gingivitis and calculus, adjusted for socio-demographic and behavioural factors. Gingivitis and calculus were highly prevalent: 79.3% in 12-year and 81.5% in 15-year olds. CS-impacts relating to calculus and/or gingivitis were reported by 26.0% of 12-year and 29.6% of 15-year olds. Except for calculus without gingivitis, calculus and/or gingivitis in any form was significantly related to any level of CS-impacts. At a moderate or higher level of CS-impacts, there were significant relationships with extensive calculus and/or gingivitis in 12-year olds and for extensive gingivitis and gingivitis without calculus in 15-year olds. Gingivitis was generally associated with any level of CS-impacts attributed to calculus and/or gingivitis. CS-impacts were related more to gingivitis than to calculus. © 2012 John Wiley & Sons A/S.

Characteristics of subgingival calculus detection by multiphoton fluorescence microscopy

NASA Astrophysics Data System (ADS)

Tung, Oi-Hong; Lee, Shyh-Yuan; Lai, Yu-Lin; Chen, How-Foo

2011-06-01

Subgingival calculus has been recognized as a major cause of periodontitis, which is one of the main chronic infectious diseases of oral cavities and a principal cause of tooth loss in humans. Bacteria deposited in subgingival calculus or plaque cause gingival inflammation, function deterioration, and then periodontitis. However, subgingival calculus within the periodontal pocket is a complicated and potentially delicate structure to be detected with current dental armamentaria, namely dental x-rays and dental probes. Consequently, complete removal of subgingival calculus remains a challenge to periodontal therapies. In this study, the detection of subgingival calculus employing a multiphoton autofluorescence imaging method was characterized in comparison with a one-photon confocal fluorescence imaging technique. Feasibility of such a system was studied based on fluorescence response of gingiva, healthy teeth, and calculus with and without gingiva covered. The multiphoton fluorescence technology perceived the tissue-covered subgingival calculus that cannot be observed by the one-photon confocal fluorescence method.

College Readiness: The Evaluation of Students Participating in the Historically Black College and University Program in Pre-Calculus and the Calculus Sequence

ERIC Educational Resources Information Center

Hall, Angela Renee

2011-01-01

This investigative research focuses on the level of readiness of Science, Technology, Engineering, and Mathematics (STEM) students entering Historically Black Colleges and Universities (HBCU) in the college Calculus sequence. Calculus is a fundamental course for STEM courses. The level of readiness of the students for Calculus can very well play a…

Concepts and Skills in High School Calculus: An Examination of a Special Case in Japan and the United States

ERIC Educational Resources Information Center

Judson, Thomas W.; Nishimori, Toshiyuki

2005-01-01

In this study we investigated above-average high school calculus students from Japan and the United States in order to determine any differences in their conceptual understanding of calculus and their ability to use algebra to solve traditional calculus problems. We examined and interviewed 18 Calculus BC students in the United States and 26…

Dental Calculus Stimulates Interleukin-1β Secretion by Activating NLRP3 Inflammasome in Human and Mouse Phagocytes

PubMed Central

Montenegro Raudales, Jorge Luis; Yoshimura, Atsutoshi; SM, Ziauddin; Kaneko, Takashi; Ozaki, Yukio; Ukai, Takashi; Miyazaki, Toshihiro; Latz, Eicke; Hara, Yoshitaka

2016-01-01

Dental calculus is a mineralized deposit associated with periodontitis. The bacterial components contained in dental calculus can be recognized by host immune sensors, such as Toll-like receptors (TLRs), and induce transcription of proinflammatory cytokines, such as IL-1β. Studies have shown that cellular uptake of crystalline particles may trigger NLRP3 inflammasome activation, leading to the cleavage of the IL-1β precursor to its mature form. Phagocytosis of dental calculus in the periodontal pocket may therefore lead to the secretion of IL-1β, promoting inflammatory responses in periodontal tissues. However, the capacity of dental calculus to induce IL-1β secretion in human phagocytes has not been explored. To study this, we stimulated human polymorphonuclear leukocytes (PMNs) and peripheral blood mononuclear cells (PBMCs) with dental calculus collected from periodontitis patients, and measured IL-1β secretion by ELISA. We found that calculus induced IL-1β secretion in both human PMNs and PBMCs. Calculus also induced IL-1β in macrophages from wild-type mice, but not in macrophages from NLRP3- and ASC-deficient mice, indicating the involvement of NLRP3 and ASC. IL-1β induction was inhibited by polymyxin B, suggesting that LPS is one of the components of calculus that induces pro-IL-1β transcription. To analyze the effect of the inorganic structure, we baked calculus at 250°C for 1 h. This baked calculus failed to induce pro-IL-1β transcription. However, it did induce IL-1β secretion in lipid A-primed cells, indicating that the crystalline structure of calculus induces inflammasome activation. Furthermore, hydroxyapatite crystals, a component of dental calculus, induced IL-1β in mouse macrophages, and baked calculus induced IL-1β in lipid A-primed human PMNs and PBMCs. These results indicate that dental calculus stimulates IL-1β secretion via NLRP3 inflammasome in human and mouse phagocytes, and that the crystalline structure has a partial role in the activation of NLRP3 inflammasome. PMID:27632566

Dental Calculus Stimulates Interleukin-1β Secretion by Activating NLRP3 Inflammasome in Human and Mouse Phagocytes.

PubMed

Montenegro Raudales, Jorge Luis; Yoshimura, Atsutoshi; Sm, Ziauddin; Kaneko, Takashi; Ozaki, Yukio; Ukai, Takashi; Miyazaki, Toshihiro; Latz, Eicke; Hara, Yoshitaka

2016-01-01

Dental calculus is a mineralized deposit associated with periodontitis. The bacterial components contained in dental calculus can be recognized by host immune sensors, such as Toll-like receptors (TLRs), and induce transcription of proinflammatory cytokines, such as IL-1β. Studies have shown that cellular uptake of crystalline particles may trigger NLRP3 inflammasome activation, leading to the cleavage of the IL-1β precursor to its mature form. Phagocytosis of dental calculus in the periodontal pocket may therefore lead to the secretion of IL-1β, promoting inflammatory responses in periodontal tissues. However, the capacity of dental calculus to induce IL-1β secretion in human phagocytes has not been explored. To study this, we stimulated human polymorphonuclear leukocytes (PMNs) and peripheral blood mononuclear cells (PBMCs) with dental calculus collected from periodontitis patients, and measured IL-1β secretion by ELISA. We found that calculus induced IL-1β secretion in both human PMNs and PBMCs. Calculus also induced IL-1β in macrophages from wild-type mice, but not in macrophages from NLRP3- and ASC-deficient mice, indicating the involvement of NLRP3 and ASC. IL-1β induction was inhibited by polymyxin B, suggesting that LPS is one of the components of calculus that induces pro-IL-1β transcription. To analyze the effect of the inorganic structure, we baked calculus at 250°C for 1 h. This baked calculus failed to induce pro-IL-1β transcription. However, it did induce IL-1β secretion in lipid A-primed cells, indicating that the crystalline structure of calculus induces inflammasome activation. Furthermore, hydroxyapatite crystals, a component of dental calculus, induced IL-1β in mouse macrophages, and baked calculus induced IL-1β in lipid A-primed human PMNs and PBMCs. These results indicate that dental calculus stimulates IL-1β secretion via NLRP3 inflammasome in human and mouse phagocytes, and that the crystalline structure has a partial role in the activation of NLRP3 inflammasome.

[Single and combining effects of Calculus Bovis and zolpidem on inhibitive neurotransmitter of rat striatum corpora].

PubMed

Liu, Ping; He, Xinrong; Guo, Mei

2010-04-01

To investigate the correlation effects between single or combined administration of Calculus Bovis or zolpidem and changes of inhibitive neurotransmitter in rat striatum corpora. Sampling from rat striatum corpora was carried out through microdialysis. The content of two inhibitive neurotransmitters in rat corpus striatum- glycine (Gly) and gama aminobutyric acid (GABA), was determined by HPLC, which involved pre-column derivation with orthophthaladehyde, reversed-phase gradient elution and fluorescence detection. GABA content of rat striatum corpora in Calculus Bovis group was significantly increased compared with saline group (P < 0.01). GABA content of zolpidem group and Calculus Boris plus zolpidem group were increased largely compared with saline group as well (P < 0.05). GABA content of Calculus Bovis group was higher than combination group (P < 0.05). GABA content of zolpidem group was not significantly different from combination group. Gly content of Calculus Bovis or zolpidem group was markedly increased compared with saline group or combination group (P < 0.05). Contents of two inhibitive neurotransmitters in rat striatum corpora were all significantly increased in Calculus Bovis group, zolpidem group and combination group. The magnitude of increase was lower in combination group than in Calculus Bovis group and Zolpidem group, suggesting that Calculus Bovis promoted encephalon inhibition is more powerful than zolpidem. The increase in two inhibitive neurotransmitters did not show reinforcing effect in combination group, suggesting that Calculus Bovis and zolpidem may compete the same receptors. Therefore, combination of Calculus Bovis containing drugs and zolpidem has no clinical significance. Calculus Bovis shouldn't as an aperture-opening drugs be used for resuscitation therapy.

Some basic results on the sets of sequences with geometric calculus

NASA Astrophysics Data System (ADS)

Türkmen, Cengiz; Başar, Feyzi

2012-08-01

As an alternative to the classical calculus, Grossman and Katz [Non-Newtonian Calculus, Lee Press, Pigeon Cove, Massachusetts, 1972] introduced the non-Newtonian calculus consisting of the branches of geometric, anageometric and bigeometric calculus. Following Grossman and Katz, we construct the field C(G) of geometric complex numbers and the concept of geometric metric. Also we give the triangle and Minkowski's inequalities in the sense of geometric calculus. Later we respectively define the sets w(G), ℓ∞(G), c(G), c0(G) and ℓp(G) of all, bounded, convergent, null and p-absolutely summable sequences, in the sense of geometric calculus and show that each of the set forms a complete vector space on the field C(G).

Extending the Phase Zero Campaign Mindset

DTIC Science & Technology

2007-01-01

activities would automatically take U.S. forces out of the fight in current operations. Instead, it would improve the calculus of the Government’s...ndu.edu Liaison officer  for U.S. State  Department  training Iraqi  police Fleet Combat Camera, Pacific (Martin Anton Edgil) Extending the Phase

Meshes optimized for discrete exterior calculus (DEC).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mousley, Sarah C.; Deakin, Michael; Knupp, Patrick

We study the optimization of an energy function used by the meshing community to measure and improve mesh quality. This energy is non-traditional because it is dependent on both the primal triangulation and its dual Voronoi (power) diagram. The energy is a measure of the mesh's quality for usage in Discrete Exterior Calculus (DEC), a method for numerically solving PDEs. In DEC, the PDE domain is triangulated and this mesh is used to obtain discrete approximations of the continuous operators in the PDE. The energy of a mesh gives an upper bound on the error of the discrete diagonal approximationmore » of the Hodge star operator. In practice, one begins with an initial mesh and then makes adjustments to produce a mesh of lower energy. However, we have discovered several shortcomings in directly optimizing this energy, e.g. its non-convexity, and we show that the search for an optimized mesh may lead to mesh inversion (malformed triangles). We propose a new energy function to address some of these issues.« less

Restricted diversity of dental calculus methanogens over five centuries, France.

PubMed

Huynh, Hong T T; Nkamga, Vanessa D; Signoli, Michel; Tzortzis, Stéfan; Pinguet, Romuald; Audoly, Gilles; Aboudharam, Gérard; Drancourt, Michel

2016-05-11

Methanogens are acknowledged archaeal members of modern dental calculus microbiota and dental pathogen complexes. Their repertoire in ancient dental calculus is poorly known. We therefore investigated archaea in one hundred dental calculus specimens collected from individuals recovered from six archaeological sites in France dated from the 14(th) to 19(th) centuries AD. Dental calculus was demonstrated by macroscopic and cone-beam observations. In 56 calculus specimens free of PCR inhibition, PCR sequencing identified Candidatus Methanobrevibacter sp. N13 in 44.6%, Methanobrevibacter oralis in 19.6%, a new Methanomassiliicoccus luminyensis-like methanogen in 12.5%, a Candidatus Nitrososphaera evergladensis-like in one and Methanoculleus bourgensis in one specimen, respectively. One Candidatus Methanobrevibacter sp. N13 dental calculus was further documented by fluorescent in situ hybridization. The prevalence of dental calculus M. oralis was significantly lower in past populations than in modern populations (P = 0.03, Chi-square test). This investigation revealed a previously unknown repertoire of archaea found in the oral cavity of past French populations as reflected in preserved dental calculus.

In vitro and clinical evaluation of optical coherence tomography for the detection of subgingival calculus and root cementum.

PubMed

Tsubokawa, Masaki; Aoki, Akira; Kakizaki, Sho; Taniguchi, Yoichi; Ejiri, Kenichiro; Mizutani, Koji; Koshy, Geena; Akizuki, Tatsuya; Oda, Shigeru; Sumi, Yasunori; Izumi, Yuichi

2018-05-24

This study evaluated the effectiveness of swept-source optical coherence tomography (ss-OCT) for detecting calculus and root cementum during periodontal therapy. Optical coherence tomography (OCT) images were taken before and after removal of subgingival calculus from extracted teeth and compared with non-decalcified histological sections. Porcine gingival sheets of various thicknesses were applied to the root surfaces of extracted teeth with calculus and OCT images were taken. OCT images were also taken before and after scaling and root planing (SRP) in human patients. In vitro, calculus was clearly detected as a white-gray amorphous structure on the root surface, which disappeared after removal. Cementum was identified as a thin, dark-gray layer. The calculus could not be clearly observed when soft tissues were present on the root surface. Clinically, supragingival calculus and cementum could be detected clearly with OCT, and subgingival calculus in the buccal cervical area of the anterior and premolar teeth was identified, which disappeared after SRP. Digital processing of the original OCT images was useful for clarifying the calculus. In conclusion, ss-OCT showed potential as a periodontal diagnostic tool for detecting cementum and subgingival calculus, although the practical applications of subgingival imaging remain limited.

Molecular symmetry with quaternions.

PubMed

Fritzer, H P

2001-09-01

A new and relatively simple version of the quaternion calculus is offered which is especially suitable for applications in molecular symmetry and structure. After introducing the real quaternion algebra and its classical matrix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism properties of the algebra are discussed. The correlation of the unit quaternions with both the Cayley-Klein and the Euler parameters through the group SU(2) is presented. Besides rotations the extension of quaternions to other important symmetry operations, reflections and the spatial inversion, is given. Finally, the power of the quaternion calculus for molecular symmetry problems is revealed by treating some examples applied to icosahedral symmetry.

Supragingival calculus in children with gastrostomy feeding: significant reduction with a caregiver-applied tartar-control dentifrice.

PubMed

Brown, Laurie M; Casamassimo, Paul S; Griffen, Ann; Tatakis, Dimitris

2006-01-01

This study assessed the anti-calculus benefit of Crest Dual Action Whitening Toothpaste in gastrostomy (GT) children compared to a control anti-caries dentifrice. A double-blind randomized crossover design was used to compare the two dentifrices. A convenience sample of 24 GT subjects, 3-12 years old, was given a consensus baseline Volpe-Manhold Index calculus score by 2 trained examiners, followed by a dental prophylaxis to remove all calculus. Each child was randomly assigned to either study or control dentifrice groups. Caregivers brushed subjects' teeth twice daily with the unlabelled dentifrice for at least 45 seconds. Calculus was scored at 8 weeks (+/- 1 week) by the same investigators. Subjects then had a prophylaxis and received the alternative dentifrice. Subjects returned 8 weeks (+/- 1 week) later for final calculus scoring. The study dentifrice significantly reduced supragingival calculus from baseline by 58% compared to control dentifrice (p<0.005 need exact p-value unless it is <.001; maybe it's reported in the paper). Calculus levels decreased by 68% over the study duration, irrespective of dentifrice. ANOVA found no significant differences in calculus scores based on gender, race, history of reflux, aspiration pneumonia, or oral intake of food. Calculus was significantly related to history of aspiration pneumonia (p<0.05 need exact p-value here). Crest Dual Action Whitening Toothpaste was effective and better than anti-caries control dentifrice in reducing calculus in GT children.

New picosecond laser emitting blue light for use in periodontology

NASA Astrophysics Data System (ADS)

Hennig, Thomas; Nieswand, Elmar; Rechmann, Peter

2001-04-01

Aim of the study was to investigate the impact of a new picosecond laser emitting blue light on tooth surfaces in order to remove calculus. The radiation may be comfortably transmitted via 25 micrometers diameter fiber optics. The resulting fluence at the tooth was found to be to low for ablation of calculus via nonlinear effects. Higher absorption of the 446 nm radiation by calculus compared to heathy tissues can provide preferential heating and evaporation of the calculus. The surface of thick calculus is irregular rough thus comprising a large interface to the surrounding cooling medium contra acting the preferential heating. In summary the study indicates the possibility flat layers of calculus by thermal effects. Carbonization in healthy tissues is the major problem concerning removal of subgingival calculus with thermal effects.

[Percentage of uric acid calculus and its metabolic character in Dongjiang River valley].

PubMed

Chong, Hong-Heng; An, Geng

2009-02-15

To study the percentage of uric acid calculus in uroliths and its metabolic character in Dongjiang River valley. To analyze the chemical composition of 290 urinary stones by infrared (IR) spectroscopy and study the ratio changes of uric acid calculus. Uric acid calculus patients and healthy people were studied. Personal characteristics, dietary habits were collected. Conditional logistic regression was used for data analysis and studied the dietary risk factors of uric acid calculus. Patients with uric acid calculus, calcium oxalate and those without urinary calculus were undergone metabolic evaluation analysis. The results of uric acid calculus patients compared to another two groups to analysis the relations between the formation of uric acid calculus and metabolism factors. Uric acid calculi were found in 53 cases (18.3%). The multiple logistic regression analysis suggested that low daily water intake, eating more salted and animal food, less vegetable were very closely associated with uric acid calculus. Comparing to calcium oxalate patients, the urine volume, the value of pH, urine calcium, urine oxalic acid were lower, but uric acid was higher than it. The value of pH, urine oxalic acid and citric acid were lower than them, but uric acid and urine calcium were higher than none urinary calculus peoples. Blood potassium and magnesium were lower than them. The percentage of uric acid stones had obvious advanced. Less daily water intake, eating salted food, eating more animal food, less vegetables and daily orange juice intake, eating sea food are the mainly dietary risk factors to the formation of uric acid calculus. Urine volume, the value of pH, citric acid, urine calcium, urine uric acid and the blood natrium, potassium, magnesium, calcium, uric acid have significant influence to the information of uric acid stones.

Dental Calculus Arrest of Dental Caries.

PubMed

Keyes, Paul H; Rams, Thomas E

An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. These observations further document the potential protective effects of dental calculus mineralization against dental caries.

Dental Calculus Arrest of Dental Caries

PubMed Central

Keyes, Paul H.; Rams, Thomas E.

2016-01-01

Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. Materials and methods A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Results Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. Conclusions These observations further document the potential protective effects of dental calculus mineralization against dental caries. PMID:27446993

[Management experience of acute renal failure induced by unilateral ureteral calculi obstruction].

PubMed

Tan, Fu-qing; Shen, Bo-hua; Xie, Li-ping; Meng, Hong-zhou; Fang, Dan-bo; Wang, Chao-jun

2013-05-28

To explore the causes and treatment options of acute renal failure induced by unilateral ureteral calculi obstruction. The clinical data of 12 cases of acute renal failure induced by unilateral ureteral calculi obstruction between August 2008 and July 2012 were reviewed retrospectively. There were 5 males and 7 females with an average age of 65.7 years. Their clinical data and treatment options were retrospectively analyzed and summarized. Seven cases showed right side ureteral calculus with hydronephrosis while another 5 presented left side ureteral calculus with hydronephrosis. Serum creatinine was higher than 310 µmol/L in 12 cases. Anuria appeared in 4 cases for 1-7 days while oliguria in 8 cases for 2-10 days. High fever was present in 11 cases, the highest of whom was 40 °C. White blood cell count increased in 10 cases (>10×10(9)/L) and decreased in 2 cases (<4 × 10(9)/L). The therapeutic options included insertion of double J stent for internal drainage (n = 1), percutaneous nephrostomy for external drainage (n = 10) and open operation (n = 1). Traditional treatments were performed to manage ureteral calculus in the above 11 cases with drainage. All cases had improved renal function after comprehensive treatment of anti-infection, antishock, rinsing stones and relieving obstruction. All 12 cases were treated successfully. Unilateral ureteral calculus may impair contralateral renal function and cause acute renal failure due to the absorption of toxin at obstructive side. The keys of management are eliminating toxin and relieving obstruction.

An implementation problem for boson fields and quantum Girsanov transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr; Obata, Nobuaki, E-mail: obata@math.is.tohoku.ac.jp

2016-08-15

We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier–Gauss and Fourier–Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.

Differential Calculus on h-Deformed Spaces

NASA Astrophysics Data System (ADS)

Herlemont, Basile; Ogievetsky, Oleg

2017-10-01

We construct the rings of generalized differential operators on the h-deformed vector space of gl-type. In contrast to the q-deformed vector space, where the ring of differential operators is unique up to an isomorphism, the general ring of h-deformed differential operators {Diff}_{h},σ(n) is labeled by a rational function σ in n variables, satisfying an over-determined system of finite-difference equations. We obtain the general solution of the system and describe some properties of the rings {Diff}_{h},σ(n).

A new method for identification of natural, artificial and in vitro cultured Calculus bovis using high-performance liquid chromatography-mass spectrometry

PubMed Central

Liu, Yonggang; Tan, Peng; Liu, Shanshan; Shi, Hang; Feng, Xin; Ma, Qun

2015-01-01

Objective: Calculus bovis have been widely used in Chinese herbology for the treatment of hyperpyrexia, convulsions, and epilepsy. Nowadays, due to the limited source and high market price, the substitutes, artificial and in vitro cultured Calculus bovis, are getting more and more commonly used. The adulteration phenomenon is serious. Therefore, it is crucial to establish a fast and simple method in discriminating the natural, artificial and in vitro cultured Calculus bovis. Bile acids, one of the main active constituents, are taken as an important indicator for evaluating the quality of Calculus bovis and the substitutes. Several techniques have been built to analyze bile acids in Calculus bovis. Whereas, as bile acids are with poor ultraviolet absorbance and high structural similarity, effective technology for identification and quality control is still lacking. Methods: In this study, high-performance liquid chromatography (HPLC) coupled with tandem mass spectrometry (LC/MS/MS) was applied in the analysis of bile acids, which effectively identified natural, artificial and in vitro cultured Calculus bovis and provide a new method for their quality control. Results: Natural, artificial and in vitro cultured Calculus bovis were differentiated by bile acids analysis. A new compound with protonated molecule at m/z 405 was found, which we called 3α, 12α-dihydroxy-7-oxo-5α-cholanic acid. This compound was discovered in in vitro cultured Calculus bovis, but almost not detected in natural and artificial Calculus bovis. A total of 13 constituents was identified. Among them, three bio-markers, including glycocholic acid, glycodeoxycholic acid and taurocholic acid (TCA) were detected in both natural and artificial Calculus bovis, but the density of TCA was different in two kinds of Calculus bovis. In addition, the characteristics of bile acids were illustrated. Conclusions: The HPLC coupled with tandem MS (LC/MS/MS) method was feasible, easy, rapid and accurate in identifying natural, artificial and in vitro cultured Calculus bovis. PMID:25829769

Tubeless versus standard PCNL in geriatric population.

PubMed

Ozturk, H

2015-10-01

Percutaneous nephrolithotomy (PCNL) is a standard, safe, and efficient method for large-volume renal calculi for all age groups. Nephrostomy tube constitutes an invaluable part of the nephrolithotomy operation. However, the nephrostomy tube has been recently replaced with ureteral catheter or double J-stent thanks to advances in urotechnology and operation equipment. The aim of the current article was to evaluate the safety and reliability of tubeless percutaneous nephrolithotomy in the geriatric population. Between January 2009 and September 2013, a total of 52 patients aged 65 years or elder with renal calculi bigger than 2cm underwent PCNL operation. The first group of 25 patients (48%) with a mean age of 70.0 years (std:±3,8) underwent tubeless PCNL whereas the second group consisting of 27 (52%) patients with a mean age of 71.3 years (std: ±4,0) underwent standard PCNL. The patients were randomly compared retrospectively in terms of burden of calculus, analgesic requirement, creatinine value, renal parenchymal thickness, Body-mass index (BMI), clavien score, length of hospitalization, and being calculus-free. The groups were found to be similar in age, BMI, and gender (P>.05). Burden of calculus, duration of operation, and rate of narcotic analgesic use were found to be statistically significantly higher in the group of Standard PCNL group than in the Tubeless PCNL group (P<.05). Length of hospital stay was 1.7 days in the group of tubeless PCNL and 2.6 days in the standard PCNL group (P<.05). No significant difference was found between the groups in terms of fall in hemoglobin, creatinine, values of parenchymal thickness, and clavien score, preoperative blood transfusion, previous SWL, location of calculi, number of access, and rate of success (P>.05). Burden of calculus was 900 mm2 (304-4232) in the standard PCNL group and 600mm(2) (220-2660) in the tubeless PCNL group with the difference being statistically significant (P=.014). Overall success was achieved in 96.0 and 96.3% of tubeless PCNL and standard PCNL patients after one session of PCNL, respectively. Tubeless percutaneous nephrolithotomy was found to be as safe and effective as standard PCNL in the geriatric population. It is recommended especially in this group of patients because of its advantages such as shorter length of hospitalization, less analgesic requirement, and earlier mobilization. Copyright © 2014 AEU. Publicado por Elsevier España, S.L.U. All rights reserved.

Maxima and Minima Without Calculus.

ERIC Educational Resources Information Center

Birnbaum, Ian

1982-01-01

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

Pulsed laser ablation of dental calculus in the near ultraviolet.

PubMed

Schoenly, Joshua E; Seka, Wolf; Rechmann, Peter

2014-02-01

Pulsed lasers emitting wavelengths near 400 nm can selectively ablate dental calculus without damaging underlying and surrounding sound dental hard tissue. Our results indicate that calculus ablation at this wavelength relies on the absorption of porphyrins endogenous to oral bacteria commonly found in calculus. Sub- and supragingival calculus on extracted human teeth, irradiated with 400-nm, 60-ns laser pulses at ≤8  J/cm2, exhibits a photobleached surface layer. Blue-light microscopy indicates this layer highly scatters 400-nm photons, whereas fluorescence spectroscopy indicates that bacterial porphyrins are permanently photobleached. A modified blow-off model for ablation is proposed that is based upon these observations and also reproduces our calculus ablation rates measured from laser profilometry. Tissue scattering and a stratified layering of absorbers within the calculus medium explain the gradual decrease in ablation rate from successive pulses. Depending on the calculus thickness, ablation stalling may occur at <5  J/cm2 but has not been observed above this fluence.

Detection, removal and prevention of calculus: Literature Review

PubMed Central

Kamath, Deepa G.; Umesh Nayak, Sangeeta

2013-01-01

Dental plaque is considered to be a major etiological factor in the development of periodontal disease. Accordingly, the elimination of supra- and sub-gingival plaque and calculus is the cornerstone of periodontal therapy. Dental calculus is mineralized plaque; because it is porous, it can absorb various toxic products that can damage the periodontal tissues. Hence, calculus should be accurately detected and thoroughly removed for adequate periodontal therapy. Many techniques have been used to identify and remove calculus deposits present on the root surface. The purpose of this review was to compile the various methods and their advantages for the detection and removal of calculus. PMID:24526823

Developing the Fundamental Theorem of Calculus. Applications of Calculus to Work, Area, and Distance Problems. [and] Atmospheric Pressure in Relation to Height and Temperature. Applications of Calculus to Atmospheric Pressure. [and] The Gradient and Some of Its Applications. Applications of Multivariate Calculus to Physics. [and] Kepler's Laws and the Inverse Square Law. Applications of Calculus to Physics. UMAP Units 323, 426, 431, 473.

ERIC Educational Resources Information Center

Lindstrom, Peter A.; And Others

This document consists of four units. The first of these views calculus applications to work, area, and distance problems. It is designed to help students gain experience in: 1) computing limits of Riemann sums; 2) computing definite integrals; and 3) solving elementary area, distance, and work problems by integration. The second module views…

The clinical anticalculus efficacy of a tartar control whitening dentifrice for the prevention of supragingival calculus in a three-month study.

PubMed

Sowinski, J; Petrone, D M; Battista, G; Petrone, M E; Crawford, R; Patel, S; DeVizio, W; Chaknis, P; Volpe, A R; Proskin, H M

1999-01-01

The objective of this double-blind clinical study was to compare the effect of a new dentifrice (Colgate Tartar Control Plus Whitening Fluoride Toothpaste) for the prevention of supragingival calculus, with that of a commercially available calculus-inhibiting dentifrice (Crest Tartar Control Toothpaste). The study involved adult male and female subjects who had pre-qualified for participation by developing sufficient supragingival calculus (greater than 7.0 on the Volpe-Manhold Calculus Index) during an eight-week screening period. Subjects received a full oral prophylaxis, and were stratified into two treatment groups balanced for age, sex and qualifying calculus score. Subjects were instructed to brush their teeth twice daily (morning and evening) for one minute with their assigned dentifrice using a soft-bristled toothbrush. Examinations for dental calculus were performed after twelve weeks' use of the study dentifrices, using the Volpe-Manhold Calculus Index, Fifty-eight (58) subjects complied with the protocol and completed the entire study. The Colgate Tartar Control Plus Whitening group exhibited a statistically significant (p < 0.001) 34.6% reduction in mean calculus score compared to the Crest Tartar Control group.

Partial Fractions via Calculus

ERIC Educational Resources Information Center

Bauldry, William C.

2018-01-01

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

The efficacy of selective calculus ablation at 400 nm: comparison to conventional calculus removal methods

NASA Astrophysics Data System (ADS)

Schoenly, Joshua E.; Seka, Wolf; Romanos, Georgios; Rechmann, Peter

A desired outcome of scaling and root planing is the complete removal of calculus and infected root tissue and preservation of healthy cementum for rapid healing of periodontal tissues. Conventional periodontal treatments for calculus removal, such as hand instrument scaling and ultrasonic scaling, often deeply scrape the surface of the underlying hard tissue and may leave behind a smear layer. Pulsed lasers emitting at violet wavelengths (specifically, 380 to 400 nm) are a potential alternative treatment since they can selectively ablate dental calculus without ablating pristine hard tissue (i.e., enamel, cementum, and dentin). In this study, light and scanning electron microscopy are used to compare and contrast the efficacy of in vitro calculus removal for several conventional periodontal treatments (hand instruments, ultrasonic scaler, and Er:YAG laser) to calculus removal with a frequency-doubled Ti:sapphire (λ = 400 nm). After calculus removal, enamel and cementum surfaces are investigated for calculus debris and damage to the underlying hard tissue surface. Compared to the smear layer, grooves, and unintentional hard tissue removal typically found using these conventional treatments, calculus removal using the 400-nm laser is complete and selective without any removal of pristine dental hard tissue. Based on these results, selective ablation from the 400-nm laser appears to produce a root surface that would be more suitable for successful healing of periodontal tissues.

Effect of non-functional teeth on accumulation of supra-gingival calculus in children.

PubMed

Ashkenazi, M; Miller, R; Levin, L

2012-10-01

To evaluate the occurrence of supra-gingival calculus in children aged 6-9 years with disuse conditions such as: presence of dental pain, open-bite or erupting teeth. A cohort of 327 children aged 7.64±2.12 (range: 6-9) years (45% girls) were screened for presence of supra-gingival calculus in relation to open bite, erupting teeth and dental pain. Presence of dental calculus was evaluated dichotomically in the buccal, palatinal/lingual and occlusal surfaces. Plaque index (PI) and gingival index (GI) were also evaluated. Supra-gingival calculus was found in 15.9% of the children mainly in the mandibular incisors. Children aged 6-7 years had a higher prevalence of calculus as compared to children aged 7-8 years (23% vs. 13.5%, p=0.057) or 8-9 years (23% vs. 12.4%, p=0.078), respectively. No statistical relation was found between plaque and gingival indices and presence of calculus. The prevalence of calculus among children with openbite was significantly higher than that of children without open-bite (29.4% vs. 10.7%, p=0.0006, OR=3.489). The prevalence of calculus among children with erupting teeth in their oral cavity was higher than that of children without erupting teeth (17.7% vs. 9%, respectively, p=0.119). No statistical correlation was found between presence of dental pain and calculus (15.4% vs. 15.9%; p=0.738). Accumulation of calculus in children aged 6-10 years was found mainly in the mandibular incisors, decreased with age and was correlated with open-bite.

Matrix-Gla Protein rs4236 [A/G] gene polymorphism and serum and GCF levels of MGP in patients with subgingival dental calculus.

PubMed

Doğan, Gülnihal Emrem; Demir, Turgut; Aksoy, Hülya; Sağlam, Ebru; Laloğlu, Esra; Yildirim, Abdulkadir

2016-10-01

Matrix-Gla Protein (MGP) is one of the major Gla-containing protein associated with calcification process. It also has a high affinity for Ca 2+ and hydroxyapatite. In this study we aimed to evaluate the MGP rs4236 [A/G] gene polymorphism in association with subgingival dental calculus. Also a possible relationship between MGP gene polymorphism and serum and GCF levels of MGP were examined. MGP rs4236 [A/G] gene polymorphism was investigated in 110 patients with or without subgingival dental calculus, using polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) techniques. Additionally, serum and GCF levels of MGP of the patients were compared according to subgingival dental calculus. Comparison of patients with and without subgingival dental calculus showed no statistically significant difference in MGP rs4236 [A/G] gene polymorphism (p=0.368). MGP concentrations in GCF of patients with subgingival dental calculus were statistically higher than those without subgingival dental calculus (p=0.032). However, a significant association was not observed between the genotypes of AA, AG and GG of the MGP rs4236 gene and the serum and GCF concentrations of MGP in subjects. In this study, it was found that MGP rs4236 [A/G] gene polymorphism was not to be associated with subgingival dental calculus. Also, that GCF MGP levels were detected higher in patients with subgingival dental calculus than those without subgingival dental calculus independently of polymorphism, may be the effect of adaptive mechanism to inhibit calculus formation. Copyright © 2016 Elsevier Ltd. All rights reserved.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

An AP Calculus Classroom Amusement Park

ERIC Educational Resources Information Center

Ferguson, Sarah

2016-01-01

Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.…

Early Vector Calculus: A Path through Multivariable Calculus

ERIC Educational Resources Information Center

Robertson, Robert L.

2013-01-01

The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)

A Historical Perspective on Teaching and Learning Calculus

ERIC Educational Resources Information Center

Doorman, Michiel; van Maanen, Jan

2008-01-01

Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of reasoning. The calculus of Leibniz brings within the reach of an ordinary student…

Subgingival calculus imaging based on swept-source optical coherence tomography

NASA Astrophysics Data System (ADS)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Lu, Chih-Wei; Jiang, Cho-Pei; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-07-01

We characterized and imaged dental calculus using swept-source optical coherence tomography (SS-OCT). The refractive indices of enamel, dentin, cementum, and calculus were measured as 1.625 +/- 0.024, 1.534 +/- 0.029, 1.570 +/- 0.021, and 2.097 +/- 0.094, respectively. Dental calculus leads strong scattering properties, and thus, the region can be identified from enamel with SS-OCT imaging. An extracted human tooth with calculus is covered with gingiva tissue as an in vitro sample for tomographic imaging.

Dental calculus image based on optical coherence tomography

NASA Astrophysics Data System (ADS)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-03-01

In this study, the dental calculus was characterized and imaged by means of swept-source optical coherence tomography (SSOCT). The refractive indices of enamel, dentin, cementum and calculus were measured as 1.625+/-0.024, 1.534+/-0.029, 1.570+/-0.021 and 1.896+/-0.085, respectively. The dental calculus lead strong scattering property and thus the region can be identified under enamel with SSOCT imaging. An extracted human tooth with calculus was covered by gingiva tissue as in vitro sample for SSOCT imaging.

Questions Revisited: A Close Examination of Calculus of Inference and Inquiry

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.; Koga, Dennis (Technical Monitor)

2003-01-01

In this paper I examine more closely the way in which probability theory, the calculus of inference, is derived from the Boolean lattice structure of logical assertions ordered by implication. I demonstrate how the duality between the logical conjunction and disjunction in Boolean algebra is lost when deriving the probability calculus. In addition, I look more closely at the other lattice identities to verify that they are satisfied by the probability calculus. Last, I look towards developing the calculus of inquiry demonstrating that there is a sum and product rule for the relevance measure as well as a Bayes theorem. Current difficulties in deriving the complete inquiry calculus will also be discussed.

Preservation of the metaproteome: variability of protein preservation in ancient dental calculus.

