Maple (Computer Algebra System) in Teaching Pre-Calculus: Example of Absolute Value Function
ERIC Educational Resources Information Center
Tuluk, Güler
2014-01-01
Modules in Computer Algebra Systems (CAS) make Mathematics interesting and easy to understand. The present study focused on the implementation of the algebraic, tabular (numerical), and graphical approaches used for the construction of the concept of absolute value function in teaching mathematical content knowledge along with Maple 9. The study…
Applications of Maple To Algebraic Cryptography.
ERIC Educational Resources Information Center
Sigmon, Neil P.
1997-01-01
Demonstrates the use of technology to enhance the appreciation of applications involving abstract algebra. The symbolic manipulator Maple can perform computations required for a linear cryptosystem. One major benefit of this process is that students can encipher and decipher messages using a linear cryptosystem without becoming confused and…
NASA Astrophysics Data System (ADS)
Nicolaides, Roy A.; Walkington, Noel J.
1996-06-01
A knowledge of one or more high level symbolic mathematics programs is rapidly becoming a necessity for mathematics users from all fields of science. The aim of this book is to provide a solid grounding in Maple, one of the best known of these programs. The authors combine efficiency and economy of exposition with a complete coverage of Maple. The book has twelve chapters, of which eight are completely accessible to anyone who has completed calculus and linear sequences as taught in American universities. These chapters cover the great majority of Maple's capabilities. There are also three chapters on Maple programming that can be read without prior programming experience, although knowledge of a high level programming language (Basic, Fortran, C etc.) will help. There is also a chapter on some relevant aspects of algebra. Above all, the book allows the reader to extract value from Maple without wasting time and effort in the learning process. It is the fastest track to expertise for Maple users in mathematics and computer science.
Born total ionisation cross sections: An algebraic computing program using Maple
NASA Astrophysics Data System (ADS)
Bartlett, Philip L.; Stelbovics, Andris T.
2003-08-01
The software described in this paper uses the Maple algebraic computing environment to calculate an analytic form for the matrix element of the plane-wave Born approximation of the electron-impact ionisation of an atomic orbital, with arbitrary orbital and angular momentum quantum numbers. The atomic orbitals are approximated by Hartree-Fock Slater functions, and the ejected electron is modelled by a hydrogenic Coulomb wave, made orthogonal to all occupied orbitals of the target atom. Clenshaw-Curtis integration techniques are then used to calculate the total ionisation cross-section. For improved performance, the numerical integrations are performed using FORTRAN by automatically converting the analytic matrix element for each orbital into a FORTRAN subroutine. The results compare favourably with experimental data for a wide range of elements, including the transition metals, with excellent convergence at high energies. Program summaryTitle of program: BIX Catalogue identifier:ADRZ Program summary URL:http://www.cpc.cs.qub.ac.uk/cpc/summaries/ADRZ Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Computers: Platform independent Operating systems: Tested on DEC Alpha Unix, Windows NT 4.0 and Windows XP Professional Edition Programming language used: Maple V Release 5.1 and FORTRAN 90 Memory required: 256 MB No. of processors used: 1 No. of bytes in distributed program, including test data, etc.:61754 Distributed format:tar gzip file Keywords: Born approximation, electron-impact ionisation cross-section, Maple, Hartree-Fock Nature of physical problem: Calculates the total electron impact ionisation cross-section for neutral and ionised atomic species using the first-Born approximation. The scattered electron is modelled by a plane wave, and the ejected electron is modelled by a hydrogenic Coulomb wave, which is made orthogonal to all occupied atomic orbitals, and the atomic orbitals are approximated by Hartree-Fock Slater
Some Unexpected Results Using Computer Algebra Systems.
ERIC Educational Resources Information Center
Alonso, Felix; Garcia, Alfonsa; Garcia, Francisco; Hoya, Sara; Rodriguez, Gerardo; de la Villa, Agustin
2001-01-01
Shows how teachers can often use unexpected outputs from Computer Algebra Systems (CAS) to reinforce concepts and to show students the importance of thinking about how they use the software and reflecting on their results. Presents different examples where DERIVE, MAPLE, or Mathematica does not work as expected and suggests how to use them as a…
NASA Astrophysics Data System (ADS)
Huf, P. A.; Carminati, J.
2015-09-01
In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment.
Maple Explorations, Perfect Numbers, and Mersenne Primes
ERIC Educational Resources Information Center
Ghusayni, B.
2005-01-01
Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.
Using Maple to Implement eLearning Integrated with Computer Aided Assessment
ERIC Educational Resources Information Center
Blyth, Bill; Labovic, Aleksandra
2009-01-01
Advanced mathematics courses have been developed and refined by the first author, using an action research methodology, for more than a decade. These courses use the computer algebra system (CAS) Maple in an "immersion mode" where all presentations and student work are done using Maple. Assignments and examinations are Maple files downloaded from…
ERIC Educational Resources Information Center
Harris, Gary A.
2000-01-01
Discusses the use of a computer algebra system in a capstone mathematics course for undergraduate mathematics majors preparing to teach secondary school mathematics. Provides sample exercises intended to demonstrate how the power of a computer algebra system such as MAPLE can contribute to desired outcomes including reinforcing and strengthening…
MAPLE Procedures For Boson Fields System On Curved Space - Time
Murariu, Gabriel
2007-04-23
Systems of interacting boson fields are an important subject in the last years. From the problem of dark matter to boson stars' study, boson fields are involved. In the general configuration, it is considered a Klein-Gordon-Maxwell-Einstein fields system for a complex scalar field minimally coupled to a gravitational one. The necessity of studying a larger number of space-time configurations and the huge volume of computations for each particular situation are some reasons for building a MAPLE procedures set for this kind of systems.
Step-by-Step Solution Possibilities in Different Computer Algebra Systems.
ERIC Educational Resources Information Center
Tonisson, Eno
This paper compares a number of different Computer Algebra Systems (CAS) in their solution of one-step and multi-step problems. The CAS programs considered include DERIVE, Maple, Mathematica, and MuPAD while the problems are taken from the final examinations of grades 9 and 12 in Estonian schools. The different outputs to one-step problems with…
Leafhopper control in filed-grown red maples with systemic insecticides
Technology Transfer Automated Retrieval System (TEKTRAN)
Red maple, a popular landscape tree, can be susceptible to foliar damage caused by potato leafhopper feeding. Typical potato leafhopper injury includes distorted leaf tissue and reduced shoot growth. This research identified systemic neonicotinoid insecticides, Allectus and Discus, which controlled...
Handheld Computer Algebra Systems in the Pre-Algebra Classroom
ERIC Educational Resources Information Center
Gantz, Linda Ann Galofaro
2010-01-01
This mixed method analysis sought to investigate several aspects of student learning in pre-algebra through the use of computer algebra systems (CAS) as opposed to non-CAS learning. This research was broken into two main parts, one which compared results from both the experimental group (instruction using CAS, N = 18) and the control group…
Li, Mengxi; Seo, Sooyoun; Karboune, Salwa
2015-11-20
Maple syrups with selected degree Brix (°Bx) (15, 30, 60) were investigated as reaction systems for levansucrase from Bacillus amyloliquefaciens. The enzymatic conversion of sucrose present in the maple syrup and the production of the transfructosylation products were assessed over a time course of 48h. At 30°C, the use of maple syrup 30°Bx led to the highest levansucrase activity (427.53μmol/mg protein/min), while maple syrup 66°Bx led to the highest converted sucrose concentration (1.53M). In maple syrup 30°Bx, oligolevans (10
Evaluation of Systemic Insecticides for Potato Leafhopper Control in Field-Grown Red Maple
Technology Transfer Automated Retrieval System (TEKTRAN)
Systemic insecticides and application methods were evaluated in two tests that began in 2005 and 2006 for control of potato leafhopper (Empoasca fabae [Harris]) on four red maple (Acer rubrum L.) cultivars and rated yearly through 2007. Treatments evaluated in this study included surface drenches o...
The Multiple Pendulum Problem via Maple[R
ERIC Educational Resources Information Center
Salisbury, K. L.; Knight, D. G.
2002-01-01
The way in which computer algebra systems, such as Maple, have made the study of physical problems of some considerable complexity accessible to mathematicians and scientists with modest computational skills is illustrated by solving the multiple pendulum problem. A solution is obtained for four pendulums with no restriction on the size of the…
Algebraic methods in system theory
NASA Technical Reports Server (NTRS)
Brockett, R. W.; Willems, J. C.; Willsky, A. S.
1975-01-01
Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.
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)
1992-05-04
DOE-MACSYMA (Project MAC''s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions. Franzmore » Lisp OPUS 38 provides the environment for the Encore, Celerity, and DEC VAX11 UNIX,SUN(OPUS) versions under UNIX and the Alliant version under Concentrix. Kyoto Common Lisp (KCL) provides the environment for the SUN(KCL),Convex, and IBM PC under UNIX and Data General under AOS/VS.« less
Lax operator algebras and integrable systems
NASA Astrophysics Data System (ADS)
Sheinman, O. K.
2016-02-01
A new class of infinite-dimensional Lie algebras, called Lax operator algebras, is presented, along with a related unifying approach to finite-dimensional integrable systems with a spectral parameter on a Riemann surface such as the Calogero-Moser and Hitchin systems. In particular, the approach includes (non-twisted) Kac-Moody algebras and integrable systems with a rational spectral parameter. The presentation is based on quite simple ideas about the use of gradings of semisimple Lie algebras and their interaction with the Riemann-Roch theorem. The basic properties of Lax operator algebras and the basic facts about the theory of the integrable systems in question are treated (and proved) from this general point of view. In particular, the existence of commutative hierarchies and their Hamiltonian properties are considered. The paper concludes with an application of Lax operator algebras to prequantization of finite-dimensional integrable systems. Bibliography: 51 titles.
Some Applications of Algebraic System Solving
ERIC Educational Resources Information Center
Roanes-Lozano, Eugenio
2011-01-01
Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact solve"…
New directions in algebraic dynamical systems
NASA Astrophysics Data System (ADS)
Schmidt, Klaus; Verbitskiy, Evgeny
2011-02-01
The logarithmic Mahler measure of certain multivariate polynomials occurs frequently as the entropy or the free energy of solvable lattice models (especially dimer models). It is also known that the entropy of an algebraic dynamical system is the logarithmic Mahler measure of the defining polynomial. The connection between the lattice models and the algebraic dynamical systems is still rather mysterious.
Lagacé, L; Jacques, M; Mafu, A A; Roy, D
2006-10-01
The susceptibility of planktonic and biofilm cells of Pseudomonas marginalis toward four commonly used biocides at different temperatures (15 and 30 degrees C) and biofilm growth times (24 and 48 h) was assessed. Using the MBEC biofilm device, biofilm production in maple sap was shown to be highly reproducible for each set of conditions tested. Biofilm formation was influenced by growth temperature and time. A temperature of 15 degrees C and incubation time of 24 h yielded fewer CFU per peg and showed fewer adhered cells and typical biofilm structures, based on scanning electron microscopy observations as compared with other conditions. Minimal biofilm eradication concentration values for P. marginalis were significantly greater (P. < 0.001) than were MBCs for planktonic cells and for every biocide tested, with the exception of minimal biofilm eradication concentration values for peracetic acid at 15 degrees C and 24 h. Sodium hypochlorite and peracetic acid sanitizers were able to eliminate P. marginalis biofilms at lower concentrations as compared with hydrogen peroxide- and quaternary ammonium-based sanitizers (P < 0.001). According to the results obtained, sodium hypochlorite and peracetic acid sanitizers would be more appropriate for maple sap collection system sanitation. PMID:17066920
Use of a Colony of Cooperating Agents and MAPLE To Solve the Traveling Salesman Problem.
ERIC Educational Resources Information Center
Guerrieri, Bruno
This paper reviews an approach for finding optimal solutions to the traveling salesman problem, a well-known problem in combinational optimization, and describes implementing the approach using the MAPLE computer algebra system. The method employed in this approach to the problem is similar to the way ant colonies manage to establish shortest…
On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations
NASA Astrophysics Data System (ADS)
Zhang, Yu-Feng; Honwah, Tam
2016-03-01
In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz-Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), and Hong Kong Research Grant Council under Grant No. HKBU202512, as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016
On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations
NASA Astrophysics Data System (ADS)
Zhang, Yu-Feng; Tam, Honwah
2016-03-01
In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz–Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), and Hong Kong Research Grant Council under Grant No. HKBU202512, as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016
ERIC Educational Resources Information Center
Ozgun-Koca, S. Ash
2010-01-01
Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…
Algebraic models of flexible manufacturing systems
NASA Astrophysics Data System (ADS)
Leskin, Aleksei Alekseevich
Various aspects of the use of mathematical methods in the development of flexible manufacturing systems are examined. Attention is given to dynamical and structural models of flexible manufacturing systems developed by using methods of algebraic and differential geometry, topology, polynomial algebra, and extreme value problem theory. The principles of model integration are discussed, and approaches are proposed for solving problems related to the selection of flexible manufacturing equipment, real-time modeling of the manufacturing process, and optimization of local automation systems. The discussion is illustrated by examples.
Digital Maps, Matrices and Computer Algebra
ERIC Educational Resources Information Center
Knight, D. G.
2005-01-01
The way in which computer algebra systems, such as Maple, have made the study of complex problems accessible to undergraduate mathematicians with modest computational skills is illustrated by some large matrix calculations, which arise from representing the Earth's surface by digital elevation models. Such problems are often considered to lie in…
Simulation of n-qubit quantum systems: A computer-algebraic approach
NASA Astrophysics Data System (ADS)
Radtke, T.; Fritzsche, S.; Surzhykov, A.
2007-03-01
During the last decade, the field of quantum computation has attracted a lot of interest and motivated many theoretical and experimental studies of n-qubit quantum systems. But apart from the promise of more efficient quantum algorithms, these investigations also revealed a number of obstacles which still have to be overcome in practice. In this context, the use of simulation programs has proved to be an appropriate method. In order to facilitate the simulation of n-qubit quantum systems, we present the Feynman software program to provide the necessary tools to define and to deal with quantum registers as well as the operators acting on them. Using an interactive design within the framework of the computer algebra system Maple, we hope that the Feynman software program will be useful not only for teaching the basic elements of quantum computing but also for studying their physical realization in the future.
Integrability of Hamiltonian systems with algebraic potentials
NASA Astrophysics Data System (ADS)
Maciejewski, Andrzej J.; Przybylska, Maria
2016-01-01
Problem of integrability for Hamiltonian systems with potentials that are algebraic thus multivalued functions of coordinates is discussed. Introducing potential as a new variable the original Hamiltonian system on 2n dimensional phase space is extended to 2 n + 1 dimensional system with rational right-hand sides. For extended system its non-canonical degenerated Poisson structure of constant rank 2n and rational Hamiltonian is identified. For algebraic homogeneous potentials of non-zero rational homogeneity degree necessary integrability conditions are formulated. These conditions are deduced from an analysis of the differential Galois group of variational equations around particular solutions of a straight line type. Obtained integrability obstructions are applied to the class of monomial homogeneous potentials. Some integrable potentials satisfying these conditions are found.
Spatial Operator Algebra for multibody system dynamics
NASA Technical Reports Server (NTRS)
Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.
1992-01-01
The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.
Symmetric linear systems - An application of algebraic systems theory
NASA Technical Reports Server (NTRS)
Hazewinkel, M.; Martin, C.
1983-01-01
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
Hyperfine structure parametrisation in Maple
NASA Astrophysics Data System (ADS)
Gaigalas, G.; Scharf, O.; Fritzsche, S.
2006-02-01
: All computers with a license of the computer algebra package MAPLE Installations: University of Kassel (Germany) Operating systems under which the program has been tested: Linux 9.0 Program language used:MAPLE, Release 7, 8 and 9 Memory required to execute with typical data: 5 MB No. of lines in distributed program, including test data, etc.: 34 300 No. of bytes in distributed program, including test data, etc.: 954 196 Distribution format: tar.gz Nature of the physical problem: Atomic state functions of an many configuration many electron atom with several open shells are defined by a number of quantum numbers, by their coupling and selection rules such as the Pauli exclusion principal or parity conservation. The matrix elements of any one-particle operator acting on these wavefunctions can be analytically integrated up to the radial part [G. Gaigalas, O. Scharf, S. Fritzsche, Central European J. Phys. 2 (2004) 720]. The decoupling of the interacting electrons is general, the obtained submatrix element holds all the peculiarities of the operator in question. These so-called submatrix elements are the key to do hyperfine structure calculations. The interaction between the electrons and the atomic nucleus leads to an additional splitting of the fine structure lines, the hyperfine structure. The leading components are the magnetic dipole interaction defining the so-called A factor and the electric quadrupole interaction, defining the so-called B factor. They express the energetic splitting of the spectral lines. Moreover, they are obtained directly by experiments and can be calculated theoretically in an ab initio approach. A semiempirical approach allows the fitting of the radial parts of the wavefunction to the experimentally obtained A and B factors. Method of solution: Extending the existing csf_LS() and asf_LS() to several open shells and implementing a data structure level_LS() for the fine structure level, the atomic environment is defined in MAPLE. It is used in
Computational algebraic geometry of epidemic models
NASA Astrophysics Data System (ADS)
Rodríguez Vega, Martín.
2014-06-01
Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.
Introducing Computer Algebra to School Teachers of Mathematics
ERIC Educational Resources Information Center
Man, Yiu-Kwong
2007-01-01
Since the last decade, the use of computer algebra systems at the Hong Kong school level is still very limited. Among various reasons behind, the lack of exposure of this kind of software to local school teachers should be taken into account. In this article, we describe how to introduce MAPLE in a BEd module of a local teacher-training programme.…
Hirdes, John P; Poss, Jeff W; Curtin-Telegdi, Nancy
2008-01-01
Background Home care plays a vital role in many health care systems, but there is evidence that appropriate targeting strategies must be used to allocate limited home care resources effectively. The aim of the present study was to develop and validate a methodology for prioritizing access to community and facility-based services for home care clients. Methods Canadian and international data based on the Resident Assessment Instrument – Home Care (RAI-HC) were analyzed to identify predictors for nursing home placement, caregiver distress and for being rated as requiring alternative placement to improve outlook. Results The Method for Assigning Priority Levels (MAPLe) algorithm was a strong predictor of all three outcomes in the derivation sample. The algorithm was validated with additional data from five other countries, three other provinces, and an Ontario sample obtained after the use of the RAI-HC was mandated. Conclusion The MAPLe algorithm provides a psychometrically sound decision-support tool that may be used to inform choices related to allocation of home care resources and prioritization of clients needing community or facility-based services. PMID:18366782
Differential/algebraic systems and matrix pencils
Gear, C.W.; Petzold, L.R.
1982-04-01
In this paper we study the numerical solution of the differential/algebraic systems F(t, y, y') = 0. Many of these systems can be solved conveniently and economically using a range of ODE methods. Others can be solved only by a small subset of ODE methods, and still others present insurmountable difficulty for all current ODE methods. We examine the first two groups of problems and indicate which methods we believe to be best for them. Then we explore the properties of the third group which cause the methods to fail. The important factor which determines the solvability of systems of linear problems is a quantity called the global nilpotency. This differs from the usual nilpotency for matrix pencils when the problem is time dependent, so that techniques based on matrix transformations are unlikely to be successful.
ERIC Educational Resources Information Center
Falcon, Raymond
2009-01-01
Teachers use action research in order to improve their teaching and student learning. This action research will analyze students' algebraic reasoning in finding values of variables in systems of equations pictorially and algebraically. This research will look at students solving linear systems of equations without knowing the algebraic algorithms.…
Integrable Hamiltonian systems on low-dimensional Lie algebras
Korotkevich, Aleksandr A
2009-12-31
For any real Lie algebra of dimension 3, 4 or 5 and any nilpotent algebra of dimension 6 an integrable Hamiltonian system with polynomial coefficients is found on its coalgebra. These systems are constructed using Sadetov's method for constructing complete commutative families of polynomials on a Lie coalgebra. Bibliography: 17 titles.
ERIC Educational Resources Information Center
Johnston, Basil
1978-01-01
Describing the Iroquoi's Maple Sugar Festival, this article details the symbolism of renewal, becoming, and regeneration celebrated by the Iroquoi as the sap from the maple trees begins to flow each year. The symbolic role of woman, the sweet sap itself, and man's fellow creatures are described. (JC)
Fock space, symbolic algebra, and analytical solutions for small stochastic systems
NASA Astrophysics Data System (ADS)
Santos, Fernando A. N.; Gadêlha, Hermes; Gaffney, Eamonn A.
2015-12-01
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.
Fock space, symbolic algebra, and analytical solutions for small stochastic systems.
Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A
2015-12-01
Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics. PMID:26764734
Redberry: a computer algebra system designed for tensor manipulation
NASA Astrophysics Data System (ADS)
Poslavsky, Stanislav; Bolotin, Dmitry
2015-05-01
In this paper we focus on the main aspects of computer-aided calculations with tensors and present a new computer algebra system Redberry which was specifically designed for algebraic tensor manipulation. We touch upon distinctive features of tensor software in comparison with pure scalar systems, discuss the main approaches used to handle tensorial expressions and present the comparison of Redberry performance with other relevant tools.
The algebraic criteria for the stability of control systems
NASA Technical Reports Server (NTRS)
Cremer, H.; Effertz, F. H.
1986-01-01
This paper critically examines the standard algebraic criteria for the stability of linear control systems and their proofs, reveals important previously unnoticed connections, and presents new representations. Algebraic stability criteria have also acquired significance for stability studies of non-linear differential equation systems by the Krylov-Bogoljubov-Magnus Method, and allow realization conditions to be determined for classes of broken rational functions as frequency characteristics of electrical network.
Revisiting Newtonian and Non-Newtonian Fluid Mechanics Using Computer Algebra
ERIC Educational Resources Information Center
Knight, D. G.
2006-01-01
This article illustrates how a computer algebra system, such as Maple[R], can assist in the study of theoretical fluid mechanics, for both Newtonian and non-Newtonian fluids. The continuity equation, the stress equations of motion, the Navier-Stokes equations, and various constitutive equations are treated, using a full, but straightforward,…
Code of Federal Regulations, 2012 CFR
2012-04-01
... § 168.140 Maple sirup. (a) Maple sirup is the liquid food derived by concentration and heat treatment of the sap of the maple tree (Acer) or by solution in water of maple sugar (mapel concrete) made...
Code of Federal Regulations, 2013 CFR
2013-04-01
... § 168.140 Maple sirup. (a) Maple sirup is the liquid food derived by concentration and heat treatment of the sap of the maple tree (Acer) or by solution in water of maple sugar (mapel concrete) made...
Code of Federal Regulations, 2011 CFR
2011-04-01
... § 168.140 Maple sirup. (a) Maple sirup is the liquid food derived by concentration and heat treatment of the sap of the maple tree (Acer) or by solution in water of maple sugar (mapel concrete) made...
Code of Federal Regulations, 2011 CFR
2011-01-01
... Yield Coverage Using Actual Production History § 1437.107 Maple sap. (a) NAP assistance for maple sap is... maple sap. (g) The actual production history for maple sap shall be recorded on the basis of gallons...
SD-CAS: Spin Dynamics by Computer Algebra System.