PubMed

Mackie, Meaghan; Hendy, Jessica; Lowe, Abigail D; Sperduti, Alessandra; Holst, Malin; Collins, Matthew J; Speller, Camilla F

2017-01-01

Proteomic analysis of dental calculus is emerging as a powerful tool for disease and dietary characterisation of archaeological populations. To better understand the variability in protein results from dental calculus, we analysed 21 samples from three Roman-period populations to compare: 1) the quantity of extracted protein; 2) the number of mass spectral queries; and 3) the number of peptide spectral matches and protein identifications. We found little correlation between the quantity of calculus analysed and total protein identifications, as well as no systematic trends between site location and protein preservation. We identified a wide range of individual variability, which may be associated with the mechanisms of calculus formation and/or post-depositional contamination, in addition to taphonomic factors. Our results suggest dental calculus is indeed a stable, long-term reservoir of proteins as previously reported, but further systematic studies are needed to identify mechanisms associated with protein entrapment and survival in dental calculus.

Recalling Prerequisite Material in a Calculus II Course to Improve Student Success

ERIC Educational Resources Information Center

Mokry, Jeanette

2016-01-01

This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…

The Path to College Calculus: The Impact of High School Mathematics Coursework

ERIC Educational Resources Information Center

Sadler, Philip; Sonnert, Gerhard

2018-01-01

This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus-- (a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? We used a data set…

The Development and Nature of Problem-Solving among First-Semester Calculus Students

ERIC Educational Resources Information Center

Dawkins, Paul Christian; Epperson, James A. Mendoza

2014-01-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate…

Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

ERIC Educational Resources Information Center

Patel, Rita Manubhai; McCombs, Paul; Zollman, Alan

2014-01-01

Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student…

The History of the Calculus

ERIC Educational Resources Information Center

Harding, Simon; Scott, Paul

2004-01-01

Calculus is a mathematical concept that is fundamental to how we understand the world around us. Whether it is in the world of technology, finance, astronomy, sociology, medicine, calculus in one form or another can be found. This brief article describes the origins of calculus in Greece, further developments by Newton and Leibniz, and the…

Polynomial Calculus: Rethinking the Role of Calculus in High Schools

ERIC Educational Resources Information Center

Grant, Melva R.; Crombie, William; Enderson, Mary; Cobb, Nell

2016-01-01

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

Calculus ABCs: A Gateway for Freshman Calculus

ERIC Educational Resources Information Center

Fulton, Scott R.

2003-01-01

This paper describes a gateway testing program designed to ensure that students acquire basic skills in freshman calculus. Students must demonstrate they have mastered standards for "Absolutely Basic Competency"--the Calculus ABCs--in order to pass the course with a grade of C or better. We describe the background, standards, and testing program.…

Unusual Case of Calculus in Floor of Mouth: A Case Report

PubMed Central

Thosar, Nilima; Jain, Eesha S

2012-01-01

Abstract Calculus consists of mineralized bacterial plaque that forms on the surfaces of natural teeth. It is supragingival or subgingival depending upon its relation with gingival margin. The two most common locations for supragingival calculus are the buccal surfaces of maxillary molars and lingual surfaces of mandibular anterior teeth. It is very important to rule out the predisposing factor for calculus formation. In the present case of an 11-year- old female child, 1.2 × 1.5 cm large indurated mass suggestive of calculus in the left side of floor of mouth was observed. After surgical removal, along with indurated mass, an embedded root fragment was seen. Biochemical analysis of the specimen detected the calcium and phosphate ions approximately equals to the level in calculus. Thus, we diagnosed it as a calculus. Oral hygiene instructions and regular follow-up was advised. How to cite this article: Bahadure RN, Thosar N, Jain ES. Unusual Case of Calculus in Floor of Mouth: A Case Report. Int J Clin Pediatr Dent 2012;5(3):223-225. PMID:25206174

Investigation of In vitro Mineral forming bacterial isolates from supragingival calculus.

PubMed

Baris, O; Demir, T; Gulluce, M

2017-12-01

Although it is known that bacterial mechanisms are involved in dental calculus formation, which is a predisposing factor in periodontal diseases, there have been few studies of such associations, and therefore, information available is limited. The purpose of this study was to isolate and identify aerobic bacteria responsible for direct calcification from supragingival calculus samples. The study was conducted using supragingival calculus samples from patients with periodontal disease, which was required as part of conventional treatment. Isolations were performed by sampling the supragingival calculus with buffer and inoculating the samples on media on which crystallization could be observed. The 16S recombinant DNA of the obtained pure cultures was then amplified and sequenced. A few bacterial species that have not previously been associated with mineralization or identified on bacterial plaque or calculus were detected. The bacteria that caused mineralization an aerobic environment are identified as Neisseria flava, Aggregatibacter segnis, Streptococcus tigurinus, and Morococcus cerebrosus. These findings proved that bacteria potentially play a role in the etiopathology of supragingival calculus. The association between the effects of the identified bacteria on periodontal diseases and calculus formation requires further studies.

Dental calculus formation in children and adolescents undergoing hemodialysis.

PubMed

Martins, Carla; Siqueira, Walter Luiz; Oliveira, Elizabeth; Nicolau, José; Primo, Laura Guimarães

2012-10-01

This study aimed to determine whether dental calculus formation is really higher among patients with chronic kidney disease undergoing hemodialysis than among controls. Furthermore, the study evaluated correlations between dental calculus formation and dental plaque, variables that are related to renal disease and/or saliva composition. The Renal Group was composed of 30 patients undergoing hemodialysis, whereas the Healthy Group had 30 clinically healthy patients. Stimulated whole saliva and parotid saliva were collected. Salivary flow rate and calcium and phosphate concentrations were determined. In the Renal Group the saliva collection was carried out before and after a hemodialysis session. Patients from both groups received intraoral exams, oral hygiene instructions, and dental scaling. Three months later, the dental calculus was measured by the Volpe-Manhold method to determine the rate of dental calculus formation. The Renal Group presented a higher rate of dental calculus formation (p < 0.01). Correlation was observed between rate of dental calculus formation and whole saliva flow rate in the Renal Group after a hemodialysis session (r = 0.44, p < 0.05). The presence of dental calculus was associated with phosphate concentration in whole saliva from the Renal Group (p < 0.05). In conclusion, patients undergoing hemodialysis presented accelerated dental calculus formation, probably due to salivary variables.

The Case for Biocalculus: Design, Retention, and Student Performance

PubMed Central

Eaton, Carrie Diaz; Highlander, Hannah Callender

2017-01-01

Calculus is one of the primary avenues for initial quantitative training of students in all science, technology, engineering, and mathematics fields, but life science students have been found to underperform in the traditional calculus setting. As a result, and because of perceived lack of its contribution to the understanding of biology, calculus is being actively cut from biology program requirements at many institutions. Here, we present an alternative: a model for learning mathematics that sees the partner disciplines as crucial to student success. We equip faculty with information to engage in dialogue within and between disciplinary departments involved in quantitative education. This includes presenting a process for interdisciplinary development and implementation of biology-oriented Calculus I courses at two institutions with different constituents, goals, and curricular constraints. When life science students enrolled in these redesigned calculus courses are compared with life science students enrolled in traditional calculus courses, students in the redesigned calculus courses learn calculus concepts and skills as well as their traditional course peers; however, the students in the redesigned courses experience more authentic life science applications and are more likely to stay and succeed in the course than their peers who are enrolled in traditional courses. Therefore, these redesigned calculus courses hold promise in helping life science undergraduate students attain Vision and Change recommended competencies. PMID:28450445

Improving student learning in calculus through applications

NASA Astrophysics Data System (ADS)

Young, C. Y.; Georgiopoulos, M.; Hagen, S. C.; Geiger, C. L.; Dagley-Falls, M. A.; Islas, A. L.; Ramsey, P. J.; Lancey, P. M.; Straney, R. A.; Forde, D. S.; Bradbury, E. E.

2011-07-01

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.

Fractal Effects in Lanchester Models of Combat

DTIC Science & Technology

2009-08-01

Lanchester models. 8. References 1 Aircraft in Warfare : The Dawn of the Fourth Arm, F W Lanchester , Constable & Co., London, 1916. 2 The Calculus of...Intermediate Asymptotics, G I Barenblatt, CUP, 1996. 14 Lanchester Models of Warfare Volumes 1 and 2, J G Taylor, Operations Research Society of America...Nagabhushana, Computers and Operations Research, 21, 615-628, 1994. 20 DSTO-TR-2331 18 Lanchester Type Models of Warfare , H K Weiss, Proc.First

The development and nature of problem-solving among first-semester calculus students

NASA Astrophysics Data System (ADS)

Dawkins, Paul Christian; Mendoza Epperson, James A.

2014-08-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem-solving performance, we observe that current instruction requires ongoing refinement to help students develop multi-register fluency and the ability to model quantitatively, as is called for in current US standards for mathematical instruction.

In vitro performance of DIAGNOdent laser fluorescence device for dental calculus detection on human tooth root surfaces.

PubMed

Rams, Thomas E; Alwaqyan, Abdulaziz Y

2017-10-01

This study assessed the reproducibility of a red diode laser device, and its capability to detect dental calculus in vitro on human tooth root surfaces. On each of 50 extracted teeth, a calculus-positive and calculus-free root surface was evaluated by two independent examiners with a low-power indium gallium arsenide phosphide diode laser (DIAGNOdent) fitted with a periodontal probe-like sapphire tip and emitting visible red light at 655 nm wavelength. Laser autofluorescence intensity readings of examined root surfaces were scored on a 0-99 scale, with duplicate assessments performed using the laser probe tip directed both perpendicular and parallel to evaluated tooth root surfaces. Pearson correlation coefficients of untransformed measurements, and kappa analysis of data dichotomized with a >40 autofluorescence intensity threshold, were calculated to assess intra- and inter-examiner reproducibility of the laser device. Mean autofluorescence intensity scores of calculus-positive and calculus-free root surfaces were evaluated with the Student's t -test. Excellent intra- and inter-examiner reproducibility was found for DIAGNOdent laser autofluorescence intensity measurements, with Pearson correlation coefficients above 94%, and kappa values ranging between 0.96 and 1.0, for duplicate readings taken with both laser probe tip orientations. Significantly higher autofluorescence intensity values were measured when the laser probe tip was directed perpendicular, rather than parallel, to tooth root surfaces. However, calculus-positive roots, particularly with calculus in markedly-raised ledges, yielded significantly greater mean DIAGNOdent laser autofluorescence intensity scores than calculus-free surfaces, regardless of probe tip orientation. DIAGNOdent autofluorescence intensity values >40 exhibited a stronger association with calculus (36.6 odds ratio) then measurements of ≥5 (20.1 odds ratio) when the laser probe tip was advanced parallel to root surfaces. Excellent intra- and inter-examiner reproducibility of autofluorescence intensity measurements was obtained with the DIAGNOdent laser fluorescence device on human tooth roots. Calculus-positive root surfaces exhibited significantly greater DIAGNOdent laser autofluorescence than calculus-free tooth roots, even with the laser probe tip directed parallel to root surfaces. These findings provide further in vitro validation of the potential utility of a DIAGNOdent laser fluorescence device for identifying dental calculus on human tooth root surfaces.

Crystalline structure of pulverized dental calculus induces cell death in oral epithelial cells.

PubMed

Ziauddin, S M; Yoshimura, A; Montenegro Raudales, J L; Ozaki, Y; Higuchi, K; Ukai, T; Kaneko, T; Miyazaki, T; Latz, E; Hara, Y

2018-06-01

Dental calculus is a mineralized deposit attached to the tooth surface. We have shown that cellular uptake of dental calculus triggers nucleotide-binding oligomerization domain-like receptor family pyrin domain-containing 3 (NLRP3) inflammasome activation, leading to the processing of the interleukin-1β precursor into its mature form in mouse and human phagocytes. The activation of the NLRP3 inflammasome also induced a lytic form of programmed cell death, pyroptosis, in these cells. However, the effects of dental calculus on other cell types in periodontal tissue have not been investigated. The aim of this study was to determine whether dental calculus can induce cell death in oral epithelial cells. HSC-2 human oral squamous carcinoma cells, HOMK107 human primary oral epithelial cells and immortalized mouse macrophages were exposed to dental calculus or 1 of its components, hydroxyapatite crystals. For inhibition assays, the cells were exposed to dental calculus in the presence or absence of cytochalasin D (endocytosis inhibitor), z-YVAD-fmk (caspase-1 inhibitor) or glyburide (NLRP3 inflammasome inhibitor). Cytotoxicity was determined by measuring lactate dehydrogenase (LDH) release and staining with propidium iodide. Tumor necrosis factor-α production was quantified by enzyme-linked immunosorbent assay. Oral epithelial barrier function was examined by permeability assay. Dental calculus induced cell death in HSC-2 cells, as judged by LDH release and propidium iodide staining. Dental calculus also induced LDH release from HOMK107 cells. Following heat treatment, dental calculus lost its capacity to induce tumor necrosis factor-α in mouse macrophages, but could induce LDH release in HSC-2 cells, indicating a major role of inorganic components in cell death. Hydroxyapatite crystals also induced cell death in both HSC-2 and HOMK107 cells, as judged by LDH release, indicating the capacity of crystal particles to induce cell death. Cell death induced by dental calculus was significantly inhibited by cytochalasin D, z-YVAD-fmk and glyburide, indicating NLRP3 inflammasome involvement. In permeability assays, dental calculus attenuated the barrier function of HSC-2 cell monolayers. Dental calculus induces pyroptotic cell death in human oral epithelial cells and the crystalline structure plays a major role in this process. Oral epithelial cell death induced by dental calculus might be important for the etiology of periodontitis. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

A Transition Course from Advanced Placement to College Calculus

ERIC Educational Resources Information Center

Lucas, Timothy A.; Spivey, Joseph

2011-01-01

In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…

Improving Calculus II and III through the Redistribution of Topics

ERIC Educational Resources Information Center

George, C. Yousuf; Koetz, Matt; Lewis, Heather A.

2016-01-01

Three years ago our mathematics department rearranged the topics in second and third semester calculus, moving multivariable calculus to the second semester and series to the third semester. This paper describes the new arrangement of topics, and how it could be adapted to calculus curricula at different schools. It also explains the benefits we…

On the Presentation of Pre-Calculus and Calculus Topics: An Alternate View

ERIC Educational Resources Information Center

Davydov, Aleksandr; Sturm-Beiss, Rachel

2008-01-01

The orders of presentation of pre-calculus and calculus topics, and the notation used, deserve careful study as they affect clarity and ultimately students' level of understanding. We introduce an alternate approach to some of the topics included in this sequence. The suggested alternative is based on years of teaching in colleges within and…

Computer Managed Instruction Homework Modules for Calculus I.

ERIC Educational Resources Information Center

Goodman-Petrushka, Sharon; Roitberg, Yael

This booklet contains 11 modules (290 multiple-choice items) designed for use in the first course of a three-course calculus sequence using the textbook "Calculus with Analytic Geometry" (Dennis G. Zill). In each module, relevant sections of the textbook are identified for users. It can, however, be used in conjunction with any calculus textbook.…

Subgingival calculus imaging based on swept-source optical coherence tomography.

PubMed

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Lu, Chih-Wei; Jiang, Cho-Pei; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-07-01

We characterized and imaged dental calculus using swept-source optical coherence tomography (SS-OCT). The refractive indices of enamel, dentin, cementum, and calculus were measured as 1.625 ± 0.024, 1.534 ± 0.029, 1.570 ± 0.021, and 2.097 ± 0.094, respectively. Dental calculus leads strong scattering properties, and thus, the region can be identified from enamel with SS-OCT imaging. An extracted human tooth with calculus is covered with gingiva tissue as an in vitro sample for tomographic imaging.

A new proof of the generalized Hamiltonian–Real calculus

PubMed Central

Gao, Hua; Mandic, Danilo P.

2016-01-01

The recently introduced generalized Hamiltonian–Real (GHR) calculus comprises, for the first time, the product and chain rules that makes it a powerful tool for quaternion-based optimization and adaptive signal processing. In this paper, we introduce novel dual relationships between the GHR calculus and multivariate real calculus, in order to provide a new, simpler proof of the GHR derivative rules. This further reinforces the theoretical foundation of the GHR calculus and provides a convenient methodology for generic extensions of real- and complex-valued learning algorithms to the quaternion domain.

Calculus detection technologies: where do we stand now?

PubMed Central

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data. PMID:25870667

Calculus detection technologies: where do we stand now?

PubMed

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data.

A large primary vaginal calculus in a woman with paraplegia.

PubMed

Avsar, Ayse Filiz; Keskin, Huseyin Levent; Catma, Tuba; Kaya, Basak; Sivaslioglu, Ahmet Akın

2013-01-01

The study aimed to report a primary vaginal stone, an extremely rare entity, without vesicovaginal fistula in a woman with disability. We describe the case of a large primary vaginal calculus in a 22-year-old woman with paraplegia, which, surprisingly, was not diagnosed until she was examined under general anesthesia during a preparation for laparoscopy for an adnexal mass. The stone had not been identified by physical examination with the patient in a recumbent position or by transabdominal ultrasonography and pelvic tomography during the preoperative preparation. Vaginoscopy was not performed because the vagina was completely filled with the mass. As a result of its size and hard consistency, a right-sided episiotomy was performed and a 136-g stone was removed using ring forceps. A vesicovaginal fistula was excluded. There was no evidence of a foreign body or other nidus on the cut section of the stone, and it was determined to be composed of 100% struvite (ammonium magnesium phosphate). Culture of urine obtained via catheter showed Escherichia coli. After the surgical removal of the calculus without complications, a program of intermittent catheterization was started. The follow-up period was uneventful, and the patient was symptom free at 6 months after the operation. We postulate that the calculus formed as a consequence of urinary contamination of the vagina in association with incontinence and prolonged maintenance in a recumbent posture. This report is important because it highlights that, although vaginal stones are very rare, their possibility should be considered in the differential diagnosis of individuals with long-term paraplegia.

Comparative clinical efficacy of three toothpastes in the control of supragingival calculus formation.

PubMed

Kraivaphan, Petcharat; Amornchat, Cholticha

2017-01-01

The purpose of this double-blind, parallel clinical study was to assess clinical efficacy in supragingival calculus formation reduction using Abhaibhubejhr Herbal Toothpaste compared to Colgate Total and Colgate Cavity Protection toothpastes. A total of 150 subjects participated in the pretest phase. All subjects were given oral soft/hard tissue evaluation, calculus examination using Volpe-Manhold calculus, and whole mouth oral prophylaxis. They received noncalculus control fluoride toothpaste and a soft-bristled toothbrush to brush for 1 min two times daily for 8 weeks. After which, subjects were given a test phase oral soft/hard tissue evaluation and calculus examination and were randomized into one of the three toothpaste groups. All subjects in the test phase received a whole mouth oral prophylaxis and were given their assigned toothpaste and a soft-bristled toothbrush to brush for 1 min two times a day for 12 weeks. Thereafter, subjects were assessed for their oral soft/hard tissue and calculus formation. Mean Volpe-Manhold calculus index scores for the Cavity Protection, Abhaibhubejhr, and Total toothpaste groups were 0.78, 0.62, and 0.48, respectively, at the 12-week test phase evaluation. Abhaibhubejhr and Total toothpaste groups show 20.51% and 38.46% significantly less calculus formation than the Cavity Protection toothpaste group ( P < 0.05). Total toothpaste group also show 22.58% significantly less calculus formation than the Abhaibhubejhr toothpaste group ( P < 0.05). The use of Colgate Total toothpaste over a 12-week period was clinically more effective than either Abhaibhubejhr or Colgate Cavity Protection toothpastes in controlling supragingival calculus formation.

Endoscopic vs. tactile evaluation of subgingival calculus.

PubMed

Osborn, Joy B; Lenton, Patricia A; Lunos, Scott A; Blue, Christine M

2014-08-01

Endoscopic technology has been developed to facilitate imagery for use during diagnostic and therapeutic phases of periodontal care. The purpose of this study was to compare the level of subgingival calculus detection using a periodontal endoscope with that of conventional tactile explorer in periodontitis subjects. A convenience sample of 26 subjects with moderate periodontitis in at least 2 quadrants was recruited from the University of Minnesota School of Dentistry to undergo quadrant scaling and root planing. One quadrant from each subject was randomized for tactile calculus detection alone and the other quadrant for tactile detection plus the Perioscope ™ (Perioscopy Inc., Oakland, Cali). A calculus index on a 0 to 3 score was performed at baseline and at 2 post-scaling and root planing visits. Sites where calculus was detected at visit 1 were retreated. T-tests were used to determine within-subject differences between Perioscope™ and tactile measures, and changes in measures between visits. Significantly more calculus was detected using the Perioscope™ vs. tactile explorer for all 3 subject visits (p<0.005). Mean changes (reduction) in calculus detection from baseline to visit 1 were statistically significant for both the Perioscope™ and tactile quadrants (p<0.0001). However, further reductions in calculus detection from visit 1 to visit 2 was only significant for the Perioscope™ quadrant (p<0.025), indicating that this methodology was able to more precisely detect calculus at this visit. It was concluded that the addition of a visual component to calculus detection via the Perioscope™ was most helpful in the re-evaluation phase of periodontal therapy. Copyright © 2014 The American Dental Hygienists’ Association.

A comparison of dental ultrasonic technologies on subgingival calculus removal: a pilot study.

PubMed

Silva, Lidia Brión; Hodges, Kathleen O; Calley, Kristin Hamman; Seikel, John A

2012-01-01

This pilot study compared the clinical endpoints of the magnetostrictive and piezoelectric ultrasonic instruments on calculus removal. The null hypothesis stated that there is no statistically significant difference in calculus removal between the 2 instruments. A quasi-experimental pre- and post-test design was used. Eighteen participants were included. The magnetostrictive and piezoelectric ultrasonic instruments were used in 2 assigned contra-lateral quadrants on each participant. A data collector, blind to treatment assignment, assessed the calculus on 6 predetermined tooth sites before and after ultrasonic instrumentation. Calculus size was evaluated using ordinal measurements on a 4 point scale (0, 1, 2, 3). Subjects were required to have size 2 or 3 calculus deposit on the 6 predetermined sites. One clinician instrumented the pre-assigned quadrants. A maximum time of 20 minutes of instrumentation was allowed with each technology. Immediately after instrumentation, the data collector then conducted the post-test calculus evaluation. The repeated analysis of variance (ANOVA) was used to analyze the pre- and post-test calculus data (p≤0.05). The null hypothesis was accepted indicating that there is no statistically significant difference in calculus removal when comparing technologies (p≤0.05). Therefore, under similar conditions, both technologies removed the same amount of calculus. This research design could be used as a foundation for continued research in this field. Future studies include implementing this study design with a larger sample size and/or modifying the study design to include multiple clinicians who are data collectors. Also, deposit removal with periodontal maintenance patients could be explored.

Science 101: How Do We Use Calculus in Science?

ERIC Educational Resources Information Center

Robertson, Bill

2014-01-01

How is calculus used in science? That might seem like an odd question to answer in a magazine intended primarily for elementary school teachers. After all, how much calculus gets used in elementary science? Here the author guesses that quite a few readers of this column do not know a whole lot about calculus and have not taken a course in…

An Analysis of College Mathematics Departments' Credit Granting Policies for Students with High School Calculus Experience

ERIC Educational Resources Information Center

Laurent, Theresa A.

2009-01-01

The purpose of this study was to investigate higher education mathematics departments' credit granting policies for students with high school calculus experience. The number of students taking calculus in high school has more than doubled since 1982 (NCES, 2007) and it is estimated that approximately 530,000 students took a calculus course in high…

A Study of Calculus Instructors' Perceptions of Approximation as a Unifying Thread of the First-Year Calculus

ERIC Educational Resources Information Center

Sofronas, Kimberly S.; DeFranco, Thomas C.; Swaminathan, Hariharan; Gorgievski, Nicholas; Vinsonhaler, Charles; Wiseman, Brianna; Escolas, Samuel

2015-01-01

This paper discusses findings from a research study designed to investigate calculus instructors' perceptions of approximation as a central concept and possible unifying thread of the first-year calculus. The study also examines the role approximation plays in participants' self-reported instructional practices. A survey was administered to 279…

What Does It Mean for a Student to Understand the First-Year Calculus? Perspectives of 24 Experts

ERIC Educational Resources Information Center

Sofronas, Kimberly S.; DeFranco, Thomas C.; Vinsonhaler, Charles; Gorgievski, Nicholas; Schroeder, Larissa; Hamelin, Chris

2011-01-01

This article presents the views of 24 nationally recognized authorities in the field of mathematics, and in particular the calculus, on student understanding of the first-year calculus. A framework emerged that includes four overarching end goals for understanding of the first-year calculus: (a) mastery of the fundamental concepts and-or skills of…

Examining related influential factors for dental calculus scaling utilization among people with disabilities in Taiwan, a nationwide population-based study.

PubMed

Lai, Hsien-Tang; Kung, Pei-Tseng; Su, Hsun-Pi; Tsai, Wen-Chen

2014-09-01

Limited studies with large samples have been conducted on the utilization of dental calculus scaling among people with physical or mental disabilities. This study aimed to investigate the utilization of dental calculus scaling among the national disabled population. This study analyzed the utilization of dental calculus scaling among the disabled people, using the nationwide data between 2006 and 2008. Descriptive analysis and logistic regression were performed to analyze related influential factors for dental calculus scaling utilization. The dental calculus scaling utilization rate among people with physical or mental disabilities was 16.39%, and the annual utilization frequency was 0.2 times. Utilization rate was higher among the female and non-aboriginal samples. Utilization rate decreased with increased age and disability severity while utilization rate increased with income, education level, urbanization of residential area and number of chronic illnesses. Related influential factors for dental calculus scaling utilization rate were gender, age, ethnicity (aboriginal or non-aboriginal), education level, urbanization of residence area, income, catastrophic illnesses, chronic illnesses, disability types, and disability severity significantly influenced the dental calculus scaling utilization rate. Copyright © 2014 Elsevier Ltd. All rights reserved.

Understanding an Adversary’s Strategic and Operational Calculus: A Late Cold War Case Study with 21st Century Applicability U.S. Views on Soviet Navy Strategy and Operations

DTIC Science & Technology

2013-08-01

principal target is domestic. It is a peculiar form of inflated Western self - esteem that turns a literature read for profit in the Soviet Union into a...17  Christopher Ford and David Rosenberg on ‘High OPINTEL’ in the Era of the...and David Rosenberg , The Admiral’s Advantage: U.S. Navy Operational Intelligence in World War II and 5 the Cold War (Annapolis, MD: Naval

Dental calculus detection using the VistaCam.

PubMed

Shakibaie, Fardad; Walsh, Laurence J

2016-12-01

The VistaCam® intra-oral camera system (Dürr Dental, Bietigheim-Bissingen, Germany) is a fluorescence system using light emitting diodes that produce a 405-nm violet light. This wavelength has potential application for detection of dental calculus based on red emissions from porphyrin molecules. This study assessed the digital scores obtained for both supragingival and subgingival calculus on 60 extracted teeth and compared these with lesions of dental caries. It has also examined the effect of saliva and blood on the fluorescence readings for dental calculus. VistaCam fluorescence scores for both supragingival (1.7-3.3) and subgingival calculus (1.3-2.4) were higher than those for sound root surfaces (0.9-1.1) and dental caries (0.9-2.2) ( p  < .05). The readings for calculus samples were not affected by the presence of saliva or blood. These results suggest that the use of violet light fluorescence could be a possible adjunct to clinical examination for deposits of dental calculus.

Preservation of the metaproteome: variability of protein preservation in ancient dental calculus

PubMed Central

Mackie, Meaghan; Hendy, Jessica; Lowe, Abigail D.; Sperduti, Alessandra; Holst, Malin; Collins, Matthew J.; Speller, Camilla F.

2017-01-01

ABSTRACT Proteomic analysis of dental calculus is emerging as a powerful tool for disease and dietary characterisation of archaeological populations. To better understand the variability in protein results from dental calculus, we analysed 21 samples from three Roman-period populations to compare: 1) the quantity of extracted protein; 2) the number of mass spectral queries; and 3) the number of peptide spectral matches and protein identifications. We found little correlation between the quantity of calculus analysed and total protein identifications, as well as no systematic trends between site location and protein preservation. We identified a wide range of individual variability, which may be associated with the mechanisms of calculus formation and/or post-depositional contamination, in addition to taphonomic factors. Our results suggest dental calculus is indeed a stable, long-term reservoir of proteins as previously reported, but further systematic studies are needed to identify mechanisms associated with protein entrapment and survival in dental calculus. PMID:29098079

The Second Law of Thermodynamics in a Historical Setting.

ERIC Educational Resources Information Center

Strnad, J.

1984-01-01

Traces the development of thermodynamics in physics, focusing on a strategy which enables students to grasp in a limited time and by means of simple calculus the main implications of the second law essential for everyday life (understanding operation of heat engines, refrigerators, heat pumps, district heating, and energy degradation). (JN)

Understanding Calculus beyond Computations: A Descriptive Study of the Parallel Meanings and Expectations of Teachers and Users of Calculus

ERIC Educational Resources Information Center

Ferguson, Leann J.

2012-01-01

Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…

Bacterial Viability within Dental Calculus: An Untrodden, Inquisitive Clinico-Patho- Microbiological Research.

PubMed

Gupta, Swati; Jain, P K; Kumra, Madhumani; Rehani, Shweta; Mathias, Yulia; Gupta, Ramakant; Mehendiratta, Monica; Chander, Anil

2016-07-01

Chronic inflammatory periodontal diseases i.e. gingivitis and periodontitis are one of the most common afflictions faced by human beings. Dental plaque, which is a pool of pathogenic microorganisms, remains to be current mainstay in etiopathogenesis. Dental calculus, which is a mineralized product of this plaque remains ignored and is considered merely as an ash heap of minor significance. However, the intriguing array in disease etiopathogenesis bulldozed researchers to suspect the role of calculus in disease chrysalis but still the viability of bacteria inside calculus and thus its pathogenicity remains an intricacy; the answer to which lies in the Pandora's Box. The present study was undertaken to investigate the viability of bacteria within dental calculus along with their identification. Also, to classify dental calculus on the basis of mineralization and to observe the variation of viable microflora found in dental calculus with the extent of mineralization and disease severity. A total of 60 samples were obtained, by harvesting two samples of supragingival calculus from each patient having chronic inflammatory periodontal disease. These samples were divided into two groups (Group A and Group B). Samples of Group A were kept non-irradiated and samples of Group B were exposed to UV radiation. The samples were categorized into less, moderately and highly mineralized according to the force required for crushing them. All the crushed calculus samples were then divided into three parts. These were used for dark-field microscopy, gram staining and bacterial cultures. Bacterial identification of the cultures obtained was also carried out by performing various biochemical assays. The present study revealed the presence of motile spirochaetes within the samples under dark-field microscope. Gram staining revealed presence of numerous gram positive cocci and gram negative bacilli. Bacterial cultures showed growth of variety of aerobic and capnophilic microorganisms. The present study concludes the presence of viable aerobic and capnophilic bacteria inside dental calculus which may reside within the lacunae and channels in the calculus.

Successful enrichment and recovery of whole mitochondrial genomes from ancient human dental calculus.

PubMed

Ozga, Andrew T; Nieves-Colón, Maria A; Honap, Tanvi P; Sankaranarayanan, Krithivasan; Hofman, Courtney A; Milner, George R; Lewis, Cecil M; Stone, Anne C; Warinner, Christina

2016-06-01

Archaeological dental calculus is a rich source of host-associated biomolecules. Importantly, however, dental calculus is more accurately described as a calcified microbial biofilm than a host tissue. As such, concerns regarding destructive analysis of human remains may not apply as strongly to dental calculus, opening the possibility of obtaining human health and ancestry information from dental calculus in cases where destructive analysis of conventional skeletal remains is not permitted. Here we investigate the preservation of human mitochondrial DNA (mtDNA) in archaeological dental calculus and its potential for full mitochondrial genome (mitogenome) reconstruction in maternal lineage ancestry analysis. Extracted DNA from six individuals at the 700-year-old Norris Farms #36 cemetery in Illinois was enriched for mtDNA using in-solution capture techniques, followed by Illumina high-throughput sequencing. Full mitogenomes (7-34×) were successfully reconstructed from dental calculus for all six individuals, including three individuals who had previously tested negative for DNA preservation in bone using conventional PCR techniques. Mitochondrial haplogroup assignments were consistent with previously published findings, and additional comparative analysis of paired dental calculus and dentine from two individuals yielded equivalent haplotype results. All dental calculus samples exhibited damage patterns consistent with ancient DNA, and mitochondrial sequences were estimated to be 92-100% endogenous. DNA polymerase choice was found to impact error rates in downstream sequence analysis, but these effects can be mitigated by greater sequencing depth. Dental calculus is a viable alternative source of human DNA that can be used to reconstruct full mitogenomes from archaeological remains. Am J Phys Anthropol 160:220-228, 2016. © 2016 The Authors American Journal of Physical Anthropology Published by Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Successful enrichment and recovery of whole mitochondrial genomes from ancient human dental calculus

PubMed Central

Ozga, Andrew T.; Nieves‐Colón, Maria A.; Honap, Tanvi P.; Sankaranarayanan, Krithivasan; Hofman, Courtney A.; Milner, George R.; Lewis, Cecil M.; Stone, Anne C.

2016-01-01

ABSTRACT Objectives Archaeological dental calculus is a rich source of host‐associated biomolecules. Importantly, however, dental calculus is more accurately described as a calcified microbial biofilm than a host tissue. As such, concerns regarding destructive analysis of human remains may not apply as strongly to dental calculus, opening the possibility of obtaining human health and ancestry information from dental calculus in cases where destructive analysis of conventional skeletal remains is not permitted. Here we investigate the preservation of human mitochondrial DNA (mtDNA) in archaeological dental calculus and its potential for full mitochondrial genome (mitogenome) reconstruction in maternal lineage ancestry analysis. Materials and Methods Extracted DNA from six individuals at the 700‐year‐old Norris Farms #36 cemetery in Illinois was enriched for mtDNA using in‐solution capture techniques, followed by Illumina high‐throughput sequencing. Results Full mitogenomes (7–34×) were successfully reconstructed from dental calculus for all six individuals, including three individuals who had previously tested negative for DNA preservation in bone using conventional PCR techniques. Mitochondrial haplogroup assignments were consistent with previously published findings, and additional comparative analysis of paired dental calculus and dentine from two individuals yielded equivalent haplotype results. All dental calculus samples exhibited damage patterns consistent with ancient DNA, and mitochondrial sequences were estimated to be 92–100% endogenous. DNA polymerase choice was found to impact error rates in downstream sequence analysis, but these effects can be mitigated by greater sequencing depth. Discussion Dental calculus is a viable alternative source of human DNA that can be used to reconstruct full mitogenomes from archaeological remains. Am J Phys Anthropol 160:220–228, 2016. © 2016 The Authors American Journal of Physical Anthropology Published by Wiley Periodicals, Inc. PMID:26989998

Comparative clinical efficacy of three toothpastes in the control of supragingival calculus formation

PubMed Central

Kraivaphan, Petcharat; Amornchat, Cholticha

2017-01-01

Objectives: The purpose of this double-blind, parallel clinical study was to assess clinical efficacy in supragingival calculus formation reduction using Abhaibhubejhr Herbal Toothpaste compared to Colgate Total and Colgate Cavity Protection toothpastes. Materials and Methods: A total of 150 subjects participated in the pretest phase. All subjects were given oral soft/hard tissue evaluation, calculus examination using Volpe-Manhold calculus, and whole mouth oral prophylaxis. They received noncalculus control fluoride toothpaste and a soft-bristled toothbrush to brush for 1 min two times daily for 8 weeks. After which, subjects were given a test phase oral soft/hard tissue evaluation and calculus examination and were randomized into one of the three toothpaste groups. All subjects in the test phase received a whole mouth oral prophylaxis and were given their assigned toothpaste and a soft-bristled toothbrush to brush for 1 min two times a day for 12 weeks. Thereafter, subjects were assessed for their oral soft/hard tissue and calculus formation. Results: Mean Volpe-Manhold calculus index scores for the Cavity Protection, Abhaibhubejhr, and Total toothpaste groups were 0.78, 0.62, and 0.48, respectively, at the 12-week test phase evaluation. Abhaibhubejhr and Total toothpaste groups show 20.51% and 38.46% significantly less calculus formation than the Cavity Protection toothpaste group (P < 0.05). Total toothpaste group also show 22.58% significantly less calculus formation than the Abhaibhubejhr toothpaste group (P < 0.05). Conclusion: The use of Colgate Total toothpaste over a 12-week period was clinically more effective than either Abhaibhubejhr or Colgate Cavity Protection toothpastes in controlling supragingival calculus formation. PMID:28435373

Selective ablation of sub- and supragingival calculus with a frequency-doubled Alexandrite laser

NASA Astrophysics Data System (ADS)

Rechmann, Peter; Hennig, Thomas

1995-05-01

In a preceding trial the absorption characteristics of subgingival calculus were calculated using fluorescence emission spectroscopy (excitation laser: N2-laser, wavelength 337 nm, pulse duration 4 ns). Subgingival calculus seems to contain chromophores absorbing in the ultraviolet spectral region up to 420 nm. The aim of the actual study was the ablation of sub- and supragingival calculus using a frequency doubled Alexandrite-laser (wavelength 377 nm, pulse duration 100 ns, repetition rate 110 Hz). Extracted human teeth presenting sub- and supragingival calculus were irradiated perpendicular to their axis with a laser fluence of 1 Jcm-2. Using a standard application protocol calculus was irradiated at the enamel surface, at the junction between enamel and root, and at the root surface (located on dentin or on cementum). During the irradiation procedure an effective water cooling-system was engaged. For light microscopical investigations undecalcified histological sections were prepared after treatment. The histological sections revealed that a selective and total removal of calculus is possible at all locations without ablation of healthy enamel, dentin or cementum. Even low fluences provide us with a high effectiveness for the ablation of calculus. Thus, based on different absorption characteristics and ablation thresholds, engaging a frequency doubled Alexandrite-laser a fast and, even more, a selective ablation of sub- and supragingival calculus is possible without adverse side effects to the surrounding tissues. Even more, microbial dental plaque can be perfectly removed.