Filip, Xenia; Filip, Claudiu
2010-11-01
A computer algebra tool for describing the Liouville-space quantum evolution of nuclear 1/2-spins is introduced and implemented within a computational framework named Spin Dynamics by Computer Algebra System (SD-CAS). A distinctive feature compared with numerical and previous computer algebra approaches to solving spin dynamics problems results from the fact that no matrix representation for spin operators is used in SD-CAS, which determines a full symbolic character to the performed computations. Spin correlations are stored in SD-CAS as four-entry nested lists of which size increases linearly with the number of spins into the system and are easily mapped into analytical expressions in terms of spin operator products. For the so defined SD-CAS spin correlations a set of specialized functions and procedures is introduced that are essential for implementing basic spin algebra operations, such as the spin operator products, commutators, and scalar products. They provide results in an abstract algebraic form: specific procedures to quantitatively evaluate such symbolic expressions with respect to the involved spin interaction parameters and experimental conditions are also discussed. Although the main focus in the present work is on laying the foundation for spin dynamics symbolic computation in NMR based on a non-matrix formalism, practical aspects are also considered throughout the theoretical development process. In particular, specific SD-CAS routines have been implemented using the YACAS computer algebra package (http://yacas.sourceforge.net), and their functionality was demonstrated on a few illustrative examples. PMID:20843716
Description of DASSL: a differential/algebraic system solver
Petzold, L.R.
1982-09-01
This paper describes a new code DASSL, for the numerical solution of implicit systems of differential/algebraic equations. These equations are written in the form F(t,y,y') = 0, and they can include systems which are substantially more complex than standard form ODE systems y' = f(t,y). Differential/algebraic equations occur in several diverse applications in the physical world. We outline the algorithms and strategies used in DASSL, and explain some of the features of the code. In addition, we outline briefly what needs to be done to solve a problem using DASSL.
Entanglement in algebraic quantum mechanics: Majorana fermion systems
NASA Astrophysics Data System (ADS)
Benatti, F.; Floreanini, R.
2016-07-01
Many-body entanglement is studied within the algebraic approach to quantum physics in systems made of Majorana fermions. In this framework, the notion of separability stems from partitions of the algebra of observables and properties of the associated correlation functions, rather than on particle tensor products. This allows a complete characterization of non-separable Majorana fermion states to be obtained. These results may have direct application in quantum metrology: using Majorana systems, sub-shot-noise accuracy in parameter estimations can be achieved without preliminary resource-consuming, state entanglement operations.
Algebraic Systems Biology: A Case Study for the Wnt Pathway.
Gross, Elizabeth; Harrington, Heather A; Rosen, Zvi; Sturmfels, Bernd
2016-01-01
Steady-state analysis of dynamical systems for biological networks gives rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here, the variety is described by a polynomial system in 19 unknowns and 36 parameters. It has degree 9 over the parameter space. This case study explores multistationarity, model comparison, dynamics within regions of the state space, identifiability, and parameter estimation, from a geometric point of view. We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics. PMID:26645985
Motivating Constraints of a Pedagogy-Embedded Computer Algebra System
ERIC Educational Resources Information Center
Dana-Picard, Thierry
2007-01-01
The constraints of a computer algebra system (CAS) generally induce limitations on its usage. Via the pedagogical features implemented in such a system, "motivating constraints" can appear, encouraging advanced theoretical learning, providing a broader mathematical knowledge and more profound mathematical understanding. We discuss this issue,…
ERIC Educational Resources Information Center
Maguire, Molly; Gunton, Ric
2000-01-01
Maple Leaf Outdoor Centre (Ontario) has added year-round outdoor education facilities and programs to help support its summer camp for disadvantaged children. Schools, youth centers, religious groups, and athletic teams conduct their own programs, collaborate with staff, or use staff-developed programs emphasizing adventure education and personal…
Equivalent Colorings with "Maple"
ERIC Educational Resources Information Center
Cecil, David R.; Wang, Rongdong
2005-01-01
Many counting problems can be modeled as "colorings" and solved by considering symmetries and Polya's cycle index polynomial. This paper presents a "Maple 7" program link http://users.tamuk.edu/kfdrc00/ that, given Polya's cycle index polynomial, determines all possible associated colorings and their partitioning into equivalence classes. These…
Quadratic algebras for three-dimensional superintegrable systems
Daskaloyannis, C. Tanoudis, Y.
2010-02-15
The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.
Computer Algebra Systems and Theorems on Real Roots of Polynomials
ERIC Educational Resources Information Center
Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.
2010-01-01
A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)
Construction of coherent states for physical algebraic systems
Hassouni, Y.; Curado, E.M.F.; Rego-Monteiro, M.A.
2005-02-01
We construct a general state which is an eigenvector of the annihilation operator of the generalized Heisenberg algebra. We show, for several systems characterized by different energy spectra, that this general state satisfies the minimal set of conditions required to obtain Klauder's minimal coherent states.
Computer Algebra Systems: Permitted but Are They Used?
ERIC Educational Resources Information Center
Pierce, Robyn; Bardini, Caroline
2015-01-01
Since the 1990s, computer algebra systems (CAS) have been available in Australia as hand-held devices designed for students with the expectation that they will be used in the mathematics classroom. The data discussed in this paper was collected as part of a pilot study that investigated first year university mathematics and statistics students'…
Computer Algebra System Calculators: Gender Issues and Teachers' Expectations
ERIC Educational Resources Information Center
Forgasz, Helen J.; Griffith, Shirly
2006-01-01
In this paper we present findings from two studies focusing on computer algebra system (CAS) calculators. In Victoria, Australia, it is currently mandatory for students to use graphics calculators in some grade 12 mathematics examinations. Since 2001, a pilot study has been conducted involving Victorian Certificate of Education (VCE) students…
T-Systems Y-Systems and Cluster Algebras:. Tamely Laced Case
NASA Astrophysics Data System (ADS)
Nakanishi, Tomoki
2011-10-01
The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently they were generalized to quantum affinizations of quantum Kac-Moody algebras associated with a wide class of generalized Cartan matrices which we say tamely laced. Furthermore, in the simply laced case, and also in the nonsimply laced case of finite type, they were identified with relations arising from cluster algebras.In this note we generalize such an identification to any tamely laced Cartan matrices, especially to the nonsimply laced ones of nonfinite type.
Keyl, Michael; Schlingemann, Dirk-M.
2010-02-15
We present an approach to a noncommutativelike phase space which allows to analyze quasifree states on the algebra of canonical anti-commutation relations (CAR) in analogy to quasifree states on the algebra of canonical commutation relations (CCR). The used mathematical tools are based on a new algebraic structure the 'Grassmann algebra of canonical anticommutation relations' (GAR algebra) which is given by the twisted tensor product of a Grassmann and a CAR algebra. As a new application, the corresponding theory provides an elegant tool for calculating the fidelity of two quasifree fermionic states which is needed for the study of entanglement distillation within fermionic systems.
The Chemical Composition of Maple Syrup
ERIC Educational Resources Information Center
Ball, David W.
2007-01-01
Maple syrup is one of several high-sugar liquids that humans consume. However, maple syrup is more than just a concentrated sugar solution. Here, we review the chemical composition of maple syrup. (Contains 4 tables and 1 figure.)
Generalized Lotka—Volterra systems connected with simple Lie algebras
NASA Astrophysics Data System (ADS)
Charalambides, Stelios A.; Damianou, Pantelis A.; Evripidou, Charalambos A.
2015-06-01
We devise a new method for producing Hamiltonian systems by constructing the corresponding Lax pairs. This is achieved by considering a larger subset of the positive roots than the simple roots of the root system of a simple Lie algebra. We classify all subsets of the positive roots of the root system of type An for which the corresponding Hamiltonian systems are transformed, via a simple change of variables, to Lotka-Volterra systems. For some special cases of subsets of the positive roots of the root system of type An, we produce new integrable Hamiltonian systems.
Spatial operator algebra framework for multibody system dynamics
NASA Technical Reports Server (NTRS)
Rodriguez, G.; Jain, Abhinandan; Kreutz, K.
1989-01-01
The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.
ERIC Educational Resources Information Center
Farley, Rosemary Carroll
2013-01-01
At Manhattan College, secondary mathematics education students take a capstone course designed specifically for them. In this course, students revisit important topics in the high school curriculum from a mathematically advanced perspective; incorporating the mathematical knowledge they have attained in their college mathematics classes to an…
Using Math With Maple Sugaring.
ERIC Educational Resources Information Center
Christenson, Gary
1984-01-01
Suggest several math activities using the simple technique of tapping a sugar maple tree for sap. Information and activities presented are useful in tapping one or two trees on school property, helping students who tap trees at home, or leading a field trip to a nearby maple sugaring site. (ERB)
Using Mathematica and Maple To Obtain Chemical Equations.
ERIC Educational Resources Information Center
Missen, Ronald W.; Smith, William R.
1997-01-01
Shows how the computer software programs Mathematica and Maple can be used to obtain chemical equations to represent the stoichiometry of a reacting system. Specific examples are included. Contains 10 references. (DKM)
Using computer algebra and SMT solvers in algebraic biology
NASA Astrophysics Data System (ADS)
Pineda Osorio, Mateo
2014-05-01
Biologic processes are represented as Boolean networks, in a discrete time. The dynamics within these networks are approached with the help of SMT Solvers and the use of computer algebra. Software such as Maple and Z3 was used in this case. The number of stationary states for each network was calculated. The network studied here corresponds to the immune system under the effects of drastic mood changes. Mood is considered as a Boolean variable that affects the entire dynamics of the immune system, changing the Boolean satisfiability and the number of stationary states of the immune network. Results obtained show Z3's great potential as a SMT Solver. Some of these results were verified in Maple, even though it showed not to be as suitable for the problem approach. The solving code was constructed using Z3-Python and Z3-SMT-LiB. Results obtained are important in biology systems and are expected to help in the design of immune therapies. As a future line of research, more complex Boolean network representations of the immune system as well as the whole psychological apparatus are suggested.
Code of Federal Regulations, 2010 CFR
2010-01-01
... limited to maple sap produced on private property for sale as sap or syrup. Eligible maple sap must be... sap must be established for the value of the sap before processing into syrup. If price data is available only for maple syrup, this data must be converted to a maple sap basis. The wholesale price for...
The Maple Products: An Outdoor Education Unit.
ERIC Educational Resources Information Center
Yaple, Charles; And Others
Designed to take advantage of the spring season, this resource packet on maple products centers upon a field lesson in harvesting and making maple syrup. The resources in this packet include: a narrative on the origins of maple sugar; an illustrated description of "old time maple sugarin'"; suggestions for pre-trip activities (history of maple…
Code of Federal Regulations, 2013 CFR
2013-01-01
... limited to maple sap produced on private property for sale as sap or syrup. Eligible maple sap must be... sap must be established for the value of the sap before processing into syrup. If price data is available only for maple syrup, this data must be converted to a maple sap basis. The wholesale price for...
Code of Federal Regulations, 2014 CFR
2014-01-01
... limited to maple sap produced on private property for sale as sap or syrup. Eligible maple sap must be... sap must be established for the value of the sap before processing into syrup. If price data is available only for maple syrup, this data must be converted to a maple sap basis. The wholesale price for...
Code of Federal Regulations, 2012 CFR
2012-01-01
... limited to maple sap produced on private property for sale as sap or syrup. Eligible maple sap must be... sap must be established for the value of the sap before processing into syrup. If price data is available only for maple syrup, this data must be converted to a maple sap basis. The wholesale price for...
Phased-mission system analysis using Boolean algebraic methods
NASA Technical Reports Server (NTRS)
Somani, Arun K.; Trivedi, Kishor S.
1993-01-01
Most reliability analysis techniques and tools assume that a system is used for a mission consisting of a single phase. However, multiple phases are natural in many missions. The failure rates of components, system configuration, and success criteria may vary from phase to phase. In addition, the duration of a phase may be deterministic or random. Recently, several researchers have addressed the problem of reliability analysis of such systems using a variety of methods. A new technique for phased-mission system reliability analysis based on Boolean algebraic methods is described. Our technique is computationally efficient and is applicable to a large class of systems for which the failure criterion in each phase can be expressed as a fault tree (or an equivalent representation). Our technique avoids state space explosion that commonly plague Markov chain-based analysis. A phase algebra to account for the effects of variable configurations and success criteria from phase to phase was developed. Our technique yields exact (as opposed to approximate) results. The use of our technique was demonstrated by means of an example and present numerical results to show the effects of mission phases on the system reliability.
Astronomy Education using the Web and a Computer Algebra System
NASA Astrophysics Data System (ADS)
Flurchick, K. M.; Culver, Roger B.; Griego, Ben
2013-04-01
The combination of a web server and a Computer Algebra System to provide students the ability to explore and investigate astronomical concepts presented in a class can help student understanding. This combination of technologies provides a framework to extend the classroom experience with independent student exploration. In this presentation we report on the developmen of this web based material and some initial results of students making use of the computational tools using webMathematica^TM. The material developed allow the student toanalyze and investigate a variety of astronomical phenomena, including topics such as the Runge-Lenz vector, descriptions of the orbits of some of the exo-planets, Bode' law and other topics related to celestial mechanics. The server based Computer Algebra System system allows for computations without installing software on the student's computer but provides a powerful environment to explore the various concepts. The current system is installed at North Carolina A&T State University and has been used in several undergraduate classes.
Parametric Equations, Maple, and Tubeplots.
ERIC Educational Resources Information Center
Feicht, Louis
1997-01-01
Presents an activity that establishes a graphical foundation for parametric equations by using a graphing output form called tubeplots from the computer program Maple. Provides a comprehensive review and exploration of many previously learned topics. (ASK)
ODE methods for the solution of differential/algebraic systems
Gear, C.W.; Petzold, L.R.
1982-09-01
In this paper we study the numerical solution of the differential/algebraic systems F(t, y, y') = 0. Many of these systems can be solved conveniently and economically using a range of ODE methods. Others can be solved only by a small subset of ODE methods, and still others present insurmountable difficulty for all current ODE methods. We examine the first two groups of problems and indicate which methods we believe to be best for them. Then we explore the properties of the third group which cause the methods to fail. We describe a reduction technique which allows systems to be reduced to ones that can be solved. It also provides a tool for the analytical study of the structure of systems.
Abedi-Fardad, J.; Rezaei-Aghdam, A.; Haghighatdoost, Gh.
2014-05-15
We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R{sup 4} and R{sup 6}. Furthermore, we construct some integrable and superintegrable Hamiltonian systems for which the symmetry Lie group is also the phase space of the system.
Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper
NASA Technical Reports Server (NTRS)
Schumann, Johann; Koga, Dennis (Technical Monitor)
1999-01-01
In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).
Algebraic versus Exponential Decoherence in Dissipative Many-Particle Systems.
Cai, Zi; Barthel, Thomas
2013-10-11
The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-1/2 chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group. For the open XXZ model, we discover that the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. This is due to a vanishing gap in the spectrum of the corresponding Liouville superoperator and can be explained on the basis of a perturbative treatment. In contrast, decoherence in the open transverse-field Ising model is found to be always exponential. In this case, the internal interactions can both facilitate and impede the environment-induced decoherence. PMID:24160582
ERIC Educational Resources Information Center
Trisler, Carmen E.
1994-01-01
Uses models to illustrate the possible "migration route" of the sugar maple in response to predicted global climate change. Curriculum activities for students are provided that specifically address the sugar maple forests of the Great Lakes regions. (ZWH)
The Design of a System to Support Exploratory Learning of Algebraic Generalisation
ERIC Educational Resources Information Center
Noss, Richard; Poulovassilis, Alexandra; Geraniou, Eirini; Gutierrez-Santos, Sergio; Hoyles, Celia; Kahn, Ken; Magoulas, George D.; Mavrikis, Manolis
2012-01-01
This paper charts the design and application of a system to support 11-14 year old students' learning of algebraic generalisation, presenting students with the means to develop their understanding of the meaning of generality, see its power for mathematics and develop algebraic ways of thinking. We focus squarely on design, while taking account of…
The Effect of an Intelligent Tutoring System (ITS) on Student Achievement in Algebraic Expression
ERIC Educational Resources Information Center
Chien, Tsai Chen; Md. Yunus, Aida Suraya; Ali, Wan Zah Wan; Bakar, Ab. Rahim
2008-01-01
In this experimental study, use of Computer Assisted Instruction (CAI) followed by use of an Intelligent Tutoring System (CAI+ITS) was compared to the use of CAI (CAI only) in tutoring students on the topic of Algebraic Expression. Two groups of students participated in the study. One group of 32 students studied algebraic expression in a CAI…
Applications of computer algebra to distributed parameter systems
NASA Technical Reports Server (NTRS)
Storch, Joel A.
1993-01-01
In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 2 2010-04-01 2010-04-01 false Maple sirup. 168.140 Section 168.140 Food and... CONSUMPTION SWEETENERS AND TABLE SIRUPS Requirements for Specific Standardized Sweeteners and Table Sirups § 168.140 Maple sirup. (a) Maple sirup is the liquid food derived by concentration and heat treatment...
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 2 2014-04-01 2014-04-01 false Maple sirup. 168.140 Section 168.140 Food and... CONSUMPTION SWEETENERS AND TABLE SIRUPS Requirements for Specific Standardized Sweeteners and Table Sirups § 168.140 Maple sirup. (a) Maple sirup is the liquid food derived by concentration and heat treatment...
ERIC Educational Resources Information Center
Cavanagh, Sean
2009-01-01
As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…
Rosen’s (M,R) system in process algebra
2013-01-01
Background Robert Rosen’s Metabolism-Replacement, or (M,R), system can be represented as a compact network structure with a single source and three products derived from that source in three consecutive reactions. (M,R) has been claimed to be non-reducible to its components and algorithmically non-computable, in the sense of not being evaluable as a function by a Turing machine. If (M,R)-like structures are present in real biological networks, this suggests that many biological networks will be non-computable, with implications for those branches of systems biology that rely on in silico modelling for predictive purposes. Results We instantiate (M,R) using the process algebra Bio-PEPA, and discuss the extent to which our model represents a true realization of (M,R). We observe that under some starting conditions and parameter values, stable states can be achieved. Although formal demonstration of algorithmic computability remains elusive for (M,R), we discuss the extent to which our Bio-PEPA representation of (M,R) allows us to sidestep Rosen’s fundamental objections to computational systems biology. Conclusions We argue that the behaviour of (M,R) in Bio-PEPA shows life-like properties. PMID:24237684
Graphs and Enhancing Maple Multiplication.
ERIC Educational Resources Information Center
Cecil, David R.; Wang, Rongdong
2002-01-01
Description of a technique in Maple programming language that automatically prints all paths of any desired length along with the name of each vertex, proceeding in order from the beginning vertex to the ending vertex for a given graph. (Author/MM)
Ladder operators and associated algebra for position-dependent effective mass systems
NASA Astrophysics Data System (ADS)
Amir, Naila; Iqbal, Shahid
2015-07-01
An algebraic treatment of shape-invariant quantum-mechanical position-dependent effective mass systems is discussed. Using shape invariance, a general recipe for construction of ladder operators and associated algebraic structure of the pertaining system, is obtained. These operators are used to find exact solutions of general one-dimensional systems with spatially varying mass. We apply our formalism to specific translationally shape-invariant potentials having position-dependent effective mass.
Lectures on algebraic system theory: Linear systems over rings
NASA Technical Reports Server (NTRS)
Kamen, E. W.
1978-01-01
The presentation centers on four classes of systems that can be treated as linear systems over a ring. These are: (1) discrete-time systems over a ring of scalars such as the integers; (2) continuous-time systems containing time delays; (3) large-scale discrete-time systems; and (4) time-varying discrete-time systems.
Filteau, Marie; Lagacé, Luc; LaPointe, Gisèle; Roy, Denis
2011-08-01
During collection, maple sap is contaminated by bacteria and fungi that subsequently colonize the tubing system. The bacterial microbiota has been more characterized than the fungal microbiota, but the impact of both components on maple sap quality remains unclear. This study focused on identifying bacterial and fungal members of maple sap and correlating microbiota composition with maple sap properties. A multiplex automated ribosomal intergenic spacer analysis (MARISA) method was developed to presumptively identify bacterial and fungal members of maple sap samples collected from 19 production sites during the tapping period. Results indicate that the fungal community of maple sap is mainly composed of yeast related to Mrakia sp., Mrakiella sp., Guehomyces pullulans, Cryptococcus victoriae and Williopsis saturnus. Mrakia, Mrakiella and Guehomyces peaks were identified in samples of all production sites and can be considered dominant and stable members of the fungal microbiota of maple sap. A multivariate analysis based on MARISA profiles and maple sap chemical composition data showed correlations between Candida sake, Janthinobacterium lividum, Williopsis sp., Leuconostoc mesenteroides, Mrakia sp., Rhodococcus sp., Pseudomonas tolaasii, G. pullulans and maple sap composition at different flow periods. This study provides new insights on the relationship between microbial community and maple sap quality. PMID:21569942
Refined algebraic quantisation in a system with nonconstant gauge invariant structure functions
Martínez-Pascual, Eric
2013-08-15
In a previous work [J. Louko and E. Martínez-Pascual, “Constraint rescaling in refined algebraic quantisation: Momentum constraint,” J. Math. Phys. 52, 123504 (2011)], refined algebraic quantisation (RAQ) within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling one momentum-type constraint was investigated. In the present work, the first steps to generalise this analysis to cases where more constraints occur are developed. The system under consideration contains two momentum-type constraints, originally abelian, where rescalings of these constraints by a non-vanishing function of the coordinates are allowed. These rescalings induce structure functions at the level of the gauge algebra. Providing a specific parametrised family of real-valued scaling functions, the implementation of the corresponding rescaled quantum momentum-type constraints is performed using RAQ when the gauge algebra: (i) remains abelian and (ii) undergoes into an algebra of a nonunimodular group with nonconstant gauge invariant structure functions. Case (ii) becomes the first example known to the author where an open algebra is handled in refined algebraic quantisation. Challenging issues that arise in the presence of non-gauge invariant structure functions are also addressed.
Pseudorational Impulse Responses — Algebraic System Theory for Distributed Parameter Systems
NASA Astrophysics Data System (ADS)
Yamamoto, Yutaka
This paper gives a comprehensive account on a class of distributed parameter systems, whose impulse response is called pseudorational. This notion was introduced by the author in 1980's, and is particularly amenable for the study of systems with bounded-time memory. We emphasize algebraic structures induced by this class of systems. Some recent results on coprimeness issues and H∞ control are discussed and illustrated.
NASA Technical Reports Server (NTRS)
Byrnes, C. I.
1980-01-01
It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.
Spontaneous PT-Symmetry Breaking for Systems of Noncommutative Euclidean Lie Algebraic Type
NASA Astrophysics Data System (ADS)
Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah
2015-11-01
We propose a noncommutative version of the Euclidean Lie algebra E 2. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of the explicitly constructed Dyson maps as a criterium, we identify the domains in the parameter space in which the Hamiltonians have real energy spectra and determine the exceptional points signifying the crossover into the different types of spontaneously broken PT-symmetric regions with pairs of complex conjugate eigenvalues. We find exceptional points which remain invariant under the deformation as well as exceptional points becoming dependent on the deformation parameter of the algebra.
Algebraic aspects of Tremblay-Turbiner-Winternitz Hamiltonian systems
NASA Astrophysics Data System (ADS)
Calzada, J. A.; Celeghini, E.; del Olmo, M. A.; Velasco, M. A.
2012-02-01
Using the factorization method we find a hierarchy of Tremblay-Turbiner-Winternitz Hamiltonians labeled by discrete indices. The shift operators (those connecting eigenfunctions of different Hamiltonians of the hierarchy) as well the ladder operators (they connect eigenstates of a determined Hamiltonian) obtained in this way close different algebraic structures that are presented here.
Fernando, Denise R; Marshall, Alan T; Lynch, Jonathan P
2016-01-01
Sugar maple and red maple are closely-related co-occurring tree species significant to the North American forest biome. Plant abiotic stress effects including nutritional imbalance and manganese (Mn) toxicity are well documented within this system, and are implicated in enhanced susceptibility to biotic stresses such as insect attack. Both tree species are known to overaccumulate foliar manganese (Mn) when growing on unbuffered acidified soils, however, sugar maple is Mn-sensitive, while red maple is not. Currently there is no knowledge about the cellular sequestration of Mn and other nutrients in these two species. Here, electron-probe x-ray microanalysis was employed to examine cellular and sub-cellular deposition of excessively accumulated foliar Mn and other mineral nutrients in vivo. For both species, excess foliar Mn was deposited in symplastic cellular compartments. There were striking between-species differences in Mn, magnesium (Mg), sulphur (S) and calcium (Ca) distribution patterns. Unusually, Mn was highly co-localised with Mg in mesophyll cells of red maple only. The known sensitivity of sugar maple to excess Mn is likely linked to Mg deficiency in the leaf mesophyll. There was strong evidence that Mn toxicity in sugar maple is primarily a symplastic process. For each species, leaf-surface damage due to biotic stress including insect herbivory was compared between sites with acidified and non-acidified soils. Although it was greatest overall in red maple, there was no difference in biotic stress damage to red maple leaves between acidified and non-acidified soils. Sugar maple trees on buffered non-acidified soil were less damaged by biotic stress compared to those on unbuffered acidified soil, where they are also affected by Mn toxicity abiotic stress. This study concluded that foliar nutrient distribution in symplastic compartments is a determinant of Mn sensitivity, and that Mn stress hinders plant resistance to biotic stress. PMID:27391424
Fernando, Denise R.; Marshall, Alan T.; Lynch, Jonathan P.
2016-01-01
Sugar maple and red maple are closely-related co-occurring tree species significant to the North American forest biome. Plant abiotic stress effects including nutritional imbalance and manganese (Mn) toxicity are well documented within this system, and are implicated in enhanced susceptibility to biotic stresses such as insect attack. Both tree species are known to overaccumulate foliar manganese (Mn) when growing on unbuffered acidified soils, however, sugar maple is Mn-sensitive, while red maple is not. Currently there is no knowledge about the cellular sequestration of Mn and other nutrients in these two species. Here, electron-probe x-ray microanalysis was employed to examine cellular and sub-cellular deposition of excessively accumulated foliar Mn and other mineral nutrients in vivo. For both species, excess foliar Mn was deposited in symplastic cellular compartments. There were striking between-species differences in Mn, magnesium (Mg), sulphur (S) and calcium (Ca) distribution patterns. Unusually, Mn was highly co-localised with Mg in mesophyll cells of red maple only. The known sensitivity of sugar maple to excess Mn is likely linked to Mg deficiency in the leaf mesophyll. There was strong evidence that Mn toxicity in sugar maple is primarily a symplastic process. For each species, leaf-surface damage due to biotic stress including insect herbivory was compared between sites with acidified and non-acidified soils. Although it was greatest overall in red maple, there was no difference in biotic stress damage to red maple leaves between acidified and non-acidified soils. Sugar maple trees on buffered non-acidified soil were less damaged by biotic stress compared to those on unbuffered acidified soil, where they are also affected by Mn toxicity abiotic stress. This study concluded that foliar nutrient distribution in symplastic compartments is a determinant of Mn sensitivity, and that Mn stress hinders plant resistance to biotic stress. PMID:27391424
Titration Calculations with Computer Algebra Software
ERIC Educational Resources Information Center
Lachance, Russ; Biaglow, Andrew
2012-01-01
This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…
The Mathlet Toolkit: Creating Dynamic Applets for Differential Equations and Dynamical Systems
ERIC Educational Resources Information Center
Decker, Robert
2011-01-01
Dynamic/interactive graphing applets can be used to supplement standard computer algebra systems such as Maple, Mathematica, Derive, or TI calculators, in courses such as Calculus, Differential Equations, and Dynamical Systems. The addition of this type of software can lead to discovery learning, with students developing their own conjectures, and…
Solving stochastic epidemiological models using computer algebra
NASA Astrophysics Data System (ADS)
Hincapie, Doracelly; Ospina, Juan
2011-06-01
Mathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world.
Geary, David C; Hoard, Mary K; Nugent, Lara; Rouder, Jeffrey N
2015-12-01
The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 ninth graders (92 girls) while controlling for parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation but not to schema memory. Frequency of fact retrieval errors was related to schema memory but not to coordinate plane or expression evaluation accuracy. The results suggest that the ANS may contribute to or be influenced by spatial-numerical and numerical-only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest that different brain and cognitive systems are engaged during the learning of different components of algebraic competence while controlling for demographic and domain general abilities. PMID:26255604
Maple Sugar Harvesting/Wild Rice Harvesting.
ERIC Educational Resources Information Center
Minneapolis Public Schools, MN.
Comprised of two separate booklets, this resource unit assists elementary teachers in explaining how the Ojibwe people harvest maple sugar and wild rice. The first booklet explains the procedure of tapping the maple trees for sap, preparation for boiling the sap, and the three forms the sugar is made into (granulated, "molded," and "taffy"). The…
Computing the Moore-Penrose Inverse of a Matrix with a Computer Algebra System
ERIC Educational Resources Information Center
Schmidt, Karsten
2008-01-01
In this paper "Derive" functions are provided for the computation of the Moore-Penrose inverse of a matrix, as well as for solving systems of linear equations by means of the Moore-Penrose inverse. Making it possible to compute the Moore-Penrose inverse easily with one of the most commonly used Computer Algebra Systems--and to have the blueprint…
Mixing Microworld and CAS Features in Building Computer Systems that Help Students Learn Algebra
ERIC Educational Resources Information Center
Nicaud, Jean-Francois; Bouhineau, Denis; Chaachoua, Hamid
2004-01-01
We present the design principles for a new kind of computer system that helps students learn algebra. The fundamental idea is to have a system based on the microworld paradigm that allows students to make their own calculations, as they do with paper and pencil, without being obliged to use commands, and to verify the correctness of these…
ERIC Educational Resources Information Center
Matsumoto, Paul S.
2014-01-01
The article describes the use of Mathematica, a computer algebra system (CAS), in a high school chemistry course. Mathematica was used to generate a graph, where a slider controls the value of parameter(s) in the equation; thus, students can visualize the effect of the parameter(s) on the behavior of the system. Also, Mathematica can show the…
ERIC Educational Resources Information Center
Naval Education and Training Program Development Center, Pensacola, FL.
This textbook is one of a series of publications designed to provide information needed by Navy personnel whose duties require an elementary and general knowledge of the fundamental concepts of number systems, logic circuits, and Boolean algebra. Topic 1, Number Systems, describes the radix; the positional notation; the decimal, binary, octal, and…
Developing a TI-92 Manual Generator Based on Computer Algebra Systems
ERIC Educational Resources Information Center
Jun, Youngcook
2004-01-01
The electronic medium suitable for mathematics learning and teaching is often designed with a notebook interface provided in a computer algebra system. Such a notebook interface facilitates a workspace for mathematical activities along with an online help system. In this paper, the proposed feature is implemented in the Mathematica's notebook…
Filteau, Marie; Lagacé, Luc; Lapointe, Gisèle; Roy, Denis
2012-03-01
Maple sap processing and microbial contamination are significant aspects that affect maple syrup quality. In this study, two sample sets from 2005 and 2008 were used to assess the maple syrup quality variation and its relationship to microbial populations, with respect to processing, production site and harvesting period. The abundance of maple sap predominant bacteria (Pseudomonas fluorescens group and two subgroups, Rahnella spp., Janthinobacterium spp., Leuconostoc mesenteroides) and yeast (Mrakia spp., Mrakiella spp.,Guehomyces pullulans) was assessed by quantitative PCR. Maple syrup properties were analyzed by physicochemical and sensorial methods. Results indicate that P. fluorescens, Mrakia spp., Mrakiella spp. G. pullulans and Rahnella spp. are stable contaminants of maple sap, as they were found for every production site throughout the flow period. Multiple factor analysis reports a link between the relative abundance of P. fluorescens group and Mrakia spp. in maple sap with maple and vanilla odor as well as flavor of maple syrup. This evidence supports the contribution of these microorganisms or a consortium of predominant microbial contaminants to the characteristic properties of maple syrup. PMID:22236761
Maple procedures for the coupling of angular momenta. IX. Wigner D-functions and rotation matrices
NASA Astrophysics Data System (ADS)
Pagaran, J.; Fritzsche, S.; Gaigalas, G.
2006-04-01
expressions to be evaluated. Licensing provisions:None Computer for which the program is designed and others on which it is operable: All computers with a license for the computer algebra package Maple [Maple is a registered trademark of Waterloo Maple Inc.] Installations:University of Kassel (Germany) Operating systems under which the program has been tested: Linux 8.2+ Program language used:MAPLE, Release 8 and 9 Memory required to execute with typical data:10-50 MB No. of lines in distributed program, including test data, etc.:52 653 No. of bytes in distributed program, including test data, etc.:1 195 346 Distribution format:tar.gzip Nature of the physical problem: The Wigner D-functions and (reduced) rotation matrices occur very frequently in physical applications. They are known not only as the (infinite) representation of the rotation group but also to obey a number of integral and summation rules, including those for their orthogonality and completeness. Instead of the direct computation of these matrices, therefore, one first often wishes to find algebraic simplifications before the computations can be carried out in practice. Reasons for new version: The RACAH program has been found an efficient tool during recent years, in order to evaluate and simplify expressions from Racah's algebra. Apart from the Wigner n-j symbols ( j=3,6,9) and spherical harmonics, we now extended the code to allow for Wigner rotation matrices. This extension will support the study of those quantum processes especially where different axis of quantization occurs in course of the theoretical deviations. Summary of revisions: In a revised version of the RACAH program [S. Fritzsche, Comput. Phys. Comm. 103 (1997) 51; S. Fritzsche, T. Inghoff, M. Tomaselli, Comput. Phys. Comm. 153 (2003) 424], we now also support the occurrence of the Wigner D-functions and reduced rotation matrices. By following our previous design, the (algebraic) properties of these rotation matrices as well as a number of
PREFACE: Infinite Dimensional Algebras and their Applications to Quantum Integrable Systems
NASA Astrophysics Data System (ADS)
Fring, Andreas; Kulish, Petr P.; Manojlović, Nenad; Nagy, Zoltán; Nunes da Costa, Joana; Samtleben, Henning
2008-05-01
This special issue is centred around the workshop Infinite Dimensional Algebras and Quantum Integrable Systems II—IDAQUIS 2007, held at the University of Algarve, Faro, Portugal in July 2007. It was the second workshop in the IDAQUIS series following a previous meeting at the same location in 2003. The latest workshop gathered around forty experts in the field reviewing recent developments in the theory and applications of integrable systems in the form of invited lectures and in a number of contributions from the participants. All contributions contain significant new results or provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants are also included. The origins of the topic of this issue can be traced back a long way to the early investigations of completely integrable systems of classical mechanics in the fundamental papers by Euler, Lagrange, Jacobi, Liouville, Kowalevski and others. By the end of the nineteenth century all interesting examples seemed to have been exhausted. A revival in the study of integrable systems began with the development of the classical inverse scattering method, or the theory of solitons. Later developments led to the basic geometrical ideas of the theory, of which infinite dimensional algebras are a key ingredient. In a loose sense one may think that all integrable systems possess some hidden symmetry. In the quantum version of these systems the representation theory of these algebras may be exploited in the description of the structure of the Hilbert space of states. Modern examples of field theoretical systems such as conformal field theories, with the Liouville model being a prominent example, affine Toda field theories and the AdS/CFT correspondence are based on algebraic structures like quantum groups, modular doubles, global conformal invariance, Hecke algebras, Kac
Structural analysis and design of multivariable control systems: An algebraic approach
NASA Technical Reports Server (NTRS)
Tsay, Yih Tsong; Shieh, Leang-San; Barnett, Stephen
1988-01-01
The application of algebraic system theory to the design of controllers for multivariable (MV) systems is explored analytically using an approach based on state-space representations and matrix-fraction descriptions. Chapters are devoted to characteristic lambda matrices and canonical descriptions of MIMO systems; spectral analysis, divisors, and spectral factors of nonsingular lambda matrices; feedback control of MV systems; and structural decomposition theories and their application to MV control systems.
ERIC Educational Resources Information Center
Buteau, Chantal; Jarvis, Daniel H.; Lavicza, Zsolt
2014-01-01
In this article, we outline the findings of a Canadian survey study (N = 302) that focused on the extent of computer algebra systems (CAS)-based technology use in postsecondary mathematics instruction. Results suggest that a considerable number of Canadian mathematicians use CAS in research and teaching. CAS use in research was found to be the…
Teaching of Real Numbers by Using the Archimedes-Cantor Approach and Computer Algebra Systems
ERIC Educational Resources Information Center
Vorob'ev, Evgenii M.
2015-01-01
Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of…
ERIC Educational Resources Information Center
Meagher, Michael
2012-01-01
The research presented here is a group case study of students learning calculus in a Computer Algebra System (CAS) environment which examines the following research questions: What are students' perceptions of the role of technology in their learning? What is the students' relationship to CAS? What is the effect of learning in a CAS environment on…
ERIC Educational Resources Information Center
Tonisson, Eno
2015-01-01
Sometimes Computer Algebra Systems (CAS) offer an answer that is somewhat different from the answer that is probably expected by the student or teacher. These (somewhat unexpected) answers could serve as a catalyst for rich mathematical discussion. In this study, over 120 equations from school mathematics were solved using 8 different CAS. Many…
ERIC Educational Resources Information Center
Maat, Siti Mistima; Zakaria, Effandi
2011-01-01
Ordinary differential equations (ODEs) are one of the important topics in engineering mathematics that lead to the understanding of technical concepts among students. This study was conducted to explore the students' understanding of ODEs when they solve ODE questions using a traditional method as well as a computer algebraic system, particularly…
Flipping an Algebra Classroom: Analyzing, Modeling, and Solving Systems of Linear Equations
ERIC Educational Resources Information Center
Kirvan, Rebecca; Rakes, Christopher R.; Zamora, Regie
2015-01-01
The present study investigated whether flipping an algebra classroom led to a stronger focus on conceptual understanding and improved learning of systems of linear equations for 54 seventh- and eighth-grade students using teacher journal data and district-mandated unit exam items. Multivariate analysis of covariance was used to compare scores on…
Examining the Use of Computer Algebra Systems in University-Level Mathematics Teaching
ERIC Educational Resources Information Center
Lavicza, Zsolt
2009-01-01
The use of Computer Algebra Systems (CAS) is becoming increasingly important and widespread in mathematics research and teaching. In this paper, I will report on a questionnaire study enquiring about mathematicians' use of CAS in mathematics teaching in three countries; the United States, the United Kingdom, and Hungary. Based on the responses…
Introducing a Computer Algebra System in Mathematics Education--Empirical Evidence from Germany
ERIC Educational Resources Information Center
Schmidt, Karsten; Kohler, Anke; Moldenhauer, Wolfgang
2009-01-01
This paper reports on the effects the use of a pocket calculator-based computer algebra system (CAS) has on the performance in mathematics of grade 11 students in Germany. A project started at 8 of about one hundred upper secondary schools in the federal state of Thuringia in 1999; 3 years later the former restrictions on the use of technology in…
A Study of the Use of a Handheld Computer Algebra System in Discrete Mathematics
ERIC Educational Resources Information Center
Powers, Robert A.; Allison, Dean E.; Grassl, Richard M.
2005-01-01
This study investigated the impact of the TI-92 handheld Computer Algebra System (CAS) on student achievement in a discrete mathematics course. Specifically, the researchers examined the differences between a CAS section and a control section of discrete mathematics on students' in-class examinations. Additionally, they analysed student approaches…
Towards Student Instrumentation of Computer-Based Algebra Systems in University Courses
ERIC Educational Resources Information Center
Stewart, Sepideh; Thomas, Michael O. J.; Hannah, John
2005-01-01
There are many perceived benefits of using technology, such as computer algebra systems, in undergraduate mathematics courses. However, attaining these benefits sometimes proves elusive. Some of the key variables are the teaching approach and the student instrumentation of the technology. This paper considers the instrumentation of computer-based…
ERIC Educational Resources Information Center
Lavicza, Zsolt
2007-01-01
Computer Algebra Systems (CAS) are increasing components of university-level mathematics education. However, little is known about the extent of CAS use and the factors influencing its integration into university curricula. Pre-university level studies suggest that beyond the availability of technology, teachers' conceptions and cultural elements…
Realizations of Galilei algebras
NASA Astrophysics Data System (ADS)
Nesterenko, Maryna; Pošta, Severin; Vaneeva, Olena
2016-03-01
All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by Shirokov. The varieties of the deformed Galilei algebras are discussed and families of one-parametric deformations are presented in explicit form. It is also shown that a number of well-known and physically interesting equations and systems are invariant with respect to the considered Galilei algebras or their deformations.
Teaching Algebra without Algebra
ERIC Educational Resources Information Center
Kalman, Richard S.
2008-01-01
Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…
Family of N-dimensional superintegrable systems and quadratic algebra structures
NASA Astrophysics Data System (ADS)
Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong
2016-01-01
Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide applications in modern physics and connection to many domains in pure and applied mathematics. We overview two new families of superintegrable Kepler-Coulomb systems with non-central terms and superintegrable Hamiltonians with double singular oscillators of type (n, N — n) in N-dimensional Euclidean space. We present their quadratic and polynomial algebras involving Casimir operators of so(N + 1) Lie algebras that exhibit very interesting decompositions Q(3) ⊕ so(N — 1), Q(3) ⊕ so(n) ⊕ so(N — n) and the cubic Casimir operators. The realization of these algebras in terms of deformed oscillator enables the determination of a finite dimensional unitary representation. We present algebraic derivations of the degenerate energy spectra of these systems and relate them with the physical spectra obtained from the separation of variables.
ERIC Educational Resources Information Center
Smith, Authella; And Others
Documentation of the Coursewriter II Function FCALC is provided. The function is designed for use on the IBM 1500 instructional system and has three major applications: 1) comparison of a numeric expression in buffer 5 with a numeric expression in buffer 0; 2) comparison of an algebraic expression in buffer 5 with an algebraic expression in buffer…
Quantum integrable systems, non-skew-symmetric r-matrices and algebraic Bethe ansatz
Skrypnyk, T.
2007-02-15
We prove the integrability of the general quantum Hamiltonian systems governed by an arbitrary non-skew-symmetric, so(3)-valued, nondynamical classical r-matrix with spectral parameters. We consider the most interesting example of these quantum integrable systems, namely, the so(3) 'generalized Gaudin systems' in detail. In the case of an arbitrary r-matrix which is 'diagonal' in the sl(2) basis we calculate the spectrum and the eigenvalues of the corresponding Hamiltonians using the algebraic Bethe ansatz technique.
Benhammouda, Brahim
2016-01-01
Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems. PMID:27330880
Using computer algebra for Yang-Baxterization applied to quantum computing
NASA Astrophysics Data System (ADS)
Vélez, Mario; Ospina, Juan
2006-05-01
Using Computer Algebra Software (Mathematica and Maple), the recently introduced topic of Yang- Baxterization applied to quantum computing, is explored from the mathematical and computational views. Some algorithms of computer algebra were elaborated with the aim to make the calculations to obtain some of results that were originally presented in the paper by Shang-Kauffman-Ge. Also certain new results about computational Yang-baxterization are presented. We obtain some Hamiltonians for hypothetical physical systems which can be realized within the domain of spin chains and certain diffusion process. We conclude that it is possible to have real physical systems on which implement, via Yang-baxterization, the standard quantum gates with topological protection. Finally some lines for future research are deligned.
Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices
Kulish, P. P.; Manojlovic, N.; Nagy, Z.
2008-02-15
A reducible representation of the Temperley-Lieb algebra is constructed on the tensor product of n-dimensional spaces. One obtains as a centralizer of this action a quantum algebra (a quasitriangular Hopf algebra) U{sub q} with a representation ring equivalent to the representation ring of the sl{sub 2} Lie algebra. This algebra U{sub q} is the symmetry algebra of the corresponding open spin chain.
NASA Astrophysics Data System (ADS)
Idzikowski, A.; Salamon, S.
2013-06-01
A general characteristics of a car hydraulic braking system (CHBS) is presented in this publication. A graphical model of properties-component objects is developed for the above-mentioned system. Moreover, four mathematical models in terms of logic, the set theory and the Boolean algebra of Boolean functions are developed. The examination is ended with a general model of the CHBS for n - Boolean variables and the construction and mathematical-technical interpretation of this model is presented.
Computer algebra and transport theory.
Warsa, J. S.
2004-01-01
Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.
Mishra, Bud
2009-01-01
Systems biology, as a subject, has captured the imagination of both biologists and systems scientists alike. But what is it? This review provides one researcher's somewhat idiosyncratic view of the subject, but also aims to persuade young scientists to examine the possible evolution of this subject in a rich historical context. In particular, one may wish to read this review to envision a subject built out of a consilience of many interesting concepts from systems sciences, logic and model theory, and algebra, culminating in novel tools, techniques and theories that can reveal deep principles in biology—seen beyond mere observations. A particular focus in this review is on approaches embedded in an embryonic program, dubbed ‘algorithmic algebraic model checking’, and its powers and limitations. PMID:19364723
Paquette, Alain; Fontaine, Bastien; Berninger, Frank; Dubois, Karine; Lechowicz, Martin J; Messier, Christian; Posada, Juan M; Valladares, Fernando; Brisson, Jacques
2012-11-01
Norway maple (Acer platanoides L), which is among the most invasive tree species in forests of eastern North America, is associated with reduced regeneration of the related native species, sugar maple (Acer saccharum Marsh) and other native flora. To identify traits conferring an advantage to Norway maple, we grew both species through an entire growing season under simulated light regimes mimicking a closed forest understorey vs. a canopy disturbance (gap). Dynamic shade-houses providing a succession of high-intensity direct-light events between longer periods of low, diffuse light were used to simulate the light regimes. We assessed seedling height growth three times in the season, as well as stem diameter, maximum photosynthetic capacity, biomass allocation above- and below-ground, seasonal phenology and phenotypic plasticity. Given the north European provenance of Norway maple, we also investigated the possibility that its growth in North America might be increased by delayed fall senescence. We found that Norway maple had significantly greater photosynthetic capacity in both light regimes and grew larger in stem diameter than sugar maple. The differences in below- and above-ground biomass, stem diameter, height and maximum photosynthesis were especially important in the simulated gap where Norway maple continued extension growth during the late fall. In the gap regime sugar maple had a significantly higher root : shoot ratio that could confer an advantage in the deepest shade of closed understorey and under water stress or browsing pressure. Norway maple is especially invasive following canopy disturbance where the opposite (low root : shoot ratio) could confer a competitive advantage. Considering the effects of global change in extending the potential growing season, we anticipate that the invasiveness of Norway maple will increase in the future. PMID:23076822
Nonnumeric Computer Applications to Algebra, Trigonometry and Calculus.
ERIC Educational Resources Information Center
Stoutemyer, David R.
1983-01-01
Described are computer program packages requiring little or no knowledge of computer programing for college algebra, calculus, and abstract algebra. Widely available computer algebra systems are listed. (MNS)
ERIC Educational Resources Information Center
Pye, Cory C.; Mercer, Colin J.
2012-01-01
The symbolic algebra program Maple and the spreadsheet Microsoft Excel were used in an attempt to reproduce the Gaussian fits to a Slater-type orbital, required to construct the popular STO-NG basis sets. The successes and pitfalls encountered in such an approach are chronicled. (Contains 1 table and 3 figures.)