Fluorescence-based calculus detection using a 405-nm excitation wavelength

NASA Astrophysics Data System (ADS)

Brede, O.; Schelle, F.; Krueger, S.; Oehme, B.; Dehn, C.; Frentzen, M.; Braun, A.

2011-03-01

The aim of this study was to assess the difference of fluorescence signals of cement and calculus using a 405 nm excitation wavelength. A total number of 20 freshly extracted teeth was used. The light source used for this study was a blue LED with a wavelength of 405nm. For each tooth the spectra of calculus and cementum were measured separately. Fluorescence light was collimated into an optical fibre and spectrally analyzed using an echelle spectrometer (aryelle 200, Lasertechnik Berlin, Germany) with an additionally bandpass (fgb 67, Edmund Industrial Optics, Karlsruhe, Germany). From these 40 measurements the median values were calculated over the whole spectrum, leading to two different median spectra, one for calculus and one for cementum. For further statistical analysis we defined 8 areas of interest (AOI) in wavelength regions, showing remarkable differences in signal strength. In 7 AOIs the intensity of the calculus spectrum differed statistically significant from the intensity of the cementum spectrum (p < 0.05). A spectral difference could be shown between calculus and cement between 600nm and 700nm. Thus, we can conclude that fluorescence of calculus shows a significant difference to the fluorescence of cement. A differentiation over the intensity is possible as well as over the spectrum. Using a wavelength of 405nm, it is possible to distinguish between calculus and cement. These results could be used for further devices to develop a method for feedback controlled calculus removal.

Taking a Quantum Leap in Cyber Deterrence

DTIC Science & Technology

2010-02-17

calculus that weighs the cost and benefit of an action. 76 According to John Mearsheimer, that decision calculus is ―a function of the costs and...frame an adversary‘s rationale and decision calculus . 82 Understanding a group‘s rationale helps frame a strategy for deterrence. Emanuel Adler...only remaining option. Mearsheimer‘s decision calculus described above indicates that if the cost of an attack is high, or the probability of

Measuring Teacher Immediacy and Communication Competence on Student Achievement in Calculus: A Sequential Explanatory Mixed Method Design

ERIC Educational Resources Information Center

Barclay, Allen C.

2012-01-01

On a national level, data indicate that about 40 percent of students in calculus courses finish with a grade of D or F, drop the course, or withdraw (Reinholz, 2009). This high failure rate has led to research studies investigating the teaching of calculus at the national level (House, 1995). Calculus courses have a history of high failure rates,…

Complete staghorn calculus in polycystic kidney disease: infection is still the cause

PubMed Central

2013-01-01

Background Kidney stones in patients with autosomal dominant polycystic kidney disease are common, regarded as the consequence of the combination of anatomic abnormality and metabolic risk factors. However, complete staghorn calculus is rare in polycystic kidney disease and predicts a gloomy prognosis of kidney. For general population, recent data showed metabolic factors were the dominant causes for staghorn calculus, but for polycystic kidney disease patients, the cause for staghorn calculus remained elusive. Case presentation We report a case of complete staghorm calculus in a polycystic kidney disease patient induced by repeatedly urinary tract infections. This 37-year-old autosomal dominant polycystic kidney disease female with positive family history was admitted in this hospital for repeatedly upper urinary tract infection for 3 years. CT scan revealed the existence of a complete staghorn calculus in her right kidney, while there was no kidney stone 3 years before, and the urinary stone component analysis showed the composition of calculus was magnesium ammonium phosphate. Conclusion UTI is an important complication for polycystic kidney disease and will facilitate the formation of staghorn calculi. As staghorn calculi are associated with kidney fibrosis and high long-term renal deterioration rate, prompt control of urinary tract infection in polycystic kidney disease patient will be beneficial in preventing staghorn calculus formation. PMID:24070202

Complete staghorn calculus in polycystic kidney disease: infection is still the cause.

PubMed

Mao, Zhiguo; Xu, Jing; Ye, Chaoyang; Chen, Dongping; Mei, Changlin

2013-08-01

Kidney stones in patients with autosomal dominant polycystic kidney disease are common, regarded as the consequence of the combination of anatomic abnormality and metabolic risk factors. However, complete staghorn calculus is rare in polycystic kidney disease and predicts a gloomy prognosis of kidney. For general population, recent data showed metabolic factors were the dominant causes for staghorn calculus, but for polycystic kidney disease patients, the cause for staghorn calculus remained elusive. We report a case of complete staghorm calculus in a polycystic kidney disease patient induced by repeatedly urinary tract infections. This 37-year-old autosomal dominant polycystic kidney disease female with positive family history was admitted in this hospital for repeatedly upper urinary tract infection for 3 years. CT scan revealed the existence of a complete staghorn calculus in her right kidney, while there was no kidney stone 3 years before, and the urinary stone component analysis showed the composition of calculus was magnesium ammonium phosphate. UTI is an important complication for polycystic kidney disease and will facilitate the formation of staghorn calculi. As staghorn calculi are associated with kidney fibrosis and high long-term renal deterioration rate, prompt control of urinary tract infection in polycystic kidney disease patient will be beneficial in preventing staghorn calculus formation.

Use of the feed additive sodium hexametaphosphate to prevent dental calculus in squirrel monkeys (Saimiri spp.).

PubMed

Brady, A G; Williams, L E; Haught, D; Abee, C R

2000-03-01

Dental calculus and associated periodontal disease are serious clinical problems in captive squirrel monkeys. Calculus begins to appear as early as 2 years of age, with subsequent development of periodontal disease, dental abscessation, tooth loss and other sequelae. When used as a feed additive, sodium hexametaphosphate (HMP) retards the growth of calculus on previously cleaned teeth in rhesus monkeys, lemurs, and other species. We wanted to determine whether HMP would reduce dental calculus in squirrel monkeys (Saimiri spp.) whose teeth had not been pre-cleaned. The study animals were divided into two groups. One received a standard diet; the other received an identical diet containing the HMP additive at a concentration effective in other primate and non-primate species that had received dental cleaning prior to treatment with HMP. Teeth were graded for extent of calculus formation at the start of the study and at 3 and 6 months during HMP treatment. We compared the results from the two groups both by total score per animal and according to tooth type (e.g., incisors versus incisors in test and control groups). At the end of 6 months, dental calculus did not differ significantly between the experimental groups. Therefore, we conclude that HMP is ineffective in squirrel monkeys with preexisting dental calculus.

Real-time detection of dental calculus by blue-LED-induced fluorescence spectroscopy.

PubMed

Qin, Y L; Luan, X L; Bi, L J; Lü, Z; Sheng, Y Q; Somesfalean, G; Zhou, C N; Zhang, Z G

2007-05-25

Successful periodontal therapy requires sensitive techniques to discriminate dental calculus from healthy teeth. The aim of the present study was to develop a fluorescence-based procedure to enable real-time detection and quantification of dental calculus. Thirty human teeth--15 teeth with sub- and supragingival calculus and 15 healthy teeth--covered with a layer of physiological saline solution or blood were illuminated by a focused blue LED light source of 405 nm. Autofluorescence spectra recorded along a randomly selected line stretching over the crown-neck-root area of each tooth were utilized to evaluate a so called calculus parameter R, which was selected to define a relationship between the integrated intensities specific for healthy teeth and for calculus in the 477-497 nm (S(A)) and 628-685 nm (S(B)) wavelength regions, respectively. Statistical analysis was performed and a cut-off threshold of R=0.2 was found to distinguish dental calculus from healthy teeth with 100% sensitivity and specificity under various experimental conditions. The results of the spectral evaluation were confirmed by clinical and histological findings. Automated real-time detection and diagnostics for clinical use were implemented by a corresponding software program written in Visual Basic language. The method enables cost-effective and reliable calculus detection, and can be further developed for imaging applications.

Differential Geometry and Lie Groups for Physicists

NASA Astrophysics Data System (ADS)

Fecko, Marián.

2006-10-01

Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke's Theorem; 9. Poincaré Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.

Differential Geometry and Lie Groups for Physicists

NASA Astrophysics Data System (ADS)

Fecko, Marián.

2011-03-01

Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke's Theorem; 9. Poincaré Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.

Extended phase graphs with anisotropic diffusion

NASA Astrophysics Data System (ADS)

Weigel, M.; Schwenk, S.; Kiselev, V. G.; Scheffler, K.; Hennig, J.

2010-08-01

The extended phase graph (EPG) calculus gives an elegant pictorial description of magnetization response in multi-pulse MR sequences. The use of the EPG calculus enables a high computational efficiency for the quantitation of echo intensities even for complex sequences with multiple refocusing pulses with arbitrary flip angles. In this work, the EPG concept dealing with RF pulses with arbitrary flip angles and phases is extended to account for anisotropic diffusion in the presence of arbitrary varying gradients. The diffusion effect can be expressed by specific diffusion weightings of individual magnetization pathways. This can be represented as an action of a linear operator on the magnetization state. The algorithm allows easy integration of diffusion anisotropy effects. The formalism is validated on known examples from literature and used to calculate the effective diffusion weighting in multi-echo sequences with arbitrary refocusing flip angles.

Selective ablation of dental calculus with a frequency-doubled Alexandrite laser

NASA Astrophysics Data System (ADS)

Rechmann, Peter; Hennig, Thomas

1996-01-01

The aim of the study was the selective removal of dental calculus by means of pulsed lasers. In a first approach the optical characteristics of subgingival calculus were calculated using fluorescence emission spectroscopy (excitation laser: N2-laser, wavelength 337 nm, pulse duration 4 ns). Subgingival calculus seems to absorb highly in the ultraviolet spectral region up to 420 nm. According to these measurements a frequency doubled Alexandrite-laser (wavelength 377 nm, pulse duration 100 ns, repetition rate 110 Hz) was used to irradiate calculus located on enamel, at the cementum enamel junction and on the root surface (located on dentin or on cementum). Irradiation was performed perpendicular to the root surface with a laser fluence of 1 Jcm-2. During the irradiation procedure an effective water cooling-system was engaged. Histological investigations were done on undecalcified sections. As a result, engaging low fluences allows a fast and strictly selective removal of subgingival calculus. Even more the investigations revealed that supragingival calculus can be removed in a strictly selective manner engaging a frequency doubled Alexandrite-laser. No adverse side effects to the surrounding tissues could be found.

Comparative study on major bioactive components in natural, artificial and in-vitro cultured Calculus Bovis.

PubMed

Yan, Shi-Kai; Wu, Yan-Wen; Liu, Run-Hui; Zhang, Wei-Dong

2007-01-01

Major bioactive components in various Calculus Bovis, including natural, artificial and in-vitro cultured Calculus Bovis, were comparatively studied. An approach of high-performance liquid chromatography coupled with ultraviolet and evaporative light scattering detections (HPLC/UV/ELSD) was established to simultaneously determinate six bioactive components thereof, including five bile acids (cholic acid, deoxycholic acid, ursodeoxycholic, chenodeoxycholic acid, hyodeoxycholic acid) and bilirubin. ELSD and UV detector were applied to detect bile acids and bilirubin respectively. The assay was performed on a C(18) column with water-acetonitrile gradient elution and the investigated constituents were authenticated by comparing retention times and mass spectra with those of reference compounds. The proposed method was applied to analyze twenty-one Calculus Bovis extraction samples, and produced data with acceptable linearity, precision, repeatability and accuracy. The result indicated the variations among Calculus Bovis samples under different developmental conditions. Artificial and in-vitro cultured Calculus Bovis, especially in-vitro cultured ones, which contain total bioactive constituents no less than natural products and have the best batch-to-batch uniformity, suffice to be used as substitutes of natural Calculus Bovis.

Putting Differentials Back into Calculus

ERIC Educational Resources Information Center

Dray, Tevian; Manogue, Corrine A.

2010-01-01

We argue that the use of differentials in introductory calculus courses is useful and provides a unifying theme, leading to a coherent view of the calculus. Along the way, we meet several interpretations of differentials, some better than others.

Study Modules for Calculus-Based General Physics. [Includes Modules 1 and 2: Dimensions and Vector Addition; Rectilinear Motion; plus a Trigonometry and Calculus Review].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

1998-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

Initialization, conceptualization, and application in the generalized (fractional) calculus.

PubMed

Lorenzo, Carl F; Hartley, Tom T

2007-01-01

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions.

On the constrained B-type Kadomtsev-Petviashvili hierarchy: Hirota bilinear equations and Virasoro symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shen, Hsin-Fu; Tu, Ming-Hsien

2011-03-15

We derive the bilinear equations of the constrained BKP hierarchy from the calculus of pseudodifferential operators. The full hierarchy equations can be expressed in Hirota's bilinear form characterized by the functions {rho}, {sigma}, and {tau}. Besides, we also give a modification of the original Orlov-Schulman additional symmetry to preserve the constrained form of the Lax operator for this hierarchy. The vector fields associated with the modified additional symmetry turn out to satisfy a truncated centerless Virasoro algebra.

Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

ERIC Educational Resources Information Center

Camporesi, Roberto

2011-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of…

Equivalent Vectors

ERIC Educational Resources Information Center

Levine, Robert

2004-01-01

The cross-product is a mathematical operation that is performed between two 3-dimensional vectors. The result is a vector that is orthogonal or perpendicular to both of them. Learning about this for the first time while taking Calculus-III, the class was taught that if AxB = AxC, it does not necessarily follow that B = C. This seemed baffling. The…

Laser fluorescence detection of subgingival calculus using the DIAGNOdent Classic versus periodontal probing.

PubMed

Shakibaie, Fardad; Walsh, Laurence J

2016-11-01

Deposits of subgingival calculus on the root surfaces of the teeth are difficult to detect with conventional methods such as tactile probing. This study compared the performance of a 655-nm wavelength laser fluorescence (LF) system (DIAGNOdent Classic with a periodontal tip) with conventional periodontal probing under defined conditions in a laboratory simulation, using an experienced examiner. Models with a total of 30 extracted teeth with varying levels of subgingival deposits scattered on their root surfaces were prepared, and silicone impression material applied to replicate periodontal soft tissues. The models were located in a phantom head, and the presence of subgingival calculus recorded at 8 points per tooth (240 sites), then the entire scoring process repeated after 1 and 2 weeks. The optimal LF threshold was determined as a fluorescence score of 7 using Receiver Operating Characteristic curves. When compared the gold standard of direct microscopic examination of roots, LF was more sensitive, specific, and accurate than tactile probing (68.3 vs. 51.7 %; 92.1 vs. 67.8; and 80.2 vs. 59.8 %, respectively), and was also more reproducible (Cohen kappa 0.60 vs. 0.39). These data support the concept of using LF as an adjunct to clinical diagnosis.

Association between chronic kidney disease and urinary calculus by stone location: a population-based study.

PubMed

Keller, Joseph J; Chen, Yi-Kuang; Lin, Herng-Ching

2012-12-01

Study Type--Disease prevalence study (cohort design) Level of Evidence 2a. What's known on the subject? and What does the study add? Several studies have estimated the potential association of urinary calculus (UC) with chronic kidney disease (CKD). However, previous literature focusing on this issue tended to evaluate the impact of kidney stones alone on incident CKD, with no studies having been conducted investigating the association between CKD and stone formation in other portions of the urological system. We found that patients with CKD were consistently more likely than comparison subjects to have been previously diagnosed with kidney calculus (odds ratio [OR] 2.10, 95% confidence interval [CI] 1.95-2.27), ureter calculus (OR 1.68, 95% CI 1.51-1.85), bladder calculus (OR 1.49, 95% CI 1.13-1.98), and unspecified calculus (OR 1.89, 95% CI 1.74-2.06). We concluded that there was an association between CKD and UC regardless of stone location. • To explore the association of chronic kidney disease (CKD) with prior kidney calculus, ureter calculus, and bladder calculus using a population-based dataset in Taiwan. Several studies have estimated the potential association of urinary calculus (UC) with CKD. However, previous literature focusing on this issue tended to evaluate the impact of kidney stones alone on incident CKD, with no studies having been conducted investigating the association between CKD and stone formation in other portions of the urological system. • We identified 21,474 patients who received their first-time diagnosis of CKD between 2001 and 2009. • The 21,474 controls were frequency-matched with cases for sex, age group, and index year. • We used conditional logistic regression analyses to compute the odds ratio (OR) and corresponding 95% confidence interval (CI) as an estimation of association between CKD and having been previously diagnosed with UC. • The results show that compared with controls, the OR of prior UC for cases was 1.91 (95% CI 1.81-2.01, P < 0.001) after adjusting for potential confounders. • Furthermore, cases were consistently more likely than controls to have been previously diagnosed with kidney calculus (OR 2.10, 95% CI 1.95-2.27), ureter calculus (OR 1.68, 95% CI 1.51-1.85), bladder calculus (OR 1.49, 95% CI 1.13-1.98), and unspecified UC (OR 1.89, 95% CI 1.74-2.06). • We concluded that there was an association between ckd and UC regardless of stone location. © 2012 BJU INTERNATIONAL.

Raw beef bones as chewing items to reduce dental calculus in Beagle dogs.

PubMed

Marx, F R; Machado, G S; Pezzali, J G; Marcolla, C S; Kessler, A M; Ahlstrøm, Ø; Trevizan, L

2016-01-01

Evaluate the effect of raw bovine cortical bone (CB) (medullary bone cross-sectioned) and marrow or epiphyseal 'spongy' bone (SB) as chew items to reduce dental calculus in adult dogs. Eight 3-year-old Beagle dogs were observed in two study periods. In the first study, the dogs each received a piece of bovine femur CB (122 ± 17 g) daily and in the second study, a piece of bovine femur SB (235 ± 27 g). The first study lasted 12 days and the second 20 days. Dental calculus was evaluated using image integration software. At the start of the studies, dental calculus covered 42.0% and 38.6% of the dental arcade areas, respectively. In study one, the chewing reduced the established dental calculus area to 27.1% (35.5% reduction) after 3 days and after 12 days the dental calculus covering was reduced to 12.3% (70.6% reduction). In study two, the dental calculus covered 16.8% (56.5% reduction) after 3 days, 7.1% (81.6% reduction) after 12 days and 4.7% (87.8% reduction) after 20 days. The CB remained largely intact after 24 h, but SB was reduced to smaller pieces and in some cases totally consumed after 24 h. No complications such as tooth fractures, pieces of bone stuck between teeth or intestinal obstructions were observed during the studies. Chewing raw bovine bones was an effective method of removing dental calculus in dogs. The SB bones removed dental calculus more efficiently in the short term. © 2016 Australian Veterinary Association.

The Legendre transform in geometric calculus

NASA Astrophysics Data System (ADS)

McClellan, Gene E.

2013-10-01

This paper explores the extension of the Legendre transform from scalar calculus to geometric calculus. In physics, the Legendre transform provides a change of variables to express equations of motion or other physical relationships in terms of the most convenient dynamical quantities for a given experimental or theoretical analysis. In classical mechanics and in field theory, the Legendre transform generates the Hamiltonian function of a system from the Lagrangian function or vice versa. In thermodynamics, the Legendre transform allows thermodynamic relationships to be written in terms of alternative sets of independent variables. In this paper, we review the properties of the Legendre transform in scalar calculus and show how an analogous transformation with similar properties may be constructed in geometric calculus.

DOE Fundamentals Handbook: Mathematics, Volume 1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclearmore » facility operations.« less

DOE Fundamentals Handbook: Mathematics, Volume 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclearmore » facility operations.« less

Calculus for a New Century: A Pump, Not a Filter. Papers Presented at a Colloquium (Washington, D.C., October 28-29, 1987). MAA Notes Number 8.

ERIC Educational Resources Information Center

Steen, Lynn Arthur, Ed.

This document, intended as a resource for calculus reform, contains 75 separate contributions, comprising a very diverse set of opinions about the shape of calculus for a new century. The authors agree on the forces that are reshaping calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory,…

Correlation of Salivary Statherin and Calcium Levels with Dental Calculus Formation: A Preliminary Study.

PubMed

Pateel, Deepak Gowda Sadashivappa; Gunjal, Shilpa; Math, Swarna Y; Murugeshappa, Devarasa Giriyapura; Nair, Sreejith Muraleedharan

2017-01-01

Salivary constituents have a wide range of functions including oral calcium homeostasis. Salivary proteins such as statherin inhibit crystal growth of calcium phosphate in supersaturated solutions and interact with several oral bacteria to adsorb on hydroxyapatite. Concurrently, saliva, which is supersaturated with respect to calcium phosphates, is the driving force for plaque mineralization and formation of calculus. Thus, the aim of the present study was to estimate and correlate salivary statherin and calcium concentration to the dental calculus formation. A cross-sectional study was conducted to assess the relationship between salivary statherin, calcium, and dental calculus among 70 subjects, aged 20-55 years. Subjects were divided into 3 groups based on the calculus scores as interpreted by Calculus Index which was followed by collection of whole saliva using Super•SAL™. Salivary calcium levels were assessed by calorimetric method using Calcium Assay kit (Cayman Chemical, Michigan, USA) and statherin levels by using ELISA Kit (Cusabio Biotech). Statherin levels showed a weak negative correlation with the calcium levels and with calculus formation. The mean salivary statherin and calcium concentration were found to be 0.96  μ g/ml and 3.87 mg/ml, respectively. Salivary statherin levels differed significantly among the three groups ( p < 0.05). Our preliminary data indicates that statherin could possibly play a role in the formation of dental calculus.

Prevention of lingual calculus formation with daily use of 6% H2O2/2% pyrophosphate whitening strips.

PubMed

Farrell, S; Barker, M L; Gerlach, R W; Putt, M S; Milleman, J L

2009-01-01

This randomized controlled clinical trial was conducted to evaluate whether daily use of a hydrogen peroxide/ pyrophosphate-containing antitartar whitening strip might safely yield clinical reductions in post-prophylaxis calculus accumulation. A three-month, randomized controlled trial was conducted to compare calculus accumulation with a daily 6% hydrogen peroxide/pyrophosphate strip versus regular brushing. After an eight-week run-in phase to identify calculus formers, a prophylaxis was administered, and 77 subjects were randomly assigned to daily strip or brushing only groups. All subjects received an anticavity dentifrice (Crest Cavity Protection) and manual brush for use throughout the three-month study; for subjects assigned to the experimental group, strip application was once daily for five minutes on the facial and lingual surfaces of the mandibular teeth. Efficacy was measured as mm calculus (VMI) before prophylaxis and after six and 12 weeks of treatment, while safety was assessed from examination and interview. Subjects ranged in age from 21-87 years, with groups balanced (p > 0.26) on pertinent demographic and behavioral parameters, and pre-prophylaxis calculus baseline mean scores (16.0 mm). At Week 6, calculus accumulation was lower in the strip group, with adjusted mean (SE) lingual VMI of 12.0 (0.87) for the strip group and 17.0 (0.88) for the brushing control. At Week 12, calculus accumulation was lower in the strip group, with adjusted mean (SE) lingual VMI of 14.3 (0.85) for the strip group and 17.2 (0.86) for the brushing control. Treatments differed significantly (p < 0.02) on calculus accumulation at both time points. A total of three subjects (8%) in the strip group and two subjects (5%) in the brushing control had mild oral irritation or tooth sensitivity during treatment; no one discontinued early due to an adverse event. Daily use of hydrogen peroxide whitening strips with pyrophosphate reduced calculus formation by up to 29% versus regular brushing, without meaningful adverse events.

A Randomized Study of Minimally Invasive Percutaneous Nephrolithotomy (MPCNL) with the aid of a patented suctioning sheath in the treatment of renal calculus complicated by pyonephrosis by one surgery.

PubMed

Huang, Jianrong; Song, Leming; Xie, Donghua; Li, Monong; Deng, Xiaolin; Hu, Min; Peng, Zuofeng; Liu, Tairong; Du, Chuance; Yao, Lei; Liu, Shengfeng; Guo, Shulin; Zhong, Jiuqing

2016-12-08

Calculus pyonephrosis is difficult to manage. The aim of this study is to explore the value of a patented suctioning sheath assisted minimally invasive percutaneous nephrolithotomy (MPCNL) in the treatment of calculus pyonephrosis. One hundred and eighty two patients with calculus pyonephrosis were randomizely divided into observation group (n = 91) and control group (n = 91). The control group was treated with MPCNL traditionally using peel-away sheath while the observation group was treated with MPCNL using the patented suctioning sheath. All the patients in the observation group underwent one stage surgical treatment, 14 patients in the control group underwent first-stage surgery with the rest of the group underwent one stage surgery. The complication rate was 12.1% in the observation group, significantly lower than the rate in the control group which was 51.6%; One surgery stone clearance in the observation group was 96.7% while it was 73.6% in the control group; operative time in the observation group was (54.5 ± 14.5) min, compared to (70.2 ± 11.7) min in the control group; the bleeding amount in the observation group was (126.4 ± 47.2) ml, compared to (321.6 ± 82.5) ml in the control group; the hospitalization duration for the observation group was (6.4 ± 2.3) days, compared to (10.6 ± 3.7) days in the control group. Comparison of the above indicators, the observation group was better than the control group with significant difference (p < 0.001 each). Minimally invasive percutaneous nephrolithotomy with the aid of the patented suctioning sheath in the treatment of calculus pyonephrosis in one surgery is economic, practical, and warrants clinical promotion. This study was registered with Chinese Clinical Trial Registry on May 18, 2016 (retrospective registration) with a trial registration number of ChiCTR-IOR-16008490 .

Calculus removal on a root cement surface by ultrashort laser pulses

NASA Astrophysics Data System (ADS)

Kraft, Johan F.; Vestentoft, Kasper; Christensen, Bjarke H.; Løvschall, Henrik; Balling, Peter

2008-01-01

Ultrashort-pulse-laser ablation of dental calculus (tartar) and cement is performed on root surfaces. The investigation shows that the threshold fluence for ablation of calculus is a factor of two to three times smaller than that of a healthy root cement surface. This indicates that ultrashort laser pulses may provide an appropriate tool for selective removal of calculus with minimal damage to the underlying root cement. Future application of an in situ profiling technique allows convenient on-line monitoring of the ablation process.

Formal Modeling of Multi-Agent Systems using the Pi-Calculus and Epistemic Logic

NASA Technical Reports Server (NTRS)

Rorie, Toinette; Esterline, Albert

1998-01-01

Multi-agent systems have become important recently in computer science, especially in artificial intelligence (AI). We allow a broad sense of agent, but require at least that an agent has some measure of autonomy and interacts with other agents via some kind of agent communication language. We are concerned in this paper with formal modeling of multi-agent systems, with emphasis on communication. We propose for this purpose to use the pi-calculus, an extension of the process algebra CCS. Although the literature on the pi-calculus refers to agents, the term is used there in the sense of a process in general. It is our contention, however, that viewing agents in the AI sense as agents in the pi-calculus sense affords significant formal insight. One formalism that has been applied to agents in the AI sense is epistemic logic, the logic of knowledge. The success of epistemic logic in computer science in general has come in large part from its ability to handle concepts of knowledge that apply to groups. We maintain that the pi-calculus affords a natural yet rigorous means by which groups that are significant to epistemic logic may be identified, encapsulated, structured into hierarchies, and restructured in a principled way. This paper is organized as follows: Section 2 introduces the pi-calculus; Section 3 takes a scenario from the classical paper on agent-oriented programming [Sh93] and translates it into a very simple subset of the n-calculus; Section 4 then shows how more sophisticated features of the pi-calculus may bc brought into play; Section 5 discusses how the pi-calculus may be used to define groups for epistemic logic; and Section 6 is the conclusion.

Composition and distribution of elements and ultrastructural topography of a human cardiac calculus.

PubMed

Cheng, Ching-Li; Chang, Hsiao-Huang; Huang, Pei-Jung; Chu, Yu-Ting; Lin, Shan-Yang

2013-04-01

Trace elements (TEs) may contribute to the formation of calculi or stones or be involved in the aetiopathogenesis of stone diseases. The compositions and spatial distribution of elements from the inner nucleus to outer crust of the cardiac calculus were investigated by energy-dispersive X-ray fluorescence (EDXRF) spectrometer. The surface topograph, distribution map of elements, elemental and chemical compositions were also determined by environmental scanning electron microscope (ESEM)-energy-dispersive X-ray (EDX) analysis. Twenty-five elements were identifiable from 18 positions on the cardiac calculus by EDXRF spectrometer, in which the highest concentrations of toxic TEs (Ni, Pt, Hg, Sn, Pb, W, Au, Al, Si) and higher levels of essential TEs (Ca, Sr, Cr, P) were detected. A moderate positive Pearson's correlation between TEs concentrations of Mg, Ca or P and location differences from centre to periphery in the cardiac calculus was observed. A positive correlation was also found for Ca/Zn and Ca/Cu, indicating the gradual increase of calcium concentration from inner nucleus to outer crust of cardiac calculus. The drop-like nodules/crystals on the surface of petrous part of cardiac calculus were observed from ESEM analysis. ESEM-EDX analysis determined the calculus to be predominantly composed of calcium hydroxyapatite and cholesterol, as indicated by the petrous surface and drop-like nodules/crystals, respectively. This composition was confirmed using a portable Raman analyser. The spatial distribution analysis indicated a gradual increase in Mg, P and Ca concentrations from the inner nucleus to the outer crust of the cardiac calculus. The major chemical compositions of calcium hydroxyapatite and cholesterol were detected on this cardiac calculus.

Study of orthophosphate, pyrophosphate, and pyrophosphatase in saliva with reference to calculus formation and inhibition.

PubMed

Pradeep, A R; Agarwal, Esha; P, Arjun Raju; Rao, M S Narayana; Faizuddin, Mohamed

2011-03-01

A large amount of calculus may hamper the efficacy of daily oral hygiene and thereby accelerate plaque formation. Salivary concentrations of orthophosphate and pyrophosphate are important in preventing calculus formation. Activity of orthophosphate, pyrophosphate, and pyrophosphatase was studied in whole saliva in calculus-forming groups and plaque-forming groups. The material for this study consists of 60 healthy individuals (age range: 15 to 30 years; mean age: 22 years). Depending on calculus index score, individuals were divided into four groups, each of 15 patients: Group 1, calculus index score 0 to 0.6; Group 2, calculus index score 0.7 to 1.8; Group 3, calculus index score 1.9 to 3; and Group 4, plaque group where index varied from 0 to 3. The saliva was collected and biochemically analyzed for concentration of orthophosphate, pyrophosphate, and pyrophosphatase. The mean values of orthophosphate in Groups 1, 2, 3, and 4 were 0.2559, 1.3639, 1.7311, and 0.1868 mM, respectively. The mean values of pyrophosphate in Groups 1, 2, 3, and 4 were 0.3258, 0.1091, 0.0314, and 0.3860 mM, respectively. The mean values of pyrophosphatase in Groups 1, 2, 3, and 4 were 10.7937, 15.4249, 27.2900, and 7.5427 units/ml, respectively. A holistic approach toward the control of periodontal disease should include antiplaque and anticalculus agents. The results are conclusive that the components orthophosphate, pyrophosphate, and pyrophosphatase present in saliva have a very significant role to play in formation and inhibition of calculus. This study reinforces the idea of using pyrophosphate and newer bisphosphonates as potential anticalculus agents.

The Case for Biocalculus: Design, Retention, and Student Performance.

PubMed

Eaton, Carrie Diaz; Highlander, Hannah Callender

2017-01-01

Calculus is one of the primary avenues for initial quantitative training of students in all science, technology, engineering, and mathematics fields, but life science students have been found to underperform in the traditional calculus setting. As a result, and because of perceived lack of its contribution to the understanding of biology, calculus is being actively cut from biology program requirements at many institutions. Here, we present an alternative: a model for learning mathematics that sees the partner disciplines as crucial to student success. We equip faculty with information to engage in dialogue within and between disciplinary departments involved in quantitative education. This includes presenting a process for interdisciplinary development and implementation of biology-oriented Calculus I courses at two institutions with different constituents, goals, and curricular constraints. When life science students enrolled in these redesigned calculus courses are compared with life science students enrolled in traditional calculus courses, students in the redesigned calculus courses learn calculus concepts and skills as well as their traditional course peers; however, the students in the redesigned courses experience more authentic life science applications and are more likely to stay and succeed in the course than their peers who are enrolled in traditional courses. Therefore, these redesigned calculus courses hold promise in helping life science undergraduate students attain Vision and Change recommended competencies. © 2017 C. D. Eaton and H. C. Highlander. CBE—Life Sciences Education © 2017 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

Site specific mineral composition and microstructure of human supra-gingival dental calculus.

PubMed

Hayashizaki, Junko; Ban, Seiji; Nakagaki, Haruo; Okumura, Akihiko; Yoshii, Saori; Robinson, Colin

2008-02-01

Dental calculus has been implicated in the aetiology of several periodontal conditions. Its prevention and removal are therefore desirable clinical goals. While it is known that calculus is very variable in chemical composition, crystallinity and crystallite size little is known about site specific variability within a dentition and between individuals. With this in mind, a study was undertaken to investigate the comparative site specific nature and composition of human dental supra-gingival dental calculus obtained from 66 male patients visiting for their dental check-up using fluorescent X-ray spectroscopy, X-ray diffractometry and Fourier transform infrared spectroscopy. The supra-gingival dental calculus formed on the lingual surfaces of lower anterior teeth and the buccal surfaces of upper molar teeth were classified into four types based on calcium phosphate phases present. There was significant difference in composition of the crystal phase types between lower and upper teeth (p<0.01). There was no significant difference in crystal size between dental calculus on anterior or molar teeth of all samples. The degree of crystallinity of dental calculus formed on the upper molar teeth was higher than that formed on the lower anterior teeth (p<0.01). The CO(3)(2-) contents in dental calculus formed on the lower anterior teeth were higher than on upper molar teeth (p<0.05) which might explain the difference in crystallinity. Magnesium and Si contents and Ca:P ratio on the other hand showed no significant difference between lower and upper teeth. It was concluded that the crystal phases, crystallinity and CO(3)(2-) contents of human dental supra-gingival dental calculus is related to its location in the mouth.

Testicular calculus: A rare case.

PubMed

Sen, Volkan; Bozkurt, Ozan; Demır, Omer; Tuna, Burcin; Yorukoglu, Kutsal; Esen, Adil

2015-01-01

Testicular calculus is an extremely rare case with unknown etiology and pathogenesis. To our knowledge, here we report the third case of testicular calculus. A 31-year-old man was admitted to our clinic with painful solid mass in left testis. After diagnostic work-up for a possible testicular tumour, he underwent inguinal orchiectomy and histopathologic examination showed a testicular calculus. Case hypothesis: Solid testicular lesions in young adults generally correspond to testicular cancer. Differential diagnosis should be done carefully. Future implications: In young adults with painful and solid testicular mass with hyperechogenic appearance on scrotal ultrasonography, testicular calculus must be kept in mind in differential diagnosis. Further reports on this topic may let us do more clear recommendations about the etiology and treatment of this rare disease.

Visual Thinking and Gender Differences in High School Calculus

ERIC Educational Resources Information Center

Haciomeroglu, Erhan Selcuk; Chicken, Eric

2012-01-01

This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…

The Integration of Biology into Calculus Courses

ERIC Educational Resources Information Center

Comar, Timothy D.

2008-01-01

This article discusses the incorporation of biological content into existing calculus courses without significantly changing the courses. This is exemplified by the common laboratory course taken by students in all first semester calculus courses at Benedictine University. Several biologically oriented projects are implemented in this laboratory…

Unisex Math: Narrowing the Gender Gap.

ERIC Educational Resources Information Center

Tapia, Martha; Marsh, George E., II

This study examined gender differences in attitudes toward mathematics of undergraduate students. The Attitudes Toward Mathematics Instrument (ATMI) was administered to students enrolled in introductory mathematics classes (Pre-Calculus, Calculus, and Business Calculus) at two Southeast universities, one a large state university and the other one…

A giant dumbbell shaped vesico-prostatic urethral calculus: a case report and review of literature.

PubMed

Prabhuswamy, Vinod Kumar; Tiwari, Rahul; Krishnamoorthy, Ramakrishnan

2013-01-01

Calculi in the urethra are an uncommon entity. Giant calculi in prostatic urethra are extremely rare. The decision about treatment strategy of calculi depends upon the size, shape, and position of the calculus and the status of the urethra. If the stone is large and immovable, it may be extracted via the perineal or the suprapubic approach. In most of the previous reported cases, giant calculi were extracted via the transvesical approach and external urethrotomy. A 38-year-old male patient presented with complaints of lower urinary tract symptoms. Further investigations showed a giant urethral calculus secondary to stricture of bulbo-membranous part of the urethra. Surgical removal of calculus was done via transvesical approach. Two calculi were found and extracted. One was a huge dumbbell calculus and the other was a smaller round calculus. This case was reported because of the rare size and the dumbbell nature of the stone. Giant urethral calculi are better managed by open surgery.

A Giant Dumbbell Shaped Vesico-Prostatic Urethral Calculus: A Case Report and Review of Literature

PubMed Central

Prabhuswamy, Vinod Kumar; Tiwari, Rahul; Krishnamoorthy, Ramakrishnan

2013-01-01

Calculi in the urethra are an uncommon entity. Giant calculi in prostatic urethra are extremely rare. The decision about treatment strategy of calculi depends upon the size, shape, and position of the calculus and the status of the urethra. If the stone is large and immovable, it may be extracted via the perineal or the suprapubic approach. In most of the previous reported cases, giant calculi were extracted via the transvesical approach and external urethrotomy. A 38-year-old male patient presented with complaints of lower urinary tract symptoms. Further investigations showed a giant urethral calculus secondary to stricture of bulbo-membranous part of the urethra. Surgical removal of calculus was done via transvesical approach. Two calculi were found and extracted. One was a huge dumbbell calculus and the other was a smaller round calculus. This case was reported because of the rare size and the dumbbell nature of the stone. Giant urethral calculi are better managed by open surgery. PMID:23762742

Estimation and quantification of human DNA in dental calculus: A pilot study.

PubMed

Singh, Udita; Goel, Saurabh

2017-01-01

Identification using DNA has proved its accuracy multiple times in the field of forensic investigations. Investigators usually rely on either teeth or bone as the DNA reservoirs. However, there are instances where the skeletal or dental remains are not available or not preserved properly. Moreover, due to religious beliefs, the family members of the dead do not allow the investigating team to damage the remains for the sole purpose of identification. To investigate the presence of human DNA in dental calculus and to quantify the amount, if present. This prospective single-blinded pilot study included twenty subjects selected from the patients visiting a dental college. The samples of dental calculus were collected from the thickest portion of calculus deposited on the lingual surfaces of mandibular incisors. These samples were decontaminated and subjected to gel electrophoresis for DNA extraction. DNA was found in 85% cases. The amount of DNA varied from 21 to 37 μg/ml of dental calculus. Dental calculus is a rich reservoir of human DNA.

Backpropagation and ordered derivatives in the time scales calculus.

PubMed

Seiffertt, John; Wunsch, Donald C

2010-08-01

Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.

Colloquium: Fractional calculus view of complexity: A tutorial

NASA Astrophysics Data System (ADS)

West, Bruce J.

2014-10-01

The fractional calculus has been part of the mathematics and science literature for 310 years. However, it is only in the past decade or so that it has drawn the attention of mainstream science as a way to describe the dynamics of complex phenomena with long-term memory, spatial heterogeneity, along with nonstationary and nonergodic statistics. The most recent application encompasses complex networks, which require new ways of thinking about the world. Part of the new cognition is provided by the fractional calculus description of temporal and topological complexity. Consequently, this Colloquium is not so much a tutorial on the mathematics of the fractional calculus as it is an exploration of how complex phenomena in the physical, social, and life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions such as differentiability are discarded and the ordinary calculus is replaced with the fractional calculus. Exemplars considered include the fractional differential equations describing the dynamics of viscoelastic materials, turbulence, foraging, and phase transitions in complex social networks.

Extended phase graphs with anisotropic diffusion.

PubMed

Weigel, M; Schwenk, S; Kiselev, V G; Scheffler, K; Hennig, J

2010-08-01

The extended phase graph (EPG) calculus gives an elegant pictorial description of magnetization response in multi-pulse MR sequences. The use of the EPG calculus enables a high computational efficiency for the quantitation of echo intensities even for complex sequences with multiple refocusing pulses with arbitrary flip angles. In this work, the EPG concept dealing with RF pulses with arbitrary flip angles and phases is extended to account for anisotropic diffusion in the presence of arbitrary varying gradients. The diffusion effect can be expressed by specific diffusion weightings of individual magnetization pathways. This can be represented as an action of a linear operator on the magnetization state. The algorithm allows easy integration of diffusion anisotropy effects. The formalism is validated on known examples from literature and used to calculate the effective diffusion weighting in multi-echo sequences with arbitrary refocusing flip angles. Copyright 2010 Elsevier Inc. All rights reserved.

Two- and three-dimensional CT measurements of urinary calculi length and width: a comparative study.

PubMed

Lidén, Mats; Thunberg, Per; Broxvall, Mathias; Geijer, Håkan

2015-04-01

The standard imaging procedure for a patient presenting with renal colic is unenhanced computed tomography (CT). The CT measured size has a close correlation to the estimated prognosis for spontaneous passage of a ureteral calculus. Size estimations of urinary calculi in CT images are still based on two-dimensional (2D) reformats. To develop and validate a calculus oriented three-dimensional (3D) method for measuring the length and width of urinary calculi and to compare the calculus oriented measurements of the length and width with corresponding 2D measurements obtained in axial and coronal reformats. Fifty unenhanced CT examinations demonstrating urinary calculi were included. A 3D symmetric segmentation algorithm was validated against reader size estimations. The calculus oriented size from the segmentation was then compared to the estimated size in axial and coronal 2D reformats. The validation showed 0.1 ± 0.7 mm agreement against reference measure. There was a 0.4 mm median bias for 3D estimated calculus length compared to 2D (P < 0.001), but no significant bias for 3D width compared to 2D. The length of a calculus in axial and coronal reformats becomes underestimated compared to 3D if its orientation is not aligned to the image planes. Future studies aiming to correlate calculus size with patient outcome should use a calculus oriented size estimation. © The Foundation Acta Radiologica 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

Development of a Math Input Interface with Flick Operation for Mobile Devices

ERIC Educational Resources Information Center

Nakamura, Yasuyuki; Nakahara, Takahiro

2016-01-01

Developing online test environments for e-learning for mobile devices will be useful to increase drill practice opportunities. In order to provide a drill practice environment for calculus using an online math test system, such as STACK, we develop a flickable math input interface that can be easily used on mobile devices. The number of taps…

Rise of the Functionals?: Mobility Air Force Developmental Teams and their Impact on Officer Education and Advancement

DTIC Science & Technology

2014-06-01

Specialists (43X/44X/45X) Chaplain (52R) Civil Engineer (32E) Combat Air Force Contracting (64P) Cyber Operations (17D) Dental (47X) Finance (65 F...assume the principal has a perfect decision making calculus . The MAF DT may actually have asymmetric information, and given the opportunity, they could

A Fresh Look at Linear Ordinary Differential Equations with Constant Coefficients. Revisiting the Impulsive Response Method Using Factorization

ERIC Educational Resources Information Center

Camporesi, Roberto

2016-01-01

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as…

Endoscopic surgery and telemedicine in microgravity: developing contingency procedures for exploratory class spaceflight.

PubMed

Jones, J A; Johnston, S; Campbell, M; Miles, B; Billica, R

1999-05-01

The risk of a urinary calculus during an extended duration mission into the reduced gravity environment of space is significant. For medical operations to develop a comprehensive strategy for the spaceflight stone risk, both preventive countermeasures and contingency management (CM) plans must be included. A feasibility study was conducted to demonstrate the potential CM technique of endoscopic ureteral stenting with ultrasound guidance for the possible in-flight urinary calculus contingency. The procedure employed the International Space Station/Human Research Facility ultrasound unit for guide wire and stent localization, a flexible cystoscope for visual guidance, and banded, biocompatible soft ureteral stents to successfully stent porcine ureters bilaterally in zero gravity (0g). The study demonstrated that downlinked endoscopic surgical and ultrasound images obtained in 0g are comparable in quality to 1g images, and therefore are useful for diagnostic clinical utility via telemedicine transmission. In order to be successful, surgical procedures in 0g require excellent positional stability of the operating surgeon, assistant, and patient, relative to one another. The technological development of medical procedures for long-duration spaceflight contingencies may lead to improved terrestrial patient care methodology and subsequently reduced morbidity.

Endoscopic surgery and telemedicine in microgravity: developing contingency procedures for exploratory class spaceflight

NASA Technical Reports Server (NTRS)

Jones, J. A.; Johnston, S.; Campbell, M.; Miles, B.; Billica, R.

1999-01-01

OBJECTIVES: The risk of a urinary calculus during an extended duration mission into the reduced gravity environment of space is significant. For medical operations to develop a comprehensive strategy for the spaceflight stone risk, both preventive countermeasures and contingency management (CM) plans must be included. METHODS: A feasibility study was conducted to demonstrate the potential CM technique of endoscopic ureteral stenting with ultrasound guidance for the possible in-flight urinary calculus contingency. The procedure employed the International Space Station/Human Research Facility ultrasound unit for guide wire and stent localization, a flexible cystoscope for visual guidance, and banded, biocompatible soft ureteral stents to successfully stent porcine ureters bilaterally in zero gravity (0g). RESULTS: The study demonstrated that downlinked endoscopic surgical and ultrasound images obtained in 0g are comparable in quality to 1g images, and therefore are useful for diagnostic clinical utility via telemedicine transmission. CONCLUSIONS: In order to be successful, surgical procedures in 0g require excellent positional stability of the operating surgeon, assistant, and patient, relative to one another. The technological development of medical procedures for long-duration spaceflight contingencies may lead to improved terrestrial patient care methodology and subsequently reduced morbidity.

An actual load forecasting methodology by interval grey modeling based on the fractional calculus.

PubMed

Yang, Yang; Xue, Dingyü

2017-07-17

The operation processes for thermal power plant are measured by the real-time data, and a large number of historical interval data can be obtained from the dataset. Within defined periods of time, the interval information could provide important information for decision making and equipment maintenance. Actual load is one of the most important parameters, and the trends hidden in the historical data will show the overall operation status of the equipments. However, based on the interval grey parameter numbers, the modeling and prediction process is more complicated than the one with real numbers. In order not lose any information, the geometric coordinate features are used by the coordinates of area and middle point lines in this paper, which are proved with the same information as the original interval data. The grey prediction model for interval grey number by the fractional-order accumulation calculus is proposed. Compared with integer-order model, the proposed method could have more freedom with better performance for modeling and prediction, which can be widely used in the modeling process and prediction for the small amount interval historical industry sequence samples. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Reflections on Our First Calculus Undergraduate Teaching Assistant

ERIC Educational Resources Information Center

Deshler, Jessica M.

2016-01-01

This article describes some reflections from the first Calculus I undergraduate teaching assistant in our department as she explored the various ways in which she was able to support both novice and experienced Calculus teachers and the effect of her experience on her academic and career plans.

Calculus Demonstrations Using MATLAB

ERIC Educational Resources Information Center

Dunn, Peter K.; Harman, Chris

2002-01-01

The note discusses ways in which technology can be used in the calculus learning process. In particular, five MATLAB programs are detailed for use by instructors or students that demonstrate important concepts in introductory calculus: Newton's method, differentiation and integration. Two of the programs are animated. The programs and the…

A Snapshot of the Calculus Classroom

ERIC Educational Resources Information Center

Weathers, Tony D.; Latterell, Carmen M.

2003-01-01

Essentially a focus group to discuss textbook related issues, a meeting of calculus instructors from a wide variety of environments was convened and sponsored by McGraw Hill to provide feedback on the current state of the calculus classroom. This paper provides a description of the group's discussions.

Improving the Instruction of Infinite Series

ERIC Educational Resources Information Center

Lindaman, Brian; Gay, A. Susan

2012-01-01

Calculus instructors struggle to teach infinite series, and students have difficulty understanding series and related concepts. Four instructional strategies, prominently used during the calculus reform movement, were implemented during a 3-week unit on infinite series in one class of second-semester calculus students. A description of each…

Interrater Agreement on Subgingival Calculus Detection Following Scaling.

ERIC Educational Resources Information Center

Pippin, David J.; Feil, Philip

1992-01-01

Two studies investigated interrater agreement among 10 clinical dental examiners who scored residual subgingival calculus after student scaling on 4,160 real and 92 manikin tooth surfaces. Interrater reliability was low. Results suggest a need in periodontics for effective examiner calibration methods and objective subgingival calculus detection…

Imagine Yourself in This Calculus Classroom

ERIC Educational Resources Information Center

Bryan, Luajean

2007-01-01

The efforts to attract students to precalculus, trigonometry, and calculus classes became more successful at the author's school when projects-based classes were offered. Data collection from an untethered hot air balloon flight for calculus students was planned to maximize enrollment. The data were analyzed numerically, graphically, and…

Hands-On Calculus

ERIC Educational Resources Information Center

Sutherland, Melissa

2006-01-01

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and…

Calculus Instructors' and Students' Discourses on the Derivative

ERIC Educational Resources Information Center

Park, Jungeun

2011-01-01

Recently, there has been an increasing interest in collegiate mathematics education, especially teaching and learning calculus (e.g., Oehrtman, Carlson, & Thompson, 2008; Speer, Smith, & Horvath, 2010). Of many calculus concepts, the derivative is known as a difficult concept for students to understand because it involves various concepts…

Advanced Algebra and Calculus. High School Mathematics Curricula. Instructor's Guide.

ERIC Educational Resources Information Center

Natour, Denise M.

This manual is an instructor's guide for the utilization of the "CCA High School Mathematics Curricula: Advanced Algebra and Calculus" courseware developed by the Computer-based Education Research Laboratory (CERL). The curriculum comprises 34 algebra lessons within 12 units and 15 calculus lessons that are computer-based and require…

Differentiated Instruction in a Calculus Curriculum for College Students in Taiwan

ERIC Educational Resources Information Center

Chen, Jing-Hua; Chen, Yi-Chou

2018-01-01

Objectives: To explore differentiated instruction within a calculus curriculum. For college students to learn concentration, motivation and the impact of academic achievement; explore the attitudes and ideas of students on differentiated instruction within a calculus curriculum; build up the diversity of mathematics education within varied…

A Cross-National Study of Calculus

ERIC Educational Resources Information Center

Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen

2015-01-01

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan…

Teaching the Calculus

ERIC Educational Resources Information Center

Sauerheber, Richard D.

2012-01-01

Methods of teaching the Calculus are presented in honour of Sir Isaac Newton, by discussing an extension of his original proofs and discoveries. The methods, requested by Newton to be used that reflect the historical sequence of the discovered Fundamental Theorems, allow first-time students to grasp quickly the basics of the Calculus from its…

The Calculus of a Vase

ERIC Educational Resources Information Center

Scherger, Nicole

2012-01-01

Of the most universal applications in integral calculus are those involved with finding volumes of solids of revolution. These profound problems are typically taught with traditional approaches of the disk and shell methods, after which most calculus curriculums will additionally cover arc length and surfaces of revolution. Even in these visibly…

Calculus and Success in a Business School

ERIC Educational Resources Information Center

Kim, Dong-gook; Garcia, Fernando; Dey, Ishita

2012-01-01

Many business schools or colleges require calculus as a prerequisite for certain classes or for continuing to upper division courses. While there are many studies investigating the relationship between performance in calculus and performance in a single course, such as economics, statistics, and finance, there are very few studies investigating…

An Introductory Calculus-Based Mechanics Investigation

ERIC Educational Resources Information Center

Allen, Bradley

2017-01-01

One challenge for the introductory physics teacher is incorporating calculus techniques into the laboratory setting. It can be difficult to strike a balance between presenting an experimental task for which calculus is essential and making the mathematics accessible to learners who may be apprehensive about applying it. One-dimensional kinematics…

How Students Use Physics to Reason about Calculus Tasks

ERIC Educational Resources Information Center

Marrongelle, Karen A.

2004-01-01

The present research study investigates how undergraduate students in an integrated calculus and physics class use physics to help them solve calculus problems. Using Zandieh's (2000) framework for analyzing student understanding of derivative as a starting point, this study adds detail to her "paradigmatic physical" context and begins to address…

The Basic Principle of Calculus?

ERIC Educational Resources Information Center

Hardy, Michael

2011-01-01

A simple partial version of the Fundamental Theorem of Calculus can be presented on the first day of the first-year calculus course, and then relied upon repeatedly in assigned problems throughout the course. With that experience behind them, students can use the partial version to understand the full-fledged Fundamental Theorem, with further…

Calculus Instructors' Responses to Prior Knowledge Errors

ERIC Educational Resources Information Center

Talley, Jana Renee

2009-01-01

This study investigates the responses to prior knowledge errors that Calculus I instructors make when assessing students. Prior knowledge is operationalized as any skill or understanding that a student needs to successfully navigate through a Calculus I course. A two part qualitative study consisting of student exams and instructor interviews was…

Resequencing Calculus

ERIC Educational Resources Information Center

Dwyer, Dave; Gruenwald, Mark; Stickles, Joe; Axtell, Mike

2018-01-01

Resequencing Calculus is a project that has reordered the typical delivery of Calculus material to better serve the needs of STEM majors. Funded twice by the National Science Foundation, this project has produced a three-semester textbook that has been piloted at numerous institutions, large and small, public and private. This paper describes the…

Transitioning from Introductory Calculus to Formal Limit Conceptions

ERIC Educational Resources Information Center

Nagle, Courtney

2013-01-01

The limit concept is a fundamental mathematical notion both for its practical applications and its importance as a prerequisite for later calculus topics. Past research suggests that limit conceptualizations promoted in introductory calculus are far removed from the formal epsilon-delta definition of limit. In this article, I provide an overview…

Utilizing Microsoft Mathematics in Teaching and Learning Calculus

ERIC Educational Resources Information Center

Oktaviyanthi, Rina; Supriani, Yani

2015-01-01

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students' achievement and the effects of the use of Microsoft…

Experimental Design: Utilizing Microsoft Mathematics in Teaching and Learning Calculus

ERIC Educational Resources Information Center

Oktaviyanthi, Rina; Supriani, Yani

2015-01-01

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students' achievement and the effects of the use of Microsoft…

Aspects of Calculus for Preservice Teachers

ERIC Educational Resources Information Center

Fothergill, Lee

2011-01-01

The purpose of this study was to compare the perspectives of faculty members who had experience teaching undergraduate calculus and preservice teachers who had recently completed student teaching in regards to a first semester undergraduate calculus course. An online survey was created and sent to recent student teachers and college mathematics…

An Excel-Aided Method for Teaching Calculus-Based Business Mathematics

ERIC Educational Resources Information Center

Liang, Jiajuan; Martin, Linda

2008-01-01

Calculus-based business mathematics is a required quantitative course for undergraduate business students in most AACSB accredited schools or colleges of business. Many business students, however, have relatively weak mathematical background or even display math-phobia when presented with calculus problems. Because of the popularity of Excel, its…

Calculus in High School--At What Cost?

ERIC Educational Resources Information Center

Sorge, D. H.; Wheatley, G. H.

1977-01-01

Evidence on the decline in preparation of entering calculus students and the relationship to high school preparation is presented, focusing on the trend toward the de-emphasis of trigonometry and analytic geometry in favor of calculus. Data on students' perception of the adequacy of their preparation are also presented. (Author/MN)

Advanced Placement Mathematics Calculus, Grade 12 Curriculum Guide.

ERIC Educational Resources Information Center

Scharf, John; And Others

This document is a guide to the advanced placement program in calculus for grade 12 in the city schools in Warren, Ohio. The program covers analytic geometry, differential and integral calculus of algebraic functions, elementary transcendental functions, and applications of differentiation and integration. The philosophy and aims of the program…

DIFFERENTIAL AND INTEGRAL CALCULUS. A TENTATIVE CURRICULUM GUIDE.

ERIC Educational Resources Information Center

BRANT, VINCENT; GERARDI, WILLIAM

A GUIDE FOR A 1-YEAR COURSE IN DIFFERENTIAL AND INTEGRAL CALCULUS PREREQUISITED KNOWLEDGE IN ALGEBRA, ANALYTIC TRIGONOMETRY, AND ELEMENTARY ANALYSIS. EACH ASSIGNMENT CONTAINED BOTH NEW AND REVIEW WORK TO REINFORCE THE NEW WORK. THERE WERE ELEVEN UNITS OF STUDY USING THE FOLLOWING FOUR BOOKS--"CALCULUS AND ANALYTIC GEOMETRY, THIRD…

Student Achievement in College Calculus, Louisiana State University 1967-1968.

ERIC Educational Resources Information Center

Scannicchio, Thomas Henry

An investigation of freshmen achievement in an introductory calculus course was performed on the basis of high school mathematics background to find predictors of college calculus grades. Overall high school academic achievement, overall high school mathematics achievement, number of high school mathematics units, pattern of college preparatory…

Recursive sequences in first-year calculus

NASA Astrophysics Data System (ADS)

Krainer, Thomas

2016-02-01

This article provides ready-to-use supplementary material on recursive sequences for a second-semester calculus class. It equips first-year calculus students with a basic methodical procedure based on which they can conduct a rigorous convergence or divergence analysis of many simple recursive sequences on their own without the need to invoke inductive arguments as is typically required in calculus textbooks. The sequences that are accessible to this kind of analysis are predominantly (eventually) monotonic, but also certain recursive sequences that alternate around their limit point as they converge can be considered.

Extending Maxwell's equations for dielectric materials using analytical principles from viscoelasticity based on the fractional calculus

NASA Astrophysics Data System (ADS)

Wharmby, Andrew William

Existing fractional calculus models having a non-empirical basis used to describe constitutive relationships between stress and strain in viscoelastic materials are modified to employ all orders of fractional derivatives between zero and one. Parallels between viscoelastic and dielectric theory are drawn so that these modified fractional calculus based models for viscoelastic materials may be used to describe relationships between electric flux density and electric field intensity in dielectric materials. The resulting fractional calculus based dielectric relaxation model is tested using existing complex permittivity data in the radio-frequency bandwidth of a wide variety of homogeneous materials. The consequences that the application of this newly developed fractional calculus based dielectric relaxation model has on Maxwell's equations are also examined through the effects of dielectric dissipation and dispersion.

Evidence for calcifying nanoparticles in gingival crevicular fluid and dental calculus in periodontitis.

PubMed

Zhang, Song-Mei; Tian, Fei; Jiang, Xin-Quan; Li, Jing; Xu, Chun; Guo, Xiao-Kui; Zhang, Fu-Qiang

2009-09-01

Calcifying nanoparticles (CNPs), also known as nanobacteria, can produce carbonate apatite on their cell walls and initiate pathologic calcification. The objective of this study was to determine whether CNPs are present in the gingival crevicular fluid (GCF) from subjects with periodontal disease and whether they can induce the pathologic calcification of primary cultured human gingival epithelial cells. GCF and dental calculus samples were collected from 10 subjects with gingivitis and 10 subjects with chronic periodontitis. CNPs in GCF and calculus filtrates were detected with nanocapture enzyme-linked immunosorbent assay kits. The CNPs in cultures of dental calculus filtrates were also identified using immunofluorescence staining, transmission electron microscopy (TEM), and chemical analysis. Pathologic changes in the CNP-treated gingival epithelial cells were observed with TEM, alizarin red staining, and disk-scanning confocal microscopy. CNPs were found in GCF samples from two subjects with chronic periodontitis. Based on chemical analysis, the surface-associated material from CNPs isolated and cultured from calculus has a composition similar to dental calculus. The pathologic calcification of CNP-treated gingival epithelial cells was also observed. Self-replicating calcifying nanoparticles can be cultured and identified from dental calculus. This raises the issue of whether CNPs contribute to the pathogenesis of periodontitis.

Dental hygiene faculty calibration in the evaluation of calculus detection.

PubMed

Garland, Kandis V; Newell, Kathleen J

2009-03-01

The purpose of this pilot study was to explore the impact of faculty calibration training on intra- and interrater reliability regarding calculus detection. After IRB approval, twelve dental hygiene faculty members were recruited from a pool of twenty-two for voluntary participation and randomized into two groups. All subjects provided two pre- and two posttest scorings of calculus deposits on each of three typodonts by recording yes or no indicating if they detected calculus. Accuracy and consistency of calculus detection were evaluated using an answer key. The experimental group received three two-hour training sessions to practice a prescribed exploring sequence and technique for calculus detection. Participants immediately corrected their answers, received feedback from the trainer, and reconciled missed areas. Intra- and interrater reliability (pre- and posttest) was determined using Cohen's Kappa and compared between groups using repeated measures (split-plot) ANOVA. The groups did not differ from pre- to posttraining (intrarater reliability p=0.64; interrater reliability p=0.20). Training had no effect on reliability levels for simulated calculus detection in this study. Recommendations for future studies of faculty calibration when evaluating students include using patients for assessing rater reliability, employing larger samples at multiple sites, and assessing the impact on students' attitudes and learning outcomes.

Alpha-synuclein is present in dental calculus but not altered in Parkinson's disease patients in comparison to controls.

PubMed

Schmid, Sabrina; Goldberg-Bockhorn, Eva; Schwarz, Silke; Rotter, Nicole; Kassubek, Jan; Del Tredici, Kelly; Pinkhardt, Elmar; Otto, Markus; Ludolph, Albert C; Oeckl, Patrick

2018-06-01

In autopsy cases staged for sporadic Parkinson's disease (PD), the neuropathology is characterized by a preclinical phase that targets the enteric nervous system of the gastrointestinal tract (GIT). Therefore, the ENS might be a source of potential (presymptomatic) PD biomarkers. In this clinically based study, we examined the alpha-synuclein (αSyn) concentration in an easily accessible protein storage medium of the GIT, dental calculus, in 21/50 patients with PD and 28/50 age- and gender-matched controls using ELISA. αSyn was detectable in dental calculus and the median concentration in the control patients was 8.6 pg/mg calculus (interquartile range 2.6-13.1 pg/mg). αSyn concentrations were significantly influenced by blood contamination and samples with a hemoglobin concentration of > 4000 ng/mL were excluded. There was no significant difference of αSyn concentrations in the dental calculus of PD patients (5.76 pg/mg, interquartile range 2.91-9.74 pg/mg) compared to those in controls (p = 0.40). The total αSyn concentration in dental calculus is not a suitable biomarker for sporadic PD. Disease-related variants such as oligomeric or phosphorylated αSyn in calculus might prove to be more specific.

The comparative clinical efficacy of pyrophosphate/triclosan, copolymer/triclosan and zinc citrate/triclosan dentifrices for the reduction of supragingival calculus formation.

PubMed

Fairbrother, K J; Kowolik, M J; Curzon, M E; Müller, I; McKeown, S; Hill, C M; Hannigan, C; Bartizek, R D; White, D J

1997-01-01

Three triclosan-containing "multi-benefit" dentifrices were compared for clinical efficacy in reducing supragingival calculus formation following a dental prophylaxis. A total of 544 subjects completed a double-blind parallel-group clinical study using the Volpe-Manhold Index (VMI) to record severity and occurrence of supragingival calculus. The study design included a pre-test period where the calculus formation rate was measured in subjects brushing with a placebo dentifrice. Following a prophylaxis, subjects were stratified for age, gender and VMI scores and assigned to one of four treatments: 1) a dentifrice containing 5.0% soluble pyrophosphate/0.145% fluoride as NaF/silica abrasive/0.28% triclosan (hereafter PPi/TCS-comparable to Crest Complete dentifrice, Procter & Gamble, UK); 2) a commercial dentifrice containing 2.0% Gantrez acid copolymer/ 0.145% fluoride as NaF/silica abrasive/0.30% triclosan (hereafter Gan/TCS-Colgate Total dentifrice, Colgate-Palmolive Company, UK); 3) a commercial dentifrice containing 0.5% zinc citrate trihydrate/0.15% fluoride as sodium monofluorophosphate/silica abrasive/0.20% triclosan (hereafter Zn/TCS-Mentadent P dentifrice, Unilever, UK); and 4) a control dentifrice comprised of 0.145% fluoride as NaF/silica abrasive (hereafter Control). Subjects were instructed to use their assigned dentifrice at least twice per day and to brush as they do normally. Supragingival calculus formation was assesed at two and four months using site-specific and whole-mouth VMI indices for both calculus severity and occurrence. Following four months of use, the PPi/TCS dentifrice provided statistically significant reductions in calculus severity (22-23%) and occurrence (15%) as compared with the Control dentifrice. The Zn/TCS dentifrice also provided significant reductions in calculus severity (17-19%) and occurrence (12-13%) as compared with the Control. The Gan/TCS produced no statistically significant reductions in calculus formation (occurrence or severity) compared with the Control. The PPi/TCS dentifrice provided statistically significant reductions in calculus severity (15-21%) and occurrence (12-16%) as compared with the Gan/TCS dentifrice. These results support the clinical effectiveness of PPi/TCS and Zn/TCS dentifrices for the reduction of supragingival dental calculus formation following a dental prophylaxis.

A non-local model of fractional heat conduction in rigid bodies

NASA Astrophysics Data System (ADS)

Borino, G.; di Paola, M.; Zingales, M.

2011-03-01

In recent years several applications of fractional differential calculus have been proposed in physics, chemistry as well as in engineering fields. Fractional order integrals and derivatives extend the well-known definitions of integer-order primitives and derivatives of the ordinary differential calculus to real-order operators. Engineering applications of fractional operators spread from viscoelastic models, stochastic dynamics as well as with thermoelasticity. In this latter field one of the main actractives of fractional operators is their capability to interpolate between the heat flux and its time-rate of change, that is related to the well-known second sound effect. In other recent studies a fractional, non-local thermoelastic model has been proposed as a particular case of the non-local, integral, thermoelasticity introduced at the mid of the seventies. In this study the autors aim to introduce a different non-local model of extended irreverible thermodynamics to account for second sound effect. Long-range heat flux is defined and it involves the integral part of the spatial Marchaud fractional derivatives of the temperature field whereas the second-sound effect is accounted for introducing time-derivative of the heat flux in the transport equation. It is shown that the proposed model does not suffer of the pathological problems of non-homogenoeus boundary conditions. Moreover the proposed model coalesces with the Povstenko fractional models in unbounded domains.

Non-Invasive Periodontal Probing Through Fourier-Domain Optical Coherence Tomography.

PubMed

Mota, Cláudia C B O; Fernandes, Luana O; Cimões, Renata; Gomes, Anderson S L

2015-09-01

Periodontitis is a multifactorial and infectious disease that may result in significant debilitation. The aim of this study is to exploit two optical coherence tomography (OCT) systems operating in the Fourier domain at different wavelengths, 930 and 1,325 nm, for structural analysis of periodontal tissue in porcine jaws. Five fresh porcine jaws were sectioned and stored in formalin before OCT analysis. Two- and three-dimensional OCT images of the tooth/gingiva interface were performed, and measurements of the gingival structures were obtained. The 930-nm OCT system operates in the spectral domain, whereas the 1,325-nm system is a swept-source model. Stereomicroscope images, the gold standard, were used for direct comparison. Through image analysis, it is possible to identify the free gingiva and the attached gingiva, the calculus deposition over tooth surfaces, and the subgingival calculus that enables the enlargement of the gingival sulcus. In addition, the gingival thickness and the gingival sulcus depth can be non-invasively measured, varying from 0.8 to 4 mm. Regarding the ability of the two OCT systems to visualize periodontal structures, the system operating at 1,325 nm shows a better performance, owing to a longer central wavelength that allows deeper tissue penetration. The results with the system at 930 nm can also be used, but some features could not be observed due to its lower penetration depth in the tissue.

A randomized controlled clinical study of the effect of daily intake of Ascophyllum nodosum alga on calculus, plaque, and gingivitis.

PubMed

van Dijken, Jan W V; Koistinen, S; Ramberg, Per

2015-07-01

The aim of this study is to evaluate, in a randomized controlled cross-over study, the effect of daily intake of the alga Ascophyllum nodosum on supragingival calculus, plaque formation, and gingival health over a 6-month period. Sixty-one adults with moderate to heavy calculus formation since their last yearly recall visit participated. In a randomized order over two 6-month periods, they swallowed two capsules daily, comprising a total of 500 mg dried marine alga powder (Ascophyllum nodosum, ProDen PlaqueOff®) or two negative control tablets. During the study, the participants maintained their regular oral habits. Their teeth were professionally cleaned at the start of each period and after the 6-month registrations. A wash out period of 1 month separated the two 6-month periods. Supragingival calculus (Volpe Manhold), gingivitis (Löe and Silness), gingival bleeding (Ainamo and Bay), and plaque (Quigley-Hein) were registered at screening and at the end of the two periods. Differences in oral health between the test and control periods were analyzed using a paired t test and Wilcoxon signed rank test. Fifty-five participants completed the study. After the alga intake, the mean calculus reduction was 52% compared to the control (p < 0.0001). Fifty-two participants showed less calculus formation in the alga group than in the control group. Plaque (p = 0.008) and gingival bleeding (p = 0.02) were also significantly less in the alga group. However, no significant difference was found between the groups for gingivitis (p = 0.13). The alga intake significantly reduced the formation of supragingival calculus and plaque and occurrence of gingival bleeding. The alga has a systemic effect on oral health. Daily intake of the alga Ascophyllum nodosum as an adjunct to customary oral hygiene showed a major reduction of supragingival calculus formation and reduced plaque formation. In addition, the calculus in the alga group was characterized by a more porous and less solid structure and was easier to remove than the calculus in the control group.

Attendance and Attainment in a Calculus Course

ERIC Educational Resources Information Center

Meulenbroek, Bernard; van den Bogaard, Maartje

2013-01-01

In this paper the relationship between attendance and attainment in a standard calculus course is investigated. Calculus could in principle be studied without attending lectures due to the wealth of material available (in hardcopy and online). However, in this study we will show that the pass rate of students attending classes regularly (>75%…

A Study of Students' Readiness to Learn Calculus

ERIC Educational Resources Information Center

Carlson, Marilyn P.; Madison, Bernard; West, Richard D.

2015-01-01

The Calculus Concept Readiness (CCR) instrument assesses foundational understandings and reasoning abilities that have been documented to be essential for learning calculus. The CCR Taxonomy describes the understandings and reasoning abilities assessed by CCR. The CCR is a 25-item multiple-choice instrument that can be used as a placement test for…

Evaluating the Use of Learning Objects for Improving Calculus Readiness

ERIC Educational Resources Information Center

Kay, Robin; Kletskin, Ilona

2010-01-01

Pre-calculus concepts such as working with functions and solving equations are essential for students to explore limits, rates of change, and integrals. Yet many students have a weak understanding of these key concepts which impedes performance in their first year university Calculus course. A series of online learning objects was developed to…

Initialized Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

The AP Calculus Exam Reading Experience: Implications for Teacher Classroom Practice and Student Comprehension

ERIC Educational Resources Information Center

Corcoran, Mimi

2017-01-01

This dissertation explores the views and experiences of high school calculus teachers and college mathematics professors on the professional development which occurs at the annual national AP Calculus exam grading. This professional development experience comes in several forms: the exam briefing sessions, the actual reading of the exams, the…

Undergraduate Course and Curriculum Development Program and Calculus and the Bridge to Calculus Program: 1993 Awards.

ERIC Educational Resources Information Center

National Science Foundation, Arlington, VA. Div. of Undergraduate Education.

The Undergraduate Course and Curriculum Development Program of the National Science Foundation supports the development of courses in all disciplines to improve the quality of undergraduate courses and curricula in science, mathematics, engineering, and technology. The purpose of the program in Curriculum Development in Mathematics: Calculus and…

Calculus in the Middle School?

ERIC Educational Resources Information Center

Barger, Rita H.; McCoy, Ann C.

2010-01-01

This article presents an example of how middle school teachers can lay a foundation for calculus. Although many middle school activities connect directly to calculus concepts, the authors have decided to look in depth at only one: the concept of change. They will show how teachers can lead their students to see and appreciate the calculus…

An Exploration of Definition and Procedural Fluency in Integral Calculus

ERIC Educational Resources Information Center

Grundmeier, Todd A.; Hansen, Jennifer; Sousa, Emily

2006-01-01

A survey was administered to calculus students who had previously been exposed to a course on integral calculus. The purpose of the survey was to explore students' understanding of the definition of a definite integral, their abilities to evaluate definite integrals, and their graphical interpretations of definite integrals. The analysis of…

The Use of Technology and Visualization in Calculus Instruction

ERIC Educational Resources Information Center

Samuels, Jason

2010-01-01

This study was inspired by a history of student difficulties in calculus, and innovation in response to those difficulties. The goals of the study were fourfold. First, to design a mathlet for students to explore local linearity. Second, to redesign the curriculum of first semester calculus around the use of technology, an emphasis on…

Problem Posing at All Levels in the Calculus Classroom

ERIC Educational Resources Information Center

Perrin, John Robert

2007-01-01

This article explores the use of problem posing in the calculus classroom using investigative projects. Specially, four examples of student work are examined, each one differing in originality of problem posed. By allowing students to explore actual questions that they have about calculus, coming from their own work or class discussion, or…

Coordinating Multiple Representations in a Reform Calculus Textbook

ERIC Educational Resources Information Center

Chang, Briana L.; Cromley, Jennifer G.; Tran, Nhi

2015-01-01

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

Calculus Challenges: An Active Learning Approach

ERIC Educational Resources Information Center

Crawford, Pam; Moseley, Daniel; Nancarrow, Mike; Ward, Erika

2018-01-01

One of the greatest challenges facing students new to calculus is the ability to persevere in the face of failure. Whether the student is choosing an integration technique or a series test, calculus is often the first course in mathematics where the path to the solution is not prescribed in an algorithmic way. At Jacksonville University we…

Descartes' Calculus of Subnormals: What Might Have Been

ERIC Educational Resources Information Center

Boudreaux, Gregory Mark; Walls, Jess E.