NASA Astrophysics Data System (ADS)
Graefe, Eva-Maria; Korsch, Hans Jürgen; Rush, Alexander
2016-04-01
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of m molecules of type A into n molecules of type B and vice versa. These Hamiltonians are analyzed in terms of generators of a polynomially deformed su(2) algebra. In the mean-field limit of large particle numbers, these systems become classical and their Hamiltonian dynamics can again be described by polynomial deformations of a Lie algebra, where quantum commutators are replaced by Poisson brackets. The Casimir operator restricts the motion to Kummer shapes, deformed Bloch spheres with cusp singularities depending on m and n . It is demonstrated that the many-particle eigenvalues can be recovered from the mean-field dynamics using a WKB-type quantization condition. The many-particle state densities can be semiclassically approximated by the time periods of periodic orbits, which show characteristic steps and singularities related to the fixed points, whose bifurcation properties are analyzed.
Max-plus Algebraic Tools for Discrete Event Systems, Static Analysis, and Zero-Sum Games
NASA Astrophysics Data System (ADS)
Gaubert, Stéphane
The max-plus algebraic approach of timed discrete event systems emerged in the eighties, after the discovery that synchronization phenomena can be modeled in a linear way in the max-plus setting. This led to a number of results, like the determination of long term characteristics (throughput, stationary regime) by spectral theory methods or the representation of the input-output behavior by rational series.
Environmental setting of Maple Creek watershed, Nebraska
Fredrick, Brian S.; Linard, Joshua I.; Carpenter, Jennifer L.
2006-01-01
The Maple Creek watershed covers a 955-square-kilometer area in eastern Nebraska, which is a region dominated by agricultural land use. The Maple Creek watershed is one of seven areas currently included in a nationwide study of the sources, transport, and fate of water and chemicals in agricultural watersheds. This study, known as the topical study of 'Agricultural Chemicals: Sources, Transport, and Fate' is part of the National Water-Quality Assessment Program being conducted by the U.S. Geological Survey. The Program is designed to describe water-quality conditions and trends based on representative surface- and ground-water resources across the Nation. The objective of the Agricultural Chemicals topical study is to investigate the sources, transport, and fate of selected agricultural chemicals in a variety of agriculturally diverse environmental settings. The Maple Creek watershed was selected for the Agricultural Chemicals topical study because its watershed represents the agricultural setting that characterizes eastern Nebraska. This report describes the environmental setting of the Maple Creek watershed in the context of how agricultural practices, including agricultural chemical applications and irrigation methods, interface with natural settings and hydrologic processes. A description of the environmental setting of a subwatershed within the drainage area of Maple Creek is included to improve the understanding of the variability of hydrologic and chemical cycles at two different scales.
ERIC Educational Resources Information Center
Abdullah, Lazim M.
2007-01-01
Computer algebra systems (CASs) have been used by thousands of teachers and students for teaching and learning algebra. They have the ability to perform efficiently almost all of the algebraic expansions and simplifications. Nevertheless, the traditional approach of using paper and pencil in acquiring procedural knowledge is still widely…
Biosensor Applications of MAPLE Deposited Lipase
Califano, Valeria; Bloisi, Francesco; Aronne, Antonio; Federici, Stefania; Nasti, Libera; Depero, Laura E.; Vicari, Luciano R. M.
2014-01-01
Matrix Assisted Pulsed Laser Evaporation (MAPLE) is a thin film deposition technique derived from Pulsed Laser Deposition (PLD) for deposition of delicate (polymers, complex biological molecules, etc.) materials in undamaged form. The main difference of MAPLE technique with respect to PLD is the target: it is a frozen solution or suspension of the (guest) molecules to be deposited in a volatile substance (matrix). Since laser beam energy is mainly absorbed by the matrix, damages to the delicate guest molecules are avoided, or at least reduced. Lipase, an enzyme catalyzing reactions borne by triglycerides, has been used in biosensors for detection of β-hydroxyacid esters and triglycerides in blood serum. Enzymes immobilization on a substrate is therefore required. In this paper we show that it is possible, using MAPLE technique, to deposit lipase on a substrate, as shown by AFM observation, preserving its conformational structure, as shown by FTIR analysis. PMID:25587426
Calculus of One and More Variables with Maple
ERIC Educational Resources Information Center
Samkova, Libuse
2012-01-01
This is a guide to using Maple in teaching fundamental calculus of one, two and three variables (limits, derivatives, integrals, etc.), also suitable for Maple beginners. It outlines one of the ways to effective use of computers in the teaching process. It scans advantages and disadvantages of using Maple in relation to students and teacher. The…
Tapping the Sugar Maple--Learning and Appreciating
ERIC Educational Resources Information Center
Malone, Charles
1976-01-01
The article discusses how to tap a maple tree. Tapping a maple tree to produce maple syrup can: (1) lead to better understanding in many subject areas, (2) develop skills through participation in a rewarding activity, and (3) help students appreciate the many important roles that trees play in our environment and daily lives. (NQ)
Variable coefficient Davey-Stewartson system with a Kac-Moody-Virasoro symmetry algebra
NASA Astrophysics Data System (ADS)
Güngör, F.; Özemir, C.
2016-06-01
We study the symmetry group properties of the variable coefficient Davey-Stewartson (vcDS) system. The Lie point symmetry algebra with a Kac-Moody-Virasoro (KMV) structure is shown to be isomorphic to that of the usual (constant coefficient) DS system if and only if the coefficients satisfy some conditions. These conditions turn out to coincide with those for the vcDS system to be transformable to the DS system by a point transformation. The equivalence group of the vcDS system is applied to pick out the integrable subsystems from a class of non-integrable ones. Additionally, the full symmetry group of the DS system is derived explicitly without exponentiating its symmetry algebra. Lump solutions (rationally localized in all directions in ℝ2) introduced by Ozawa for the DS system are shown to hold even for the vcDS system precisely when the system belongs to the integrable class, i.e., equivalent to the DS system. These solutions can be used for establishing exact blow-up solutions in finite time in the space L2(ℝ2) in the focusing case.
NASA Astrophysics Data System (ADS)
Marquette, Ian
2015-04-01
Four new families of two-dimensional quantum superintegrable systems are constructed from k-step extension of the harmonic oscillator and the radial oscillator. Their wavefunctions are related with Hermite and Laguerre exceptional orthogonal polynomials (EOP) of type III. We show that ladder operators obtained from alternative construction based on combinations of supercharges in the Krein-Adler and Darboux Crum (or state deleting and creating) approaches can be used to generate a set of integrals of motion and a corresponding polynomial algebra that provides an algebraic derivation of the full spectrum and total number of degeneracies. Such derivation is based on finite dimensional unitary representations (unirreps) and doesn't work for integrals build from standard ladder operators in supersymmetric quantum mechanics (SUSYQM) as they contain singlets isolated from excited states. In this paper, we also rely on a novel approach to obtain the finite dimensional unirreps based on the action of the integrals of motion on the wavefunctions given in terms of these EOP. We compare the results with those obtained from the Daskaloyannis approach and the realizations in terms of deformed oscillator algebras for one of the new families in the case of 1-step extension. This communication is a review of recent works.
Marquette, Ian; Quesne, Christiane
2015-06-15
We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformed oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.
NASA Astrophysics Data System (ADS)
Marquette, Ian; Quesne, Christiane
2015-06-01
We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformed oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.
NASA Astrophysics Data System (ADS)
Konopelchenko, B. G.; Ortenzi, G.
2011-11-01
The local properties of the families of algebraic subsets Wg in the Birkhoff strata Σ2g of Gr(2) containing the hyperelliptic curves of genus g are studied. It is shown that the tangent spaces Tg for Wg are isomorphic to the linear spaces of 2-coboundaries. Particular subsets in Wg are described by the integrable dispersionless coupled KdV systems of hydrodynamical type defining a special class of 2-cocycles and 2-coboundaries in Tg. It is demonstrated that the blows-ups of such 2-cocycles and 2-coboundaries and gradient catastrophes for associated integrable systems are interrelated.
Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems
NASA Technical Reports Server (NTRS)
Downie, John D.; Goodman, Joseph W.
1989-01-01
The accuracy requirements of optical processors in adaptive optics systems are determined by estimating the required accuracy in a general optical linear algebra processor (OLAP) that results in a smaller average residual aberration than that achieved with a conventional electronic digital processor with some specific computation speed. Special attention is given to an error analysis of a general OLAP with regard to the residual aberration that is created in an adaptive mirror system by the inaccuracies of the processor, and to the effect of computational speed of an electronic processor on the correction. Results are presented on the ability of an OLAP to compete with a digital processor in various situations.
Omar, Mohamed A
2014-01-01
Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations. PMID:25045732
Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator
Omar, Mohamed A.
2014-01-01
Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations. PMID:25045732
NASA Astrophysics Data System (ADS)
Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.
2012-10-01
We present a set of software routines in Maple 14 for solving first order ordinary differential equations (FOODEs). The package implements the Prelle-Singer method in its original form together with its extension to include integrating factors in terms of elementary functions. The package also presents a theoretical extension to deal with all FOODEs presenting Liouvillian solutions. Applications to ODEs taken from standard references show that it solves ODEs which remain unsolved using Maple's standard ODE solution routines. New version program summary Program title: PSsolver Catalogue identifier: ADPR_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADPR_v2_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.: 2302 No. of bytes in distributed program, including test data, etc.: 31962 Distribution format: tar.gz Programming language: Maple 14 (also tested using Maple 15 and 16). Computer: Intel Pentium Processor P6000, 1.86 GHz. Operating system: Windows 7. RAM: 4 GB DDR3 Memory Classification: 4.3. Catalogue identifier of previous version: ADPR_v1_0 Journal reference of previous version: Comput. Phys. Comm. 144 (2002) 46 Does the new version supersede the previous version?: Yes Nature of problem: Symbolic solution of first order differential equations via the Prelle-Singer method. Solution method: The method of solution is based on the standard Prelle-Singer method, with extensions for the cases when the FOODE contains elementary functions. Additionally, an extension of our own which solves FOODEs with Liouvillian solutions is included. Reasons for new version: The program was not running anymore due to changes in the latest versions of Maple. Additionally, we corrected/changed some bugs/details that were hampering the smoother functioning of the routines. Summary
NASA Astrophysics Data System (ADS)
Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.
2012-10-01
We present a set of software routines in Maple 14 for solving first order ordinary differential equations (FOODEs). The package implements the Prelle-Singer method in its original form together with its extension to include integrating factors in terms of elementary functions. The package also presents a theoretical extension to deal with all FOODEs presenting Liouvillian solutions. Applications to ODEs taken from standard references show that it solves ODEs which remain unsolved using Maple's standard ODE solution routines. New version program summary Program title: PSsolver Catalogue identifier: ADPR_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADPR_v2_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.: 2302 No. of bytes in distributed program, including test data, etc.: 31962 Distribution format: tar.gz Programming language: Maple 14 (also tested using Maple 15 and 16). Computer: Intel Pentium Processor P6000, 1.86 GHz. Operating system: Windows 7. RAM: 4 GB DDR3 Memory Classification: 4.3. Catalogue identifier of previous version: ADPR_v1_0 Journal reference of previous version: Comput. Phys. Comm. 144 (2002) 46 Does the new version supersede the previous version?: Yes Nature of problem: Symbolic solution of first order differential equations via the Prelle-Singer method. Solution method: The method of solution is based on the standard Prelle-Singer method, with extensions for the cases when the FOODE contains elementary functions. Additionally, an extension of our own which solves FOODEs with Liouvillian solutions is included. Reasons for new version: The program was not running anymore due to changes in the latest versions of Maple. Additionally, we corrected/changed some bugs/details that were hampering the smoother functioning of the routines. Summary
Using geometric algebra to understand pattern rotations in multiple mirror optical systems
Hanlon, J.; Ziock, H.
1997-05-01
Geometric Algebra (GA) is a new formulation of Clifford Algebra that includes vector analysis without notation changes. Most applications of Ga have been in theoretical physics, but GA is also a very good analysis tool for engineering. As an example, the authors use GA to study pattern rotation in optical systems with multiple mirror reflections. The common ways to analyze pattern rotations are to use rotation matrices or optical ray trace codes, but these are often inconvenient. The authors use GA to develop a simple expression for pattern rotation that is useful for designing or tolerancing pattern rotations in a multiple mirror optical system by inspection. Pattern rotation is used in many optical engineering systems, but it is not normally covered in optical system engineering texts. Pattern rotation is important in optical systems such as: (1) the 192 beam National ignition Facility (NIF), which uses square laser beams in close packed arrays to cut costs; (2) visual optical systems, which use pattern rotation to present the image to the observer in the appropriate orientation, and (3) the UR90 unstable ring resonator, which uses pattern rotation to fill a rectangular laser gain region and provide a filled-in laser output beam.
Engineering Mathematics Assessment Using "MapleTA"
ERIC Educational Resources Information Center
Jones, Ian S.
2008-01-01
The assessment of degree level engineering mathematics students using the computer-aided assessment package MapleTA is discussed. Experience of academic and practical issues for both online coursework and examination assessments is presented, hopefully benefiting other academics in this novel area of activity. (Contains 6 figures and 1 table.)
Ophthalmoplegia in Maple Syrup Urine Disease
ERIC Educational Resources Information Center
Zee, David S.; And Others
1974-01-01
Reported is the case of a female infant whose early symptom of ophthalmoplegia (paralysis of one or more motor nerves in the eye) led to eventual diagnosis and treatment for maple syrup urine disease, a condition in which early dietary restrictions can prevent severe mental retardation and neurologic disability. (DB)
MAPLE activities and applications in gas sensors
NASA Astrophysics Data System (ADS)
Jelínek, Miroslav; Remsa, Jan; Kocourek, Tomáš; Kubešová, Barbara; Schůrek, Jakub; Myslík, Vladimír
2011-11-01
During the last decade, many groups have grown thin films of various organic materials by the cryogenic Matrix Assisted Pulsed Laser Evaporation (MAPLE) technique with a wide range of applications. This contribution is focused on the summary of our results with deposition and characterization of thin films of fibrinogen, pullulan derivates, azo-polyurethane, cryoglobulin, polyvinyl alcohol, and bovine serum albumin dissolved in physiological serum, dimethyl sulfoxide, sanguine plasma, phosphate buffer solution, H2O, ethylene glycol, and tert-butanol. MAPLE films were characterized using FTIR, AFM, Raman scattering, and SEM. For deposition, a special hardware was developed including a unique liquid nitrogen cooled target holder. Overview of MAPLE thin film applications is given. We studied SnAcAc, InAcAc, SnO2, porphyrins, and polypyrrole MAPLE fabricated films as small resistive gas sensors. Sensors were tested with ozone, nitrogen dioxide, hydrogen, and water vapor gases. In the last years, our focus was on the study of fibrinogen-based scaffolds for application in tissue engineering, wound healing, and also as a part of layers for medical devices.
The development of an algebraic multigrid algorithm for symmetric positive definite linear systems
Vanek, P.; Mandel, J.; Brezina, M.
1996-12-31
An algebraic multigrid algorithm for symmetric, positive definite linear systems is developed based on the concept of prolongation by smoothed aggregation. Coarse levels are generated automatically. We present a set of requirements motivated heuristically by a convergence theory. The algorithm then attempts to satisfy the requirements. Input to the method are the coefficient matrix and zero energy modes, which are determined from nodal coordinates and knowledge of the differential equation. Efficiency of the resulting algorithm is demonstrated by computational results on real world problems from solid elasticity, plate blending, and shells.
Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra
Dey, Sanjib Fring, Andreas Mathanaranjan, Thilagarajah
2014-07-15
We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean–Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schrödinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy spectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices. -- Highlights: •Different PT-symmetries lead to qualitatively different systems. •Construction of non-perturbative Dyson maps and isospectral Hermitian counterparts. •Numerical discussion of the eigenvalue spectra for one of the E(2)-systems. •Established link to systems studied in the context of optical lattices. •Setup for the E(3)-algebra is provided.
Assessing Elementary Algebra with STACK
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2007-01-01
This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…
MAMA: an algebraic map for the secular dynamics of planetesimals in tight binary systems
NASA Astrophysics Data System (ADS)
Leiva, A. M.; Correa-Otto, J. A.; Beaugé, C.
2013-12-01
We present an algebraic map (MAMA) for the dynamical and collisional evolution of a planetesimal swarm orbiting the main star of a tight binary system. The orbital evolution of each planetesimal is dictated by the secular perturbations of the secondary star and gas drag due to interactions with a protoplanetary disc. The gas disc is assumed eccentric with a constant precession rate. Gravitational interactions between the planetesimals are ignored. All bodies are assumed coplanar. A comparison with full N-body simulations shows that the map is of the order of 102 times faster, while preserving all the main characteristics of the full system. In a second part of the work, we apply multiparticle algebraic map for accretion (MAMA) to the γ-Cephei, searching for friendly scenarios that may explain the formation of the giant planet detected in this system. For low-mass protoplanetary discs, we find that a low-eccentricity static disc aligned with the binary yields impact velocities between planetesimals below the disruption threshold. All other scenarios appear hostile to planetary formation.
ERIC Educational Resources Information Center
Levy, Alissa Beth
2012-01-01
The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…
Algebraic solutions of shape-invariant position-dependent effective mass systems
NASA Astrophysics Data System (ADS)
Amir, Naila; Iqbal, Shahid
2016-06-01
Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with position-dependent effective mass is discussed. We quantize the Hamiltonian of the pertaining system by using symmetric ordering of the operators concerning momentum and the spatially varying mass, initially proposed by von Roos and Lévy-Leblond. The algebraic method, used to obtain the solutions, is based on the concepts of supersymmetric quantum mechanics and shape invariance. In order to exemplify the general formalism a class of non-linear oscillators has been considered. This class includes the particular example of a one-dimensional oscillator with different position-dependent effective mass profiles. Explicit expressions for the eigenenergies and eigenfunctions in terms of generalized Hermite polynomials are presented. Moreover, properties of these modified Hermite polynomials, like existence of generating function and recurrence relations among the polynomials have also been studied. Furthermore, it has been shown that in the harmonic limit, all the results for the linear harmonic oscillator are recovered.
NASA Astrophysics Data System (ADS)
Putnam, Ian F.
2010-03-01
We investigate the C*-algebras associated to aperiodic structures called model sets obtained by the cut-and-project method. These C*-algebras are Morita equivalent to crossed product C*-algebras obtained from dynamics on a disconnected version of the internal space. This construction may be made from more general data, which we call a hyperplane system. From a hyperplane system, others may be constructed by a process of reduction and we show how the C*-algebras involved are related to each other. In particular, there are natural elements in the Kasparov KK-groups for the C*-algebra of a hyperplane system and that of its reduction. The induced map on K-theory fits in a six-term exact sequence. This provides a new method of the computation of the K-theory of such C*-algebras which is done completely in the setting of non-commutative geometry.
Family with intermittent maple syrup urine disease
Valman, H. B.; Patrick, A. D.; Seakins, J. W. T.; Platt, J. W.; Gompertz, D.
1973-01-01
A family is described in which the 3 children presented with episodes of severe metabolic acidosis secondary to minor infections. 2 of them died, and 1 of these was severely retarded. The sole surviving child is 6 years old and is normal with respect to physical and mental development. Gas chromatography of the urine obtained during episodes of ketoacidosis showed the keto and hydroxy acids characteristic of maple syrup urine disease, and thin layer chromatography of the plasma and urine showed greatly increased concentrations of the branched chain amino acids. The urine and plasma of the surviving child was chromatographically normal between episodes. The leucocyte branched chain keto acid decarboxylase activity in this patient and her father was reduced. The range of features in this family with intermittent maple syrup urine disease illustrates the necessity for prompt and careful investigation of metabolic acidosis of unknown aetiology. PMID:4693464
Teaching of real numbers by using the Archimedes-Cantor approach and computer algebra systems
NASA Astrophysics Data System (ADS)
Vorob'ev, Evgenii M.
2015-11-01
Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of CAS. In the case of real numbers, the Archimedes-Cantor approach satisfies this requirement. The name of Archimedes brings back the exhaustion method. Cantor's name reminds us of the use of Cauchy rational sequences to represent real numbers. The usage of CAS with the Archimedes-Cantor approach enables the discussion of various representations of real numbers such as graphical, decimal, approximate decimal with precision estimates, and representation as points on a straight line. Exercises with numbers such as e, π, the golden ratio ϕ, and algebraic irrational numbers can help students better understand the real numbers. The Archimedes-Cantor approach also reveals a deep and close relationship between real numbers and continuity, in particular the continuity of functions.
New developments in the numerical solution of differential/algebraic systems
Petzold, L.R.
1987-04-01
In this paper we survey some recent developments in the numerical solution of nonlinear differential/algebraic equation (DAE) systems of the form 0 = F(t,y,y'), where the initial values of y are known and par. deltaF/par. deltay' may be singular. These systems arise in the simulation of electrical networks, as well as in many other applications. DAE systems include standard form ODEs as a special case, but they also include problems which are in many ways quite different from ODEs. We examine the classification of DAE systems according to the degree of singularity of the system, and present some results on the analytical structure of these systems. We give convergence results for backward differentiation formulas applied to DAEs and examine some of the software issues involved in the numerical solution of DAEs. One-step methods are potentially advantageous for solving DAE systems with frequent discontinuities. However, recent results indicate that there is a reduction in the order of accuracy of many implicit Runge-Kutta methods even for simple DAE systems. We examine the current state of solving DAE systems by implicit Runge-Kutta methods. Finding a consistent set of initial conditions is often a problem for DAEs arising in applications. We explore some numerical methods for obtaining a consistent set of initial conditions. 21 refs.
ERIC Educational Resources Information Center
Gonzalez-Vega, Laureano
1999-01-01
Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)
ERIC Educational Resources Information Center
Marshall, Neil; Buteau, Chantal; Jarvis, Daniel H.; Lavicza, Zsolt
2012-01-01
We present a comparative study of a literature review of 326 selected contributions (Buteau, Marshall, Jarvis & Lavicza, 2010) to an international (US, UK, Hungary) survey of mathematicians (Lavicza, 2008) regarding the use of Computer Algebra Systems (CAS) in post-secondary mathematics education. The comparison results are organized with respect…
ERIC Educational Resources Information Center
Tonisson, Eno; Lepp, Marina
2015-01-01
The answers offered by computer algebra systems (CAS) can sometimes differ from those expected by the students or teachers. The comparison of the students' answers and CAS answers could provide ground for discussion about equivalence and correctness. Investigating the students' comparison of the answers gives the possibility to study different…
Phase noise in oscillators as differential-algebraic systems with colored noise sources
NASA Astrophysics Data System (ADS)
Demir, Alper
2004-05-01
Oscillators are key components of many kinds of systems, particularly electronic and opto-electronic systems. Undesired perturbations, i.e. noise, in practical systems adversely affect the spectral and timing properties of the signals generated by oscillators resulting in phase noise and timing jitter, which are key performance limiting factors, being major contributors to bit-error-rate (BER) of RF and possibly optical communication systems, and creating synchronization problems in clocked and sampled-data electronic systems. In this paper, we review our work on the theory and numerical methods for nonlinear perturbation and noise analysis of oscillators described by a system of differential-algebraic equations (DAEs) with white and colored noise sources. The bulk of the work reviewed in this paper first appeared in [1], then in [2] and [3]. Prior to the work mentioned above, we developed a theory and numerical methods for nonlinear perturbation and noise analysis of oscillators described by a system of ordinary differential equations (ODEs) with white noise sources only [4, 5]. In this paper, we also discuss some open problems and issues in the modeling and analysis of phase noise both in free running oscillators and in phase/injection-locked ones.
Marquette, Ian
2013-07-15
We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.
Aprepro - Algebraic Preprocessor
2005-08-01
Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.