2013-01-01

Rene Descartes' method for finding tangents (equivalently, subnormals) depends on geometric and algebraic properties of a family of circles intersecting a given curve. It can be generalized to establish a calculus of subnormals, an alternative to the calculus of Newton and Leibniz. Here we prove subnormal counterparts of the well-known…

On Flipping the Classroom in Large First Year Calculus Courses

ERIC Educational Resources Information Center

Jungic, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy

2015-01-01

Over the course of two years, 2012-2014, we have implemented a "flipping" the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of…

A Methodology in the Teaching Process of Calculus and Its Motivation.

ERIC Educational Resources Information Center

Vasquez-Martinez, Claudio-Rafael

The development of calculus and science by being permanent, didactic, demands on one part an analytical, deductive study and on another an application of methods, rhochrematics, resources, within calculus, which allows to dialectically conform knowledge in its different phases and to test the results. For the purpose of this study, the motivation…

Inversion exercises inspired by mechanics

NASA Astrophysics Data System (ADS)

Groetsch, C. W.

2016-02-01

An elementary calculus transform, inspired by the centroid and gyration radius, is introduced as a prelude to the study of more advanced transforms. Analysis of the transform, including its inversion, makes use of several key concepts from basic calculus and exercises in the application and inversion of the transform provide practice in the use of technology in calculus.

The Association of Precollege Use of Calculators with Student Performance in College Calculus

ERIC Educational Resources Information Center

Mao, Yi; White, Tyreke; Sadler, Philip M.; Sonnert, Gerhard

2017-01-01

This study investigates how the use of calculators during high school mathematics courses is associated with student performance in introductory college calculus courses in the USA. Data were drawn from a nationally representative sample of 7087 students enrolled in college calculus at 134 colleges and universities. They included information about…

The Development of Prerequisite Notions for an Introductory Conception of a Functional Limit

ERIC Educational Resources Information Center

Nagle, Courtney Rose

2012-01-01

The limit concept plays a foundational role in calculus, appearing in the definitions of the two main ideas of introductory calculus, derivatives and integrals. Previous research has focused on three stages of students' development of limit ideas: the premathematical stage, the introductory calculus stage, and the transition from introductory…

Calculus: An Active Approach with Projects.

ERIC Educational Resources Information Center

Hilbert, Steve; And Others

Ithaca College, in New York, has developed and tested a projects-based first-year calculus course over the last 3 years which uses the graphs of functions and physical phenomena to illustrate and motivate the major concepts of calculus and to introduce students to mathematical modeling. The course curriculum is designed to: (1) emphasize on the…

Student Created Calculus Movies Using Computers and the TI-92.

ERIC Educational Resources Information Center

Sher, Lawrence; Wilkinson, Patricia

The Mathematics Department at Borough of Manhattan Community College (BMCC) (New York) has been actively involved since 1988 in a serious and successful program to improve instruction, understanding, and retention for women and minority students in calculus courses. One result of this work has been students creating calculus animations using…

Analyzing Conceptual Gains in Introductory Calculus with Interactively-Engaged Teaching Styles

ERIC Educational Resources Information Center

Thomas, Matthew

2013-01-01

This dissertation examines the relationship between an instructional style called Interactive-Engagement (IE) and gains on a measure of conceptual knowledge called the Calculus Concept Inventory (CCI). The data comes from two semesters of introductory calculus courses (Fall 2010 and Spring 2011), consisting of a total of 482 students from the…

Educating about Sustainability while Enhancing Calculus

ERIC Educational Resources Information Center

Pfaff, Thomas J.

2011-01-01

We give an overview of why it is important to include sustainability in mathematics classes and provide specific examples of how to do this for a calculus class. We illustrate that when students use "Excel" to fit curves to real data, fundamentally important questions about sustainability become calculus questions about those curves. (Contains 5…

Commentary on A General Curriculum in Mathematics for Colleges.

ERIC Educational Resources Information Center

Committee on the Undergraduate Program in Mathematics, Berkeley, CA.

This document constitutes a complete revision of the report of the same name first published in 1965. A new list of basic courses is described, consisting of Calculus I, Calculus II, Elementary Linear Algebra, Multivariable Calculus I, Linear Algebra, and Introductory Modern Algebra. Commentaries outline the content and spirit of these courses in…

Online Homework in Calculus I: Friend or Foe?

ERIC Educational Resources Information Center

Halcrow, Cheryl; Dunnigan, Gerri

2012-01-01

This article describes a quantitative and qualitative assessment from a study done on the possible effectiveness of including an online homework component in first-semester calculus. Two instructors, each teaching two sections of Calculus I, agreed to treat one of their sections as an experimental group and the other as a control group. Students…

Modelling the Landing of a Plane in a Calculus Lab

ERIC Educational Resources Information Center

Morante, Antonio; Vallejo, Jose A.

2012-01-01

We exhibit a simple model of a plane landing that involves only basic concepts of differential calculus, so it is suitable for a first-year calculus lab. We use the computer algebra system Maxima and the interactive geometry software GeoGebra to do the computations and graphics. (Contains 5 figures and 1 note.)

Coordinating Multiple Representations in a Reform Calculus Textbook

ERIC Educational Resources Information Center

Chang, Briana L.; Cromley, Jennifer G.; Tran, Nhi

2016-01-01

Coordination of multiple representations (CMR) is widely recognized as a critical skill in mathematics and is frequently demanded in reform calculus textbooks. However, little is known about the prevalence of coordination tasks in such textbooks. We coded 707 instances of CMR in a widely used reform calculus textbook and analyzed the distributions…

Plaque, gingival bleeding and calculus formation after supragingival scaling with and without polishing: a randomised clinical trial.

PubMed

Zanatta, Fabricio Batistin; Pinto, Tatiana Militz; Kantorski, Karla Zanini; Rösing, Cassiano Kuchenbecker

2011-01-01

The aim of this study was to compare the effect of polishing after scaling and root planing on supragingival plaque, calculus formation, and gingival bleeding. The study was designed as a split-mouth randomised clinical trial. Seventy-six patients were submitted to supragingival scaling on the six mandibular anterior teeth with manual curettes until a smooth surface was achieved. Subsequently, quadrants were randomly selected to be polished (test) or not (control) with a rubber cup and pumice. One, two and three weeks following treatment, a blinded examiner evaluated the visible plaque index, gingival bleeding index and the presence of supragingival calculus on the lingual tooth surfaces. The results showed that unpolished surfaces exhibited higher mean percentages of visible plaque in the third week. No statistically significant differences were observed between unpolished and polished sites related to gingival bleeding. Calculus formation was higher on unpolished sites than on polished sites at 2 and 3 weeks. Dental polishing after supragingival scaling contributed to reducing plaque and calculus formation. Polishing exerts an inhibitory effect on plaque and calculus formation.

Light and scanning electron microscope investigations comparing calculus removal using an Er:YAG laser and a frequency-doubled alexandrite laser

NASA Astrophysics Data System (ADS)

Rechmann, Peter; Hennig, Thomas; Sadegh, Hamid M. M.; Goldin, Dan S.

1997-05-01

With respect to lasers emitting within the mid-IR spectral domain fiber applicators are being developed. Intended is the use of these lasers in periodontal therapy and their application inside the gingival pocket. Aim of the study presented here is to compare the effect of an Er:YAG laser on dental calculus with the results following irradiation with a frequency doubled Alexandrite laser. The surface of freshly extracted wisdom teeth and of extracted teeth suffering from severe periodontitis were irradiated with both laser wavelengths using a standardized application protocol. Calculus on the enamel surface, at the enamel cementum junction and on the root surface was irradiated. For light microscope investigations undecalcified histological sections were prepared after treatment. For the scanning electron microscope teeth were dried in alcohol and sputtered with gold. Investigations revealed that with both laser systems calculus can be removed. Using the frequency doubled Alexandrite laser selective removal of calculus is possible while engaging the Er:YAG laser even at lowest energies necessary for calculus removal healthy cementum is ablated without control.

On flipping first-semester calculus: a case study

NASA Astrophysics Data System (ADS)

Petrillo, Joseph

2016-05-01

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are 'flipping' (or inverting) their classrooms. By flipping, we mean administering course content outside of the classroom and replacing the traditional in-class lectures with discussion, practice, group work, and other elements of active learning. This paper presents the major results from a three-year study of a flipped, first-semester calculus course at a small, comprehensive, American university with a well-known engineering programme. The data we have collected help quantify the positive and substantial effects of our flipped calculus course on failure rates, scores on the common final exam, student opinion of calculus, teacher impact on measurable outcomes, and success in second-semester calculus. While flipping may not be suitable for every teacher, every student, and in every situation, this report provides some evidence that it may be a viable option for those seeking an alternative to the traditional lecture model.

Dental calculus: the calcified biofilm and its role in disease development.

PubMed

Akcalı, Aliye; Lang, Niklaus P

2018-02-01

Dental calculus represents the first fossilized record of bacterial communities as a testimony of evolutionary biology. The development of dental calculus is a dynamic process that starts with a nonmineralized biofilm which eventually calcifies. Nonmineralized dental biofilm entraps particles from the oral cavity, including large amounts of oral bacteria, human proteins, viruses and food remnants, and preserves their DNA. The process of mineralization involves metabolic activities of the bacterial colonies and strengthens the attachment of nonmineralized biofilms to the tooth surface. From a clinical point of view, dental calculus always harbors a living, nonmineralized biofilm, jeopardizing the integrity of the dento-gingival or implanto-mucosal unit. This narrative review presents a brief historical overview of dental calculus formation and its clinical relevance in modern periodontal practice. © 2017 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Characterization of calculus migration during Ho:YAG laser lithotripsy by high speed camera using suspended pendulum method

NASA Astrophysics Data System (ADS)

Zhang, Jian James; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Chia, Ray W. J.; Hasenberg, Tom

2014-03-01

Calculus migration is a common problem during ureteroscopic laser lithotripsy procedure to treat urolithiasis. A conventional experimental method to characterize calculus migration utilized a hosting container (e.g. a "V" grove or a test tube). These methods, however, demonstrated large variation and poor detectability, possibly attributing to friction between the calculus and the container on which the calculus was situated. In this study, calculus migration was investigated using a pendulum model suspended under water to eliminate the aforementioned friction. A high speed camera was used to study the movement of the calculus which covered zero order (displacement), 1st order (speed) and 2nd order (acceleration). A commercialized, pulsed Ho:YAG laser at 2.1 um, 365-um core fiber, and calculus phantom (Plaster of Paris, 10×10×10mm cube) were utilized to mimic laser lithotripsy procedure. The phantom was hung on a stainless steel bar and irradiated by the laser at 0.5, 1.0 and 1.5J energy per pulse at 10Hz for 1 second (i.e., 5, 10, and 15W). Movement of the phantom was recorded by a high-speed camera with a frame rate of 10,000 FPS. Maximum displacement was 1.25+/-0.10, 3.01+/-0.52, and 4.37+/-0.58 mm for 0.5, 1, and 1.5J energy per pulse, respectively. Using the same laser power, the conventional method showed <0.5 mm total displacement. When reducing the phantom size to 5×5×5mm (1/8 in volume), the displacement was very inconsistent. The results suggested that using the pendulum model to eliminate the friction improved sensitivity and repeatability of the experiment. Detailed investigation on calculus movement and other causes of experimental variation will be conducted as a future study.

Investigation into the optimum beam shape and fluence for selective ablation of dental calculus at lambda = 400 nm.

PubMed

Schoenly, Joshua E; Seka, Wolf; Rechmann, Peter

2010-01-01

A frequency-doubled Ti:sapphire laser is shown to selectively ablate dental calculus. The optimal transverse shape of the laser beam, including its variability under water-cooling, is determined for selective ablation of dental calculus. Intensity profiles under various water-cooling conditions were optically observed. The 400-nm laser was coupled into a multimode optical fiber using an f = 2.5-cm lens and light-shaping diffuser. Water-cooling was supplied coaxially around the fiber. Five human tooth samples (four with calculus and one pristine) were irradiated perpendicular to the tooth surface while the tooth was moved back and forth at 0.3 mm/second, varying between 20 and 180 iterations. The teeth were imaged before and after irradiation using light microscopy with a flashing blue light-emitting diode (LED). An environmental scanning electron microscope imaged each tooth after irradiation. High-order super-Gaussian intensity profiles are observed at the output of a fiber coiled around a 4-in. diameter drum. Super-Gaussian beams have a more-homogenous fluence distribution than Gaussian beams and have a higher energy efficiency for selective ablation. Coaxial water-cooling does not noticeably distort the intensity distribution within 1 mm from the optical fiber. In contrast, lasers focused to a Gaussian cross section (< or =50-microm diameter) without fiber propagation and cooled by a water spray are heavily distorted and may lead to variable ablation. Calculus is preferentially ablated at high fluences (> or =2 J/cm(2)); below this fluence, stalling occurs because of photo-bleaching of the calculus. Healthy dental hard tissue is not removed at fluences < or =3 J/cm(2). Supplying laser light to a tooth using an optical fiber with coaxial water-cooling is determined to be the most appropriate method when selectively removing calculus with a frequency-doubled Ti:sapphire laser. Fluences over 2 J/cm(2) are required to remove calculus efficiently since photo-bleaching stalls calculus removal below that value.

Investigation Into the Optimum Beam Shape and Fluence for Selective Ablation of Dental Calculus at lambda = 400 nm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schoenly, J.E.; Seka. W.; Rechmann, P.

A frequency-doubled Ti:sapphire laser is shown to selectively ablate dental calculus. The optimal transverse shape of the laser beam, including its variability under water-cooling, is determined for selective ablation of dental calculus. Intensity profiles under various water-cooling conditions were optically observed. The 400-nm laser was coupled into a multimode optical fiber using an f = 2.5-cm lens and light-shaping diffuser. Water-cooling was supplied coaxially around the fiber. Five human tooth samples (four with calculus and one pristine) were irradiated perpendicular to the tooth surface while the tooth was moved back and forth at 0.3 mm/second, varying between 20 and 180more » iterations. The teeth were imaged before and after irradiation using light microscopy with a flashing blue light-emitting diode (LED). An environmental scanning electron microscope imaged each tooth after irradiation. High-order super-Gaussian intensity profiles are observed at the output of a fiber coiled around a 4-in. diameter drum. Super-Gaussian beams have a morehomogenous fluence distribution than Gaussian beams and have a higher energy efficiency for selective ablation. Coaxial water-cooling does not noticeably distort the intensity distribution within 1 mm from the optical fiber. In contrast, lasers focused to a Gaussian cross section (<=50-mm diameter) without fiber propagation and cooled by a water spray are heavily distorted and may lead to variable ablation. Calculus is preferentially ablated at high fluences (>= 2 J/cm^2); below this fluence, stalling occurs because of photo-bleaching of the calculus. Healthy dental hard tissue is not removed at fluences <=3 J/cm^2. Supplying laser light to a tooth using an optical fiber with coaxial water-cooling is determined to be the most appropriate method when selectively removing calculus with a frequency-doubled Ti:sapphire laser. Fluences over 2 J/cm^2 are required to remove calculus efficiently since photo-bleaching stalls calculus removal below that value.« less

A fractional calculus perspective of distributed propeller design

NASA Astrophysics Data System (ADS)

Tenreiro Machado, J.; Galhano, Alexandra M.

2018-02-01

A new generation of aircraft with distributed propellers leads to operational performances superior to those exhibited by standard designs. Computational simulations and experimental tests show a reduction of fuel consumption and noise. This paper proposes an analogy between aerodynamics and electrical circuits. The model reveals properties similar to those of fractional-order systems and gives a deeper insight into the dynamics of multi-propeller coupling.

Formally verifying Ada programs which use real number types

NASA Technical Reports Server (NTRS)

Sutherland, David

1986-01-01

Formal verification is applied to programs which use real number arithmetic operations (mathematical programs). Formal verification of a program P consists of creating a mathematical model of F, stating the desired properties of P in a formal logical language, and proving that the mathematical model has the desired properties using a formal proof calculus. The development and verification of the mathematical model are discussed.

Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory

DTIC Science & Technology

2017-03-01

calculus, applied mathematics, Director’s Research Initiative 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18... research of Svenkeson et al.4 Section 2 is Accomplishments and Section 3 is the Conclusion. 2. Accomplishments 2.1 Prescribed External Forcing To study ...ARL-TR-7959 MAR 2017 US Army Research Laboratory Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman

Dynamic Battlefield Visualization: Knowledge Management in a Complex, Emergent PMESII-PT Battlefield

DTIC Science & Technology

2009-06-01

organizations was articulated over two decades ago by Jerome Bruner (1986). Specifically, he argued that humans employ two distinctive modes of...narrative knowledge underscored by the writings of Jerome Bruner , Karl Weick, Laurence Prusak, and John Seely Brown. Finally, it consistently supports...a known battle calculus) and ambiguity (pattern/trend analysis to reveal operational variances or to discover influence mechanisms that can be

Heat exchanger expert system logic

NASA Technical Reports Server (NTRS)

Cormier, R.

1988-01-01

The reduction is described of the operation and fault diagnostics of a Deep Space Network heat exchanger to a rule base by the application of propositional calculus to a set of logic statements. The value of this approach lies in the ease of converting the logic and subsequently implementing it on a computer as an expert system. The rule base was written in Process Intelligent Control software.

Measuring Quality of the ANSF

DTIC Science & Technology

2011-03-01

own efforts to remain good stewards of these resources. Manpower further constrains our actions and ability to produce quality and will only become...literate will directly benefit operational effectiveness (e.g., orders and directives) and steward - ship of personnel and equipment (e.g., supply...Unfortunately, many don’t realize this statement of fact and do not account for it in their calculus when assessing the quality of the ANSF. Our

Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena

NASA Astrophysics Data System (ADS)

Atangana, Abdon; Gómez-Aguilar, J. F.

2018-04-01

To answer some issues raised about the concept of fractional differentiation and integration based on the exponential and Mittag-Leffler laws, we present, in this paper, fundamental differences between the power law, exponential decay, Mittag-Leffler law and their possible applications in nature. We demonstrate the failure of the semi-group principle in modeling real-world problems. We use natural phenomena to illustrate the importance of non-commutative and non-associative operators under which the Caputo-Fabrizio and Atangana-Baleanu fractional operators fall. We present statistical properties of generator for each fractional derivative, including Riemann-Liouville, Caputo-Fabrizio and Atangana-Baleanu ones. The Atangana-Baleanu and Caputo-Fabrizio fractional derivatives show crossover properties for the mean-square displacement, while the Riemann-Liouville is scale invariant. Their probability distributions are also a Gaussian to non-Gaussian crossover, with the difference that the Caputo Fabrizio kernel has a steady state between the transition. Only the Atangana-Baleanu kernel is a crossover for the waiting time distribution from stretched exponential to power law. A new criterion was suggested, namely the Atangana-Gómez fractional bracket, that helps describe the energy needed by a fractional derivative to characterize a 2-pletic manifold. Based on these properties, we classified fractional derivatives in three categories: weak, mild and strong fractional differential and integral operators. We presented some applications of fractional differential operators to describe real-world problems and we proved, with numerical simulations, that the Riemann-Liouville power-law derivative provides a description of real-world problems with much additional information, that can be seen as noise or error due to specific memory properties of its power-law kernel. The Caputo-Fabrizio derivative is less noisy while the Atangana-Baleanu fractional derivative provides an excellent description, due to its Mittag-Leffler memory, able to distinguish between dynamical systems taking place at different scales without steady state. The study suggests that the properties of associativity and commutativity or the semi-group principle are just irrelevant in fractional calculus. Properties of classical derivatives were established for the ordinary calculus with no memory effect and it is a failure of mathematical investigation to attempt to describe more complex natural phenomena using the same notions.

Dual-Energy Computed Tomography Gemstone Spectral Imaging: A Novel Technique to Determine Human Cardiac Calculus Composition.

PubMed

Cheng, Ching-Li; Chang, Hsiao-Huang; Ko, Shih-Chi; Huang, Pei-Jung; Lin, Shan-Yang

2016-01-01

Understanding the chemical composition of any calculus in different human organs is essential for choosing the best treatment strategy for patients. The purpose of this study was to assess the capability of determining the chemical composition of a human cardiac calculus using gemstone spectral imaging (GSI) mode on a single-source dual-energy computed tomography (DECT) in vitro. The cardiac calculus was directly scanned on the Discovery CT750 HD FREEdom Edition using GSI mode, in vitro. A portable fiber-optic Raman spectroscopy was also applied to verify the quantitative accuracy of the DECT measurements. The results of spectral DECT measurements indicate that effective Z values in 3 designated positions located in this calculus were 15.02 to 15.47, which are close to values of 15.74 to 15.86, corresponding to the effective Z values of calcium apatite and hydroxyapatite. The Raman spectral data were also reflected by the predominant Raman peak at 960 cm for hydroxyapatite and the minor peak at 875 cm for calcium apatite. A potential single-source DECT with GSI mode was first used to examine the morphological characteristics and chemical compositions of a giant human cardiac calculus, in vitro. The CT results were consistent with the Raman spectral data, suggesting that spectral CT imaging techniques could be accurately used to diagnose and characterize the compositional materials in the cardiac calculus.

Giant ureteric and staghorn calculi in a young adult Nigerian male: a case report.

PubMed

Gali, B M; Ali, A; Ibrahim, A G; Bakari, A; Minoza, K

2010-01-01

Ureteric calculi are usually small and solitary.The term giant has been applied to ureteric calculi that aremore than five cms in length and/or 50g or more in weight. These are uncommon and may present with few or no urological symptoms and might be ignored or be missed. To present a rare case of a giant left ureteric calculus associated with an ipsilateral staghorn calculus. A 31-year-old Nigerian male presented with recurrent left abdominal pain, dysuria, urinary frequency, and fever which had been on for 10 years. Patient was clinically evaluated. He had plain abdominal X-rays, abdominal ultrasonography and intravenous urography. He had to undergo nephrouterorectomy. Patient took analgesics and antibiotics purchased from patent chemist shops for relief of symptoms by himself. He was fit except for a hard cylindrical mass felt arising from the pelvis. Abdomino-pelvic ultrasound scan, plain abdominal X-ray and Intravenous urogram showed a giant ureteric calculus with an ipsilateral staghorn calculus in a nonfunctioning hydronephrotic left kidney. There was no evidence of underlying anatomic or metabolic abnormalities. He had left nephroureterectomy. The ureteric calculus measured 10.5 x 3.0cm and weighed 20.1gm. Giant ureteric calculi are rare. The association giant ureteric calculus with an ipsilateral staghorn renal calculus without underlying anatomic abnormalities appear not have been reported earlier.

Improving Student Success in Calculus I Using a Co-Requisite Calculus I Lab

ERIC Educational Resources Information Center

Vestal, Sharon Schaffer; Brandenburger, Thomas; Furth, Alfred

2015-01-01

This paper describes how one university mathematics department was able to improve student success in Calculus I by requiring a co-requisite lab for certain groups of students. The groups of students required to take the co-requisite lab were identified by analyzing student data, including Math ACT scores, ACT Compass Trigonometry scores, and…

Areas and Volumes in Pre-Calculus

ERIC Educational Resources Information Center

Jarrett, Joscelyn A.

2008-01-01

This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

Effects of Clicker Use on Calculus Students' Mathematics Anxiety

ERIC Educational Resources Information Center

Batchelor, John

2015-01-01

This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught…

The Role of Cognitive Ability and Preferred Mode of Processing in Students' Calculus Performance

ERIC Educational Resources Information Center

Haciomeroglu, Erhan Selcuk

2015-01-01

The present study sought to design calculus tasks to determine students' preference for visual or analytic processing as well as examine the role of preferred mode of processing in calculus performance and its relationship to spatial ability and verbal-logical reasoning ability. Data were collected from 150 high school students who were enrolled…

Using Dynamic Tools to Develop an Understanding of the Fundamental Ideas of Calculus

ERIC Educational Resources Information Center

Verzosa, Debbie; Guzon, Angela Fatima; De Las Peñas, Ma. Louise Antonette N.

2014-01-01

Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the…

Instructional Experiences That Align with Conceptual Understanding in the Transition from High School Mathematics to College Calculus

ERIC Educational Resources Information Center

Wade, Carol H.; Sonnert, Gerhard; Sadler, Philip M.; Hazari, Zahra

2017-01-01

Using data from the first National study on high school preparation for college calculus success, the Factors Influencing College Success in Mathematics (FICSMath) project, this article connects student high school instructional experiences to college calculus performance. The findings reported here reveal that students were better prepared for…

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendices; Index.

Promoting Students' Ability to Think Conceptually in Calculus

ERIC Educational Resources Information Center

Zerr, Ryan J.

2010-01-01

An overview is given of three conceptual lessons that can be incorporated into any first-semester calculus class. These lessons were developed to help promote calculus students' ability to think conceptually, in particular with regard to the role that infinity plays in the subject. A theoretical basis for the value of these lessons is provided,…

Preparatory Year Program Courses as Predictors of First Calculus Course Grade

ERIC Educational Resources Information Center

Yushau, B; Omar, M. H

2007-01-01

This study investigates the effect of the preparatory year program courses on the first calculus course (Calculus I) at King Fahd University of Petroleum and Minerals (KFUPM). The data consists of more than 2,000 bilingual Arab university students studying in the English language, tracked over seven semesters. These students represent over 70% of…

Relativistic Kinetics from the Bondi "K"-Calculus

ERIC Educational Resources Information Center

Dasgupta, Ananda

2007-01-01

The Bondi K-calculus is a delightful method that has been used to provide rich insights into relativistic kinematics. In this paper, we will try to show how several important results of relativistic kinetics can be derived simply by using this approach. In addition, we will also indicate how the K-calculus can be used to simplify certain…

Studies in Mathematics, Volume XV. Calculus and Science.

ERIC Educational Resources Information Center

Twersky, Victor

This book is designed to illustrate how one general method of calculus is used in many different sciences and how different methods of calculus have furthered the development of essentially one field of science. The material is written so that it could serve as a math-science supplement for many courses. Chapters included are: (1) Introduction;…

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendix.

Fluorescence spectroscopy of dental calculus

NASA Astrophysics Data System (ADS)

Bakhmutov, D.; Gonchukov, S.; Sukhinina, A.

2010-05-01

The aim of the present study was to investigate the fluorescence properties of dental calculus in comparison with the properties of adjacent unaffected tooth structure using both lasers and LEDs in the UV-visible range for fluorescence excitation. The influence of calculus color on the informative signal is demonstrated. The optimal spectral bands of excitation and registration of the fluorescence are determined.

Implementing Projects in Calculus on a Large Scale at the University of South Florida

ERIC Educational Resources Information Center

Fox, Gordon A.; Campbell, Scott; Grinshpan, Arcadii; Xu, Xiaoying; Holcomb, John; Bénéteau, Catherine; Lewis, Jennifer E.; Ramachandran, Kandethody

2017-01-01

This paper describes the development of a program of project-based learning in Calculus courses at a large urban research university. In this program, students developed research projects in consultation with a faculty advisor in their major, and supervised by their calculus instructors. Students wrote up their projects in a prescribed format…

Improving Student Learning of Calculus Topics via Modified Just-in-Time Teaching Methods

ERIC Educational Resources Information Center

Natarajan, Rekha; Bennett, Andrew

2014-01-01

Although the use of traditional just-in-time teaching techniques has long been viewed positively by students and instructors in undergraduate calculus courses, past studies in this area have not addressed gains in student achievement with respect to specific calculus topics. This paper investigates the latter by administering modified just-in-time…

Calculus: A Computer Oriented Presentation, Part 1 [and] Part 2.

ERIC Educational Resources Information Center

Stenberg, Warren; Walker, Robert J.

Parts one and two of a one-year computer-oriented calculus course (without analytic geometry) are presented. The ideas of calculus are introduced and motivated through computer (i.e., algorithmic) concepts. An introduction to computing via algorithms and a simple flow chart language allows the book to be self-contained, except that material on…

Towards the Development of an Automated Learning Assistant for Vector Calculus: Integration over Planar Regions

ERIC Educational Resources Information Center

Yaacob, Yuzita; Wester, Michael; Steinberg, Stanly

2010-01-01

This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a…

Disappearing renal calculus.

PubMed

Cui, Helen; Thomas, Johanna; Kumar, Sunil

2013-04-10

We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging.

Tablet PC: A Preliminary Report on a Tool for Teaching Calculus

ERIC Educational Resources Information Center

Gorgievski, Nicholas; Stroud, Robert; Truxaw, Mary; DeFranco, Thomas

2005-01-01

This study examined students' perceptions of the Tablet PC as an instructional tool for teaching Calculus. A thirteen item survey was developed by the researchers and administered to 103 students in an introductory Calculus course at a large university in the Northeast of the United States. The purpose of this survey was to collect data regarding…

On flipping the classroom in large first year calculus courses

NASA Astrophysics Data System (ADS)

Jungić, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy

2015-05-01

Over the course of two years, 2012--2014, we have implemented a 'flipping' the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of both instructors and students.

Resequencing Skills and Concepts in Applied Calculus Using the Computer as a Tool.

ERIC Educational Resources Information Center

Heid, M. Kathleen

1988-01-01

During the first 12 weeks of an applied calculus course, two classes of college students studied calculus concepts using graphical and symbol-manipulation computer programs to perform routine manipulations. Three weeks were spent on skill development. Students showed better understanding of concepts and performed almost as well on routine skills.…

Teaching Children How to Include the Inversion Principle in Their Reasoning about Quantitative Relations

ERIC Educational Resources Information Center

Nunes, Terezinha; Bryant, Peter; Evans, Deborah; Bell, Daniel; Barros, Rossana

2012-01-01

The basis of this intervention study is a distinction between numerical calculus and relational calculus. The former refers to numerical calculations and the latter to the analysis of the quantitative relations in mathematical problems. The inverse relation between addition and subtraction is relevant to both kinds of calculus, but so far research…

A case-control study on the association between bladder cancer and prior bladder calculus.

PubMed

Chung, Shiu-Dong; Tsai, Ming-Chieh; Lin, Ching-Chun; Lin, Herng-Ching

2013-03-15

Bladder calculus is associated with chronic irritation and inflammation. As there is substantial documentation that inflammation can play a direct role in carcinogenesis, to date the relationship between stone formation and bladder cancer (BC) remains unclear. This study aimed to examine the association between BC and prior bladder calculus using a population-based dataset. This case-control study included 2,086 cases who had received their first-time diagnosis of BC between 2001 and 2009 and 10,430 randomly selected controls without BC. Conditional logistic regressions were employed to explore the association between BC and having been previously diagnosed with bladder calculus. Of the sampled subjects, bladder calculus was found in 71 (3.4%) cases and 105 (1.1%) controls. Conditional logistic regression analysis revealed that the odds ratio (OR) of having been diagnosed with bladder calculus before the index date for cases was 3.42 (95% CI = 2.48-4.72) when compared with controls after adjusting for monthly income, geographic region, hypertension, diabetes, coronary heart disease, and renal disease, tobacco use disorder, obesity, alcohol abuse, and schistosomiasis, bladder outlet obstruction, and urinary tract infection. We further analyzed according to sex and found that among males, the OR of having been previously diagnosed with bladder calculus for cases was 3.45 (95% CI = 2.39-4.99) that of controls. Among females, the OR was 3.05 (95% CI = 1.53-6.08) that of controls. These results add to the evidence surrounding the conflicting reports regarding the association between BC and prior bladder calculus and highlight a potential target population for bladder cancer screening.

[Melamine related urinary calculus and acute renal failure in infants].

PubMed

Sun, Ning; Shen, Ying; Sun, Qiang; Li, Xu-ran; Jia, Li-qun; Zhang, Gui-ju; Zhang, Wei-ping; Chen, Zhi; Fan, Jian-feng; Jiang, Ye-ping; Feng, Dong-chuan; Zhang, Rui-feng; Zhu, Xiao-yu; Xiao, Hong-zhan

2008-11-01

To summarize clinical characteristics, diagnosis and treatment of infants with urinary calculus and acute renal failure developed after being fed with melamine tainted formula milk. Data of infant patients with urinary calculus and acute renal failure due to melamine tainted formula milk admitted to the Beijing Children's Hospital affiliated to the Capital Medical University and the Xuzhou Children's Hospital in 2008 were used to analyze the epidemiological characteristics, clinical manifestations, image features as well as effects of 4 types of therapies. All the 34 infants with urinary calculus were complicated with acute renal failure, their blood urea nitrogen (BUN) was (24.1 +/- 8.2) mmol/L and creatinine (Cr) was (384.2 +/- 201.2) micromol/L. The chemical analysis on the urinary calculus sampled from 14 of the infants showed that the calculus contained melamine and acidum uricum. The time needed for the four types of therapies for returning Cr to normal was (3.5 +/- 1.9) d for cystoscopy group, (2.7 +/- 1.1) d for lithotomy group, (3.8 +/- 2.3) d for dialysis group, and (2.7 +/- 1.6) d for medical treatment group, which had no statistically significant difference (P = 0.508). Renal failure of all the 34 infants was relieved within 1 to 7 days, averaging (3.0 +/- 1.8) d. Melamine tainted formula milk may cause urinary calculus and obstructive acute renal failure. It is suggested that firstly the patients with urinary calculus complicated with acute renal failure should be treated with dialysis or medication to correct electrolyte disturbances, in particular hyperkalemia, and then relieve the obstruction with available medical and surgical methods as soon as possible. It is observed that the short term prognosis is satisfactory.

Potential of shock waves to remove calculus and biofilm.

PubMed

Müller, Philipp; Guggenheim, Bernhard; Attin, Thomas; Marlinghaus, Ernst; Schmidlin, Patrick R

2011-12-01

Effective calculus and biofilm removal is essential to treat periodontitis. Sonic and ultrasonic technologies are used in several scaler applications. This was the first feasibility study to assess the potential of a shock wave device to remove calculus and biofilms and to kill bacteria. Ten extracted teeth with visible subgingival calculus were treated with either shock waves for 1 min at an energy output of 0.4 mJ/mm(2) at 3 Hz or a magnetostrictive ultrasonic scaler at medium power setting for 1 min, which served as a control. Calculus was determined before and after treatment planimetrically using a custom-made software using a grey scale threshold. In a second experiment, multispecies biofilms were formed on saliva-preconditioned bovine enamel discs during 64.5 h. They were subsequently treated with shock waves or the ultrasonic scaler (N = 6/group) using identical settings. Biofilm detachment and bactericidal effects were then assessed. Limited efficiency of the shock wave therapy in terms of calculus removal was observed: only 5% of the calculus was removed as compared to 100% when ultrasound was used (P ≤ 0.0001). However, shock waves were able to significantly reduce adherent bacteria by three orders of magnitude (P ≤ 0.0001). The extent of biofilm removal by the ultrasonic device was statistically similar. Only limited bactericidal effects were observed using both methods. Within the limitations of this preliminary study, the shock wave device was not able to reliably remove calculus but had the potential to remove biofilms by three log steps. To increase the efficacy, technical improvements are still required. This novel noninvasive intervention, however, merits further investigation.

Surgical removal of a large vaginal calculus formed after a tension-free vaginal tape procedure.

PubMed

Zilberlicht, Ariel; Feiner, Benjamin; Haya, Nir; Auslender, Ron; Abramov, Yoram

2016-11-01

Vaginal calculus is a rare disorder which has been reported in association with urethral diverticulum, urogenital sinus anomaly, bladder exstrophy and the tension-free vaginal tape (TVT) procedure. We report a 42-year-old woman who presented with persistent, intractable urinary tract infection (UTI) following a TVT procedure. Cystoscopy demonstrated an eroded tape with the formation of a bladder calculus, and the patient underwent laser cystolithotripsy and cystoscopic resection of the tape. Following this procedure, her UTI completely resolved and she remained asymptomatic for several years. Seven years later she presented with a solid vaginal mass. Pelvic examination followed by transvaginal ultrasonography and magnetic resonance imaging demonstrated a large vaginal calculus located at the lower third of the anterior vaginal wall adjacent to the bladder neck. This video presents the transvaginal excision and removal of the vaginal calculus.

Rare calcium oxalate monohydrate calculus attached to the wall of the renal pelvis.

PubMed

Grases, Felix; Costa-Bauza, Antonia; Prieto, Rafael M; Saus, Carlos; Servera, Antonio; García-Miralles, Reyes; Benejam, Joan

2011-04-01

Most renal calculi can be classified using well-established criteria in a manner that reflects both composition and fine structure under specific pathophysiological conditions. However, when a large patient population is considered, rare renal calculi invariably appear, some of which have never been classified; careful study is required to establish stone etiology in such cases. The patient in the present case report formed two types of calculi. One was attached on the wall of the renal pelvis near the ureter and part of the calculus was embedded inside pelvic renal tissue. The calculus developed on an ossified calcification located in the pelvis tissue. Current knowledge on the development of calcification in soft tissues suggests a pre-existing injury as an inducer of its development. A mechanism of calculus formation is proposed. The second stone was a typical jack-stone calculus. © 2011 The Japanese Urological Association.

Adiabatic elimination for systems with inertia driven by compound Poisson colored noise.