Monitoring the Health of Sugar Maple, "Acer Saccharum"
ERIC Educational Resources Information Center
Carlson, Martha
2013-01-01
The sugar maple, "Acer saccharum," is projected to decline and die in 88 to 100 percent of its current range in the United States. An iconic symbol of the northeastern temperate forest and a dominant species in this forest, the sugar maple is identified as the most sensitive tree in its ecosystem to rising temperatures and a warming…
Algebraic integrability: a survey.
Vanhaecke, Pol
2008-03-28
We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863
Acceleration of multiple solution of a boundary value problem involving a linear algebraic system
NASA Astrophysics Data System (ADS)
Gazizov, Talgat R.; Kuksenko, Sergey P.; Surovtsev, Roman S.
2016-06-01
Multiple solution of a boundary value problem that involves a linear algebraic system is considered. New approach to acceleration of the solution is proposed. The approach uses the structure of the linear system matrix. Particularly, location of entries in the right columns and low rows of the matrix, which undergo variation due to the computing in the range of parameters, is used to apply block LU decomposition. Application of the approach is considered on the example of multiple computing of the capacitance matrix by method of moments used in numerical electromagnetics. Expressions for analytic estimation of the acceleration are presented. Results of the numerical experiments for solution of 100 linear systems with matrix orders of 1000, 2000, 3000 and different relations of variated and constant entries of the matrix show that block LU decomposition can be effective for multiple solution of linear systems. The speed up compared to pointwise LU factorization increases (up to 15) for larger number and order of considered systems with lower number of variated entries.
ERIC Educational Resources Information Center
Schaufele, Christopher; Zumoff, Nancy
Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…
Virasoro algebra in the KN algebra; Bosonic string with fermionic ghosts on Riemann surfaces
Koibuchi, H. )
1991-10-10
In this paper the bosonic string model with fermionic ghosts is considered in the framework of the KN algebra. The authors' attentions are paid to representations of KN algebra and a Clifford algebra of the ghosts. The authors show that a Virasoro-like algebra is obtained from KN algebra when KN algebra has certain antilinear anti-involution, and that it is isomorphic to the usual Virasoro algebra. The authors show that there is an expected relation between a central charge of this Virasoro-like algebra and an anomaly of the combined system.
NASA Astrophysics Data System (ADS)
Lisitsyn, Ya. V.; Shapovalov, A. V.
1998-05-01
A study is made of the possibility of reducing quantum analogs of Hamiltonian systems to Lie algebras. The procedure of reducing classical systems to orbits in a coadjoint representation based on Lie algebra is well-known. An analog of this procedure for quantum systems described by linear differential equations (LDEs) in partial derivatives is proposed here on the basis of the method of noncommutative integration of LDEs. As an example illustrating the procedure, an examination is made of nontrivial systems that cannot be integrated by separation of variables: the Gryachev-Chaplygin hydrostat and the Kovalevskii gyroscope. In both cases, the problem is reduced to a system with a smaller number of variables.
Prado, Julia; Quesada, Carlos; Gosney, Michael; Mickelbart, Michael V; Sadof, Clifford
2015-06-01
Although leaf nitrogen (N) has been shown to increase the suitability of hosts to herbivorous arthropods, the responses of these pests to N fertilization on susceptible and resistant host plants are not well characterized. This study determined how different rates of N fertilization affected injury caused by the potato leafhopper (Empoasca fabae Harris) and the abundance of maple spider mite (Oligonychus aceris (Shimer)) on 'Red Sunset' red maple (Acer rubrum) and 'Autumn Blaze' Freeman maple (Acer×freemanii) during two years in Indiana. N fertilization increased leaf N concentration in both maple cultivars, albeit to a lesser extent during the second year of the study. Overall, Red Sunset maples were more susceptible to E. fabae injury than Autumn Blaze, whereas Autumn Blaze maples supported higher populations of O. aceris. Differences in populations of O. aceris were attributed to differences between communities of stigmaeid and phytoseiid mites on each cultivar. Injury caused by E. fabae increased with N fertilization in a dose-dependent manner in both cultivars. Although N fertilization increased the abundance of O. aceris on both maple cultivars, there was no difference between the 20 and 40 g rates. We suggest the capacity of N fertilization to increase O. aceris on maples could be limited at higher trophic levels by the community of predatory mites. PMID:26470249
A Maple package for improved global mapping forecast
NASA Astrophysics Data System (ADS)
Carli, H.; Duarte, L. G. S.; da Mota, L. A. C. P.
2014-03-01
We present a Maple implementation of the well known global approach to time series analysis and some further developments designed to improve the computational efficiency of the forecasting capabilities of the approach. This global approach can be summarized as being a reconstruction of the phase space, based on a time ordered series of data obtained from the system. After that, using the reconstructed vectors, a portion of this space is used to produce a mapping, a polynomial fitting, through a minimization procedure, that represents the system and can be employed to forecast further entries for the series. In the present implementation, we introduce a set of commands, tools, in order to perform all these tasks. For example, the command VecTS deals mainly with the reconstruction of the vector in the phase space. The command GfiTS deals with producing the minimization and the fitting. ForecasTS uses all these and produces the prediction of the next entries. For the non-standard algorithms, we here present two commands: IforecasTS and NiforecasTS that, respectively deal with the one-step and the N-step forecasting. Finally, we introduce two further tools to aid the forecasting. The commands GfiTS and AnalysTS, basically, perform an analysis of the behavior of each portion of a series regarding the settings used on the commands just mentioned above. Catalogue identifier: AERW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERW_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.: 3001 No. of bytes in distributed program, including test data, etc.: 95018 Distribution format: tar.gz Programming language: Maple 14. Computer: Any capable of running Maple Operating system: Any capable of running Maple. Tested on Windows ME, Windows XP, Windows 7. RAM: 128 MB
Matrix Algebra for GPU and Multicore Architectures (MAGMA) for Large Petascale Systems
Dongarra, Jack J.; Tomov, Stanimire
2014-03-24
The goal of the MAGMA project is to create a new generation of linear algebra libraries that achieve the fastest possible time to an accurate solution on hybrid Multicore+GPU-based systems, using all the processing power that future high-end systems can make available within given energy constraints. Our efforts at the University of Tennessee achieved the goals set in all of the five areas identified in the proposal: 1. Communication optimal algorithms; 2. Autotuning for GPU and hybrid processors; 3. Scheduling and memory management techniques for heterogeneity and scale; 4. Fault tolerance and robustness for large scale systems; 5. Building energy efficiency into software foundations. The University of Tennessee’s main contributions, as proposed, were the research and software development of new algorithms for hybrid multi/many-core CPUs and GPUs, as related to two-sided factorizations and complete eigenproblem solvers, hybrid BLAS, and energy efficiency for dense, as well as sparse, operations. Furthermore, as proposed, we investigated and experimented with various techniques targeting the five main areas outlined.
Structural characterization of MAPLE deposited lipase biofilm
NASA Astrophysics Data System (ADS)
Aronne, Antonio; Ausanio, Giovanni; Bloisi, Francesco; Calabria, Raffaela; Califano, Valeria; Fanelli, Esther; Massoli, Patrizio; Vicari, Luciano R. M.
2014-11-01
Lipases (triacylglycerol ester hydrolases) are enzymes used in several industrial applications. Enzymes immobilization can be used to address key issues limiting widespread application at industrial level. Immobilization efficiency is related to the ability to preserve the native conformation of the enzyme. MAPLE (Matrix Assisted Pulsed Laser Evaporation) technique, a laser deposition procedure for treating organic/polymeric/biomaterials, was applied for the deposition of lipase enzyme in an ice matrix, using near infrared laser radiation. Microscopy analysis showed that the deposition occurred in micrometric and submicrometric clusters with a wide size distribution. AFM imaging showed that inter-cluster regions are uniformly covered with smaller aggregates of nanometric size. Fourier transform infrared spectroscopy was used for both recognizing the deposited material and analyzing its secondary structure. Results showed that the protein underwent reversible self-association during the deposition process. Actually, preliminary tests of MAPLE deposited lipase used for soybean oil transesterification with isopropyl alcohol followed by gas chromatography-mass spectrometry gave results consistent with undamaged deposition of lipase.
NASA Astrophysics Data System (ADS)
Cooper, Cameron I.; Pearson, Paul T.
2012-02-01
In higher education, many high-enrollment introductory courses have evolved into "gatekeeper" courses due to their high failure rates. These courses prevent many students from attaining their educational goals and often become graduation roadblocks. At the authors' home institution, general chemistry has become a gatekeeper course in which approximately 25% of students do not pass. This failure rate in chemistry is common, and often higher, at many other institutions of higher education, and mathematical deficiencies are perceived to be a large contributing factor. This paper details the development of a highly accurate predictive system that identifies students at the beginning of the semester who are "at-risk" for earning a grade of C- or below in chemistry. The predictive accuracy of this system is maximized by using a genetically optimized neural network to analyze the results of a diagnostic algebra test designed for a specific population. Once at-risk students have been identified, they can be helped to improve their chances of success using techniques such as concurrent support courses, online tutorials, "just-in-time" instructional aides, study skills, motivational interviewing, and/or peer mentoring.
Development of a GNSS water vapour tomography system using algebraic reconstruction techniques
NASA Astrophysics Data System (ADS)
Bender, Michael; Dick, Galina; Ge, Maorong; Deng, Zhiguo; Wickert, Jens; Kahle, Hans-Gert; Raabe, Armin; Tetzlaff, Gerd
2011-05-01
A GNSS water vapour tomography system developed to reconstruct spatially resolved humidity fields in the troposphere is described. The tomography system was designed to process the slant path delays of about 270 German GNSS stations in near real-time with a temporal resolution of 30 min, a horizontal resolution of 40 km and a vertical resolution of 500 m or better. After a short introduction to the GPS slant delay processing the framework of the GNSS tomography is described in detail. Different implementations of the iterative algebraic reconstruction techniques (ART) used to invert the linear inverse problem are discussed. It was found that the multiplicative techniques (MART) provide the best results with least processing time, i.e., a tomographic reconstruction of about 26,000 slant delays on a 8280 cell grid can be obtained in less than 10 min. Different iterative reconstruction techniques are compared with respect to their convergence behaviour and some numerical parameters. The inversion can be considerably stabilized by using additional non-GNSS observations and implementing various constraints. Different strategies for initialising the tomography and utilizing extra information are discussed. At last an example of a reconstructed field of the wet refractivity is presented and compared to the corresponding distribution of the integrated water vapour, an analysis of a numerical weather model (COSMO-DE) and some radiosonde profiles.
Definite Integrals, Some Involving Residue Theory Evaluated by Maple Code
Bowman, Kimiko o
2010-01-01
The calculus of residue is applied to evaluate certain integrals in the range (-{infinity} to {infinity}) using the Maple symbolic code. These integrals are of the form {integral}{sub -{infinity}}{sup {infinity}} cos(x)/[(x{sup 2} + a{sup 2})(x{sup 2} + b{sup 2}) (x{sup 2} + c{sup 2})]dx and similar extensions. The Maple code is also applied to expressions in maximum likelihood estimator moments when sampling from the negative binomial distribution. In general the Maple code approach to the integrals gives correct answers to specified decimal places, but the symbolic result may be extremely long and complex.
NASA Astrophysics Data System (ADS)
Wu, P. K.; Ringeisen, B. R.; Krizman, D. B.; Frondoza, C. G.; Brooks, M.; Bubb, D. M.; Auyeung, R. C. Y.; Piqué, A.; Spargo, B.; McGill, R. A.; Chrisey, D. B.
2003-04-01
Two techniques for transferring biomaterial using a pulsed laser beam were developed: matrix-assisted pulsed laser evaporation (MAPLE) and MAPLE direct write (MDW). MAPLE is a large-area vacuum based technique suitable for coatings, i.e., antibiofouling, and MDW is a localized deposition technique capable of fast prototyping of devices, i.e., protein or tissue arrays. Both techniques have demonstrated the capability of transferring large (mol wt>100 kDa) molecules in different forms, e.g., liquid and gel, and preserving their functions. They can deposit patterned films with spatial accuracy and resolution of tens of μm and layering on a variety of substrate materials and geometries. MDW can dispense volumes less than 100 pl, transfer solid tissues, fabricate a complete device, and is computed aided design/computer aided manufacturing compatible. They are noncontact techniques and can be integrated with other sterile processes. These attributes are substantiated by films and arrays of biomaterials, e.g., polymers, enzymes, proteins, eucaryotic cells, and tissue, and a dopamine sensor. These examples, the instrumentation, basic mechanisms, a comparison with other techniques, and future developments are discussed.
Adaptive Algebraic Multigrid Methods
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
Higher level twisted Zhu algebras
Ekeren, Jethro van
2011-05-15
The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper, we consider the general setup of a vertex algebra V, graded by {Gamma}/Z for some subgroup {Gamma} of R containing Z, and with a Hamiltonian operator H having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level p Zhu algebras Zhu{sub p,{Gamma}}(V), and we prove the following theorems: For each p, there is a bijection between the irreducible Zhu{sub p,{Gamma}}(V)-modules and the irreducible {Gamma}-twisted positive energy V-modules, and V is ({Gamma}, H)-rational if and only if all its Zhu algebras Zhu{sub p,{Gamma}}(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for H. We provide an explicit description of the level p Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra Vir{sup c} and the universal affine Kac-Moody vertex algebra V{sup k}(g) at non-critical level. We also compute the inverse limits of these directed systems of algebras.
Invariant classification of second-order conformally flat superintegrable systems
NASA Astrophysics Data System (ADS)
Capel, J. J.; Kress, J. M.
2014-12-01
In this paper we continue the work of Kalnins et al in classifying all second-order conformally-superintegrable (Laplace-type) systems over conformally flat spaces, using tools from algebraic geometry and classical invariant theory. The results obtained show, through Stäckel equivalence, that the list of known nondegenerate superintegrable systems over three-dimensional conformally flat spaces is complete. In particular, a seven-dimensional manifold is determined such that each point corresponds to a conformal class of superintegrable systems. This manifold is foliated by the nonlinear action of the conformal group in three dimensions. Two systems lie in the same conformal class if and only if they lie in the same leaf of the foliation. This foliation is explicitly described using algebraic varieties formed from representations of the conformal group. The proof of these results rely heavily on Gröbner basis calculations using the computer algebra software packages Maple and Singular.
Dynamics of the inverse MAPLE nanoparticle deposition process
NASA Astrophysics Data System (ADS)
Steiner, Matthew A.; Fitz-Gerald, James M.
2015-05-01
Matrix-assisted pulsed laser evaporation (MAPLE) is a processing technique by which laser-sensitive materials are dissolved or placed into colloidal solution with a strongly absorbing sacrificial solvent, which when frozen into a solid target and irradiated under vacuum disperses the undamaged solute material onto a desired substrate. We present an inversion of the original MAPLE process, where the irradiation of metal-based acetate precursors in solution with UV transparent water results in the deposition of inorganic nanoparticles. A theory is forwarded to explain the underlying multiscale sequence of events that control the inverse MAPLE process from acetate decomposition to nanoparticle formation and subsequent ejection. Support for this theory is provided through the analysis of deposited nanoparticles and by novel characterization of MAPLE targets post-irradiation via cryostage scanning electron microscopy. Ejection is shown to proceed through the same phase-explosion mechanism that drives conventional MAPLE, relating the two techniques and advancing the broader understanding of MAPLE deposition processes.
The possible role of air quality in sugar maple decline
Linzon, S.N. )
1987-01-01
The decline of sugar maple (Acer saccharum L.) was first reported to occur in North America in 1913. A review of the literature on the occurrence of sugar maple decline and the associated causal agents was made in 1986 based on 189 reports. No single cause for the decline was identified with a number of diverse factors being reported to be involved. These factors included defoliating insects, drought, nutritional deficiencies, improper woodlot management, secondary root rot organisms, road salt and acidic precipitation. In the Provinces of Quebec and Ontario, Canada, intensive studies into the occurrence and etiology of sugar maple decline commenced in the early 1980s. Maple syrup producers in both provinces complained that sugar maple trees were declining and dying in greater numbers than usual and suspected that air pollution, including acidic precipitation, was involved. This paper describes the symptoms associated with sugar maple decline, the surveys underway in both provinces, and the field and experimental studies being carried out to determine the role of air quality.
Examinations in the Final Year of Transition to Mathematical Methods Computer Algebra System (CAS)
ERIC Educational Resources Information Center
Leigh-Lancaster, David; Les, Magdalena; Evans, Michael
2010-01-01
2009 was the final year of parallel implementation for Mathematical Methods Units 3 and 4 and Mathematical Methods (CAS) Units 3 and 4. From 2006-2009 there was a common technology-free short answer examination that covered the same function, algebra, calculus and probability content for both studies with corresponding expectations for key…
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1991-01-01
The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.
Sugar Maple Pigments Through the Fall and the Role of Anthocyanin as an Analytical Tool
NASA Astrophysics Data System (ADS)
Lindgren, E.; Rock, B.; Middleton, E.; Aber, J.
2008-12-01
Sugar maple habitat is projected to almost disappear in future climate scenarios. In fact, many institutions state that these trees are already in decline. Being able to detect sugar maple health could prove to be a useful analytical tool to monitor changes in phenology. Anthocyanin, a red pigment found in sugar maples, is thought to be a universal indicator of plant stress. It is very prominent in the spring during the first flush of leaves, as well as in the fall as leaves senesce. Determining an anthocyanin index that could be used with satellite systems will provide a greater understanding of tree phenology and the distribution of plant stress, both over large areas as well as changes over time. The utilization of anthocyanin for one of it's functions, prevention of oxidative stress, may fluctuate in response to changing climatic conditions that occur during senescence or vary from year to year. By monitoring changes in pigment levels and antioxidant capacity through the fall, one may be able to draw conclusions about the ability to detect anthocyanin remotely from space-based systems, and possibly determine a more specific function for anthocyanin during fall senescence. These results could then be applied to track changes in tree stress.
ERIC Educational Resources Information Center
Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott
2007-01-01
Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…
NASA Astrophysics Data System (ADS)
Ahunov, Roman R.; Kuksenko, Sergey P.; Gazizov, Talgat R.
2016-06-01
A multiple solution of linear algebraic systems with dense matrix by iterative methods is considered. To accelerate the process, the recomputing of the preconditioning matrix is used. A priory condition of the recomputing based on change of the arithmetic mean of the current solution time during the multiple solution is proposed. To confirm the effectiveness of the proposed approach, the numerical experiments using iterative methods BiCGStab and CGS for four different sets of matrices on two examples of microstrip structures are carried out. For solution of 100 linear systems the acceleration up to 1.6 times, compared to the approach without recomputing, is obtained.
Monitoring the health of sugar maple, Acer saccharum
NASA Astrophysics Data System (ADS)
Carlson, Martha
The sugar maple, Acer saccharum, is projected to decline and die in 88 to 100 percent of its current range in the United States. An iconic symbol of the northeastern temperate forest and a dominant species in this forest, the sugar maple is identified as the most sensitive tree in its ecosystem to rising temperatures and a warming climate. This study measures the health of sugar maples on 12 privately owned forests and at three schools in New Hampshire. Laboratory quantitative analyses of leaves, buds and sap as well as qualitative measures of leaf and bud indicate that record high beat in 2012 stressed the sugar maple. The study identifies several laboratory and qualitative tests of health which seem most sensitive and capable of identifying stress early when intervention in forest management or public policy change might counter decline of the species. The study presents evidence of an unusual atmospheric pollution event which defoliated sugar maples in 2010. The study examines the work of citizen scientists in Forest Watch, a K-12 school program in which students monitor the impacts of ozone on white pine, Pinus strobus, another keystone species in New Hampshire's forest. Finally, the study examines three simple measurements of bud, leaf and the tree's acclimation to light. The findings of these tests illuminate findings in the first study. And they present examples of what citizen scientists might contribute to long-term monitoring of maples. A partnership between science and citizens is proposed to begin long-term monitoring and to report on the health of sugar maples.
Bifurcation diagram and the discriminant of a spectral curve of integrable systems on Lie algebras
Konyaev, Andrei Yu
2010-11-11
A bifurcation diagram is a stratified (in general, nonclosed) set and is one of the efficient tools of studying the topology of the Liouville foliation. In the framework of the present paper, the coincidence of the closure of a bifurcation diagram {Sigma}-bar of the moment map defined by functions obtained by the method of argument shift with the closure of the discriminant D-bar{sub z} of a spectral curve is proved for the Lie algebras sl(n+1), sp(2n), so(2n+1), and g{sub 2}. Moreover, it is proved that these sets are distinct for the Lie algebra so(2n). Bibliography: 22 titles.
Bifurcation diagram and the discriminant of a spectral curve of integrable systems on Lie algebras
NASA Astrophysics Data System (ADS)
Konyaev, Andrei Yu
2010-11-01
A bifurcation diagram is a stratified (in general, nonclosed) set and is one of the efficient tools of studying the topology of the Liouville foliation. In the framework of the present paper, the coincidence of the closure of a bifurcation diagram \\overline\\Sigma of the moment map defined by functions obtained by the method of argument shift with the closure of the discriminant \\overline D_z of a spectral curve is proved for the Lie algebras \\operatorname{sl}(n+1), \\operatorname{sp}(2n), \\operatorname{so}(2n+1), and \\operatorname{g}_2. Moreover, it is proved that these sets are distinct for the Lie algebra \\operatorname{so}(2n). Bibliography: 22 titles.
SUSY QM, symmetries and spectrum generating algebras for two-dimensional systems
Martinez, D. Mota, R.D.
2008-04-15
We show in a systematic and clear way how factorization methods can be used to construct the generators for hidden and dynamical symmetries. This is shown by studying the 2D problems of hydrogen atom, the isotropic harmonic oscillator and the radial potential A{rho}{sup 2{zeta}}{sup -2} - B{rho}{sup {zeta}}{sup -2}. We show that in these cases the non-compact (compact) algebra corresponds to so(2, 1) (su(2))
Analytical solution using computer algebra of a biosensor for detecting toxic substances in water
NASA Astrophysics Data System (ADS)
Rúa Taborda, María. Isabel
2014-05-01
In a relatively recent paper an electrochemical biosensor for water toxicity detection based on a bio-chip as a whole cell was proposed and numerically solved and analyzed. In such paper the kinetic processes in a miniaturized electrochemical biosensor system was described using the equations for specific enzymatic reaction and the diffusion equation. The numerical solution shown excellent agreement with the measured data but such numerical solution is not enough to design efficiently the corresponding bio-chip. For this reason an analytical solution is demanded. The object of the present work is to provide such analytical solution and then to give algebraic guides to design the bio-sensor. The analytical solution is obtained using computer algebra software, specifically Maple. The method of solution is the Laplace transform, with Bromwich integral and residue theorem. The final solution is given as a series of Bessel functions and the effective time for the bio-sensor is computed. It is claimed that the analytical solutions that were obtained will be very useful to predict further current variations in similar systems with different geometries, materials and biological components. Beside of this the analytical solution that we provide is very useful to investigate the relationship between different chamber parameters such as cell radius and height; and electrode radius.
ERIC Educational Resources Information Center
Dougherty, Shaun M.; Goodman, Joshua S.; Hill, Darryl V.; Litke, Erica G.; Page, Lindsay C.