PubMed

Li, Tiejun; Min, Bin; Wang, Zhiming

2014-02-01

We consider the dynamics of systems driven by compound Poisson colored noise in the presence of inertia. We study the limit when the frictional relaxation time and the noise autocorrelation time both tend to zero. We show that the Itô and Marcus stochastic calculuses naturally arise depending on these two time scales, and an extra intermediate type occurs when the two time scales are comparable. This leads to three different limiting regimes which are supported by numerical simulations. Furthermore, we establish that when the resulting compound Poisson process tends to the Wiener process in the frequent jump limit the Itô and Marcus calculuses, respectively, tend to the classical Itô and Stratonovich calculuses for Gaussian white noise, and the crossover type calculus tends to a crossover between the Itô and Stratonovich calculuses. Our results would be very helpful for understanding relevant experiments when jump type noise is involved.

Success in Introductory Calculus: The Role of High School and Pre-Calculus Preparation

ERIC Educational Resources Information Center

Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles

2017-01-01

Calculus at the college level has significant potential to serve as a pump for increasing the number of students majoring in STEM fields. It is a foundation course for all STEM majors and, if mastered well, should provide students with a positive and successful first-year experience and gateway into more advanced courses. Studies have shown that a…

Development of Curriculum Units as Basic Course for Calculus Provided for Freshmen with Low Academic Achievement

ERIC Educational Resources Information Center

Lue, Yuang-Tswong

2015-01-01

This study was to design, develop, and investigate instructional units for freshmen with low academic achievement to learn before they study calculus. Because the concepts, skills, and theories of function are fundamental for the calculus course but the below average students were not familiar with the basic knowledge and ability in function when…

Improving Student Success in Calculus at Seattle University

ERIC Educational Resources Information Center

Carter, J. D.; Helliwell, D.; Henrich, Allison; Principe, M.; Sloughter, J. M.

2016-01-01

Finding ways to improve student success in calculus is a critically important step on the path to supporting students who are pursuing degrees in STEM fields. Far too many students fail calculus 1 and are pushed to drop their majors in technical fields. One way of addressing this issue is by following a program that was pioneered at University of…

An Evaluative Calculus Project: Applying Bloom's Taxonomy to the Calculus Classroom

ERIC Educational Resources Information Center

Karaali, Gizem

2011-01-01

In education theory, Bloom's taxonomy is a well-known paradigm to describe domains of learning and levels of competency. In this article I propose a calculus capstone project that is meant to utilize the sixth and arguably the highest level in the cognitive domain, according to Bloom et al.: evaluation. Although one may assume that mathematics is…

Incorporating Inquiry-Based Learning in the Calculus Sequence: A Most Challenging Endeavour

ERIC Educational Resources Information Center

McLoughlin, M. Padraig M. M.

2009-01-01

A course in the Calculus sequence is arguably the most difficult course in which inquiry-based learning (IBL) can be achieved with any degree of success within the curriculum in part due to: (1) the plethora of majors taking Calculus to which the sequence relates to their majors in what is considered an "applied" manner; and (2) the…

Evaluating Views of Lecturers on the Consistency of Teaching Content with Teaching Approach: Traditional versus Reform Calculus

ERIC Educational Resources Information Center

Sevimli, Eyup

2016-01-01

This study aims to evaluate the consistency of teaching content with teaching approaches in calculus on the basis of lecturers' views. In this sense, the structures of the examples given in two commonly used calculus textbooks, both in traditional and reform classrooms, are compared. The content analysis findings show that the examples in both…

A Useful Demonstration of Calculus in a Physics High School Laboratory

ERIC Educational Resources Information Center

Alvarez, Gustavo; Schulte, Jurgen; Stockton, Geoffrey; Wheeler, David

2018-01-01

The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an…

Disappearing renal calculus

PubMed Central

Cui, Helen; Thomas, Johanna; Kumar, Sunil

2013-01-01

We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging. PMID:23580676

Calculus, Part 3, Student's Text, Unit No. 70. Revised Edition.

ERIC Educational Resources Information Center

Beck, A.; And Others

This is part three of a three-part SMSG calculus text for high school students. One of the goals of the text is to present calculus as a mathematical discipline as well as presenting its practical uses. The authors emphasize the importance of being able to interpret the concepts and theory in terms of models to which they apply. The text…

Students' Conceptual Knowledge of Limits in Calculus: A Two-Part Constructivist Case Study

ERIC Educational Resources Information Center

Adams, Margaret Smolinka

2013-01-01

This case study investigated students' conceptual knowledge of limits in calculus by implementing semi-structured interviews. The constructivist learning principles of Piaget and Inhelder as well as theories of understanding by Skemp guided the study. In Phase I, a pilot study was conducted with 15 students from a Calculus III class. By using…

Fluorescence detection of dental calculus

NASA Astrophysics Data System (ADS)

Gonchukov, S.; Biryukova, T.; Sukhinina, A.; Vdovin, Yu

2010-11-01

This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 - 645 nm and 340 - 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy.

Revised Bloom's taxonomy and integral calculus: unpacking the knowledge dimension

NASA Astrophysics Data System (ADS)

Radmehr, Farzad; Drake, Michael

2017-11-01

In this paper, the knowledge dimension for Revised Bloom's taxonomy (RBT) is unpacked for integral calculus. As part of this work, the 11 subtypes of the knowledge dimension are introduced, and through document analysis of chapter 4 of the RBT handbook, these subtypes are defined. Then, by consulting materials frequently used for teaching integral calculus, each subtype is exemplified. The developed dimension may enable or enhance opportunities for dialogue between lecturers, teachers, and researchers about how to develop and align educational objectives, teaching activities, and assessments in integral calculus, or how metacognition and metacognitive knowledge could be used to support teaching and learning.

Representing and reasoning about program in situation calculus

NASA Astrophysics Data System (ADS)

Yang, Bo; Zhang, Ming-yi; Wu, Mao-nian; Xie, Gang

2011-12-01

Situation calculus is an expressive tool for modeling dynamical system in artificial intelligence, changes in a dynamical world is represented naturally by the notions of action, situation and fluent in situation calculus. Program can be viewed as a discrete dynamical system, so it is possible to model program with situation calculus. To model program written in a smaller core programming language CL, notion of fluent is expanded for representing value of expression. Together with some functions returning concerned objects from expressions, a basic action theory of CL programming is constructed. Under such a theory, some properties of program, such as correctness and termination can be reasoned about.

Dental calculus evidence of Taï Forest Chimpanzee plant consumption and life history transitions

NASA Astrophysics Data System (ADS)

Power, Robert C.; Salazar-García, Domingo C.; Wittig, Roman M.; Freiberg, Martin; Henry, Amanda G.

2015-10-01

Dental calculus (calcified dental plaque) is a source of multiple types of data on life history. Recent research has targeted the plant microremains preserved in this mineralised deposit as a source of dietary and health information for recent and past populations. However, it is unclear to what extent we can interpret behaviour from microremains. Few studies to date have directly compared the microremain record from dental calculus to dietary records, and none with long-term observation dietary records, thus limiting how we can interpret diet, food acquisition and behaviour. Here we present a high-resolution analysis of calculus microremains from wild chimpanzees (Pan troglodytes verus) of Taï National Park, Côte d’Ivoire. We test microremain assemblages against more than two decades of field behavioural observations to establish the ability of calculus to capture the composition of diet. Our results show that some microremain classes accumulate as long-lived dietary markers. Phytolith abundance in calculus can reflect the proportions of plants in the diet, yet this pattern is not true for starches. We also report microremains can record information about other dietary behaviours, such as the age of weaning and learned food processing techniques like nut-cracking.

Dental calculus evidence of Taï Forest Chimpanzee plant consumption and life history transitions.

PubMed

Power, Robert C; Salazar-García, Domingo C; Wittig, Roman M; Freiberg, Martin; Henry, Amanda G

2015-10-19

Dental calculus (calcified dental plaque) is a source of multiple types of data on life history. Recent research has targeted the plant microremains preserved in this mineralised deposit as a source of dietary and health information for recent and past populations. However, it is unclear to what extent we can interpret behaviour from microremains. Few studies to date have directly compared the microremain record from dental calculus to dietary records, and none with long-term observation dietary records, thus limiting how we can interpret diet, food acquisition and behaviour. Here we present a high-resolution analysis of calculus microremains from wild chimpanzees (Pan troglodytes verus) of Taï National Park, Côte d'Ivoire. We test microremain assemblages against more than two decades of field behavioural observations to establish the ability of calculus to capture the composition of diet. Our results show that some microremain classes accumulate as long-lived dietary markers. Phytolith abundance in calculus can reflect the proportions of plants in the diet, yet this pattern is not true for starches. We also report microremains can record information about other dietary behaviours, such as the age of weaning and learned food processing techniques like nut-cracking.

Near-ultraviolet removal rates for subgingival dental calculus at different irradiation angles.

PubMed

Schoenly, Joshua E; Seka, Wolf D; Rechmann, Peter

2011-07-01

The laser ablation rate of subgingival dental calculus irradiated at a 400-nm-wavelength, 7.4-mJ pulse energy, and 85- and 20-deg irradiation angles is measured using laser triangulation. Three-dimensional images taken before and after irradiation create a removal map with 6-μm axial resolution. Fifteen human teeth with subgingival calculus are irradiated in vitro under a cooling water spray with an ∼300-μm-diam, tenth-order super-gaussian beam. The average subgingival calculus removal rates for irradiation at 85 and 20 deg are 11.1±3.6 and 11.5±5.9 μm∕pulse, respectively, for depth removal and 4.5±1.7×10(5) and 4.8±2.3×10(5) μm(3)∕pulse, respectively, for volume removal. The ablation rate is constant at each irradiation site but varies between sites because of the large differences in the physical and optical properties of calculus. Comparison of the average depth- and volume-removal rates does not reveal any dependence on the irradiation angle and is likely due to the surface topology of subgingival calculus samples that overshadows any expected angular dependence.

Kinetics of canine dental calculus crystallization: an in vitro study on the influence of inorganic components of canine saliva.

PubMed

Borah, Ballav M; Halter, Timothy J; Xie, Baoquan; Henneman, Zachary J; Siudzinski, Thomas R; Harris, Stephen; Elliott, Matthew; Nancollas, George H

2014-07-01

This work identifies carbonated hydroxyapatite (CAP) as the primary component of canine dental calculus, and corrects the long held belief that canine dental calculus is primarily CaCO3 (calcite). CAP is known to be the principal crystalline component of human dental calculus, suggesting that there are previously unknown similarities in the calcification that occurs in these two unique oral environments. In vitro kinetic experiments mimicking the inorganic components of canine saliva have examined the mechanisms of dental calculus formation. The solutions were prepared so as to mimic the inorganic components of canine saliva; phosphate, carbonate, and magnesium ion concentrations were varied individually to investigate the roll of these ions in controlling the nature of the phases that is nucleated. To date, the inorganic components of the canine oral systems have not been investigated at concentrations that mimic those in vivo. The mineral composition of the synthetic calculi grown under these conditions closely resembled samples excised from canines. This finding adds new information about calculus formation in humans and canines, and their sensitivity to chemicals used to treat these conditions. Copyright © 2014 Elsevier Inc. All rights reserved.

Near-ultraviolet removal rates for subgingival dental calculus at different irradiation angles

NASA Astrophysics Data System (ADS)

Schoenly, Joshua E.; Seka, Wolf D.; Rechmann, Peter

2011-07-01

The laser ablation rate of subgingival dental calculus irradiated at a 400-nm-wavelength, 7.4-mJ pulse energy, and 85- and 20-deg irradiation angles is measured using laser triangulation. Three-dimensional images taken before and after irradiation create a removal map with 6-μm axial resolution. Fifteen human teeth with subgingival calculus are irradiated in vitro under a cooling water spray with an ~300-μm-diam, tenth-order super-Gaussian beam. The average subgingival calculus removal rates for irradiation at 85 and 20 deg are 11.1+/-3.6 and 11.5+/-5.9 μm/pulse, respectively, for depth removal and 4.5+/-1.7×105 and 4.8+/-2.3×105 μm3/pulse, respectively, for volume removal. The ablation rate is constant at each irradiation site but varies between sites because of the large differences in the physical and optical properties of calculus. Comparison of the average depth- and volume-removal rates does not reveal any dependence on the irradiation angle and is likely due to the surface topology of subgingival calculus samples that overshadows any expected angular dependence.

Calculus domains modelled using an original bool algebra based on polygons

NASA Astrophysics Data System (ADS)

Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.

2016-08-01

Analytical and numerical computer based models require analytical definitions of the calculus domains. The paper presents a method to model a calculus domain based on a bool algebra which uses solid and hollow polygons. The general calculus relations of the geometrical characteristics that are widely used in mechanical engineering are tested using several shapes of the calculus domain in order to draw conclusions regarding the most effective methods to discretize the domain. The paper also tests the results of several CAD commercial software applications which are able to compute the geometrical characteristics, being drawn interesting conclusions. The tests were also targeting the accuracy of the results vs. the number of nodes on the curved boundary of the cross section. The study required the development of an original software consisting of more than 1700 computer code lines. In comparison with other calculus methods, the discretization using convex polygons is a simpler approach. Moreover, this method doesn't lead to large numbers as the spline approximation did, in that case being required special software packages in order to offer multiple, arbitrary precision. The knowledge resulted from this study may be used to develop complex computer based models in engineering.

Dental calculus evidence of Taï Forest Chimpanzee plant consumption and life history transitions

PubMed Central

Power, Robert C.; Salazar-García, Domingo C.; Wittig, Roman M.; Freiberg, Martin; Henry, Amanda G.

2015-01-01

Dental calculus (calcified dental plaque) is a source of multiple types of data on life history. Recent research has targeted the plant microremains preserved in this mineralised deposit as a source of dietary and health information for recent and past populations. However, it is unclear to what extent we can interpret behaviour from microremains. Few studies to date have directly compared the microremain record from dental calculus to dietary records, and none with long-term observation dietary records, thus limiting how we can interpret diet, food acquisition and behaviour. Here we present a high-resolution analysis of calculus microremains from wild chimpanzees (Pan troglodytes verus) of Taï National Park, Côte d’Ivoire. We test microremain assemblages against more than two decades of field behavioural observations to establish the ability of calculus to capture the composition of diet. Our results show that some microremain classes accumulate as long-lived dietary markers. Phytolith abundance in calculus can reflect the proportions of plants in the diet, yet this pattern is not true for starches. We also report microremains can record information about other dietary behaviours, such as the age of weaning and learned food processing techniques like nut-cracking. PMID:26481858

[Does carbonate originate from carbonate-calcium crystal component of the human urinary calculus?].

PubMed

Yuzawa, Masayuki; Nakano, Kazuhiko; Kumamaru, Takatoshi; Nukui, Akinori; Ikeda, Hitoshi; Suzuki, Kazumi; Kobayashi, Minoru; Sugaya, Yasuhiro; Morita, Tatsuo

2008-09-01

It gives important information in selecting the appropriate treatment for urolithiasis to confirm the component of urinary calculus. Presently component analysis of the urinary calculus is generally performed by infrared spectroscopy which is employed by companies providing laboratory testing services in Japan. The infrared spectroscopy determines the molecular components from the absorption spectra in consequence of atomic vibrations. It has the drawback that an accurate crystal structure cannot be analyzed compared with the X-ray diffraction method which analyzes the crystal constituent based on the diffraction of X-rays on crystal lattice. The components of the urinary calculus including carbonate are carbonate apatite and calcium carbonate such as calcite. Although the latter is reported to be very rare component in human urinary calculus, the results by infrared spectroscopy often show that calcium carbonate is included in calculus. The infrared spectroscopy can confirm the existence of carbonate but cannot determine whether carbonate is originated from carbonate apatite or calcium carbonate. Thus, it is not clear whether calcium carbonate is included in human urinary calculus component in Japan. In this study, we examined human urinary calculus including carbonate by use of X-ray structural analysis in order to elucidate the origin of carbonate in human urinary calculus. We examined 17 human calculi which were reported to contain calcium carbonate by infrared spectroscopy performed in the clinical laboratory. Fifteen calculi were obtained from urinary tract, and two were from gall bladder. The stones were analyzed by X-ray powder method after crushed finely. The reports from the clinical laboratory showed that all urinary culculi consisted of calcium carbonate and calcium phosphate, while the gallstones consisted of calcium carbonate. But the components of all urinary calculi were revealed to be carbonate apatite by X-ray diffraction. The components of gallstones were shown to be calcium carbonate (one calcite and the other aragonite) not only by infrared spectroscopy but by X-ray diffraction. It was shown that component analysis of the calculus could be more accurately performed by adding X-ray diffraction method to infrared spectroscopy. It was shown that calcium carbonate existed in a gallstone. As for the carbonate in human urinary calculi, present study showed that it was not calcium carbonate origin but carbonate apatite origin.

Calculus migration characterization during Ho:YAG laser lithotripsy by high-speed camera using suspended pendulum method.

PubMed

Zhang, Jian James; Rajabhandharaks, Danop; Xuan, Jason Rongwei; Chia, Ray W J; Hasenberg, Thomas

2017-07-01

Calculus migration is a common problem during ureteroscopic laser lithotripsy procedure to treat urolithiasis. A conventional experimental method to characterize calculus migration utilized a hosting container (e.g., a "V" grove or a test tube). These methods, however, demonstrated large variation and poor detectability, possibly attributed to the friction between the calculus and the container on which the calculus was situated. In this study, calculus migration was investigated using a pendulum model suspended underwater to eliminate the aforementioned friction. A high-speed camera was used to study the movement of the calculus which covered zero order (displacement), first order (speed), and second order (acceleration). A commercialized, pulsed Ho:YAG laser at 2.1 μm, a 365-μm core diameter fiber, and a calculus phantom (Plaster of Paris, 10 × 10 × 10 mm 3 ) was utilized to mimic laser lithotripsy procedure. The phantom was hung on a stainless steel bar and irradiated by the laser at 0.5, 1.0, and 1.5 J energy per pulse at 10 Hz for 1 s (i.e., 5, 10, and 15 W). Movement of the phantom was recorded by a high-speed camera with a frame rate of 10,000 FPS. The video data files are analyzed by MATLAB program by processing each image frame and obtaining position data of the calculus. With a sample size of 10, the maximum displacement was 1.25 ± 0.10, 3.01 ± 0.52, and 4.37 ± 0.58 mm for 0.5, 1, and 1.5 J energy per pulse, respectively. Using the same laser power, the conventional method showed <0.5 mm total displacement. When reducing the phantom size to 5 × 5 × 5 mm 3 (one eighth in volume), the displacement was very inconsistent. The results suggested that using the pendulum model to eliminate the friction improved sensitivity and repeatability of the experiment. A detailed investigation on calculus movement and other causes of experimental variation will be conducted as a future study.

A clinical and SEM evaluation of the efficiency of sofscale gel and hand scaling and hand scaling alone.

PubMed

Thomas, K; Vandana, K L; Reddy, V Ramesh

2002-01-01

The purpose of this study is to compose between hand scaling with abd without the calculus solvent gel (sofscale) and ultrasonic instrumentation at clinical and SEM level. 30 patients belonging to the age group of 17-50 year were selected. Patients selected were subjected to three different scaling modalities namely hand scaling (control), hand scaling using sofscale (Experimental quadrant A) and ultrasonic scaling (Experimental quadrant B), in three different quadrants. Case report forms were used to document the tooth sensitivity, soft tissue pain after scaling, patient preference of instrumentation, ease of calculus removal, patient comfort, soft tissue irritation, time taken for scaling, Bleeding while scaling, pre and post operative sulcus bleeding index. In addition to the clinical criteria, the teeth treated were extracted and evaluated using the scanning electron microscope to show potential effects on cemntal surfaces. No difference in tooth sensitivity was appreciated between control and experimental quadrant A. There was a higher degree of tooth sensitivity when treated with ultrasonic. Patients in control group appreciated a higher degree of soft tissue pain. Hand scaling using softscale produced a lesser amount of pain and treatment with ultrasoincs was the least painful. Most of the patients preferred ultrasonic scaling (70%) Calculus removal was easier. Hand scaling using sofscale gel results in more patient comfort when compared to hand scaling alone. There was no significant difference in patient comfort between handscaling using sofscale and ultrasonic scaling. The percentage of reduction of sulcus bleeding index showed no difference between the 3 scaling modalities SEM evaluation revealed that there was no significant difference the 3 scaling modalities in relation to residual calculus, cleaning efficiency and damage to the root surface. This study concluded that treatment with sofscale gel appears to be safe and effective method for removal calculus as this did not damage cemental surfaces, nor did it cause any damage to soft tissue. "Your tratar is your calcified hate. Not only the microflora in your oral cavity but also your muddled thoughts, your obstinate squinting backward, the way you regree when you mean to progress, in other words, the tendency of your diseased gums to form germ catching pockets, all that, the sum of dental picture and psyche, betrays you, it is stored up violence, full of murdero us designs" Gunter Grass.

Effect of Ramadan fasting on urinary risk factors for calculus formation.

PubMed

Miladipour, Amir Hossein; Shakhssalim, Nasser; Parvin, Mahmoud; Azadvari, Mohaddeseh

2012-01-01

Even though dehydration could aggravate formation of urinary calculi, the effects of fluid and food restriction on calculus formation is not thoroughly defined. The purpose of this study is to evaluate the effects of fluid and food restriction in Ramadan fasting on urinary factors in kidney and urinary calculus formation. Fifty-seven men aged 30 to 55 years old, including 37 recurrent calcium calculus formers and 20 with no history of kidney calculi were evaluated for blood tests, ultrasonography investigations, urinalysis, urine culture, and also 24-hour urine collection test. Metabolites including calcium, oxalate, citrate, uric acid, magnesium, phosphate, potassium, sodium, and creatinine were measured before and during Ramadan fasting. The values of calculus-precipitating solutes as well as inhibitory factors were documented thoroughly. Total excretion of calcium, phosphate, and magnesium in 24-hour urine and also urine volume during fasting were significantly lower than those in the nonfasting period. Urine concentration of calcium during fasting was significantly lower than nonfasting (P < .001). Urine concentrations of uric acid, citrate, phosphate, sodium, and potassium during fasting were significantly higher than nonfasting. Uric acid supersaturation was accentuated, and calcium phosphate supersaturation was decreased significantly during fasting. There was no significant increase in calcium oxalate supersaturation during the fasting period. Fasting during Ramadan has different effects on total excretion and concentrations of urinary precipitate and inhibitory factors contributing to calculus formation. We did not find enough evidence in favor of increased risks of calculus formation during Ramadan fasting.

[Giant prostatic calculus with neurogenic bladder disease and prostate diverticulum: a case report and review of the literature].

PubMed

Li, Xiao-Shi; Quan, Chang-Yi; Li, Gang; Cai, Qi-Liang; Hu, Bin; Wang, Jiu-Wei; Niu, Yuan-Jie

2013-02-01

To study the etiology, clinical manifestation, diagnosis and treatment of giant prostatic calculus with neurogenic bladder disease and prostate diverticulum. We retrospectively analyzed the clinical data of a case of giant prostatic calculus with neurogenic bladder disease and prostate diverticulum and reviewed the relevant literature. The patient was a 37-year-old man, with urinary incontinence for 22 years and intermittent dysuria with frequent micturition for 9 years, aggravated in the past 3 months. He had received surgery for spina bifida and giant vesico-prostatic calculus. The results of preoperative routine urinary examination were as follows: WBC 17 -20/HPF, RBC 12 - 15/HPF. KUB, IVU and pelvic CT revealed spina bifida occulta, neurogenic bladder and giant prostatic calculus. The patient underwent TURP and transurethral lithotripsy with holmium-YAG laser. The prostatic calculus was carbonate apatite in composition. Urinary dynamic images at 2 weeks after surgery exhibited significant improvement in the highest urine flow rate and residual urine volume. Seventeen months of postoperative follow-up showed dramatically improved urinary incontinence and thicker urine stream. Prostate diverticulum with prostatic giant calculus is very rare, and neurogenic bladder may play a role in its etiology. Cystoscopy is an accurate screening method for its diagnosis. For the young patients and those who wish to retain sexual function, TURP combined with holmium laser lithotripsy can be employed, and intraoperative rectal examination should be taken to ensure complete removal of calculi.

Drinking water composition and incidence of urinary calculus: introducing a new index.

PubMed

Basiri, Abbas; Shakhssalim, Nasser; Khoshdel, Ali Reza; Pakmanesh, Hamid; Radfar, Mohammad Hadi

2011-01-01

INTRODUCTION. We searched for a pathophysiologically based feature of major water electrolytes, which may define water quality better than the water hardness, respecting urinary calculus formation. MATERIALS AND METHODS. Utilizing a multistage stratified sampling, 2310 patients were diagnosed in the imaging centers of the provincial capitals in Iran between 2007 and 2008. These were composed of 1755 patients who were settled residents of 24 provincial capitals. Data on the regional drinking water composition, obtained from an accredited registry, and their relationships with the region's incidence of urinary calculi were evaluated by metaregression models. The stone risk index (defined as the ratio of calcium to magnesium-bicarbonate product in drinking water) was used to assess the risk of calculus formation. RESULTS. No correlation was found between the urinary calculus incidence and the amount of calcium, bicarbonate, or the total hardness of the drinking water. In contrast, water magnesium had a marginally significant nonlinear inverse relationship with the incidence of the disease in the capitals (R(2) = 26%, P = .05 for a power model). The stone risk index was associated nonlinearly with the calculus incidence (R(2) = 28.4%, P = .04). CONCLUSIONS. Urinary calculus incidence was inversely related with drinking water magnesium content. We introduced a new index constructed on the foundation of a pathophysiologically based formula; the stone risk index had a strong positive association with calculus incidence. This index can have therapeutic and preventive applications, yet to be confirmed by clinical trials.

High levels of heavy metal accumulation in dental calculus of smokers: a pilot inductively coupled plasma mass spectrometry study.

PubMed

Yaprak, E; Yolcubal, I; Sinanoğlu, A; Doğrul-Demiray, A; Guzeldemir-Akcakanat, E; Marakoğlu, I

2017-02-01

Various trace elements, including toxic heavy metals, may exist in dental calculus. However, the effect of environmental factors on heavy metal composition of dental calculus is unknown. Smoking is a major environmental source for chronic toxic heavy metal exposition. The aim of this study is to compare toxic heavy metal accumulation levels in supragingival dental calculus of smokers and non-smokers. A total of 29 supragingival dental calculus samples were obtained from non-smoker (n = 14) and smoker (n = 15) individuals. Subjects with a probability of occupational exposure were excluded from the study. Samples were analyzed by inductively coupled plasma mass spectrometry in terms of 26 metals and metalloids, including toxic heavy metals. Toxic heavy metals, arsenic (p < 0.05), cadmium (p < 0.05), lead (p < 0.01), manganese (p < 0.01) and vanadium (p < 0.01) levels were significantly higher in smokers than non-smokers. The levels of other examined elements were similar in both groups (p > 0.05). Within the limitations of this study, it can be concluded that the elementary composition of dental calculus may be affected by environmental factors such as tobacco smoke. Therefore, dental calculus may be utilized as a non-invasive diagnostic biological material for monitoring chronic oral heavy metal exposition. However, further studies are required to evaluate its diagnostic potential. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Correlation between calcium and phosphate levels to calculus accumulation on coronary heart disease patients

NASA Astrophysics Data System (ADS)

Cahaya, Cindy; Masulili, Sri Lelyati C.; Lessang, Robert; Radi, Basuni

2017-02-01

Coronary Artery Disease (CAD) or Coronary Heart Disease (CHD) is a disease that happened because of blood flow being blocked by atherosclerosis. Atherosclerosis is a process of hardening of the arteries which characterized by thickening and loss of elasticity of the intimal layer of vascular wall, by lipid deposit. Periodontitis is a chronic multifactorial inflammatory disease caused by microorganism and characterized by progressive destruction of the tooth supporting apparatus leading to tooth loss. Many studies use saliva as a valuable source for clinically information, as an asset for early diagnosis, prognostic and reviewer for pascatherapy status. Dental calculus had happened as a consequence of saliva supersaturation by calcium and phosphate. Salivary flow rate and its composition influence the formation of calculus. Increasing salivary calcium levels is characteristic of periodontitis patients. An important hipotesis in Cardiology is chronic infections contribute in atherosclerosis. Objective: To analyse the correlation between calcium and phosphate levels in saliva to calculus accumulation on CHD patients. Result: Correlation analysis between salivary calcium levels with calculus accumulation in patients with CHD and non-CHD showed no significant p value, p=0.59 and p=0.518. Correlation analysis between salivary phosphate levels and calculus accumulation showed no significant p value, p=0.836 for CHD patients and p=0.484 for non-CHD patients. Conclusion: There are no correlation between calcium levels and phosphate levels with calculus accumulation in CHD patients. Further research need to be done.

EARLINET Single Calculus Chain - overview on methodology and strategy

NASA Astrophysics Data System (ADS)

D'Amico, G.; Amodeo, A.; Baars, H.; Binietoglou, I.; Freudenthaler, V.; Mattis, I.; Wandinger, U.; Pappalardo, G.

2015-11-01

In this paper we describe the EARLINET Single Calculus Chain (SCC), a tool for the automatic analysis of lidar measurements. The development of this tool started in the framework of EARLINET-ASOS (European Aerosol Research Lidar Network - Advanced Sustainable Observation System); it was extended within ACTRIS (Aerosol, Clouds and Trace gases Research InfraStructure Network), and it is continuing within ACTRIS-2. The main idea was to develop a data processing chain that allows all EARLINET stations to retrieve, in a fully automatic way, the aerosol backscatter and extinction profiles starting from the raw lidar data of the lidar systems they operate. The calculus subsystem of the SCC is composed of two modules: a pre-processor module which handles the raw lidar data and corrects them for instrumental effects and an optical processing module for the retrieval of aerosol optical products from the pre-processed data. All input parameters needed to perform the lidar analysis are stored in a database to keep track of all changes which may occur for any EARLINET lidar system over the time. The two calculus modules are coordinated and synchronized by an additional module (daemon) which makes the whole analysis process fully automatic. The end user can interact with the SCC via a user-friendly web interface. All SCC modules are developed using open-source and freely available software packages. The final products retrieved by the SCC fulfill all requirements of the EARLINET quality assurance programs on both instrumental and algorithm levels. Moreover, the manpower needed to provide aerosol optical products is greatly reduced and thus the near-real-time availability of lidar data is improved. The high-quality of the SCC products is proven by the good agreement between the SCC analysis, and the corresponding independent manual retrievals. Finally, the ability of the SCC to provide high-quality aerosol optical products is demonstrated for an EARLINET intense observation period.

Mathematical Modeling of Diverse Phenomena

NASA Technical Reports Server (NTRS)

Howard, J. C.

1979-01-01

Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.

Spinors: A Mathematica package for doing spinor calculus in General Relativity

NASA Astrophysics Data System (ADS)

Gómez-Lobo, Alfonso García-Parrado; Martín-García, José M.

2012-10-01

The Spinors software is a Mathematica package which implements 2-component spinor calculus as devised by Penrose for General Relativity in dimension 3+1. The Spinors software is part of the xAct system, which is a collection of Mathematica packages to do tensor analysis by computer. In this paper we give a thorough description of Spinors and present practical examples of use. Program summary Program title: Spinors Catalogue identifier: AEMQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 117039 No. of bytes in distributed program, including test data, etc.: 300404 Distribution format: tar.gz Programming language: Mathematica. Computer: Any computer running Mathematica 7.0 or higher. Operating system: Any operating system compatible with Mathematica 7.0 or higher. RAM: 94Mb in Mathematica 8.0. Classification: 1.5. External routines: Mathematica packages xCore, xPerm and xTensor which are part of the xAct system. These can be obtained at http://www.xact.es. Nature of problem: Manipulation and simplification of spinor expressions in General Relativity. Solution method: Adaptation of the tensor functionality of the xAct system for the specific situation of spinor calculus in four dimensional Lorentzian geometry. Restrictions: The software only works on 4-dimensional Lorentzian space-times with metric of signature (1, -1, -1, -1). There is no direct support for Dirac spinors. Unusual features: Easy rules to transform tensor expressions into spinor ones and back. Seamless integration of abstract index manipulation of spinor expressions with component computations. Running time: Under one second to handle and canonicalize standard spinorial expressions with a few dozen indices. (These expressions arise naturally in the transformation of a spinor expression into a tensor one or vice versa.)

Analysis of Errors and Misconceptions in the Learning of Calculus by Undergraduate Students

ERIC Educational Resources Information Center

Muzangwa, Jonatan; Chifamba, Peter

2012-01-01

This paper is going to analyse errors and misconceptions in an undergraduate course in Calculus. The study will be based on a group of 10 BEd. Mathematics students at Great Zimbabwe University. Data is gathered through use of two exercises on Calculus 1&2.The analysis of the results from the tests showed that a majority of the errors were due…

Assessment of Peer-Led Team Learning in Calculus I: A Five-Year Study

ERIC Educational Resources Information Center

Merkel, John Conrad; Brania, Abdelkrim

2015-01-01

This five-year study of the peer-led team learning (PLTL) paradigm examined its implementation in a Calculus I course at an all-male HBCU institution. For this study we set up a strong control group and measured the effect of PLTL in the teaching and learning of Calculus I through two points of measure: retention and success rates and learning…

Security Modeling and Correctness Proof Using Specware and Isabelle

DTIC Science & Technology

2008-12-01

proving requires substantial knowledge and experience in logical calculus . 15. NUMBER OF PAGES 146 14. SUBJECT TERMS Formal Method, Theorem...although the actual proving requires substantial knowledge and experience in logical calculus . vi THIS PAGE INTENTIONALLY LEFT BLANK vii TABLE OF...formal language and provides tools for proving those formulas in a logical calculus ” [5]. We are demonstrating in this thesis that a specification in

Study Modules for Calculus-Based General Physics. [Includes Modules 24-26: Electric Potential; Ohm's Law; and Capacitors].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Using an Advanced Graphing Calculator in the Teaching and Learning of Calculus

ERIC Educational Resources Information Center

Leng, Ng Wee

2011-01-01

The purpose of this study was to investigate how the use of TI-Nspire[TM] could enhance the teaching and learning of calculus. A conceptual framework for the use of TI-Nspire[TM] for learning calculus in a mathematics classroom is proposed that describes the interactions among the students, TI-Nspire[TM], and the learning tasks, and how they lead…

What Is Old Is New Again: A Systemic Approach to the Challenges of Calculus Instruction

ERIC Educational Resources Information Center

Carreon, Fernando; DeBacker, Stephen; Kessenich, Paul; Kubena, Angela; LaRose, P. Gavin

2018-01-01

In the abstract for "Calculus for a New Century: A Pump, Not a Filter," Lynn Steen wrote: "The authors agree on the forces that are reshaping calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory, yet disagree about new content emphases. They agree that the neglect of…

Collaborate and Innovate: One Department's Perspective on Factors Supporting and Sustaining Pedagogical Change in Calculus I

ERIC Educational Resources Information Center

Schroeder, Larissa Bucchi; McGivney-Burelle, Jean; Haruta, Mako E.; Xue, Fei

2018-01-01

At the University of Hartford we transformed our approach to Calculus I--moving it away from a lecture-dominant format to one that focuses squarely on students solving problems and discussing and presenting their mathematical ideas for the majority of class time. In this article, we discuss our Flipping Calculus project and how a departmental…

Unusual Giant Prostatic Urethral Calculus

PubMed Central

Bello, A.; Maitama, H. Y.; Mbibu, N. H.; Kalayi, G. D.; Ahmed, A.

2010-01-01

Giant vesico-prostatic urethral calculus is uncommon. Urethral stones rarely form primarily in the urethra, and they are usually associated with urethral strictures, posterior urethral valve or diverticula. We report a case of a 32-year-old man with giant vesico-prostatic (collar-stud) urethral stone presenting with sepsis and bladder outlet obstruction. The clinical presentation, management, and outcome of the giant prostatic urethral calculus are reviewed. PMID:22091328

A phenomenological calculus of Wiener description space.

PubMed

Richardson, I W; Louie, A H

2007-10-01

The phenomenological calculus is a categorical example of Robert Rosen's modeling relation. This paper is an alligation of the phenomenological calculus and generalized harmonic analysis, another categorical example. Our epistemological exploration continues into the realm of Wiener description space, in which constitutive parameters are extended from vectors to vector-valued functions of a real variable. Inherent in the phenomenology are fundamental representations of time and nearness to equilibrium.

Using `min' and `max' functions in calculus teaching

NASA Astrophysics Data System (ADS)

Satianov, Pavel; Dagan, Miriam; Amram, Meirav

2015-08-01

In this paper, we discuss the use of the min and max functions in teaching calculus to engineering students. Our experience illustrates that such functions have great possibilities in the development of a student's analytical thinking. The types of problems we present here are not common in most instructional texts, which lead us to suggest that the paper will be interesting and useful to calculus lecturers.

Diagnosis and treatment of melamine-associated urinary calculus complicated with acute renal failure in infants and young children.

PubMed

Sun, Ning; Shen, Ying; Sun, Qiang; Li, Xu-ran; Jia, Li-qun; Zhang, Gui-ju; Zhang, Wei-ping; Chen, Zhi; Fan, Jian-feng; Jiang, Ye-ping; Feng, Dong-chuan; Zhang, Rui-feng; Zhu, Xiao-yu; Xiao, Hong-zhan

2009-02-05

Infants in some areas of China developed urinary lithiasis after being fed with powdered milk that was tainted with melamine in 2008 and very small proportion of the infants developed acute renal failure caused by urinary tract calculus obstruction. The aim of this article was to summarize clinical characteristics, diagnosis and treatment of infants with urinary calculus and acute renal failure developed after being fed with melamine tainted formula milk. Data of infant patients with urinary calculus and acute renal failure due to melamine tainted formula milk admitted to the Beijing Children's Hospital Affiliated to the Capital Medical University and the Xuzhou Children's Hospital in 2008 were used to analyze the epidemiological characteristics, clinical manifestations, imaging features as well as effects of 4 types of therapies. All the 34 infants with urinary calculus were complicated with acute renal failure, their blood urea nitrogen (BUN) was (24.1+/-8.2) mmol/L and creatinine (Cr) was (384.2+/-201.2) micromol/L. The chemical analysis on the urinary calculus sampled from 15 of the infants showed that the calculus contained melamine and acidum uricum. The time needed for the four types of therapies for returning Cr to normal was (3.5+/-1.9) days for cystoscopy group, (2.7+/-1.1) days for lithotomy group, (3.8+/-2.3) days for dialysis group, and (2.7+/-1.6) days for medical treatment group, which had no statistically significant difference (P=0.508). Renal failure of all the 34 infants was relieved within 1 to 7 days, averaging (3.00+/-1.78) days. Melamine tainted formula milk may cause urinary calculus and obstructive acute renal failure. It is suggested that firstly the patients with urinary calculus complicated with acute renal failure should be treated with dialysis or medication to correct electrolyte disturbance, in particular hyperkalemia, and then relieve the obstruction with available medical and surgical methods as soon as possible. It was observed that the short-term prognosis was satisfactory.

Identification of Actinobacillus actinomycetemcomitans, Treponema denticola and Porphyromonas gingivalis within human dental calculus: a pilot investigation.

PubMed

Calabrese, Nicolino; Galgut, Peter; Mordan, Nicola

2007-10-01

Dental calculus is considered to be simply a "plaque-retentive factor", and therefore only a secondary aetiological factor in the pathogenesis of periodontitis. Recent studies have suggested a more active role for calculus. Our objective was to demonstrate the presence of periodontal pathogens in the non-mineralised areas of supra- and subgingival dental calculus. Subjects for the study were derived from patients with substantial amounts of supragingival calculus in the lower anterior region who had moderate periodontal disease, having been referred to the periodontal department at the Eastman Dental Hospital for periodontal care. Calculus was removed in as large pieces as possible by the use of a sickle or a push scaler placed underneath the apical or facial border of the calculus and fracturing it from the tooth surface in a single stroke. The orientation and absence of dental plaque was confirmed using light microscopy for each sample prior to inclusion in this study. Samples were prepared for transmission electron microscopic (TEM) observation after immunogold staining with polyclonal antibodies for the presence of Actinobacillus actinomycetemcomitans (A. a.), Porphyromonas gingivalis (P. g.) and Treponema denticola (T. d.). Most of the samples contained at least one of the bacterial species examined, either in the lacunae or in the covering dental plaque. T. d. was the most frequently identified species and was found in nearly all of the subgingival samples, whilstA. a. was rarely observed. In this limited study, supra- and subgingival dental calculus appears to be capable of maintaining periodontal pathogens within the deep recesses of its structural lacunae and channels. Therefore, calculus could possibly play a relevant role in the aetiology and pathogenesis of periodontitis. The presence of T. d. in the majority of specimens requires further investigation as its pathogenic potential may be underestimated in current published microbiological research, and further work is required to determine its role in the pathogenesis of periodontal diseases. However, further work by way of a large-scale definitive study is necessary to confirm the results of this investigation.

Model-order reduction of lumped parameter systems via fractional calculus

NASA Astrophysics Data System (ADS)

Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio

2018-04-01

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.

Symbolic computer vector analysis

NASA Technical Reports Server (NTRS)

Stoutemyer, D. R.

1977-01-01

A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.

Primary vaginal calculus in a middle-aged woman with mental and physical disabilities.

PubMed

Ikeda, Yuji; Oda, Katsutoshi; Matsuzawa, Naoki; Shimizu, Ken

2013-07-01

Vaginal calculi are rarely encountered and are often misdiagnosed as bladder calculi because of the difficulty in achieving an appropriate diagnosis. Most vaginal calculi result from the presence of a urethrovaginal fistula; those occurring in the absence of such fistulas are extremely rare. We present a case of a 42-year-old bedridden woman with mental and physical disabilities who had been misdiagnosed for a decade as having a bladder calculus. We removed the calculus nonsurgically and the analyzed the components. Results demonstrated the presence of a primary vaginal calculus. Vaginal calculi may occasionally occur in disabled women, but further investigation of the etiology of such calculi is required.

Large bladder calculus masking a stone in single-system ureterocele.

PubMed

Bhaskar, Ved; Sinha, Rahul Janak; Purkait, Bimalesh; Singh, Vishwajeet

2017-06-14

Ureterocele in an elderly is a rare entity. The presence of stone within ureterocele along with a large bladder calculus is an even rarer presentation. This phenomenon has not been reported so far to the best of our knowledge. We present an unusual case of a large bladder calculus with a concomitant stone in the associated ureterocele. The diagnosis was missed in the first instance due to the masking effect by the larger bladder calculus. Herein, we discuss this case and its management. © BMJ Publishing Group Ltd (unless otherwise stated in the text of the article) 2017. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

A cross-national study of calculus

NASA Astrophysics Data System (ADS)

Chai, Jun; Friedler, Louis M.; Wolff, Edward F.; Li, Jun; Rhea, Karen

2015-05-01

The results from a cross-national study comparing calculus performance of students at East China Normal University (ECNU) in Shanghai and students at the University of Michigan before and after their first university calculus course are presented. Overall, ECNU significantly outperformed Michigan on both the pre- and post-tests, but the Michigan students showed a larger gain and normalized gain, and hence narrowed the gap. ECNU's superior performance was especially striking on the subset of problems requiring only a pre-calculus background. On those, Michigan's post-test scores were below ECNU's pre-test scores and, indeed, ECNU's higher performance on both the overall pre-test and overall post-test is attributable to its success on these problems.

The feasibility of using microwave-induced thermoacoustic tomography for detection and evaluation of renal calculi.

PubMed

Cao, Caijun; Nie, Liming; Lou, Cunguang; Xing, Da

2010-09-07

Imaging of renal calculi is important for patients who suffered a urinary calculus prior to treatment. The available imaging techniques include plain x-ray, ultrasound scan, intravenous urogram, computed tomography, etc. However, the visualization of a uric acid calculus (radiolucent calculi) is difficult and often impossible by the above imaging methods. In this paper, a new detection method based on microwave-induced thermoacoustic tomography was developed to detect the renal calculi. Thermoacoustic images of calcium oxalate and uric acid calculus were compared with their x-ray images. The microwave absorption differences among the calcium oxalate calculus, uric acid calculus and normal kidney tissue could be evaluated by the amplitude of the thermoacoustic signals. The calculi hidden in the swine kidney were clearly imaged with excellent contrast and resolution in the three orthogonal thermoacoustic images. The results indicate that thermoacoustic imaging may be developed as a complementary method for detecting renal calculi, and its low cost and effective feature shows high potential for clinical applications.

The calculus of differences: Effects of a psychosocial, cultural, and pedagogical intervention in an all women's university calculus class

NASA Astrophysics Data System (ADS)

Steele, Diana F.; Levin, Amy K.; Blecksmith, Richard; Shahverdian, Jill

2005-10-01

The purpose of this study was to investigate the ways in which a multi-layered women's calculus course influenced the participants' learning of mathematics. This study, conducted in a state university in the Midwestern region of the United States, revealed not only that women in this particular section of calculus were likely to select careers that involved mathematics, but that the focus on peer support, psychosocial issues such as self-confidence, and pedagogy helped the young women overcome gender barriers, as well as barriers of class, poverty, and race. In this article we provide some of the relevant quantitative statistics and relate the stories of two particular women through excerpts from interviews, student artefacts, and participant observation data. We selected these young women because they faced multiple barriers to success in Calculus I and might not have completed the course or taken additional mathematics courses without the support structures that were fundamental to the course.

Profile of Metacognition of Mathematics Pre-Service Teachers in Understanding the Concept of Integral Calculus with Regard Gender Differences

NASA Astrophysics Data System (ADS)

Misu, L.; Budayasa, I. K.; Lukito, A.

2018-01-01

This research is to describe metacognition profile of female and male mathematics’ pre-service teachers in understanding the concept of integral calculus. The subjects of this study are one female and 1 male mathematics’ pre-service teachers who have studied integral calculus. This research type is an explorative study with the qualitative approach. The main data collection of this research was obtained by using Interview technique. In addition, there are supporting data which is the result of the written work of research subjects (SP) in understanding the question of integral calculus. The results of this study are as follows: There is a difference in metacognition profiles between male and female mathematics’ pre-service teachers in the understanding concept of integral calculus in the interpreting category, especially the definite integral concept. While in the category of exemplifying, there is no difference in metacognition profile between male and female mathematics’ pre-service teachers either the definite integral concept and the indefinite integral concept.

Study Modules for Calculus-Based General Physics. [Includes Modules 11-14: Collisions; Equilibrium of Rigid Bodies; Rotational Dynamics; and Fluid Mechanics].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Vaginal Calculus in a Woman With Mixed Urinary Incontinence and Vaginal Mesh Exposure.

PubMed

Winkelman, William D; Rabban, Joseph T; Korn, Abner P

2016-01-01

Vaginal calculi are extremely rare and are most commonly encountered in the setting of an urethrovaginal or vesicovaginal fistula. We present a case of a 72-year-old woman with mixed urinary incontinence and vaginal mesh exposure incidentally found to have a large vaginal calculus. We removed the calculus surgically and analyzed the components. Results demonstrated the presence of ammonium-magnesium phosphate hexahydrate and carbonate apatite.

Study Modules for Calculus-Based General Physics. [Includes Modules 8-10: Conservation of Energy; Impulse and Momentum; and Rotational Motion].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Deriving the Work Done by an Inverse Square Force in Non-Calculus-Based Introductory Physics Courses

ERIC Educational Resources Information Center

Hu, Ben Yu-Kuang

2012-01-01

I describe a method of evaluating the integral of 1/r[superscript 2] with respect to r that uses only algebra and the concept of area underneath a curve, and which does not formally employ any calculus. This is useful for algebra-based introductory physics classes (where the use of calculus is forbidden) to derive the work done by the force of one…

Future Directions in Fractional Calculus Research and Applications

DTIC Science & Technology

2017-10-31

Report: Future Directions in Fractional Calculus Research and Applications The views, opinions and/or findings contained in this report are those of the...SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 REPORT...Future Directions in Fractional Calculus Research and Applications Report Term: 0-Other Email: mcubed@msu.edu Distribution Statement: 1-Approved for

Study Modules for Calculus-Based General Physics. [Includes Modules 3-5: Planar Motion; Newton's Laws; and Vector Multiplication].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Study Modules for Calculus-Based General Physics. [Includes Modules 27-30: Direct-Current Circuits; Magnetic Forces; Ampere's Law; and Faraday's Law].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules indlude study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Functional Itô versus Banach space stochastic calculus and strict solutions of semilinear path-dependent equations

NASA Astrophysics Data System (ADS)

Cosso, Andrea; Russo, Francesco

2016-11-01

Functional Itô calculus was introduced in order to expand a functional F(t,Xṡ+t,Xt) depending on time t, past and present values of the process X. Another possibility to expand F(t,Xṡ+t,Xt) consists in considering the path Xṡ+t = {Xx+t,x ∈ [-T, 0]} as an element of the Banach space of continuous functions on C([-T, 0]) and to use Banach space stochastic calculus. The aim of this paper is threefold. (1) To reformulate functional Itô calculus, separating time and past, making use of the regularization procedures which match more naturally the notion of horizontal derivative which is one of the tools of that calculus. (2) To exploit this reformulation in order to discuss the (not obvious) relation between the functional and the Banach space approaches. (3) To study existence and uniqueness of smooth solutions to path-dependent partial differential equations which naturally arise in the study of functional Itô calculus. More precisely, we study a path-dependent equation of Kolmogorov type which is related to the window process of the solution to an Itô stochastic differential equation with path-dependent coefficients. We also study a semilinear version of that equation.

Cadmium Profiles in Dental Calculus: a Cross-Sectional Population-Based Study in Hunan Province of China.

PubMed

Zhang, Bo; Tan, Xiaodan; Zhang, Kunlun

2018-01-24

We aimed to investigate whether the cadmium concentrations differ in human dental calculus obtained from the residents with no smoking living in the contaminated area and those with no smoking living in noncontaminated area. In total, there were 260 samples of dental calculus from the adults (n = 50) with no smoking living in contaminated area, the adults (n = 60) with no smoking living in mountainous area, and the adults (n = 150) with no smoking living in low altitude area in Hunan province of China. All samples were analyzed by inductively coupled plasma mass spectrometry (ICP-MS) for cadmium levels. The cadmium levels in dental calculus were significantly higher in the adults with no smoking living in contaminated area than those living in mountainous area and in low altitude area (p < 0.01). The cadmium levels in dental calculus were also higher in the adults with no smoking living in low altitude area than those living in mountainous region (p < 0.01). The results suggested that measuring cadmium levels in dental calculus may be a useful noninvasive method for analysis of environmental exposure to cadmium in the human oral cavity. The low altitude region may have an area contaminated with cadmium in Hunan province of China.

Effect of occlusal calculus utilized as a potential "biological sealant" in special needs patients with gastric feeding tubes: a qualitative in vitro contrast to pit and fissure sealant restorations.

PubMed

Owens, Barry M; Sharp, Harry K; Fourmy, Emily E; Phebus, Jeffrey G

2016-01-01

The aim of this case report and in vitro investigation was to evaluate the marginal microleakage of intact occlusal calculus of primary molars extracted from a special needs patient who received nutrition via a gastric feeding tube. An adolescent with a history of developmental disturbance presented for routine dental care in a hospital facility. Prophylaxis was performed, and 2 mandibular permanent molars were restored. Five primary molars were extracted due to mobility and delayed retention. Heavy deposits of intact calculus were present on the occlusal surfaces of the primary teeth. The extracted teeth were immersed in methylene blue dye solution, invested in acrylic resin, sectioned into blocks, and photographed at 20× and 40× magnification. Previously photographed calculus-free molars with pit and fissure sealants were reviewed and served as contrasting "restorations." The occlusal calculus on the primary teeth extracted from the patient absorbed the dye, while the comparison teeth containing pit and fissure sealants exhibited varying degrees of marginal dye penetration (microleakage). No marginal microleakage was noted in the calculus specimens, indicating that this substrate may serve as a "natural" occlusal surface sealant and that its removal from occlusal surfaces during routine oral prophylaxis may be unnecessary.

Beyond food: The multiple pathways for inclusion of materials into ancient dental calculus.

PubMed

Radini, Anita; Nikita, Efthymia; Buckley, Stephen; Copeland, Les; Hardy, Karen

2017-01-01

Dental calculus (mineralized dental plaque) was first recognised as a potentially useful archaeological deposit in the 1970s, though interest in human dental calculus as a resource material has increased sharply in the past few years. The majority of recent research has focused on the retrieval of plant microfossils embedded in its matrix and interpretation of these finds as largely the result of deliberate consumption of plant-derived food. However, while most of the material described in published works does represent food, dental calculus is in fact a "depositional environment" as material can enter the mouth from a range of sources. In this respect, it therefore represents an archaeological deposit that can also contain extensive non-dietary debris. This can comprise a wide variety of cultural and environmental material which reaches the mouth and can become embedded in dental calculus through alternative pathways. Here, we explore the human behaviors and activities besides eating that can generate a flux of particles into the human mouth, the broad range of additional cultural and environmental information that can be obtained through the analysis and contextualisation of this material, and the implications of the additional pathways by which material can become embedded in dental calculus. © 2017 American Association of Physical Anthropologists.

Ancient DNA analysis of dental calculus.

PubMed

Weyrich, Laura S; Dobney, Keith; Cooper, Alan

2015-02-01

Dental calculus (calcified tartar or plaque) is today widespread on modern human teeth around the world. A combination of soft starchy foods, changing acidity of the oral environment, genetic pre-disposition, and the absence of dental hygiene all lead to the build-up of microorganisms and food debris on the tooth crown, which eventually calcifies through a complex process of mineralisation. Millions of oral microbes are trapped and preserved within this mineralised matrix, including pathogens associated with the oral cavity and airways, masticated food debris, and other types of extraneous particles that enter the mouth. As a result, archaeologists and anthropologists are increasingly using ancient human dental calculus to explore broad aspects of past human diet and health. Most recently, high-throughput DNA sequencing of ancient dental calculus has provided valuable insights into the evolution of the oral microbiome and shed new light on the impacts of some of the major biocultural transitions on human health throughout history and prehistory. Here, we provide a brief historical overview of archaeological dental calculus research, and discuss the current approaches to ancient DNA sampling and sequencing. Novel applications of ancient DNA from dental calculus are discussed, highlighting the considerable scope of this new research field for evolutionary biology and modern medicine. Copyright © 2014 Elsevier Ltd. All rights reserved.

Analysis of root surface properties by fluorescence/Raman intensity ratio.

PubMed

Nakamura, Shino; Ando, Masahiro; Hamaguchi, Hiro-O; Yamamoto, Matsuo

2017-11-01

The aim of this study is to evaluate the existence of residual calculus on root surfaces by determining the fluorescence/Raman intensity ratio. Thirty-two extracted human teeth, partially covered with calculus on the root surface, were evaluated by using a portable Raman spectrophotometer, and a 785-nm, 100-mW laser was applied for fluorescence/Raman excitation. The collected spectra were normalized to the hydroxyapatite Raman band intensity at 960 cm -1 . Raman spectra were recorded from the same point after changing the focal distance of the laser and the target radiating angle. In seven teeth, the condition of calculus, cementum, and dentin were evaluated. In 25 teeth, we determined the fluorescence/Raman intensity ratio following three strokes of debridement. Raman spectra collected from the dentin, cementum, and calculus were different. After normalization, spectra values were constant. The fluorescence/Raman intensity ratio of calculus region showed significant differences compared to the cementum and dentin (p < 0.05). The fluorescence/Raman intensity ratio decreased with calculus debridement. For this analysis, the delta value was defined as the difference between the values before and after three strokes, with the final 2 delta values close to zero, indicating a gradual asymptotic curve and the change in intensity ratio approximating that of individual constants. Fluorescence/Raman intensity ratio was effectively used to cancel the angle- and distance-dependent fluctuations of fluorescence collection efficiency during measurement. Changes in the fluorescence/Raman intensity ratio near zero suggested that cementum or dentin was exposed, and calculus removed.

The dental calculus metabolome in modern and historic samples.

PubMed

Velsko, Irina M; Overmyer, Katherine A; Speller, Camilla; Klaus, Lauren; Collins, Matthew J; Loe, Louise; Frantz, Laurent A F; Sankaranarayanan, Krithivasan; Lewis, Cecil M; Martinez, Juan Bautista Rodriguez; Chaves, Eros; Coon, Joshua J; Larson, Greger; Warinner, Christina

2017-01-01

Dental calculus is a mineralized microbial dental plaque biofilm that forms throughout life by precipitation of salivary calcium salts. Successive cycles of dental plaque growth and calcification make it an unusually well-preserved, long-term record of host-microbial interaction in the archaeological record. Recent studies have confirmed the survival of authentic ancient DNA and proteins within historic and prehistoric dental calculus, making it a promising substrate for investigating oral microbiome evolution via direct measurement and comparison of modern and ancient specimens. We present the first comprehensive characterization of the human dental calculus metabolome using a multi-platform approach. Ultra performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS) quantified 285 metabolites in modern and historic (200 years old) dental calculus, including metabolites of drug and dietary origin. A subset of historic samples was additionally analyzed by high-resolution gas chromatography-MS (GC-MS) and UPLC-MS/MS for further characterization of metabolites and lipids. Metabolite profiles of modern and historic calculus were compared to identify patterns of persistence and loss. Dipeptides, free amino acids, free nucleotides, and carbohydrates substantially decrease in abundance and ubiquity in archaeological samples, with some exceptions. Lipids generally persist, and saturated and mono-unsaturated medium and long chain fatty acids appear to be well-preserved, while metabolic derivatives related to oxidation and chemical degradation are found at higher levels in archaeological dental calculus than fresh samples. The results of this study indicate that certain metabolite classes have higher potential for recovery over long time scales and may serve as appropriate targets for oral microbiome evolutionary studies.

Anti-calculus activity of a toothpaste with microgranules.

PubMed

Chesters, R K; O'Mullane, D M; Finnerty, A; Huntington, E; Jones, P R

1998-09-01

The objective of the trial was to determine the efficacy of the proven anticalculus active system (zinc citrate trihydrate [ZCT] and triclosan), when the ZCT is delivered from microgranules incorporated in a silica-based toothpaste containing 1450 ppm F as sodium fluoride. A monadic, single-blind, two phase design clinical trial was used to compare the effect of the test and a negative control fluoridated toothpaste on the formation of supragingival calculus. Male and female calculus-forming volunteers, aged 18 or over, were recruited for the study following a 2-week screening phase. All subjects were given a scale and polish of their eight lower anterior teeth at the start of both the pre-test and test phases. Subjects were supplied with a silica-based 1450 F ppm fluoridated toothpaste with no anti-calculus active for use during an 8-week pre-test phase. Calculus was assessed at the end of the pre-test and test phases using the Volpe-Manhold index (VMI). Subjects were stratified according to their pre-test VMI score (8-10, 10.5-12, > 12) and gender and then allocated at random to test or negative control toothpaste groups. Subjects with < 8 mm of calculus were excluded from further participation. The outcome variable was the mean VMI score for the test and negative control groups. The test toothpaste caused a statistically significant 30% reduction in calculus compared with the control paste after a 13-week use. No adverse events were reported during the study. The incorporation of the ZCT in microgranules did not adversely affect the anticalculus activity of the new formulation.

Introduction to Plasma Physics

NASA Astrophysics Data System (ADS)

Gurnett, Donald A.; Bhattacharjee, Amitava

2017-03-01

Preface; 1. Introduction; 2. Characteristic parameters of a plasma; 3. Single particle motions; 4. Waves in a cold plasma; 5. Kinetic theory and the moment equations; 6. Magnetohydrodynamics; 7. MHD equilibria and stability; 8. Discontinuities and shock waves; 9. Electrostatic waves in a hot unmagnetized plasma; 10. Waves in a hot magnetized plasma; 11. Nonlinear effects; 12. Collisional processes; Appendix A. Symbols; Appendix B. Useful trigonometric identities; Appendix C. Vector differential operators; Appendix D. Vector calculus identities; Index.

Lipschitz and Besov spaces in quantum calculus

NASA Astrophysics Data System (ADS)

Nemri, Akram; Selmi, Belgacem

2016-08-01

The purpose of this paper is to investigate the harmonic analysis on the time scale 𝕋q, q ∈ (0, 1) to introduce q-weighted Besov spaces subspaces of Lp(𝕋 q) generalizing the classical one. Further, using an example of q-weighted wα,β(.; q) which is introduced and studied. We give a new characterization of the q-Besov space using q-Poisson kernel and the g1 Littlewood-Paley operator.

Modelling Team Adversarial Actions in UAV Operations

DTIC Science & Technology

2007-11-01

support for the dynamic creation and destruction of entities is the history dependent automata ( HDA ) [9] which evolved from an algorithmic structure for...checking bi-similarity of π- calculus agents. The authors define HDA as automata which perform actions that can carry information generated in the...past history of the system. The states, transitions and labels of the HDA are enriched with sets of local names. Thus, each transition can refer to the

An Introduction to Lagrangian Differential Calculus.

ERIC Educational Resources Information Center

Schremmer, Francesca; Schremmer, Alain

1990-01-01

Illustrates how Lagrange's approach applies to the differential calculus of polynomial functions when approximations are obtained. Discusses how to obtain polynomial approximations in other cases. (YP)

Study Modules for Calculus-Based General Physics. [Includes Modules 18-20: Sound; Temperature, Heat, and Thermodynamics: First Law; and Kinetic Theory of Gases].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Study Modules for Calculus-Based General Physics. [Includes Modules 31-34: Inductance; Wave Properties of Light; Interference; and Introduction to Quantum Physics].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is Part of a series of 41 Calculus Based Physics (CBP) modules totaling about 1,000 Pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized courses in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Dental Calculus and the Evolution of the Human Oral Microbiome.

PubMed

Warinner, Christina

2016-07-01

Characterizing the evolution of the oral microbiome is a challenging, but increasingly feasible, task. Recently, dental calculus has been shown to preserve ancient biomolecules from the oral microbiota, host tissues and diet for tens of thousands of years. As such, it provides a unique window into the ancestral oral microbiome. This article reviews recent advancements in ancient dental calculus research and emerging insights into the evolution and ecology of the human oral microbiome.

Ureterolithotripsy for a Ureteral Calculus at the Ureteroureterostomy of a Renal-transplant Recipient.

PubMed

Mitsui, Yosuke; Wada, Koichiro; Araki, Motoo; Yoshioka, Takashi; Ariyoshi, Yuichi; Nishimura, Shingo; Kobayashi, Yasuyuki; Sasaki, Katsumi; Watanabe, Toyohiko; Nasu, Yasutomo

2017-10-01

We describe a 40-year-old living-donor renal-transplant recipient who underwent successful ureterolithotripsy. He had been on hemodialysis for >15 years pre-transplant and underwent ureteroureterostomy along with the surgery. One year post-transplant, ultrasound examination demonstrated hydronephrosis, and CT showed a 6-mm ureteral calculus at the ureteroureterostomy site. No pain and no elevated serum creatinine were present. As the ureter was easily accessed, we performed a ureterolithotripsy, which would confirm whether a suture caused the calculus. Despite ureteral tortuosity, laser stone fragmentation succeeded. The calculus was completely removed with an antegrade guidewire. Mild postoperative ureteral stenosis resolved with a temporary ureteral stent without balloon dilation. Ureterolithotripsy is effective even in renal transplant recipients with ureteroureterostomy.

Laser ablation of dental calculus at 400 nm using a Ti:sapphire laser

NASA Astrophysics Data System (ADS)

Schoenly, Joshua E.; Seka, Wolf; Rechmann, Peter

2009-02-01

A Nd:YAG laser-pumped, frequency-doubled Ti:sapphire laser is used for selective ablation of calculus. The laser provides <=25 mJ at 400 nm (60-ns pulse width, 10-Hz repetition rate). The laser is coupled into an optical multimode fiber coiled around a 4-in.-diam drum to generate a top-hat output intensity profile. With coaxial water cooling, this is ideal for efficient, selective calculus removal. This is in stark contrast with tightly focused Gaussian beams that are energetically inefficient and lead to irreproducible results. Calculus is well ablated at high fluences >=2J/cm2 stalling occurs below this fluence because of photobleaching. Healthy hard tissue is not removed at fluences <=3 J/cm2.

Projectile motion without calculus

NASA Astrophysics Data System (ADS)

Rizcallah, Joseph A.

2018-07-01

Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are kept at a fairly elementary level, some, such as determining the safe domain, involve not so elementary techniques, which can hardly be assumed of the targeted audience. In the literature, several attempts have been undertaken to avoid calculus altogether and keep the exposition entirely within the realm of algebra and/or geometry. In this paper, we propose yet another non-calculus approach which uses the projectile’s travel times to shed new light on these problems and provide instructors with an alternate method to address them with their students.

Pre- and Post-Conditions Expressed in Variants of the Modal µ-Calculus

NASA Astrophysics Data System (ADS)

Tanabe, Yoshinori; Sekizawa, Toshifusa; Yuasa, Yoshifumi; Takahashi, Koichi

Properties of Kripke structures can be expressed by formulas of the modal µ-calculus. Despite its strong expressive power, the validity problem of the modal µ-calculus is decidable, and so are some of its variants enriched by inverse programs, graded modalities, and nominals. In this study, we show that the pre- and post-conditions of transformations of Kripke structures, such as addition/deletion of states and edges, can be expressed using variants of the modal µ-calculus. Combined with decision procedures we have developed for those variants, the properties of sequences of transformations on Kripke structures can be deduced. We show that these techniques can be used to verify the properties of pointer-manipulating programs.

The giant calculus within the prostatic urethra.

PubMed

Demir, Omer; Kefi, Aykut; Cahangirov, Asif; Cihan, Ahmet; Obuz, Funda; Esen, Adil Ahmet; Celebi, Ilhan

2011-08-01

The giant calculus within the prostatic urethra is a rare clinical entity in the young population. Most of the calculi within the urethra migrate from the urinary bladder and obliterate the urethra. These stones are often composed of calcium phosphate or calcium oxalate. The decision of treatment strategy is affected by the size, shape and position of the calculus and by the status of the urethra. If the stone is large and immovable, it may be extracted via the perineal or the suprapubic approach. In most cases, the giant calculi were extracted via the transvesical approach and external urethrotomy. Our case is the biggest prostatic calculus, known in the literature so far, which was treated endoscopically by the combination of laser and the pneumatic lithotriptor.

Multidimensional Simulation Applied to Water Resources Management

NASA Astrophysics Data System (ADS)

Camara, A. S.; Ferreira, F. C.; Loucks, D. P.; Seixas, M. J.

1990-09-01

A framework for an integrated decision aiding simulation (IDEAS) methodology using numerical, linguistic, and pictorial entities and operations is introduced. IDEAS relies upon traditional numerical formulations, logical rules to handle linguistic entities with linguistic values, and a set of pictorial operations. Pictorial entities are defined by their shape, size, color, and position. Pictorial operators include reproduction (copy of a pictorial entity), mutation (expansion, rotation, translation, change in color), fertile encounters (intersection, reunion), and sterile encounters (absorption). Interaction between numerical, linguistic, and pictorial entities is handled through logical rules or a simplified vector calculus operation. This approach is shown to be applicable to various environmental and water resources management analyses using a model to assess the impacts of an oil spill. Future developments, including IDEAS implementation on parallel processing machines, are also discussed.

Prevalence of gingivitis and calculus in 12-year-old Puerto Ricans: a cross-sectional study.

PubMed

Elias-Boneta, Augusto R; Ramirez, Karol; Rivas-Tumanyan, Sona; Murillo, Margarita; Toro, Milagros J

2018-01-19

Gingivitis is a common oral health problem. Untreated gingivitis may progress to periodontitis, a common cause of tooth loss. The prevalence of gingivitis and calculus among Puerto Rican children is unknown. Understanding this prevalence can support early public health preventative strategies. This study aims to estimate the prevalence of gingivitis and calculus among 12-year-old Puerto Ricans by health region and to explore differences in distribution by school type (proxy for socio-economic status) and gender. A probability-based sample of 113 schools was selected proportional to enrollment size and stratified by health region, school type, and gender. Two trained examiners evaluated the presence of gingivitis and both supragingival and subgingival dental calculus. Gingivitis was defined as the presence of gingival bleeding upon gentle probing (BOP) in at least one site, and the extent of the problem was classified according to the percentage of teeth whose gingiva presented BOP (limited: 25-49% of the teeth tested; extensive: >50% of teeth tested). Logistic and linear regression models, adjusted for health regions, were used to compare gingivitis and calculus prevalence and extent between genders and school types. Gingivitis was found in 80.41% of the 1586 children evaluated. Urban-public schoolchildren had a slightly higher prevalence (83.24%) compared to private (79.15%, p = 0.16); those in rural-public (77.59%) and private schools had similar prevalence (p = 0.15). Extensive gingivitis was present in 60.81% of all children. The mean percentage of sites presenting BOP (BOP%) was 17.79%. Rural and urban public schoolchildren presented significantly higher BOP% compared to children from private schools (p = 0.0005, p = 0.002, respectively). Dental calculus was detected in 61.59% of the sample, boys presenting significantly higher (p = 0.005) total and supragingival calculus. Rural-public schoolchildren had a significantly higher prevalence of subgingival calculus compared to private schoolchildren (p = 0.02). Gingivitis prevalence is higher among 12-year-old Puerto Ricans compared to data reported for U.S. adolescents. Public schoolchildren presented significantly higher BOP% sites compared to private schoolchildren. Boys presented a significantly higher total and supragingival calculus prevalence than girls. Oral health disparities related to gender and school type were identified by this study. Studies exploring the reasons for these disparities are recommended.

Women 1.5 Times More Likely to Leave STEM Pipeline after Calculus Compared to Men: Lack of Mathematical Confidence a Potential Culprit.

PubMed

Ellis, Jessica; Fosdick, Bailey K; Rasmussen, Chris

2016-01-01

The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this pathway and has been shown to often dissuade people from pursuing STEM fields. We examine the characteristics of students who begin college interested in STEM and either persist or switch out of the calculus sequence after taking Calculus I, and hence either continue to pursue a STEM major or are dissuaded from STEM disciplines. The data come from a unique, national survey focused on mainstream college calculus. Our analyses show that, while controlling for academic preparedness, career intentions, and instruction, the odds of a woman being dissuaded from continuing in calculus is 1.5 times greater than that for a man. Furthermore, women report they do not understand the course material well enough to continue significantly more often than men. When comparing women and men with above-average mathematical abilities and preparedness, we find women start and end the term with significantly lower mathematical confidence than men. This suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that if women persisted in STEM at the same rate as men starting in Calculus I, the number of women entering the STEM workforce would increase by 75%.

Women 1.5 Times More Likely to Leave STEM Pipeline after Calculus Compared to Men: Lack of Mathematical Confidence a Potential Culprit

PubMed Central

Ellis, Jessica; Fosdick, Bailey K.; Rasmussen, Chris

2016-01-01

The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this pathway and has been shown to often dissuade people from pursuing STEM fields. We examine the characteristics of students who begin college interested in STEM and either persist or switch out of the calculus sequence after taking Calculus I, and hence either continue to pursue a STEM major or are dissuaded from STEM disciplines. The data come from a unique, national survey focused on mainstream college calculus. Our analyses show that, while controlling for academic preparedness, career intentions, and instruction, the odds of a woman being dissuaded from continuing in calculus is 1.5 times greater than that for a man. Furthermore, women report they do not understand the course material well enough to continue significantly more often than men. When comparing women and men with above-average mathematical abilities and preparedness, we find women start and end the term with significantly lower mathematical confidence than men. This suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that if women persisted in STEM at the same rate as men starting in Calculus I, the number of women entering the STEM workforce would increase by 75%. PMID:27410262

A double blind randomised controlled clinical trial comparing a novel anti-stain and calculus reducing dentifrice with a standard fluoride dentifrice.

PubMed

Jowett, Adrian K; Marlow, Ian; Rawlinson, Andrew

2013-04-01

This clinical trial tested the anti-stain efficacy at 3 and 6 months of a novel, sodium polyaspartate-containing, anti-stain dentifrice. In addition, the efficacy of the new dentifrice in controlling gingival inflammation and inhibition of calculus deposition was tested. Participants were recruited to this double blind randomised control clinical trial, and allocated to either test or control groups. The presence of stain and calculus were entry criteria. Measurements of stain, calculus and gingival inflammation were recorded using the Shaw and Murray Stain score, Volpe-Manhold Calculus score and the Modified Gingival Index respectively. Measurements were made at baseline, prior to the removal of stain and calculus, and after 3 and 6 months. Missing data were imputed by and the outcomes were analysed using univariate analysis. At three months, toothpaste containing sodium polyaspartate was better (difference of mean 1.13 with SEM 0.57) than control for the control of dental stain (p<0.05). Stain scores also showed a trend in favour of the test product (difference of mean 1.03 with SEM 0.78) at six months (p>0.05). There was no difference between toothpastes with respect to calculus deposition or gingival inflammation. Toothpaste containing sodium polyaspartate was more effective than a control toothpaste at preventing deposition of dental stain for 3 months after professional tooth cleaning but showed no significant effect at 6 months. Sodium polyaspartate toothpaste was more effective than a control toothpaste at preventing dental stain formation and maybe helpful in controlling staining between episodes of scaling and polishing. Copyright © 2012 Elsevier Ltd. All rights reserved.

A Default Temporal Logic for Regulatory Conformance Checking

DTIC Science & Technology

2008-04-01

proofs. In Section 4.3, we provide an axiomatization using Fitting’s sequent calculus [25]. Completeness is proved in Section 4.4. We conclude, in...axiomatize RefL. 4.3 Sequent Calculus We use Fitting’s sequent calculus [25]. A sequent is a statement of the form Γ → ∆, where Γ and ∆ are finite sets of...T.D., Vail, M.W., Anton , A.I.: Towards regulatory compliance: Extracting rights and obligations to align requirements with regulations. In

Generalized Cartan Calculus in general dimension

DOE PAGES

Wang, Yi -Nan

2015-07-22

We develop the generalized Cartan Calculus for the groups G = SL(2,R) × R +, SL(5,R) and SO(5,5). They are the underlying algebraic structures of d=9,7,6 exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincar\\'e lemmas in this new differential geometry is also discussed. Lastly, we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.