2015-01-01
Taking algebra by eighth grade is considered an important milestone on the pathway to college readiness. We highlight a collaboration to investigate one district's effort to increase middle school algebra course-taking. In 2010, the Wake County Public Schools began assigning middle school students to accelerated math and eighth-grade algebra based…
Phenylbutyrate therapy for maple syrup urine disease
Brunetti-Pierri, Nicola; Lanpher, Brendan; Erez, Ayelet; Ananieva, Elitsa A.; Islam, Mohammad; Marini, Juan C.; Sun, Qin; Yu, Chunli; Hegde, Madhuri; Li, Jun; Wynn, R. Max; Chuang, David T.; Hutson, Susan; Lee, Brendan
2011-01-01
Therapy with sodium phenylacetate/benzoate or sodium phenylbutyrate in urea cycle disorder patients has been associated with a selective reduction in branched-chain amino acids (BCAA) in spite of adequate dietary protein intake. Based on this clinical observation, we investigated the potential of phenylbutyrate treatment to lower BCAA and their corresponding α-keto acids (BCKA) in patients with classic and variant late-onset forms of maple syrup urine disease (MSUD). We also performed in vitro and in vivo experiments to elucidate the mechanism for this effect. We found that BCAA and BCKA are both significantly reduced following phenylbutyrate therapy in control subjects and in patients with late-onset, intermediate MSUD. In vitro treatment with phenylbutyrate of control fibroblasts and lymphoblasts resulted in an increase in the residual enzyme activity, while treatment of MSUD cells resulted in the variable response which did not simply predict the biochemical response in the patients. In vivo phenylbutyrate increases the proportion of active hepatic enzyme and unphosphorylated form over the inactive phosphorylated form of the E1α subunit of the branched-chain α-keto acid dehydrogenase complex (BCKDC). Using recombinant enzymes, we show that phenylbutyrate prevents phosphorylation of E1α by inhibition of the BCKDC kinase to activate BCKDC overall activity, providing a molecular explanation for the effect of phenylbutyrate in a subset of MSUD patients. Phenylbutyrate treatment may be a valuable treatment for reducing the plasma levels of neurotoxic BCAA and their corresponding BCKA in a subset of MSUD patients and studies of its long-term efficacy are indicated. PMID:21098507
Results of Using Algebra Tiles as Meaningful Representations of Algebra Concepts.
ERIC Educational Resources Information Center
Sharp, Janet M.
Mathematical meanings can be developed when individuals construct translations between algebra symbol systems and physical systems that represent one another. Previous research studies indicated (1) few high school students connect whole number manipulations to algebraic manipulations and (2) students who encounter algebraic ideas through…
Development of a more efficient maple syrup evaporator. Final report
Parsons, D.
1982-11-30
The goal of this project was to retrofit a traditional wood-fired maple syrup evaporator to make more efficient use of the wood fuel. A sap preheater was constructed that used waste heat from the steam to preheat the incoming sap. The preheater was tested on the evaporator and 8% more water was processed. There were some problems that will be discussed in the body of the report. A sap pan with fins incorporated into the bottom (described in the 1st and 2nd quarterly reports) was built but was not tested because the fins could not be properly sealed at the ends. Put more simply, it leaked. The bulk of time and energy was spent designing, building, and installing the forced draft and heat exchanger system (refer to 3rd quarterly report). A squirrel cage blower forced fresh air through twelve pipes that were arranged in the stack to the firebox and a draft inducer was mounted on top of the stack. With this arrangement plus the preheater 27% more water was processed than the original rig with the same amount of wood.
Skrypnyk, T.
2009-03-15
We construct quantum integrable systems associated with non-skew-symmetric gl(2)-valued classical r-matrices. We find a new explicit multiparametric family of such the non-skew-symmetric classical r-matrices. We consider two classes of examples of the corresponding integrable systems, namely generalized Gaudin systems with and without an external magnetic field. In the case of arbitrary r-matrices diagonal in a standard gl(2)-basis, we calculate the spectrum of the corresponding quantum integrable systems using the algebraic Bethe ansatz. We apply these results to a construction of integrable fermionic models and obtain a wide class of integrable Bardeen-Cooper-Schrieffer (BCS)-type fermionic Hamiltonians containing the pairing and electrostatic interaction terms. We also consider special cases when the corresponding integrable Hamiltonians contain only pairing interaction term and are exact analogs of the 'reduced BCS Hamiltonian' of Richardson.
Technology Transfer Automated Retrieval System (TEKTRAN)
Air injection (AI) is a maple sap processing technology reported to increase the efficiency of maple syrup production by increasing production of more economically valuable light-colored maple syrup, and reducing development of loose scale mineral precipitates in syrup, and scale deposits on evapora...
Maple syrup-production, composition, chemistry, and sensory characteristics.
Perkins, Timothy D; van den Berg, Abby K
2009-01-01
Maple syrup is made from sap exuded from stems of the genus Acer during the springtime. Sap is a dilute solution of primarily water and sucrose, with varying amounts of amino and organic acids and phenolic substances. When concentrated, usually by heating, a series of complex reactions produce a wide variety of flavor compounds that vary due to processing and other management factors, seasonal changes in sap chemistry, and microbial contamination. Color also forms during thermal evaporation. Flavor and color together are the primary factors determining maple syrup grade, and syrup can range from very light-colored and delicate-flavored to very dark-colored and strong-flavored. PMID:19389608
Static algebraic solitons in Korteweg-de Vries type systems and the Hirota transformation.
Burde, G I
2011-08-01
Some effects in the soliton dynamics governed by higher-order Korteweg-de Vries (KdV) type equations are discussed. This is done based on the exact explicit solutions of the equations derived in the paper. It is shown that some higher order KdV equations possessing multisoliton solutions also admit steady state solutions in terms of algebraic functions describing localized patterns. Solutions including both those static patterns and propagating KdV-like solitons are combinations of algebraic and hyperbolic functions. It is shown that the localized structures behave like static solitons upon collisions with regular moving solitons, with their shape remaining unchanged after the collision and only the position shifted. These phenomena are not revealed in common multisoliton solutions derived using inverse scattering or Hirota's method. The solutions of the higher-order KdV type equations were obtained using a method devised for obtaining soliton solutions of nonlinear evolution equations. This method can be combined with Hirota's method with a modified representation of the solution which allows the results to be extended to multisoliton solutions. The prospects for applying the methods to soliton equations not of KdV type are discussed. PMID:21929136
Multiobjective algebraic synthesis of neural control systems by implicit model following.
Ferrari, Silvia
2009-03-01
The advantages brought about by using classical linear control theory in conjunction with neural approximators have long been recognized in the literature. In particular, using linear controllers to obtain the starting neural control design has been shown to be a key step for the successful development and implementation of adaptive-critic neural controllers. Despite their adaptive capabilities, neural controllers are often criticized for not providing the same performance and stability guarantees as classical linear designs. Therefore, this paper develops an algebraic synthesis procedure for designing dynamic output-feedback neural controllers that are closed-loop stable and meet the same performance objectives as any classical linear design. The performance synthesis problem is addressed by deriving implicit model-following algebraic relationships between model matrices, obtained from the classical design, and the neural control parameters. Additional linear matrix inequalities (LMIs) conditions for closed-loop exponential stability of the neural controller are derived using existing integral quadratic constraints (IQCs) for operators with repeated slope-restricted nonlinearities. The approach is demonstrated by designing a recurrent neural network controller for a highly maneuverable tailfin-controlled missile that meets multiple design objectives, including pole placement for transient tuning, H(infinity) and H(2) performance in the presence of parameter uncertainty, and command-input tracking. PMID:19203887
The Exocenter of a Generalized Effect Algebra
NASA Astrophysics Data System (ADS)
Foulis, David J.; Pulmannová, Sylvia
2011-12-01
Elements of the exocenter of a generalized effect algebra (GEA) correspond to decompositions of the GEA as a direct sum and thus the exocenter is a generalization to GEAs of the center of an effect algebra. The exocenter of a GEA is shown to be a boolean algebra, and the notion of a hull mapping for an effect algebra is generalized to a hull system for a GEA. We study Dedekind orthocompleteness of GEAs and extend to GEAs the notion of a centrally orthocomplete effect algebra.
Twisted Quantum Toroidal Algebras
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Liu, Rongjia
2014-09-01
We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.
Kalay, Berfin; Demiralp, Metin
2015-12-31
This proceedings paper aims to show the efficiency of an expectation value identity for a given algebraic function operator which is assumed to be depending pn only position operator. We show that this expectation value formula becomes enabled to determine the eigenstates of the quantum system Hamiltonian as long as it is autonomous and an appropriate basis set in position operator is used. This approach produces a denumerable infinite recursion which may be considered as revisited but at the same time generalized form of the recursions over the natural number powers of the position operator. The content of this short paper is devoted not only to the formulation of the new method but also to show that this novel approach is capable of catching the eigenvalues and eigenfunctions for Hydrogen-like systems, beyond that, it can give a hand to us to reveal the wavefunction structure. So it has also somehow a confirmative nature.
Algebraic vs physical N = 6 3-algebras
Cantarini, Nicoletta; Kac, Victor G.
2014-01-15
In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.
Quantum algebra of N superspace
Hatcher, Nicolas; Restuccia, A.; Stephany, J.
2007-08-15
We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.
CHICKEN COOP AND BROAD LEAF MAPLE, LOOKING NORTHEAST. Three chicken ...
CHICKEN COOP AND BROAD LEAF MAPLE, LOOKING NORTHEAST. Three chicken coops on the farm were used by both chickens and turkeys. The yards around the buildings were once fenced in to give the poultry brooding space. - Kineth Farm, Chicken Coop, 19162 STATE ROUTE 20, Coupeville, Island County, WA
Student's Lab Assignments in PDE Course with MAPLE.
ERIC Educational Resources Information Center
Ponidi, B. Alhadi
Computer-aided software has been used intensively in many mathematics courses, especially in computational subjects, to solve initial value and boundary value problems in Partial Differential Equations (PDE). Many software packages were used in student lab assignments such as FORTRAN, PASCAL, MATLAB, MATHEMATICA, and MAPLE in order to accelerate…
FACTORS INFLUENCING FALL FOLIAGE COLOR EXPRESSION IN SUGAR MAPLE TREES.
Abstract: We evaluated factors influencing red autumn coloration in leaves of sugar maple (Acer saccharum Marsh.) by measuring mineral nutrition and carbohydrate concentrations, moisture content, and phenology of color development of leaves from 16 mature open-grown trees on 12 d...
Semiclassical states on Lie algebras
Tsobanjan, Artur
2015-03-15
The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.
NASA Technical Reports Server (NTRS)
Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.
1999-01-01
This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, Inc., Reston, VA.
This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…
Sequential products on effect algebras
NASA Astrophysics Data System (ADS)
Gudder, Stan; Greechie, Richard
2002-02-01
A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined. The properties of sequential products on Hilbert space effect algebras are discussed. For a general SEA, relationships between sequential independence, coexistence and compatibility are given. It is shown that the sharp elements of a SEA form an orthomodular poset. The sequential center of a SEA is discussed and a characterization of when the sequential center is isomorphic to a fuzzy set system is presented. It is shown that the existence, of a sequential product is a strong restriction that eliminates many effect algebras from being SEA's. For example, there are no finite nonboolean SEA's, A measure of sharpness called the sharpness index is studied. The existence of horizontal sums of SEA's is characterized and examples of horizontal sums and tensor products are presented.
Figueroa-O'Farrill, Jose Miguel
2009-11-15
We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern-Simons theories with matter.
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
Philip, Bobby; Chartier, Dr Timothy
2012-01-01
methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.
Explicit travelling waves and invariant algebraic curves
NASA Astrophysics Data System (ADS)
Gasull, Armengol; Giacomini, Hector
2015-06-01
We introduce a precise definition of algebraic travelling wave solution of n-th order partial differential equations and prove that the only algebraic travelling waves solutions for the celebrated Fisher-Kolmogorov equation are the ones found in 1979 by Ablowitz and Zeppetella. This question is equivalent to study when an associated one-parameter family of planar ordinary differential systems has invariant algebraic curves.
Binomial and Poisson Mixtures, Maximum Likelihood, and Maple Code
Bowman, Kimiko o; Shenton, LR
2006-01-01
The bias, variance, and skewness of maximum likelihoood estimators are considered for binomial and Poisson mixture distributions. The moments considered are asymptotic, and they are assessed using the Maple code. Question of existence of solutions and Karl Pearson's study are mentioned, along with the problems of valid sample space. Large samples to reduce variances are not unusual; this also applies to the size of the asymptotic skewness.
Phenolic glycosides from sugar maple (Acer saccharum) bark.
Yuan, Tao; Wan, Chunpeng; González-Sarrías, Antonio; Kandhi, Vamsikrishna; Cech, Nadja B; Seeram, Navindra P
2011-11-28
Four new phenolic glycosides, saccharumosides A-D (1-4), along with eight known phenolic glycosides, were isolated from the bark of sugar maple (Acer saccharum). The structures of 1-4 were elucidated on the basis of spectroscopic data analysis. All compounds isolated were evaluated for cytotoxicity effects against human colon tumorigenic (HCT-116 and Caco-2) and nontumorigenic (CCD-18Co) cell lines. PMID:22032697
Classical and quantum Kummer shape algebras
NASA Astrophysics Data System (ADS)
Odzijewicz, A.; Wawreniuk, E.
2016-07-01
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras, here called Kummer shape algebras. The resolution of identity for a wide class of reproducing kernels is found. A number of examples, illustrating this theory, are also presented.
Assessing the Factors of Regional Growth Decline of Sugar Maple
NASA Astrophysics Data System (ADS)
Bishop, D. A.; Beier, C. M.; Pederson, N.; Lawrence, G. B.; Stella, J. C.; Sullivan, T. J.
2014-12-01
Sugar maple (Acer saccharum Marsh) is among the most ecologically, economically and culturally important trees in North America, but has experienced a decline disease across much of its range. We investigated the climatic and edaphic factors associated with A. saccharum growth in the Adirondack Mountains (USA) using a well-replicated tree-ring network incorporating a range of soil fertility (base cation availability). We found that nearly 3 in 4 A. saccharum trees exhibited declining growth rates during the last several decades, regardless of tree age or size. Although diameter growth was consistently higher on base-rich soils, the negative trends in growth were largely consistent across the soil chemistry gradient. Sensitivity of sugar maple growth to climatic variability was overall weaker than expected, but were also non-stationary during the 20th century. We observed increasingly positive responses to late-winter precipitation, increasingly negative responses to growing season temperatures, and strong positive responses to moisture availability during the 1960s drought that became much weaker during the recent pluvial. Further study is needed of these factors and their interactions as potential mechanisms for sugar maple growth decline.
Statecharts Via Process Algebra
NASA Technical Reports Server (NTRS)
Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance
1999-01-01
Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics
Inhibitory effect of maple syrup on the cell growth and invasion of human colorectal cancer cells.
Yamamoto, Tetsushi; Uemura, Kentaro; Moriyama, Kaho; Mitamura, Kuniko; Taga, Atsushi
2015-04-01
Maple syrup is a natural sweetener consumed by individuals of all ages throughout the world. Maple syrup contains not only carbohydrates such as sucrose but also various components such as organic acids, amino acids, vitamins and phenolic compounds. Recent studies have shown that these phenolic compounds in maple syrup may possess various activities such as decreasing the blood glucose level and an anticancer effect. In this study, we examined the effect of three types of maple syrup, classified by color, on the cell proliferation, migration and invasion of colorectal cancer (CRC) cells in order to investigate whether the maple syrup is suitable as a phytomedicine for cancer treatment. CRC cells that were administered maple syrup showed significantly lower growth rates than cells that were administered sucrose. In addition, administration of maple syrup to CRC cells caused inhibition of cell invasion, while there was no effect on cell migration. Administration of maple syrup clearly inhibited AKT phosphorylation, while there was no effect on ERK phosphorylation. These data suggest that maple syrup might inhibit cell proliferation and invasion through suppression of AKT activation and be suitable as a phytomedicine for CRC treatment, with fewer adverse effects than traditional chemotherapy. PMID:25647359
I CAN Learn[R] Pre-Algebra and Algebra. What Works Clearinghouse Intervention Report
ERIC Educational Resources Information Center
What Works Clearinghouse, 2009
2009-01-01
The I CAN Learn[R] Education System is an interactive, self-paced, mastery-based software system that includes the I CAN Learn[R] Fundamentals of Math (5th-6th grade math) curriculum, the I CAN Learn[R] Pre-Algebra curriculum, and the I CAN Learn[R] Algebra curriculum. College algebra credit is also available to students in participating schools…
Learning Algebra in a Computer Algebra Environment
ERIC Educational Resources Information Center
Drijvers, Paul
2004-01-01
This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…
Commutative algebraic methods for controllability of discrete-time polynomial systems
NASA Astrophysics Data System (ADS)
Kawano, Yu; Ohtsuka, Toshiyuki
2016-02-01
In this paper, we consider controllability of discrete-time polynomial systems. First, we present a forward accessibility (local reachability) condition that can be verified in finite time, in contrast to conventional conditions. Second, we give a backward accessibility (local controllability) condition for an invertible system and a condition to verify invertibility. Finally, we derive sufficient conditions to test whether the forward accessible system is reachable and to test the backward accessible system is controllable.
Difficulties in initial algebra learning in Indonesia
NASA Astrophysics Data System (ADS)
Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja
2014-12-01
Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.
Banach Algebras Associated to Lax Pairs
NASA Astrophysics Data System (ADS)
Glazebrook, James F.
2015-04-01
Lax pairs featuring in the theory of integrable systems are known to be constructed from a commutative algebra of formal pseudodifferential operators known as the Burchnall- Chaundy algebra. Such pairs induce the well known KP flows on a restricted infinite-dimensional Grassmannian. The latter can be exhibited as a Banach homogeneous space constructed from a Banach *-algebra. It is shown that this commutative algebra of operators generating Lax pairs can be associated with a commutative C*-subalgebra in the C*-norm completion of the *-algebra. In relationship to the Bose-Fermi correspondence and the theory of vertex operators, this C*-algebra has an association with the CAR algebra of operators as represented on Fermionic Fock space by the Gelfand-Naimark-Segal construction. Instrumental is the Plücker embedding of the restricted Grassmannian into the projective space of the associated Hilbert space. The related Baker and tau-functions provide a connection between these two C*-algebras, following which their respective state spaces and Jordan-Lie-Banach algebras structures can be compared.
Elementary Algebra Connections to Precalculus
ERIC Educational Resources Information Center
Lopez-Boada, Roberto; Daire, Sandra Arguelles
2013-01-01
This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…
Moving frames and prolongation algebras
NASA Technical Reports Server (NTRS)
Estabrook, F. B.
1982-01-01
Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less
NASA Technical Reports Server (NTRS)
Iachello, Franco
1995-01-01
An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.
Orientation in operator algebras
Alfsen, Erik M.; Shultz, Frederic W.
1998-01-01
A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457
Developing Thinking in Algebra
ERIC Educational Resources Information Center
Mason, John; Graham, Alan; Johnson-Wilder, Sue
2005-01-01
This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…
Connecting Arithmetic to Algebra
ERIC Educational Resources Information Center
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
Applied Algebra Curriculum Modules.
ERIC Educational Resources Information Center
Texas State Technical Coll., Marshall.
This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…
Profiles of Algebraic Competence
ERIC Educational Resources Information Center
Humberstone, J.; Reeve, R.A.
2008-01-01
The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…
Ternary Virasoro - Witt algebra.
Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham
2008-01-01
A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.
Is Algebra Really Difficult for All Students?
ERIC Educational Resources Information Center
Egodawatte, Gunawardena
2009-01-01
Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…
NASA Astrophysics Data System (ADS)
Baykara, N. A.
2015-12-01
Recent studies on quantum evolutionary problems in Demiralp's group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.
Baykara, N. A.
2015-12-31
Recent studies on quantum evolutionary problems in Demiralp’s group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.
Upper bound for the length of commutative algebras
Markova, Ol'ga V
2009-12-31
By the length of a finite system of generators for a finite-dimensional associative algebra over an arbitrary field one means the least positive integer k such that the words of length not exceeding k span this algebra (as a vector space). The maximum length for the systems of generators of an algebra is referred to as the length of the algebra. In the present paper, an upper bound for the length of a commutative algebra in terms of a function of two invariants of the algebra, the dimension and the maximal degree of the minimal polynomial for the elements of the algebra, is obtained. As a corollary, a formula for the length of the algebra of diagonal matrices over an arbitrary field is obtained. Bibliography: 8 titles.
NASA Technical Reports Server (NTRS)
Shapiro, Bruce E.; Levchenko, Andre; Meyerowitz, Elliot M.; Wold, Barbara J.; Mjolsness, Eric D.
2003-01-01
Cellerator describes single and multi-cellular signal transduction networks (STN) with a compact, optionally palette-driven, arrow-based notation to represent biochemical reactions and transcriptional activation. Multi-compartment systems are represented as graphs with STNs embedded in each node. Interactions include mass-action, enzymatic, allosteric and connectionist models. Reactions are translated into differential equations and can be solved numerically to generate predictive time courses or output as systems of equations that can be read by other programs. Cellerator simulations are fully extensible and portable to any operating system that supports Mathematica, and can be indefinitely nested within larger data structures to produce highly scaleable models.
Computer algebra and operators
NASA Technical Reports Server (NTRS)
Fateman, Richard; Grossman, Robert
1989-01-01
The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.
NASA Technical Reports Server (NTRS)
Anderson, B. D. O.; Brockett, R. W.; Byrnes, C. I.; Ghosh, B. K.; Stevens, P. K.
1983-01-01
The extent to which feedback can alter the dynamic characteristics (e.g., instability, oscillations) of a control system, possibly operating in one or more modes (e.g., failure versus nonfailure of one or more components) is examined.
QUALITY ASSURANCE ASPECTS OF THE JOINT USA-CANADA NORTH AMERICAN SUGAR MAPLE DECLINE PROJECT
The North American Sugar Maple Decline Project was implemented in 1988 in response to concerns about the condition of sugar maple (Acer saccharum Marsh) in the United States and Canada. ata collection for the project involved at least 15 federal, state, and provincial crews from ...
America's Native Sweet: Chippewa Treaties and the Right to Harvest Maple Sugar.
ERIC Educational Resources Information Center
Keller, Robert H.
1989-01-01
Argues in favor of a Chippewa right to harvest maple sap from trees on federal land. Discusses the history of Indian production of and trade in maple sugar, examines relevant treaties, and draws parallels with tribal rights to fish and harvest wild rice. Contains 91 references. (SV)
Passive Maple-Seed Robotic Fliers for Education, Research and Entrepreneurship
ERIC Educational Resources Information Center
Aslam, D. M.; Abu-Ageel, A.; Alfatlawi, M.; Varney, M. W.; Thompson, C. M.; Aslam, S. K.
2014-01-01
As inspirations from flora and fauna have led to many advances in modern technology, the concept of drawing ideas from nature for design should be reflected in engineering education. This paper focuses on a maple-seed robotic flier (MRF) with various complexities, a robotic platform modeled after the samaras of maple or ash trees, to teach STEM…
Computer subroutine ISUDS accurately solves large system of simultaneous linear algebraic equations
NASA Technical Reports Server (NTRS)
Collier, G.
1967-01-01
Computer program, an Iterative Scheme Using a Direct Solution, obtains double precision accuracy using a single-precision coefficient matrix. ISUDS solves a system of equations written in matrix form as AX equals B, where A is a square non-singular coefficient matrix, X is a vector, and B is a vector.
Thermodynamics. [algebraic structure
NASA Technical Reports Server (NTRS)
Zeleznik, F. J.
1976-01-01
The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.
Inequalities, Assessment and Computer Algebra
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2015-01-01
The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in…
ERIC Educational Resources Information Center
Bosse, Michael J.; Ries, Heather; Chandler, Kayla
2012-01-01
Secondary school mathematics teachers often need to answer the "Why do we do that?" question in such a way that avoids confusion and evokes student interest. Understanding the properties of number systems can provide an avenue to better grasp algebraic structures, which in turn builds students' conceptual knowledge of secondary mathematics. This…
Exploring Algebraic Misconceptions with Technology
ERIC Educational Resources Information Center
Sakow, Matthew; Karaman, Ruveyda
2015-01-01
Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…
An Introduction to Algebraic Multigrid
Falgout, R D
2006-04-25
Algebraic multigrid (AMG) solves linear systems based on multigrid principles, but in a way that only depends on the coefficients in the underlying matrix. The author begins with a basic introduction to AMG methods, and then describes some more recent advances and theoretical developments
Using PROC GLIMMIX to Analyze the Animal Watch, a Web-Based Tutoring System for Algebra Readiness
ERIC Educational Resources Information Center
Barbu, Otilia C.
2012-01-01
In this study, I investigated how proficiently seventh-grade students enrolled in two Southwestern schools solve algebra word problems. I analyzed various factors that could affect this proficiency and explored the differences between English Learners (ELs) and native English Primary students (EPs). I collected the data as part of the Animal Watch…
Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems
NASA Technical Reports Server (NTRS)
Downie, John D.
1990-01-01
A ground-based adaptive optics imaging telescope system attempts to improve image quality by detecting and correcting for atmospherically induced wavefront aberrations. The required control computations during each cycle will take a finite amount of time. Longer time delays result in larger values of residual wavefront error variance since the atmosphere continues to change during that time. Thus an optical processor may be well-suited for this task. This paper presents a study of the accuracy requirements in a general optical processor that will make it competitive with, or superior to, a conventional digital computer for the adaptive optics application. An optimization of the adaptive optics correction algorithm with respect to an optical processor's degree of accuracy is also briefly discussed.
Combinatorial MAPLE gradient thin film assemblies signalling to human osteoblasts.
Axente, Emanuel; Sima, Felix; Elena Sima, Livia; Erginer, Merve; Eroglu, Mehmet S; Serban, Natalia; Ristoscu, Carmen; Petrescu, Stefana M; Toksoy Oner, Ebru; Mihailescu, Ion N
2014-09-01
There is increased interest in smart bioactive materials to control tissue regeneration for the engineering of cell instructive scaffolds. We introduced combinatorial matrix-assisted pulsed laser evaporation (C-MAPLE) as a new method for the fabrication of organic thin films with a compositional gradient. Synchronized C-MAPLE of levan and oxidized levan was employed to assemble a two-compound biopolymer film structure. The gradient of the film composition was validated by fluorescence microscopy. In this study, we investigated the cell response induced by the compositional gradient using imaging of early osteoblast attachment and analysis of signalling phosphoprotein expression. Cells attached along the gradient in direct proportion to oxidized levan concentration. During this process distinct areas of the binary gradient have been shown to modulate the osteoblasts' extracellular signal-regulated kinase signalling with different propensity. The proposed fabrication method results in the preparation of a new bioactive material, which could control the cell signalling response. This approach can be extended to screen new bioactive interfaces for tissue regeneration. PMID:24867882
Red edge spectral measurements from sugar maple leaves
NASA Technical Reports Server (NTRS)
Vogelmann, J. E.; Rock, B. N.; Moss, D. M.
1993-01-01
Many sugar maple stands in the northeastern United States experienced extensive insect damage during the 1988 growing season. Chlorophyll data and high spectral resolution spectrometer laboratory reflectance data were acquired for multiple collections of single detached sugar maple leaves variously affected by the insect over the 1988 growing season. Reflectance data indicated consistent and diagnostic differences in the red edge portion (680-750 nm) of the spectrum among the various samples and populations of leaves. These included differences in the red edge inflection point (REIP), a ratio of reflectance at 740-720 nm (RE3/RE2), and a ratio of first derivative values at 715-705 nm (D715/D705). All three red edge parameters were highly correlated with variation in total chlorophyll content. Other spectral measures, including the Normalized Difference Vegetation Index (NDVI) and the Simple Vegetation Index Ratio (VI), also varied among populations and over the growing season, but did not correlate well with total chlorophyll content. Leaf stacking studies on light and dark backgrounds indicated REIP, RE3/RE2 and D715/D705 to be much less influenced by differences in green leaf biomass and background condition than either NDVI or VI.
[GENETIC AND METABOLIC URGENCIES IN THE NEONATAL INTENSIVE CARE UNIT: MAPLE SYRUP URINE DISEASE].
Páez Rojas, Paola Liliana; Suarez Obando, Fernando
2015-01-01
Maple syrup urine disease (MSUD) is a hereditary disorder of branched chain amino/keto acid metabolism, caused by a decreased activity of the branched-chain alpha- ketoacid dehydrogenase complex (BCKAD), which leads to abnormal elevated plasma concentrations of branched-chain amino acids (BCAAs) clinically manifested as a heavy burden for Central Nervous system. The toxic accumulation of substrates promotes the development of a severe and rapidly progressive neonatal encephalopathy if treatment is not immediately given. This disorder has a specific medical management in acute phase in order to minimize mortality and morbidity. For all those reasons, it is important to include the MSUD as a possible diagnosis in a encephalopathic newborn. We present a colombian newborn with classical MSUD with fatal outcome as an example of metabolic emergency and a differential diagnosis in the encephalopathic newborn. PMID:26262748
[Lists of food exchanges for use in phenylketonuria and maple-syrup urine disease].
Jiménez Soto, Z
1993-09-01
Phenylketonuria (PKU) and maple syrup urine disease (MSUD) are disorders of the amino acid metabolism. Treatment of PKU and MSUD, is based on the restriction of the involved amino acids. Diet must begin very early in life in order to prevent neurological sequelae. A wrong dietary produce central nervous system damage. The first clinical manifestations are unexplained failure to thrive, vomiting, feeding difficulties, lethargy, coma, acidosis and irritability. The most severe consequence is impaired mental development. The standard exchange foods list (EFL) used in outpatient clinics, is designed for developed countries, and contains foods that are not available in our countries. Therefore, we provide in this article a EFL, based on food that are frequently used in Central America, with data of existing food composition tables. This list is currently being used by the Costa Rica national Children's Hospital Metabolic Disease Unit. PMID:8779622
NASA Astrophysics Data System (ADS)
Surzhykov, Andrey; Koval, Peter; Fritzsche, Stephan
2005-01-01
Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen-like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb-field) solutions, here we present the DIRAC program which has been developed originally for studying the properties and dynamical behavior of the (hydrogen-like) ions. In the present version, a set of MAPLE procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the DIRAC program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion-atom and ion-photon collisions. Program summaryTitle of program:DIRAC Catalogue number: ADUQ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Computer for which the program is designed and has been tested: All computers with a license of the computer algebra package MAPLE [1] Program language used: Maple 8 and 9 No. of lines in distributed program, including test data, etc.:2186 No. of bytes in distributed program, including test data, etc.: 162 591 Distribution format: tar gzip file CPC Program Library subprograms required: None Nature of the physical problem: Analytical solutions of the hydrogen atom are widely used in very different fields of physics [2,3]. Despite of the rather simple structure
A Richer Understanding of Algebra
ERIC Educational Resources Information Center
Foy, Michelle
2008-01-01
Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…
Algebraic method for finding equivalence groups
NASA Astrophysics Data System (ADS)
Bihlo, Alexander; Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O.
2015-06-01
The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the corresponding equivalence algebra. Two versions of the method are presented, where the first involves the automorphism group of this algebra and the second is based on a list of its megaideals. We illustrate the megaideal-based version of the method with the computation of the complete equivalence group of a class of nonlinear wave equations with applications in nonlinear elasticity.
Structure of classical affine and classical affine fractional W-algebras
Suh, Uhi Rinn
2015-01-15
We introduce a classical BRST complex (See Definition 3.2.) and show that one can construct a classical affine W-algebra via the complex. This definition clarifies that classical affine W-algebras can be considered as quasi-classical limits of quantum affine W-algebras. We also give a definition of a classical affine fractional W-algebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional W-algebra has two compatible λ-brackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional W-algebra is associated to a minimal nilpotent, we describe explicit forms of free generators and compute λ-brackets between them. Provided some assumptions on a classical affine fractional W-algebra, we find an infinite sequence of integrable systems related to the algebra, using the generalized Drinfel’d and Sokolov reduction.
Connecting Algebra and Chemistry.
ERIC Educational Resources Information Center
O'Connor, Sean
2003-01-01
Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)
Muhr, Jan; Messier, Christian; Delagrange, Sylvain; Trumbore, Susan; Xu, Xiaomei; Hartmann, Henrik
2016-03-01
While trees store substantial amounts of nonstructural carbon (NSC) for later use, storage regulation and mobilization of stored NSC in long-lived organisms like trees are still not well understood. At two different sites with sugar maple (Acer saccharum), we investigated ascending sap (sugar concentration, δ(13) C, Δ(14) C) as the mobilized component of stored stem NSC during early springtime. Using the bomb-spike radiocarbon approach we were able to estimate the average time elapsed since the mobilized carbon (C) was originally fixed from the atmosphere and to infer the turnover time of stem storage. Sites differed in concentration dynamics and overall δ(13) C, indicating different growing conditions. The absence of temporal trends for δ(13) C and Δ(14) C indicated sugar mobilization from a well-mixed pool with average Δ(14) C consistent with a mean turnover time (TT) of three to five years for this pool, with only minor differences between the sites. Sugar maple trees hence appear well buffered against single or even several years of negative plant C balance from environmental stress such as drought or repeated defoliation by insects. Manipulative investigations (e.g. starvation via girdling) combined with Δ(14) C measurements of this mobilized storage pool will provide further new insights into tree storage regulation and functioning. PMID:26639654
NASA Astrophysics Data System (ADS)
Kipps, Mark R.
1994-03-01
The modeling of power systems has been primarily driven by the commercial power utility industry. These models usually involve the assumption that system bus voltage and frequency are constant. However, in applications such as shipboard power systems this infinite bus assumption is not valid. This thesis investigates the modeling of a synchronous generator and various loads in a modular fashion on a finite bus. The simulation presented allows the interconnection of multiple state-space models via a bus voltage model. The major difficulty encountered in building a model which computes bus voltage at each time step is that bus voltage is a function of current and current derivative terms. Bus voltage is also an input to the state equations which produce the current and current derivatives. This creates an algebraic loop which is a form of implicit differential equation. A routine has been developed by Linda Petzold of Lawrence Livermore Laboratory for solving these types of equations. The routine, called Differential Algebraic System Solver (DASSL), has been implemented in a pre-release version of the software Advanced Continuous Simulation Language (ACSL) and has been made available to the Naval Postgraduate School on a trial basis. An isolated power system is modeled using this software and the DASSL routine. The system response to several dynamic situations is studied and the results are presented.
Filtering Algebraic Multigrid and Adaptive Strategies
Nagel, A; Falgout, R D; Wittum, G
2006-01-31
Solving linear systems arising from systems of partial differential equations, multigrid and multilevel methods have proven optimal complexity and efficiency properties. Due to shortcomings of geometric approaches, algebraic multigrid methods have been developed. One example is the filtering algebraic multigrid method introduced by C. Wagner. This paper proposes a variant of Wagner's method with substantially improved robustness properties. The method is used in an adaptive, self-correcting framework and tested numerically.
Toward robust scalable algebraic multigrid solvers.
Waisman, Haim; Schroder, Jacob; Olson, Luke; Hiriyur, Badri; Gaidamour, Jeremie; Siefert, Christopher; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen
2010-10-01
This talk highlights some multigrid challenges that arise from several application areas including structural dynamics, fluid flow, and electromagnetics. A general framework is presented to help introduce and understand algebraic multigrid methods based on energy minimization concepts. Connections between algebraic multigrid prolongators and finite element basis functions are made to explored. It is shown how the general algebraic multigrid framework allows one to adapt multigrid ideas to a number of different situations. Examples are given corresponding to linear elasticity and specifically in the solution of linear systems associated with extended finite elements for fracture problems.
Imperfect Cloning Operations in Algebraic Quantum Theory
NASA Astrophysics Data System (ADS)
Kitajima, Yuichiro
2015-01-01
No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal -imperfect cloning operation which tolerates a finite loss of fidelity in the cloned state, and show that an individual system's algebra of observables is abelian if and only if there is a universal -imperfect cloning operation in the case where the loss of fidelity is less than . Therefore in this case no universal -imperfect cloning operation is possible in algebraic quantum theory.
ERIC Educational Resources Information Center
Merlin, Ethan M.
2013-01-01
This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…
NASA Technical Reports Server (NTRS)
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…
Intellectual performance of children with maple syrup urine disease.
Hilliges, C; Awiszus, D; Wendel, U
1993-02-01
The intellectual performance of 22 children aged 3-16 years with maple syrup urine disease (MSUD) was assessed and compared to a group of early treated phenylketonuria (PKU) children and normal subjects matched by age, sex, nationality, and socio-economic status. All subjects were tested by one examiner only using the age related versions of the non-verbal Snijders-Oomen intelligence test. The mean IQ (+/- SD) score was 74 +/- 14 (range 50-103) in patients with MSUD, 101 +/- 12 (range 87-125) in early treated PKU patients, and 107 +/- 9 (range 90-122) in normal subjects. Intercorrelations indicated that length of time after birth that plasma leucine concentration remained > 1 mmol/l and quality of long-term metabolic control have important influences on IQ. PMID:8444223
Semigroups And Computer Algebra In Discrete Structures
NASA Astrophysics Data System (ADS)
Bijev, G.
2010-10-01
Some concepts in semigroup theory are interpreted in discrete structures such as finite lattices, binary relations, and finite semilattices. An algebraic approach to the pseudoinverse generalization problem in Boolean vector spaces is used. By analogy with the linear spaces in the linear algebra semilattice homomorphisms, isomorphisms, projections on Boolean vector spaces are defined and some properties of them are investigated in detail. Maps, corresponding to them in the linear algebra, are connected with matrices and their pseudouinverse. Important properties of these maps, which are essential for solving linear systems, remain the same in the Boolean vector spaces. Stochastic experiments using the maps defined and computer algebra methods have been made for solving linear equations Ax = b. The Hamming distance between b and the projection p(b) = Ax of b is equal or close to the least possible one, if the system has no solutions.
mMaple: A Photoconvertible Fluorescent Protein for Use in Multiple Imaging Modalities
McEvoy, Ann L.; Hoi, Hiofan; Bates, Mark; Platonova, Evgenia; Cranfill, Paula J.; Baird, Michelle A.; Davidson, Michael W.; Ewers, Helge; Liphardt, Jan; Campbell, Robert E.
2012-01-01
Recent advances in fluorescence microscopy have extended the spatial resolution to the nanometer scale. Here, we report an engineered photoconvertible fluorescent protein (pcFP) variant, designated as mMaple, that is suited for use in multiple conventional and super-resolution imaging modalities, specifically, widefield and confocal microscopy, structured illumination microscopy (SIM), and single-molecule localization microscopy. We demonstrate the versatility of mMaple by obtaining super-resolution images of protein organization in Escherichia coli and conventional fluorescence images of mammalian cells. Beneficial features of mMaple include high photostability of the green state when expressed in mammalian cells and high steady state intracellular protein concentration of functional protein when expressed in E. coli. mMaple thus enables both fast live-cell ensemble imaging and high precision single molecule localization for a single pcFP-containing construct. PMID:23240015
Semigroups and computer algebra in algebraic structures
NASA Astrophysics Data System (ADS)
Bijev, G.
2012-11-01
Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X')B of the complement operator (') on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (') is an isomorphism between Boolean semilattices, the generalized complement operator is homomorphism in the general case. The map fA,B and its general inverse (fA,B)+ have quite similar properties to those in the linear algebra and are useful for solving linear equations in Boolean matrix algebras. For binary relations on a finite set, necessary and sufficient conditions for the equation αξβ = γ to have a solution ξ are proved. A generalization of Green's equivalence relations in semigroups for rectangular matrices is proposed. Relationships between them and the Moore-Penrose inverses are investigated. It is shown how any generalized Green's H-class could be constructed by given its corresponding linear subspaces and converted into a group isomorphic to a linear group. Some information about using computer algebra methods concerning this paper is given.
2003-06-03
The ALGEBRA II program allows the user to manipulate data from a finite element analysis before it is plotted by evaluating algebraic expressions. The equation variables are dependent on the input database variable names. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database which can be read by plot programs. Code is written in a portable form as possible. Fortran codemore » is written in ANSI Standard FORTRAN-77. Machine-specific routines are limited in number and are grouped together to minimize the time required to adapt them to a new system. SEACAS codes has been ported to several Unix systems.« less
NASA Astrophysics Data System (ADS)
Günther, Uwe; Kuzhel, Sergii
2010-10-01
Gauged \\ {P}\\ {T} quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan decompositions. A Lie-triple structure is found and an interpretation as \\ {P}\\ {T}-symmetrically generalized Jaynes-Cummings model is possible with close relation to recently studied cavity QED setups with transmon states in multilevel artificial atoms. For models with Abelian gauge potentials a hidden Clifford algebra structure is found and used to obtain the fundamental symmetry of Krein space-related J-self-adjoint extensions for PTQM setups with ultra-localized potentials.
Lie algebra extensions of current algebras on S3
NASA Astrophysics Data System (ADS)
Kori, Tosiaki; Imai, Yuto
2015-06-01
An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.
Leibniz algebras associated with representations of filiform Lie algebras
NASA Astrophysics Data System (ADS)
Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.
2015-12-01
In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.
Single axioms for Boolean algebra.
McCune, W.
2000-06-30
Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction techniques were applied to find axioms of lengths 105, 131, 111, and 127, respectively, each with six variables.
Kreutzweiser, David P; Good, Kevin P; Chartrand, Derek T; Scarr, Taylor A; Thompson, Dean G
2008-01-01
The systemic insecticide imidacloprid may be applied to deciduous trees for control of the Asian longhorned beetle, an invasive wood-boring insect. Senescent leaves falling from systemically treated trees contain imidacloprid concentrations that could pose a risk to natural decomposer organisms. We examined the effects of foliar imidacloprid concentrations on decomposer organisms by adding leaves from imidacloprid-treated sugar maple trees to aquatic and terrestrial microcosms under controlled laboratory conditions. Imidacloprid in maple leaves at realistic field concentrations (3-11 mg kg(-1)) did not affect survival of aquatic leaf-shredding insects or litter-dwelling earthworms. However, adverse sublethal effects at these concentrations were detected. Feeding rates by aquatic insects and earthworms were reduced, leaf decomposition (mass loss) was decreased, measurable weight losses occurred among earthworms, and aquatic and terrestrial microbial decomposition activity was significantly inhibited. Results of this study suggest that sugar maple trees systemically treated with imidacloprid to control Asian longhorned beetles may yield senescent leaves with residue levels sufficient to reduce natural decomposition processes in aquatic and terrestrial environments through adverse effects on non-target decomposer organisms. PMID:18396551
Coreflections in Algebraic Quantum Logic
NASA Astrophysics Data System (ADS)
Jacobs, Bart; Mandemaker, Jorik
2012-07-01
Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.
Developing Algebraic Thinking.
ERIC Educational Resources Information Center
Alejandre, Suzanne
2002-01-01
Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)
Algebraic Semantics for Narrative
ERIC Educational Resources Information Center
Kahn, E.
1974-01-01
This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
Covariant deformed oscillator algebras
NASA Technical Reports Server (NTRS)
Quesne, Christiane
1995-01-01
The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
NASA Astrophysics Data System (ADS)
Hiley, B. J.
In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.
NASA Astrophysics Data System (ADS)
Cristescu, R.; Visan, A.; Socol, G.; Surdu, A. V.; Oprea, A. E.; Grumezescu, A. M.; Chifiriuc, M. C.; Boehm, R. D.; Yamaleyeva, D.; Taylor, M.; Narayan, R. J.; Chrisey, D. B.
2016-06-01
The purpose of this study was to investigate the interactions between microorganisms, including the planktonic and adherent organisms, and biopolymer (polyvinylpyrrolidone), flavonoid (quercetin dihydrate and resveratrol)-biopolymer, and silver nanoparticles-biopolymer composite thin films that were deposited using matrix assisted pulsed laser evaporation (MAPLE). A pulsed KrF* excimer laser source was used to deposit the aforementioned composite thin films, which were characterized using Fourier transform infrared spectroscopy (FT-IR), infrared microscopy (IRM), scanning electron microscopy (SEM), Grazing incidence X-ray diffraction (GIXRD) and atomic force microscopy (AFM). The antimicrobial activity of thin films was quantified using an adapted disk diffusion assay against Gram-positive and Gram-negative bacteria strains. FT-IR, AFM and SEM studies confirmed that MAPLE may be used to fabricate thin films with chemical properties corresponding to the input materials as well as surface properties that are appropriate for medical use. The silver nanoparticles and flavonoid-containing films exhibited an antimicrobial activity both against Gram-positive and Gram-negative bacterial strains demonstrating the potential use of these hybrid systems for the development of novel antimicrobial strategies.
DG Poisson algebra and its universal enveloping algebra
NASA Astrophysics Data System (ADS)
Lü, JiaFeng; Wang, XingTing; Zhuang, GuangBin
2016-05-01
In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.
Nagai, Noriaki; Yamamoto, Tetsushi; Tanabe, Wataru; Ito, Yoshimasa; Kurabuchi, Satoshi; Mitamura, Kuniko; Taga, Atsushi
2015-01-01
We investigate whether maple syrup is a suitable sweetener in the management of type 2 diabetes using the Otsuka Long-Evans Tokushima Fatty (OLETF) rat. The enhancement in plasma glucose (PG) and glucose absorption in the small intestine were lower after the oral administration of maple syrup than after sucrose administration in OLETF rats, and no significant differences were observed in insulin levels. These data suggested that maple syrup might inhibit the absorption of glucose from the small intestine and preventing the enhancement of PG in OLETF rats. Therefore, maple syrup might help in the prevention of type 2 diabetes. PMID:25757438
Climate Change in the School Yard: Monitoring the Health of Acer Saccharum with A Maple Report Card
NASA Astrophysics Data System (ADS)
Carlson, M.; Diller, A.; Rock, B. N.
2012-12-01
K-12 Teachers and students engage in authentic science and a research partnership with scientists in Maple Watch, a University of New Hampshire outreach program. Maple Watch is a hands-on, inquiry-based program in which students learn about climate change and air quality as well as many other environmental stress factors which may affect the health of sugar maple. The iconic New England tree is slated to lose 52% of its range in this century. Maple Watch builds on the 20-year record of Forest Watch, a K-12 program in which students and teachers have contributed annual research specimens and data to a UNH study of tropospheric ozone and its impact on white pine (Pinus strobus). Maple Watch students monitor sugar maples (Acer saccharum) year-round for signals of strain and disease. Students report the first run in sap season, bud burst and leaf development, and leaf senescence and fall. Across New England the timing of these phenologic events is changing with climate warming. Students assess maple health with simple measures of leaf development in May, leaf senescence in early fall and bud quality in late fall. Simple student arithmetic rankings of leaf and bud health correlate with chlorophyll content and spectral reflectance measures that students can analyze and compare with researchers at UNH. Grading their trees for each test on a one-two-three scale, students develop a Maple Report Card for each type of measurement, which presents an annual portrait of tree health. Year-by-year, schools across the sugar maple's 31 million acre range could monitor changes in tree health. The change over time in maple health can be graphed in parallel with the Goddard Space Institute's Common Sense Climate Index. Four teachers, listed as co-authors here, began a pilot study with Maple Watch in 2010, contributing sap samples and sharing curricular activities with UNH. Pilot Maple Watch schools already manage stands of sugar maples and make maple syrup and are assisting in training
NASA Astrophysics Data System (ADS)
Kharcheva, Anastasia V.
2014-01-01
The work is devoted to the spectral measurements of maple leaves. Fresh green leaves of maple were investigated in spring and summer, healthy leaves and leaves affected by fungal diseases - during the fall color change. F685/F740 parameter values for healthy and diseased maple leaves were found, as well as the change of this parameter during the growing season. The concentration of chlorophylls a and b and carotenoids in ethanol extracts of maple leaves with different pigmentation were calculated by absorption spectroscopy and the ratio of Chl a / Chl b was found.