Some problems in fractal differential equations

NASA Astrophysics Data System (ADS)

Su, Weiyi

2016-06-01

Based upon the fractal calculus on local fields, or p-type calculus, or Gibbs-Butzer calculus ([1],[2]), we suggest a constructive idea for "fractal differential equations", beginning from some special examples to a general theory. However, this is just an original idea, it needs lots of later work to support. In [3], we show example "two dimension wave equations with fractal boundaries", and in this note, other examples, as well as an idea to construct fractal differential equations are shown.

Study Modules for Calculus-Based General Physics. [Includes Modules 21-23: Second Law and Entropy; Coulomb's Law and the Electric Field; and Flux and Gauss' Law].

ERIC Educational Resources Information Center

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Hermeneutics of differential calculus in eighteenth-century northern Germany.

PubMed

Blanco, Mónica

2008-01-01

This paper applies comparative textbook analysis to studying the mathematical development of differential calculus in northern German states during the eighteenth century. It begins with describing how the four textbooks analyzed presented the foundations of calculus and continues with assessing the influence each of these foundational approaches exerted on the resolution of problems, such as the determination of tangents and extreme values, and even on the choice of coordinates for both algebraic and transcendental curves.

Discrete Calculus as a Bridge between Scales

NASA Astrophysics Data System (ADS)

Degiuli, Eric; McElwaine, Jim

2012-02-01

Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310

The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alpay, Daniel, E-mail: dany@math.bgu.ac.il; Kimsey, David P., E-mail: dpkimsey@gmail.com; Colombo, Fabrizio, E-mail: fabrizio.colombo@polimi.it

In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The lack of a suitable notion ofmore » spectrum was a major obstruction to fully understand the spectral theorem for quaternionic normal operators. A prime motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti-self adjoint quaternionic operators which play a crucial role in the quaternionic quantum mechanics.« less

The Profit Motive: The Bane of Mathematics Education.

ERIC Educational Resources Information Center

Koblitz, Neal

1992-01-01

Discusses the lack of calculus textbook improvements even though there have been complaints about them from students and professors. Argues against using commercial textbooks in calculus instruction. (ASK)

Laser Ablation of Dental Calculus Around 400 nm Using a Ti:Sapphire Laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schoenly, J.; Seka, W.; Rechmann, P.

2009-10-19

A Nd:YAG laser-pumped, frequency-doubled Ti:sapphire laser is used for selective ablation of calculus. The laser provides ≤25 mJ at 400 nm (60-ns pulse width, 10-Hz repetition rate). The laser is coupled into an optical multimode fiber coiled around a 4-in.-diam drum to generate a top-hat output intensity profile. With coaxial water cooling, this is ideal for efficient, selective calculus removal. This is in stark contrast with tightly focused Gaussian beams that are energetically inefficient and lead to irreproducible results. Calculus is well ablated at high fluences ≥2 J/cm^2; stalling occurs below this fluence because of photobleaching. Healthy hard tissue ismore » not removed at fluences ≤3 J/cm^2.« less

A Tutorial Review on Fractal Spacetime and Fractional Calculus

NASA Astrophysics Data System (ADS)

He, Ji-Huan

2014-11-01

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

Means and Variances without Calculus

ERIC Educational Resources Information Center

Kinney, John J.

2005-01-01

This article gives a method of finding discrete approximations to continuous probability density functions and shows examples of its use, allowing students without calculus access to the calculation of means and variances.

Tactical Synthesis Of Efficient Global Search Algorithms

NASA Technical Reports Server (NTRS)

Nedunuri, Srinivas; Smith, Douglas R.; Cook, William R.

2009-01-01

Algorithm synthesis transforms a formal specification into an efficient algorithm to solve a problem. Algorithm synthesis in Specware combines the formal specification of a problem with a high-level algorithm strategy. To derive an efficient algorithm, a developer must define operators that refine the algorithm by combining the generic operators in the algorithm with the details of the problem specification. This derivation requires skill and a deep understanding of the problem and the algorithmic strategy. In this paper we introduce two tactics to ease this process. The tactics serve a similar purpose to tactics used for determining indefinite integrals in calculus, that is suggesting possible ways to attack the problem.

Stochastic Calculus and Differential Equations for Physics and Finance

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2013-02-01

1. Random variables and probability distributions; 2. Martingales, Markov, and nonstationarity; 3. Stochastic calculus; 4. Ito processes and Fokker-Planck equations; 5. Selfsimilar Ito processes; 6. Fractional Brownian motion; 7. Kolmogorov's PDEs and Chapman-Kolmogorov; 8. Non Markov Ito processes; 9. Black-Scholes, martingales, and Feynman-Katz; 10. Stochastic calculus with martingales; 11. Statistical physics and finance, a brief history of both; 12. Introduction to new financial economics; 13. Statistical ensembles and time series analysis; 14. Econometrics; 15. Semimartingales; References; Index.

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Geometric constrained variational calculus. II: The second variation (Part I)

NASA Astrophysics Data System (ADS)

Massa, Enrico; Bruno, Danilo; Luria, Gianvittorio; Pagani, Enrico

2016-10-01

Within the geometrical framework developed in [Geometric constrained variational calculus. I: Piecewise smooth extremals, Int. J. Geom. Methods Mod. Phys. 12 (2015) 1550061], the problem of minimality for constrained calculus of variations is analyzed among the class of differentiable curves. A fully covariant representation of the second variation of the action functional, based on a suitable gauge transformation of the Lagrangian, is explicitly worked out. Both necessary and sufficient conditions for minimality are proved, and reinterpreted in terms of Jacobi fields.

Computer-Aided Transformation of PDE Models: Languages, Representations, and a Calculus of Operations

DTIC Science & Technology

2016-01-05

discretizations . We maintain that what is clear at the mathematical level should be equally clear in computation. In this small STIR project, we separate the...concerns of describing and discretizing such models by defining an input language representing PDE, including steady-state and tran- sient, linear and...solvers, such as [8, 9], focused on the solvers themselves and particular families of discretizations (e. g. finite elements), and now it is natural to

Riemann-Liouville Fractional Calculus of Certain Finite Class of Classical Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Malik, Pradeep; Swaminathan, A.

2010-11-01

In this work we consider certain class of classical orthogonal polynomials defined on the positive real line. These polynomials have their weight function related to the probability density function of F distribution and are finite in number up to orthogonality. We generalize these polynomials for fractional order by considering the Riemann-Liouville type operator on these polynomials. Various properties like explicit representation in terms of hypergeometric functions, differential equations, recurrence relations are derived.

Air Force Leadership Study: The Need for Deliberate Development

DTIC Science & Technology

2012-02-01

Skills, 1. For future military operating environment studies, see Stephen J . Zaccaro, Richard J . Klimoski, and Lisa A. Boyce, The Changing U.S...fresh-voice -2176107.html. 13. Stephen J . Hagel et al., The Future of Global US Air Force Basing 2010– 2040, unpublished manuscript (Maxwell AFB, AL...it included the senior commanders of Amer- ica’s primary allies. Marshall’s simple calculus was Conner’s and, now, Eisenhower’s: If the United States

Optimal Collision Avoidance Trajectories for Unmanned/Remotely Piloted Aircraft

DTIC Science & Technology

2014-12-26

projected operational tempos (OPTEMPOs)” [15]. The Oce of the Secretary of Defense (OSD) Unmanned Systems Roadmap [15] goes on to say that the airspace...methods [63]. In an indirect method, the researcher derives the first- order necessary conditions for optimality “via the calculus of variations and...region around the ownship using a variation of a superquadric. From [116], the standard equation for a superellipsoid appears as: ✓ x a1 ◆ 2 ✏ 2

One Answer to "What Is Calculus?"

ERIC Educational Resources Information Center

Shilgalis, Thomas W.

1979-01-01

A number of questions are posed that can be answered with the aid of calculus. These include best value problems, best shape problems, problems involving integration, and growth and decay problems. (MP)

Catwalk: First-Semester Calculus.

ERIC Educational Resources Information Center

Speiser, Bob; Walter, Chuck

1994-01-01

Describes the use of time-lapse photographs of a running cat as a model to investigate the concepts of function and derivative in a college calculus course. Discusses student difficulties and implications for teachers. (MKR)

Limit Interchange and L'Hopital's Rule

ERIC Educational Resources Information Center

Ecker, Michael W.

2011-01-01

Conventional application of these two calculus staples is stretched here, somewhat recreationally, but also to raise solid questions about the role of limit interchange in analysis--without, however, delving any deeper than first-year Calculus.

A Discrete Approach to Computer-Oriented Calculus.

ERIC Educational Resources Information Center

Gordon, Sheldon P.

1979-01-01

Some of the implications and advantages of an instructional approach using results from the calculus of finite differences and finite sums, both for motivation and as tools leading to applications, are discussed. (MP)

Case Study: Students’ Symbolic Manipulation in Calculus Among UTHM Students

NASA Astrophysics Data System (ADS)

Ali, Maselan; Sufahani, Suliadi; Ahmad, Wan N. A. W.; Ghazali Kamardan, M.; Saifullah Rusiman, Mohd; Che-Him, Norziha

2018-04-01

Words are symbols representing certain aspects of mathematics. The main purpose of this study is to gain insight into students’ symbolic manipulation in calculus among UTHM students. This study make use the various methods in collecting data which are documentation, pilot study, written test and follow up individual interviews. Hence, the results analyzed and interpreted based on action-process-object-schema framework which is based on Piaget’s ideas of reflective abstraction, the concept of relational and instrumental understanding and the zone of proximal development idea. The students’ reply in the interview session is analyzed and then the overall performance is discussed briefly to relate with the students flexibility in symbolic manipulation in linking to the graphical idea, the students interpretation towards different symbolic structure in calculus and the problem that related to overgeneralization in their calculus problems solving.

Surface area and volume determination of subgingival calculus using laser fluorescence.

PubMed

Shakibaie, Fardad; Walsh, Laurence J

2014-03-01

Visible red (655 nm) laser fluorescence (LF) devices are currently used for identifying deposits of subgingival calculus on the root surfaces of teeth during dental examination and treatment; however, it is not known how the fluorescence readings produced by commercially available LF systems correlate to the nature of the deposits. This laboratory study explored the correlation between LF digital readings and the surface area and volume of subgingival calculus deposits on teeth. A collection of 30 extracted human posterior teeth with various levels of subgingival deposits of calculus across 240 sites were used in a clinical simulation, with silicone impression material used to replicate periodontal soft tissues. The teeth were scored by two examiners by using three commercial LF systems (DIAGNOdent, DIAGNOdent Pen and KEY3). The silicone was removed, and the teeth were removed for photography at × 20 magnification under white or ultraviolet light. The surface area, thickness, and volume were calculated, and both linear least squares regression and nonlinear (Spearman's rank method) correlation coefficients were determined. Visible red LF digital readings showed better correlation to calculus volume than to surface area. Overall, the best performance was found for the KEY3 system (Spearman coefficient 0.59), compared to the Classic DIAGNOdent (0.56) and the DIAGNOdent Pen (0.49). These results indicate that while visible red LF systems vary somewhat in performance, their LF readings provide a useful estimation of the volume of subgingival calculus deposits present on teeth.

A clinical investigation of the efficacy of two dentifrices for the reduction of supragingival calculus formation.

PubMed

Schiff, Thomas; Delgado, Evaristo; DeVizio, William; Proskin, Howard M

2008-01-01

The objective of this double-blind clinical study, conducted in harmony with Volpe-Manhold design for studies of dental calculus, was to compare the efficacy of a dentifrice containing 0.3% triclosan/2.0% polyvinylmethyl ether/maleic acid (PVM/MA) copolymer/0.243% sodium fluoride in a 17% dual silica base (Colgate Total Advanced Toothpaste) to that of a commercially available dentifrice containing 0.243% sodium fluoride in a silica base (Crest Cavity Protection Toothpaste) with respect to the reduction of supragingival calculus formation. Adult male and female subjects from the San Francisco area were entered into the eight-week pre-test phase of the study. Subjects received an evaluation of oral soft and hard tissues and were given a complete oral prophylaxis. They were provided with a non-tartar control placebo dentifrice and a soft-bristled adult toothbrush, and were instructed to brush their teeth twice daily (morning and evening) for one minute. After eight weeks of using the placebo dentifrice, subjects were examined for baseline supragingival calculus formation using the Volpe-Manhold Calculus Index. Qualifying subjects were randomized into two treatment groups which were balanced for gender and baseline calculus scores. All subjects entered into the twelve-week test phase were given a complete oral prophylaxis, and were provided with their assigned dentifrice and a soft-bristled adult toothbrush for home use. Subjects were instructed to brush their teeth for one minute twice daily (in the morning and evening). Prior to each study visit, subjects refrained from brushing their teeth and eating and drinking for four hours. Seventy-seven (77) subjects complied with the protocol and completed the study. At the twelve-week examination, the Test Dentifrice group presented a mean Volpe-Manhold Calculus Index score of 13.22 and the Control Dentifrice group presented a score of 20.29. After twelve weeks of product use, the Test Dentifrice group exhibited 34.8% less supragingival calculus formation than the Control Dentifrice group (statistically significant at p < 0.05). The overall results of this double-blind clinical study support the conclusion that after twelve weeks' use of a dentifrice containing 0.3% triclosan/2.0% PVM/MA copolymer/0.243% sodium fluoride in a 17% dual silica base provides significantly greater control of supragingival calculus formation relative to that of a commercially available dentifrice containing 0.243% sodium fluoride in a silica base.

A physically based connection between fractional calculus and fractal geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Butera, Salvatore, E-mail: sg.butera@gmail.com; Di Paola, Mario, E-mail: mario.dipaola@unipa.it

2014-11-15

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalousmore » dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry.« less

Enabling quaternion derivatives: the generalized HR calculus

PubMed Central

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C.; Mandic, Danilo P.

2015-01-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis. PMID:26361555

Enabling quaternion derivatives: the generalized HR calculus.

PubMed

Xu, Dongpo; Jahanchahi, Cyrus; Took, Clive C; Mandic, Danilo P

2015-08-01

Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective function. The recent HR calculus is a step forward and provides a way to calculate derivatives and gradients of both analytic and non-analytic functions of quaternion variables; however, the HR calculus can become cumbersome in complex optimization problems due to the lack of rigorous product and chain rules, a consequence of the non-commutativity of quaternion algebra. To address this issue, we introduce the generalized HR (GHR) derivatives which employ quaternion rotations in a general orthogonal system and provide the left- and right-hand versions of the quaternion derivative of general functions. The GHR calculus also solves the long-standing problems of product and chain rules, mean-value theorem and Taylor's theorem in the quaternion field. At the core of the proposed GHR calculus is quaternion rotation, which makes it possible to extend the principle to other functional calculi in non-commutative settings. Examples in statistical learning theory and adaptive signal processing support the analysis.

Fluorescence properties of human teeth and dental calculus for clinical applications

NASA Astrophysics Data System (ADS)

Lee, Yong-Keun

2015-04-01

Fluorescent emission of human teeth and dental calculus is important for the esthetic rehabilitation of teeth, diagnosis of dental caries, and detection of dental calculus. The purposes of this review were to summarize the fluorescence and phosphorescence of human teeth by ambient ultraviolet (UV) light, to investigate the clinically relevant fluorescence measurement methods in dentistry, and to review the fluorescence of teeth and dental calculus by specific wavelength light. Dentine was three times more phosphorescent than enamel. When exposed to light sources containing UV components, the fluorescence of human teeth gives them the quality of vitality, and fluorescent emission with a peak of 440 nm is observed. Esthetic restorative materials should have fluorescence properties similar to those of natural teeth. Based on the fluorescence of teeth and restorative materials as determined with a spectrophotometer, a fluorescence parameter was defined. As to the fluorescence spectra by a specific wavelength, varied wavelengths were investigated for clinical applications, and several methods for the diagnosis of dental caries and the detection of dental calculus were developed. Since fluorescent properties of dental hard tissues have been used and would be expanded in diverse fields of clinical practice, these properties should be investigated further, embracing newly developed optical techniques.

Dental calculus is associated with death from heart infarction.

PubMed

Söder, Birgitta; Meurman, Jukka H; Söder, Per-Östen

2014-01-01

We studied whether the amount of dental calculus is associated with death from heart infarction in the dental infection-atherosclerosis paradigm. Participants were 1676 healthy young Swedes followed up from 1985 to 2011. At the beginning of the study all subjects underwent oral clinical examination including dental calculus registration scored with calculus index (CI). Outcome measure was cause of death classified according to WHO International Classification of Diseases. Unpaired t-test, Chi-square tests, and multiple logistic regressions were used. Of the 1676 participants, 2.8% had died during follow-up. Women died at a mean age of 61.5 years and men at 61.7 years. The difference in the CI index score between the survivors versus deceased patients was significant by the year 2009 (P < 0.01). In multiple regression analysis of the relationship between death from heart infarction as a dependent variable and CI as independent variable with controlling for age, gender, dental visits, dental plaque, periodontal pockets, education, income, socioeconomic status, and pack-years of smoking, CI score appeared to be associated with 2.3 times the odds ratio for cardiac death. The results confirmed our study hypothesis by showing that dental calculus indeed associated statistically with cardiac death due to infarction.

Fluorescence properties of human teeth and dental calculus for clinical applications.

PubMed

Lee, Yong-Keun

2015-04-01

Fluorescent emission of human teeth and dental calculus is important for the esthetic rehabilitation of teeth, diagnosis of dental caries, and detection of dental calculus. The purposes of this review were to summarize the fluorescence and phosphorescence of human teeth by ambient ultraviolet (UV) light, to investigate the clinically relevant fluorescence measurement methods in dentistry, and to review the fluorescence of teeth and dental calculus by specific wavelength light. Dentine was three times more phosphorescent than enamel. When exposed to light sources containing UV components, the fluorescence of human teeth gives them the quality of vitality, and fluorescent emission with a peak of 440 nm is observed. Esthetic restorative materials should have fluorescence properties similar to those of natural teeth. Based on the fluorescence of teeth and restorative materials as determined with a spectrophotometer, a fluorescence parameter was defined. As to the fluorescence spectra by a specific wavelength, varied wavelengths were investigated for clinical applications, and several methods for the diagnosis of dental caries and the detection of dental calculus were developed. Since fluorescent properties of dental hard tissues have been used and would be expanded in diverse fields of clinical practice, these properties should be investigated further, embracing newly developed optical techniques.

Selective near-UV ablation of subgingival dental calculus: measurement of removal rates

NASA Astrophysics Data System (ADS)

Schoenly, J. E.; Seka, W.; Rechmann, P.

2010-02-01

A noncontact profilometer (laser triangulation) was used to measure the removal rates of subgingival dental calculus irradiated with a frequency-doubled Ti:sapphire laser (60-ns pulse duration, 400-nm wavelength, 10-Hz repetition rate, 7-mJ pulse energy). Profilometer traces before and after irradiation were used to create a removal map with 4-μm axial and 15-μm transverse resolution. Twenty-three teeth (15 with calculus and 8 pristine) were irradiated at 90° and 45° under a cooling water spray with a super-Gaussian beam (~300-μm diameter). Subgingival calculus was selectively removed at 5.6 and 4.0 J/cm2 for 90° and 45°, respecetively, within a range of rates, between 2 to 9 μm/pulse. These ablation rates were constant during these exposures. For comparison, pristine cementum irradiated for 10 min at the same peak fluence and pulse repetition rate showed only craters, 15 to 50 μm deep, corresponding to an equivalent removal rate three orders of magnitude smaller than that obtained for calculus. Pristine enamel was not removed under the same irradiation conditions.

Electron microscopy of octacalcium phosphate in the dental calculus.

PubMed

Kakei, Mitsuo; Sakae, Toshiro; Yoshikawa, Masayoshi

2009-12-01

The purpose of this study was to morphologically demonstrate the presence of octacalcium phosphate in the dental calculus by judging from the crystal lattice image and its rapid transformation into apatite crystal, as part of our serial studies on biomineral products. We also aimed to confirm whether the physical properties of octacalcium phosphate are identical with those of the central dark lines observed in crystals of ordinary calcifying hard tissues. Electron micrographs showed that crystals of various sizes form in the dental calculus. The formation of each crystal seemed to be closely associated with the organic substance, possibly originating from degenerated microorganisms at the calcification front. Many crystals had an 8.2-A lattice interval, similar to that of an apatite crystal. Furthermore, some crystals clearly revealed an 18.7-A lattice interval and were vulnerable to electron bombardment. After electron beam exposure, this lattice interval was quickly altered to about half (i.e. 8.2 A), indicating structural conversion. Consequently, a number of apatite crystals in the dental calculus are possibly created by a conversion mechanism involving an octacalcium phosphate intermediate. However, we also concluded that the calcification process in the dental calculus is not similar to that of ordinary calcifying hard tissues.

Selective Near-UV Ablation of Subgingival Dental Calculus: Measurement of Removal Rates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schoenly, J.E.; Seka, W.; Rechmann, P.

A noncontact profilometer (laser triangulation) was used to measure the removal rates of subgingival dental calculus irradiated with a frequency-doubled Ti:sapphire laser (60-ns pulse duration, 400-nm wavelength, 10-Hz repetition rate, 7-mJ pulse energy). Profilometer traces before and after irradiation were used to create a removal map with 4-μm axial and 15-μm transverse resolution. Twenty-three teeth (15 with calculus and 8 pristine) were irradiated at 90° and 45° under a cooling water spray with a super-Gaussian beam (~300-μm diameter). Subgingival calculus was selectively removed at 5.6 and 4.0 J/cm2 for 90° and 45°, respecetively, within a range of rates, between 2more » to 9 μm/pulse. These ablation rates were constant during these exposures. For comparison, pristine cementum irradiated for 10 min at the same peak fluence and pulse repetition rate showed only craters, 15 to 50 μm deep, corresponding to an equivalent removal rate three orders of magnitude smaller than that obtained for calculus. Pristine enamel was not removed under the same irradiation conditions.« less

Effect of a pre-brush mounthrinse containing triclosan and a copolymer on calculus formation: a three-month clinical study in Thailand.

PubMed

Triratana, T; Kraivaphan, P; Tandhachoon, K; Rustogi, K; Volpe, A R; Petrone, M

1995-01-01

A three-month, double-blind, parallel clinical study was conducted on a population of Thai adults to evaluate the effect of the twice daily use of a commercially available pre-brush mouthrinse on supragingival calculus formation. The mouthrinse test product contained 0.03% triclosan and 0.13% PVM/MA copolymer with the absence of fluoride. The subjects were initially examined for calculus using the Volpe-Manhold procedure. All subjects received an oral prophylaxis and were assigned to the use of either 1) a triclosan-copolymer mouthrinse, or 2) a matching flavored/colored water placebo mouthrinse. Subjects were instructed to rinse twice daily with 10 cc of the assigned mouthrinse for 1 minute, followed by brushing with the provided toothpaste containing fluoride for 45 seconds. After three months of using the assigned mouthrinse, the subjects were reexamined for calculus formation. The results indicated that the subjects using triclosan/copolymer mouthrinse had 23.17% less supragingival calculus than the placebo mouthrinse subjects. This reduction was statistically significant at the 99% or greater (F = 24.35, p<0.001) level of confidence.

Making an Interactive Calculus Textbook.

ERIC Educational Resources Information Center

Larson, Timothy R.

1995-01-01

Presents a case study of the design and production of "Interactive Calculus," an interactive multimedia textbook. Discusses reasons for using multimedia textbooks; what an interactive textbook is; content, organization, graphic design, authoring and composition; and work flow. (AEF)

Cartooning in Algebra and Calculus

ERIC Educational Resources Information Center

Moseley, L. Jeneva

2014-01-01

This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

A Giant Urethral Calculus.

PubMed

Sigdel, G; Agarwal, A; Keshaw, B W

2014-01-01

Urethral calculi are rare forms of urolithiasis. Majority of the calculi are migratory from urinary bladder or upper urinary tract. Primary urethral calculi usually occur in presence of urethral stricture or diverticulum. In this article we report a case of a giant posterior urethral calculus measuring 7x3x2 cm in a 47 years old male. Patient presented with acute retention of urine which was preceded by burning micturition and dribbling of urine for one week. The calculus was pushed in to the bladder through the cystoscope and was removed by suprapubic cystolithotomy.

An intrahepatic calculus superimposed over the right renal shadow: a case of mistaken identity.

PubMed

Learney, Robert M; Shrotri, Nitin

2010-08-01

A 36-year-old Caucasian British woman presented with a classic case of right renal colic. Initial plain abdominal radiography and intravenous urography identified an 8 x 5 mm calculus apparently lying within a right lower pole calyx. Following failed extracorporeal lithotripsy and flexible ureterorenoscopy, cross-sectional imaging revealed a misdiagnosis by superposition of an intrahepatic calculus over the right renal shadow. This case serves to support cross-sectional imaging in the diagnosis of renal calculi. Copyright 2010 Elsevier Inc. All rights reserved.

Mathematics preparation for medical school: do all premedical students need calculus?

PubMed

Nusbaum, Neil J

2006-01-01

The premedical student confronts a disparate set of required and recommended courses from the various medical schools to which the student might apply. Students may feel compelled to take courses such as calculus even though most medical schools do not require it and even though it may not be related to either undergraduate academic plans or the core academic needs of the typical future physician. Basic mathematical knowledge--a knowledge of algebra, statistics, and overall numeracy--are each more important for most future physicians than is the traditional calculus course.

Extreme value problems without calculus: a good link with geometry and elementary maths

NASA Astrophysics Data System (ADS)

Ganci, Salvatore

2016-11-01

Some classical examples of problem solving, where an extreme value condition is required, are here considered and/or revisited. The search for non-calculus solutions appears pedagogically useful and intriguing as shown through a rich literature. A teacher, who teaches both maths and physics, (as happens in Italian High schools) can find in these kinds of problems a mind stimulating exercise compared with the standard solution obtained by the differential calculus. A good link between the geometric and analytical explanations is so established.

ECG artifact cancellation in surface EMG signals by fractional order calculus application.

PubMed

Miljković, Nadica; Popović, Nenad; Djordjević, Olivera; Konstantinović, Ljubica; Šekara, Tomislav B

2017-03-01

New aspects for automatic electrocardiography artifact removal from surface electromyography signals by application of fractional order calculus in combination with linear and nonlinear moving window filters are explored. Surface electromyography recordings of skeletal trunk muscles are commonly contaminated with spike shaped artifacts. This artifact originates from electrical heart activity, recorded by electrocardiography, commonly present in the surface electromyography signals recorded in heart proximity. For appropriate assessment of neuromuscular changes by means of surface electromyography, application of a proper filtering technique of electrocardiography artifact is crucial. A novel method for automatic artifact cancellation in surface electromyography signals by applying fractional order calculus and nonlinear median filter is introduced. The proposed method is compared with the linear moving average filter, with and without prior application of fractional order calculus. 3D graphs for assessment of window lengths of the filters, crest factors, root mean square differences, and fractional calculus orders (called WFC and WRC graphs) have been introduced. For an appropriate quantitative filtering evaluation, the synthetic electrocardiography signal and analogous semi-synthetic dataset have been generated. The examples of noise removal in 10 able-bodied subjects and in one patient with muscle dystrophy are presented for qualitative analysis. The crest factors, correlation coefficients, and root mean square differences of the recorded and semi-synthetic electromyography datasets showed that the most successful method was the median filter in combination with fractional order calculus of the order 0.9. Statistically more significant (p < 0.001) ECG peak reduction was obtained by the median filter application compared to the moving average filter in the cases of low level amplitude of muscle contraction compared to ECG spikes. The presented results suggest that the novel method combining a median filter and fractional order calculus can be used for automatic filtering of electrocardiography artifacts in the surface electromyography signal envelopes recorded in trunk muscles. Copyright © 2017 Elsevier Ireland Ltd. All rights reserved.

Preparing Future College Instructors: The Role of Graduate Student Teaching Assistants (GTAs) in Successful College Calculus Programs

NASA Astrophysics Data System (ADS)

Ellis, Jessica Fabricant

Graduate student Teaching Assistants (GTAs) contribute to calculus instruction in two ways: as the primary teacher and as recitation leaders. GTAs can also be viewed as the next generation of mathematics instructors. Thus, in addition to their immediate contribution to the landscape of Calculus 1 instruction, GTAs will contribute significantly to the long-term state of calculus in their future occupations. However, their preparation for these roles varies widely and is often minimal. In this study, I first compare the mathematical beliefs, instructional practices, and student success of GTAs to other Calculus 1 instructors. I then provide rich descriptions for three GTA professional development (PD) programs that prepare graduate students as course instructors, as recitation leaders, and as future faculty. I then investigate the instructional practices and mathematical beliefs of graduate students coming from these three PD programs. I conclude this work with a description of a framework for GTA-PD programs. To accomplish this work, I conducted a mixed-method analysis on national survey data and case study data from four doctoral granting institutions. These four institutions were chosen because of their higher-than-expected student success in Calculus 1. The results of these analyses indicate that graduate students teach in more innovative ways than other instructors, though their students were less successful. Among the four case study institutions, I identified three models of GTA-PD, each of which appeared successful in accomplishing their goals. These goals included transitioning graduate students into the role of instructor, preparing graduate students to implement an innovative approach to Calculus 1, and supporting graduate students as recitation leaders. These analyses also led to the development of a framework to be used to characterize, evaluate, and consider the implementation of graduate student professional development programs. This GTA-PD framework is thus one of the major contributions put forth by this dissertation.

LOOP CALCULUS AND BELIEF PROPAGATION FOR Q-ARY ALPHABET: LOOP TOWER

DOE Office of Scientific and Technical Information (OSTI.GOV)

CHERTKOV, MICHAEL; CHERNYAK, VLADIMIR

Loop calculus introduced in [1], [2] constitutes a new theoretical tool that explicitly expresses symbol Maximum-A-Posteriori (MAP) solution of a general statistical inference problem via a solution of the Belief Propagation (BP) equations. This finding brought a new significance to the BP concept, which in the past was thought of as just a loop-free approximation. In this paper they continue a discussion of the Loop Calculus, partitioning the results into three Sections. In Section 1 they introduce a new formulation of the Loop Calculus in terms of a set of transformations (gauges) that keeping the partition function of the problemmore » invariant. The full expression contains two terms referred to as the 'ground state' and 'excited states' contributions. The BP equations are interpreted as a special (BP) gauge fixing condition that emerges as a special orthogonality constraint between the ground state and excited states, which also selects loop contributions as the only surviving ones among the excited states. In Section 2 they demonstrate how the invariant interpretation of the Loop Calculus, introduced in Section 1, allows a natural extension to the case of a general q-ary alphabet, this is achieved via a loop tower sequential construction. The ground level in the tower is exactly equivalent to assigning one color (out of q available) to the 'ground state' and considering all 'excited' states colored in the remaining (q-1) colors, according to the loop calculus rule. Sequentially, the second level in the tower corresponds to selecting a loop from the previous step, colored in (q-1) colors, and repeating the same ground vs excited states splitting procedure into one and (q-2) colors respectively. The construction proceeds till the full (q-1)-levels deep loop tower (and the corresponding contributions to the partition function) are established. In Section 3 they discuss an ultimate relation between the loop calculus and the Bethe-Free energy variational approach of [3].« less

Effectiveness of a mouthrinse containing active ingredients in addition to chlorhexidine and triclosan compared with chlorhexidine and triclosan rinses on plaque, gingivitis, supragingival calculus and extrinsic staining.

PubMed

Kumar, S; Patel, S; Tadakamadla, J; Tibdewal, H; Duraiswamy, P; Kulkarni, S

2013-02-01

To assess the effectiveness of three different mouthrinses--chlorhexidine, triclosan + sodium fluoride and chlorhexidine + triclosan + sodium fluoride + zinc chloride--on plaque, calculus, gingivitis and stains and to evaluate the occurrence of adverse effects with these three treatments. Forty-eight healthy subjects participated in a double-blind, randomized, parallel experiment and were randomly allocated to any one of the three experimental mouthrinses: group A (0.2% chlorhexidine (CHX) gluconate), group B (0.03% triclosan + 0.025% sodium fluoride (NaF) + 12% ethyl alcohol) or group C (0.2% CHX + 0.3% triclosan + 0.3% NaF + 0.09% Zn chloride (ZnCl(2)). All the subjects were assessed for gingivitis, plaque, supragingival calculus and extrinsic stains at baseline and at the end of the 21-day experimental period. There was a significant difference (P = 0.046) in the effectiveness for the prevention of gingivitis and plaque, with subjects of group A and group C presenting least and highest gingival and plaque scores, respectively. Significant differences (P = 0.03) were observed for the accumulation of supragingival calculus where the deposition of calculus in group A was nearly double that of the group B, and group B was most effective in the prevention of supragingival calculus. Highest deposition of extrinsic stains was in the group A followed by group C and group B. There was no significant difference between the three treatments for adverse events' occurrence. CHX mouthrinse was most effective in controlling plaque and gingivitis but caused greatest deposition of extrinsic stains. Supragingival calculus deposition was least in triclosan + NaF group followed by CHX + triclosan + NaF + ZnCl(2) and CHX. More than half of the subjects reported adverse events during the experimental phase. © 2012 John Wiley & Sons A/S.

An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order

PubMed Central

Almeida, Ricardo

2013-01-01

We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type. PMID:24319382

ATHLI16: the ATHens Lidar Intercomparison campaign

NASA Astrophysics Data System (ADS)

Amodeo, Aldo; D'Amico, Giuseppe; Giunta, Aldo; Papagiannopoulos, Nikolaos; Papayannis, Alex; Argyrouli, Athina; Mylonaki, Maria; Tsaknakis, Georgios; Kokkalis, Panos; Soupiona, Ourania; Tzanis, Chris

2018-04-01

The results of the ATHLI16 (ATHens Lidar Intercomparison) campaign, held in Athens from 26/09 to 07/10 2016 are presented. The campaign was performed within the Lidar Calibration Centre activities (EU H2020 ACTRIS-2 project) to assess the performance of the EOLE lidar system (NTUA, Athens, Greece), operating within EARLINET, by comparing against the EARLINET reference lidar system MUSA (CNR-IMAA, Potenza, Italy). For both lidars only products retrieved by the EARLINET Single Calculus Chain have been compared.

Methods of Contemporary Gauge Theory

NASA Astrophysics Data System (ADS)

Makeenko, Yuri

2002-08-01

Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.

Methods of Contemporary Gauge Theory

NASA Astrophysics Data System (ADS)

Makeenko, Yuri

2005-11-01

Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.

The Calculus of War: The Role and Use of Quantitative Decision Aids at the Tactical Level of War

DTIC Science & Technology

1993-01-01

significantly. Ceilings of unbroken clouds came down to only several hundred feet altitude. Blowing sand mixed with heavy oil smoke to further obscure...Analysts go off into the murky world of materiel marketing . Allow the OR scientists return to the pure mode of enhancing combat operations. If necessary...Roots of Stategy , Book 2 (Harrisburg, Pa.: Stackpole Books, 1987), p. 66. 36 Larry H. Addington, The Patterns of War Since the 18th Century

Iraqi Perspectives Project. A View of Operation Iraqi Freedom from Saddam’s Senior Leadership

DTIC Science & Technology

2006-01-01

nation’s history and culture . Thus, the Iraqi response to threats and the invasion of Coalition forces was a function of how Saddam and his minions...had been shaped by violence. Being a product of a violent political culture does not ab- solve Saddam for his role over the past three decades. He was...calculus, the United States was unwilling to undertake any action that could result in even small numbers of Americans being sent home in body bags

[Case report of live threatening complications due to self insertion of foreign body into the vagina for masturbation purpose].

PubMed

Kuzaka, Bolesław; Kobryń, Andrzej; Niemierko, Maciej; Czaplicki, Maciej

2009-01-01

Authors have reported a case report of life threatening complications due to insertion of foreign bodies into the vagina, because of masturbation purpose. In this case subsequently came to perforation of the urinary bladder by the huge calculus that developed over the foreign body, and next to the peritoneum with development peritonitis and acute renal insufficiency with the need of dialysotherapy. After a number of surgical operations, the patient with a definitive percutaneous nephrostomy was discharged.

Summer Research Apprentice Program report. [Summer Research Apprentice Program

DOE Office of Scientific and Technical Information (OSTI.GOV)

Curington, B.

1982-01-01

The Summer Research Apprentice Program is designed to provide students with their first look at college life while preparing them for possible careers in mathematics, science and engineering. The 23 students, enrolled as college freshmen for 8 hours of college credit, took courses in Trigonometry, College Algebra and introduction to Research (4 students were enrolled in Calculus 1 instead of Trigonometry and College Albebra). During this third year of operation, refinements were made in both the administration of the program and in the method of implementation.

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

NASA Astrophysics Data System (ADS)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

Using Student-Made Games to Learn Mathematics

ERIC Educational Resources Information Center

Gallegos, Irene; Flores, Alfinio

2010-01-01

First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

Forest Carbon Uptake and the Fundamental Theorem of Calculus

ERIC Educational Resources Information Center

Zobitz, John

2013-01-01

Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.

Calculus Student Descending a Staircase.

ERIC Educational Resources Information Center

Mueller, William

1999-01-01

Common student attitudes toward reform methods are conveyed through the thoughts of a student leaving a multivariable calculus exam and musings range over textbooks, homework, workload, group work, writing, noncomputational problems, instructional problems, instructional styles, and classroom activities. (Author/ASK)