Fundamental Theorems of Algebra for the Perplexes
ERIC Educational Resources Information Center
Poodiak, Robert; LeClair, Kevin
2009-01-01
The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…
FAST TRACK COMMUNICATION: Kac Moody algebras and controlled chaos
NASA Astrophysics Data System (ADS)
Wesley, Daniel H.
2007-02-01
Compactification can control chaotic Mixmaster behaviour in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac Moody algebras. We show that different compactifications define 'mutations' of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by Lorentzian (but not hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi Yau, or M theory on a manifold of G2 holonomy.
Affine Vertex Operator Algebras and Modular Linear Differential Equations
NASA Astrophysics Data System (ADS)
Arike, Yusuke; Kaneko, Masanobu; Nagatomo, Kiyokazu; Sakai, Yuichi
2016-05-01
In this paper, we list all affine vertex operator algebras of positive integral levels whose dimensions of spaces of characters are at most 5 and show that a basis of the space of characters of each affine vertex operator algebra in the list gives a fundamental system of solutions of a modular linear differential equation. Further, we determine the dimensions of the spaces of characters of affine vertex operator algebras whose numbers of inequivalent simple modules are not exceeding 20.
Algebras of Measurements: The Logical Structure of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Lehmann, Daniel; Engesser, Kurt; Gabbay, Dov M.
2006-04-01
In quantum physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute.
Biochemical correlates of neuropsychiatric illness in maple syrup urine disease
Muelly, Emilie R.; Moore, Gregory J.; Bunce, Scott C.; Mack, Julie; Bigler, Don C.; Morton, D. Holmes; Strauss, Kevin A.
2013-01-01
Maple syrup urine disease (MSUD) is an inherited disorder of branched chain amino acid metabolism presenting with neonatal encephalopathy, episodic metabolic decompensation, and chronic amino acid imbalances. Dietary management enables survival and reduces risk of acute crises. Liver transplantation has emerged as an effective way to eliminate acute decompensation risk. Psychiatric illness is a reported MSUD complication, but has not been well characterized and remains poorly understood. We report the prevalence and characteristics of neuropsychiatric problems among 37 classical MSUD patients (ages 5–35 years, 26 on dietary therapy, 11 after liver transplantation) and explore their underlying mechanisms. Compared with 26 age-matched controls, MSUD patients were at higher risk for disorders of cognition, attention, and mood. Using quantitative proton magnetic resonance spectroscopy, we found lower brain glutamate, N-acetylaspartate (NAA), and creatine concentrations in MSUD patients, which correlated with specific neuropsychiatric outcomes. Asymptomatic neonatal course and stringent longitudinal biochemical control proved fundamental to optimizing long-term mental health. Neuropsychiatric morbidity and neurochemistry were similar among transplanted and nontransplanted MSUD patients. In conclusion, amino acid dysregulation results in aberrant neural networks with neurochemical deficiencies that persist after transplant and correlate with neuropsychiatric morbidities. These findings may provide insight into general mechanisms of psychiatric illness. PMID:23478409
Acrodermatitis dysmetabolica in an infant with maple syrup urine disease.
Flores, K; Chikowski, R; Morrell, D S
2016-08-01
Acrodermatitis dysmetabolica (AD) is a rare, newly termed, and poorly understood disease that appears to be clinically similar to acrodermatitis enteropathica (AE). Both diseases are characterized by the triad of periorificial and acral dermatitis, diarrhoea, and alopecia. Unlike AE, which is caused by zinc deficiency, AD is caused by numerous metabolic disorders. One such disorder is maple syrup urine disease (MSUD), a genetic deficiency of branched chain α-ketoacid dehydrogenase, the enzyme that degrades the branched-chain amino acids (BCAAs) isoleucine, leucine and valine. Treatment involves restricting BCAAs to prevent accumulation. We report a case of an infant being treated for MSUD, who developed the triad of AE/AD after a period of poor BCAA formula intake. The child was found to have low isoleucine and normal zinc levels. Increasing the isoleucine dose improved the eruption, thus the diagnosis of AD secondary to isoleucine deficiency was made. This case emphasizes the importance of carefully balancing BCAA levels while treating MSUD, as deficiency can precipitate AD. PMID:27334242
Sugar Maple Phenology: Anthocyanin Production During Leaf Senescence
NASA Astrophysics Data System (ADS)
Lindgren, E.; Rock, B.
2007-12-01
The Northeastern United States is known for its brilliant fall foliage colors. Foliage is responsible for a billion dollar tourism industry. Many comment that past years have not resulted in the amazing color displays seen historically. As sugar maple trees senesce they contribute bright red leaves to the mural of oranges, yellows, and greens. The pigment that produces the red color, anthocyanin, is synthesized in the fall as chlorophyll slowly degrades. Remote sensing data from LandSat during fall senescence can help investigate this event by quantifying color change and intensity. This data can then be compared to ground validation efforts in several study plots. The results will help answer the question, "Why do leaves turn red?" One hypothesis is that this pigment acts as a photoprotectant and screens leaves from UV light. It is possible that an increase in tropospheric ozone has negatively affected fall foliage due to the increased reflection of UV light before it reaches the trees; thereby reducing the leaves need to produce anthocyanin. Another hypothesis is that production of anthocyanin is linked to temperature, with maximum synthesis occurring during cold evenings and moderate days. Temperature changes caused by climate change could also be affecting anthocyanin. Through observing these changes by remote sensing and ground experiments, more can be learned about this phenological stage and why it happens.
NASA Astrophysics Data System (ADS)
Lannes, A.; Teunissen, P. J. G.
2011-05-01
The first objective of this paper is to show that some basic concepts used in global navigation satellite systems (GNSS) are similar to those introduced in Fourier synthesis for handling some phase calibration problems. In experimental astronomy, the latter are at the heart of what is called `phase closure imaging.' In both cases, the analysis of the related structures appeals to the algebraic graph theory and the algebraic number theory. For example, the estimable functions of carrier-phase ambiguities, which were introduced in GNSS to correct some rank defects of the undifferenced equations, prove to be `closure-phase ambiguities:' the so-called `closure-delay' (CD) ambiguities. The notion of closure delay thus generalizes that of double difference (DD). The other estimable functional variables involved in the phase and code undifferenced equations are the receiver and satellite pseudo-clock biases. A related application, which corresponds to the second objective of this paper, concerns the definition of the clock information to be broadcasted to the network users for their precise point positioning (PPP). It is shown that this positioning can be achieved by simply having access to the satellite pseudo-clock biases. For simplicity, the study is restricted to relatively small networks. Concerning the phase for example, these biases then include five components: a frequency-dependent satellite-clock error, a tropospheric satellite delay, an ionospheric satellite delay, an initial satellite phase, and an integer satellite ambiguity. The form of the PPP equations to be solved by the network user is then similar to that of the traditional PPP equations. As soon as the CD ambiguities are fixed and validated, an operation which can be performed in real time via appropriate decorrelation techniques, estimates of these float biases can be immediately obtained. No other ambiguity is to be fixed. The satellite pseudo-clock biases can thus be obtained in real time. This is
NASA Astrophysics Data System (ADS)
Kuzmin, Dmitri; Möller, Matthias; Gurris, Marcel
Flux limiting for hyperbolic systems requires a careful generalization of the design principles and algorithms introduced in the context of scalar conservation laws. In this chapter, we develop FCT-like algebraic flux correction schemes for the Euler equations of gas dynamics. In particular, we discuss the construction of artificial viscosity operators, the choice of variables to be limited, and the transformation of antidiffusive fluxes. An a posteriori control mechanism is implemented to make the limiter failsafe. The numerical treatment of initial and boundary conditions is discussed in some detail. The initialization is performed using an FCT-constrained L 2 projection. The characteristic boundary conditions are imposed in a weak sense, and an approximate Riemann solver is used to evaluate the fluxes on the boundary. We also present an unconditionally stable semi-implicit time-stepping scheme and an iterative solver for the fully discrete problem. The results of a numerical study indicate that the nonlinearity and non-differentiability of the flux limiter do not inhibit steady state convergence even in the case of strongly varying Mach numbers. Moreover, the convergence rates improve as the pseudo-time step is increased.
Twisted vertex algebras, bicharacter construction and boson-fermion correspondences
Anguelova, Iana I.
2013-12-15
The boson-fermion correspondences are an important phenomena on the intersection of several areas in mathematical physics: representation theory, vertex algebras and conformal field theory, integrable systems, number theory, cohomology. Two such correspondences are well known: the types A and B (and their super extensions). As a main result of this paper we present a new boson-fermion correspondence of type D-A. Further, we define a new concept of twisted vertex algebra of order N, which generalizes super vertex algebra. We develop the bicharacter construction which we use for constructing classes of examples of twisted vertex algebras, as well as for deriving formulas for the operator product expansions, analytic continuations, and normal ordered products. By using the underlying Hopf algebra structure we prove general bicharacter formulas for the vacuum expectation values for two important groups of examples. We show that the correspondences of types B, C, and D-A are isomorphisms of twisted vertex algebras.
Biogeochemical Drivers of Sugar Maple Mortality at the Species-Range Scale
NASA Astrophysics Data System (ADS)
Perry, C. H.; Zimmerman, P. L.
2012-12-01
The decline of sugar maple in the northern United States is causing concern in the resource management community, and several studies have identified soil properties that are linked to the observation of dead/dying trees (Hallett et al. 2006; Horsley et al. 2000; Long et al. 2009; St.Clair et al. 2008). Unfortunately, the sample of trees supporting these studies tends to be purposive in nature; soil properties generally are assessed only on those plots where dead trees are observed. In this study, we used more than 200 plots from the USDA Forest Service's FIADB (USDA Forest Service 2012; Woudenberg et al. 2010), including the phase 3 soils data (O'Neill et al. 2005; Woodall et al. 2010), to analyze a broader population of sugar maple (alive and dead) across a wide range of soil types. This population of plots has a highly skewed, zero-inflated distribution: the number of plots in the sample without dead trees is an order of magnitude greater than the number of plots with dead trees. One effective method of analysis is a two-stage approach. In the first stage, the response variable is the presence or absence of dead sugar maple; the inferential space is the entire population of plots with sugar maple trees. The second stage uses the relative abundance of dead sugar maple as the response variable; in this case, inference is restricted to those plots where dead sugar maple trees are observed. In both sets of models, basal area and geology are significant predictors of dead sugar maple. The most significant soil variables vary between these two inferential spaces. Our model of the presence/absence of sugar maple death included the molar ratio of Mg:Mn; when conditional on the presence of dead sugar maple, our model includes the molar ratio of Ca:Al, along with exchangeable Na and Mg percentages. Multimodel inference (Burnham and Anderson 2002) assists the assessment of predictors within and between the two stages.
Stiff-Roberts, Adrienne D.; Pate, Ryan; McCormick, Ryan; Lantz, Kevin R.
2012-07-30
Resonant infrared matrix-assisted pulsed laser evaporation (RIR-MAPLE) is a variation of pulsed laser deposition that is useful for organic-based thin films because it reduces material degradation by selective absorption of infrared radiation in the host matrix. A unique emulsion-based RIR-MAPLE approach has been developed that reduces substrate exposure to solvents and provides controlled and repeatable organic thin film deposition. In order to establish emulsion-based RIR-MAPLE as a preferred deposition technique for conjugated polymer or hybrid nanocomposite optoelectronic devices, studies have been conducted to demonstrate the value added by the approach in comparison to traditional solution-based deposition techniques, and this work will be reviewed. The control of hybrid nanocomposite thin film deposition, and the photoconductivity in such materials deposited using emulsion-based RIR-MAPLE, will also be reviewed. The overall result of these studies is the demonstration of emulsion-based RIR-MAPLE as a viable option for the fabrication of conjugated polymer and hybrid nanocomposite optoelectronic devices that could yield improved device performance.
Changes in mRNA and protein content of SO sub 2 -fumigated maple leaves
Stinemetz, C.L. ); Roberts, B.R.; Schnipke, V.M. )
1989-04-01
The effect of acute SO{sub 2} fumigation on foliar DNA, RNA, and protein levels in 2-yr-old containerized Acer seedlings was examined. While DNA content did not change appreciably in either SO{sub 2}-sensitive red maple (A. rubrum L.) or SO{sub 2}-tolerant silver maple (A. saccharinum L.), significant reductions in mRNA (35% for red maple; 21% for silver maple) were observed after 54 h fumigation (6 h/day {times} 3 days/wk {times} 3 wk) at 2.5 ppm SO{sub 2}. Reductions in mRNA and protein content were accompanied by a corresponding decline in net photosynthesis (Pn). The data from this study suggest that acute SO{sub 2} fumigation alters Pn in red and silver maple by disrupting molecular events, and that species sensitivity for these particular Acer spp may be related to the degree of change associated with mRNA and total protein content.
Regional growth decline of sugar maple (Acer saccharum) and its potential causes
Bishop, Daniel A.; Beier, Colin M.; Pederson, Neil; Lawrence, Gregory B.; Stella, John C; Sullivan, Timothy J.
2015-01-01
Sugar maple (Acer saccharum Marsh) has experienced poor vigor, regeneration failure, and elevated mortality across much of its range, but there has been relatively little attention to its growth rates. Based on a well-replicated dendrochronological network of range-centered populations in the Adirondack Mountains (USA), which encompassed a wide gradient of soil fertility, we observed that the majority of sugar maple trees exhibited negative growth trends in the last several decades, regardless of age, diameter, or soil fertility. Such growth patterns were unexpected, given recent warming and increased moisture availability, as well as reduced acidic deposition, which should have favored growth. Mean basal area increment was greater on base-rich soils, but these stands also experienced sharp reductions in growth. Growth sensitivity of sugar maple to temperature and precipitation was non-stationary during the last century, with overall weaker relationships than expected. Given the favorable competitive status and age structure of the Adirondack sugar maple populations sampled, evidence of widespread growth reductions raises concern over this ecologically and economically important tree. Further study will be needed to establish whether growth declines of sugar maple are occurring more widely across its range.
NASA Astrophysics Data System (ADS)
Roitman, Michael
2008-08-01
In this paper we prove that for any commutative (but in general non-associative) algebra A with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra V = V0 Å V2 Å V3 Å ¼, such that dim V0 = 1 and V2 contains A. We can choose V so that if A has a unit e, then 2e is the Virasoro element of V, and if G is a finite group of automorphisms of A, then G acts on V as well. In addition, the algebra V can be chosen with a non-degenerate invariant bilinear form, in which case it is simple.
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
2016-01-01
This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
Protein and leucine metabolism in maple syrup urine disease
Thompson, G.N.; Bresson, J.L.; Pacy, P.J.; Bonnefont, J.P.; Walter, J.H.; Leonard, J.V.; Saudubray, J.M.; Halliday, D. )
1990-04-01
Constant infusions of (13C)leucine and (2H5)phenylalanine were used to trace leucine and protein kinetics, respectively, in seven children with maple syrup urine disease (MSUD) and eleven controls matched for age and dietary protein intake. Despite significant elevations of plasma leucine (mean 351 mumol/l, range 224-477) in MSUD subjects, mean whole body protein synthesis (3.78 +/- 0.42 (SD) g.kg-1. 24 h-1) and catabolism (4.07 +/- 0.46) were similar to control values (3.69 +/- 0.50 and 4.09 +/- 0.50, respectively). The relationship between phenylalanine and leucine fluxes was also similar in MSUD subjects (mean phenylalanine-leucine flux ratio 0.35 +/- 0.07) and previously reported adult controls (0.33 +/- 0.02). Leucine oxidation was undetectable in four of the MSUD subjects and very low in the other three (less than 4 mumol.kg-1.h-1; controls 13-20). These results show that persistent elevation in leucine concentration has no effect on protein synthesis. The marked disturbance in leucine metabolism in MSUD did not alter the relationship between rates of catabolism of protein to phenylalanine and leucine, which provides further support for the validity of the use of a single amino acid to trace whole body protein metabolism. The minimal leucine oxidation in MSUD differs from findings in other inborn metabolic errors and indicates that in patients with classical MSUD there is no significant route of leucine disposal other than through protein synthesis.
Federal Register 2010, 2011, 2012, 2013, 2014
2010-09-17
... From the Federal Register Online via the Government Publishing Office DEPARTMENT OF ENERGY Federal Energy Regulatory Commission Maple Analytics, LLC; Supplemental Notice That Initial Market- Based Rate... notice in the above-referenced proceeding of Maple Analytics, LLC's application for market-based...
ERIC Educational Resources Information Center
Bal, Tara L.
2013-01-01
Sugar Maple, "Acer saccharum" Marsh., is one of the most valuable trees in the northern hardwood forests. Severe dieback was recently reported by area foresters in the western Upper Great Lakes Region. Sugar Maple has had a history of dieback over the last 100 years throughout its range and different variables have been identified as…
ERIC Educational Resources Information Center
Scanlan, Martin
2016-01-01
This case describes Maple Hills Elementary, a K-8 school in a rural farming community of the Midwest. As a community, Maple Hills has historically experienced a narrow range of diversity across race, ethnicity, language, and religion. Residents have predominantly been White, with German and English heritage, speak English as a mother tongue, and…
Computer Program For Linear Algebra
NASA Technical Reports Server (NTRS)
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
NASA Astrophysics Data System (ADS)
Bouwknegt, Peter
1988-06-01
We investigate extensions of the Virasoro algebra by a single primary field of integer or halfinteger conformal dimension Δ. We argue that for vanishing structure constant CΔΔΔ, the extended conformal algebra can only be associative for a generic c-value if Δ=1/2, 1, 3/2, 2 or 3. For the other Δ<=5 we compute the finite set of allowed c-values and identify the rational solutions. The case CΔΔΔ≠0 is also briefly discussed. I would like to thank Kareljan Schoutens for discussions and Sander Bais for a careful reading of the manuscript.
Ecology of red maple swamps in the glaciated northeast: A community profile
Golet, F.C.; Calhoun, A.J.K.; DeRagon, W.R.; Lowry, D.J.; Gold, A.J.
1993-06-01
The report is part of a series of profiles on the ecology of wetland and deepwater habitats. This particular profile addresses red maple swamps in the glaciated northeastern United States. Red maple (Acer rubrum) swamp is a dominant wetland type in most of the region; it reaches the greatest abundance in southern New England and northern New Jersey; where it comprises 60-80% of all inland wetlands. Red maple swamps occur in a wide variety of hydrogeologic settings, from small, isolated basins in till or glaciofluvial deposits to extensive wetland complexes on glacial lake beds, and from hillside seeps to stream floodplains and lake edges. Individual swamps may be seasonally flooded, temporarily flooded, or seasonally saturated, and soils may be mineral or organic. As many as five distinct vegetation layers may occur in these swamps, including trees, saplings, shrubs, herbs, and ground cover plants such as bryophytes and clubmosses.
Bragg, D.C.; Stokke, D.D.
1994-01-01
Birdseye grain distortions in sugar maple must be identified to capture the full value of a timber sale throughout the economic range of birdseye's occurrence. Even when relatively common, birdseye veneer typically makes up less than 1 percent of the harvested volume, but may account for one-half of the value of the sale. Field identification of birdseye sugar maple is critical for two principal reasons: (1) it allows for the enumeration of a valuable resource that may influence management decisions, and (2) it may prevent improper manufacturing of logs at the job site. Both factors should help increase overall timber sale return. The objective of the paper is to provide a background on birdseye sugar maples and a detailed sequential methodology for field identification of birdseye in standing trees.
Ecology of red maple swamps in the glaciated northeast: A community profile
Golet, F.C.; Calhoun, A.J.K.; DeRagon, W.R.; Lowry, D.J.; Gold, A.J.
1993-06-01
In many areas of the glaciated northeastern United States, forested wetlands dominated by red maple (Acer rubrum) cover more of the landscape than all other nontidal wetland types combined. Yet surprisingly little of their ecology, functions, or social significance has been documented. Bogs, salt marshes, Atlantic white cedar swamps, and other less common types of wetlands have received considerable attention from scientists, but, except for botanical surveys, red maple swamps have been largely ignored. The report conveys what is known about these common wetlands and identifies topics most in need of investigation. Red maple swamps are so abundant and so widely distributed in the Northeast that their physical, chemical, and biological properties range widely as well, and their values to society are diverse. The central focus of the U.S. Fish and Wildlife Service community profile series is the plant and animal communities of wetlands and deepwater habitats.
Four Lie algebras associated with R6 and their applications
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Tam, Honwah
2010-09-01
The first part in the paper reads that a three-dimensional Lie algebra is first introduced, whose corresponding loop algebra is constructed, for which isospectral problems are established. By employing zero curvature equations, a modified Kaup-Newell (mKN) soliton hierarchy of evolution equations is obtained. The corresponding hereditary operator and Hamiltonian structure are worked out, respectively. Then two types of enlarging semisimple Lie algebras isomorphic to the linear space R6 are followed to construct, one of them is a complex Lie algebra. Their corresponding loop algebras are also given so that two types of new isospectral problems are introduced to generate two kinds of integrable couplings of the above mKN hierarchy. The hereditary operators, Hamiltonian structures of the hierarchies are produced again, respectively. The exact computing formulas of the constant γ appearing in the trace identity and the variational identity are derived under the semisimple algebras. The second part of this paper is devoted to constructing two kinds of Lie algebras by using product of complex vectors, which are also isomorphic to the linear space R6. Then we make use of the corresponding loop algebras to produce two integrable hierarchies along with bi-Hamiltonian structures. From various aspects, we give some ways for constructing Lie algebras which have extensive applications in generating integrable Hamiltonian systems.
Effects of pesticide application on arthropod pests of nursery-grown maples.
Prado, Julia; Quesada, Carlos; Sadof, Clifford
2014-04-01
Insecticides used against potato leafhopper, Empoasca fabae (Harris) (Homoptera: Cicadellidae), have been reported to cause problems with maple spider mite, Oligonychus aceris (Shimer) (Acarina: Tetranychidae), on nursery-grown 'Red Sunset' red maple and 'Autumn Blaze' Freeman maple. To test this, we conducted two experiments on field-grown trees in nurseries. In the first, the effects of early-season pesticide applications were examined during 2009. The second experiment was conducted in 2010 to compare effects of using threshold levels of one, three, or six leafhoppers per branch to time applications. Pesticide applications reduced abundance and damage by leafhoppers in both cultivars, but increased populations of O. aceris on Autumn Blaze during 2009. In contrast, on Red Sunset, populations of O. aceris did not increase after insecticide applications. In 2010, insecticide applications did not increase abundance of O. aceris on Autumn Blaze because use of treatment thresholds to manage leafhoppers greatly reduced numbers of trees requiring treatment for leafhoppers. Two phytoseiid mites, Neoseiulus fallacis (Garman) and Typhlodromus caudiglans (Schuster), and one stigmaeid, Zetzellia mali (Ewing), were identified as the principal predators of O. aceris on maple leaves. Insecticide applications had no significant effects on the total abundance of predatory mites on either Red Sunset or Autumn Blaze maples in 2009 or 2010. However, populations of predator Z. mali were higher during both years on Red Sunset than on Autumn Blaze. These results suggest that both early-season pesticide use and cultivar can affect the likelihood of secondary outbreaks of spider mites on maples. PMID:24772553
Stability of Linear Equations--Algebraic Approach
ERIC Educational Resources Information Center
Cherif, Chokri; Goldstein, Avraham; Prado, Lucio M. G.
2012-01-01
This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…
Teaching Arithmetic and Algebraic Expressions
ERIC Educational Resources Information Center
Subramaniam, K.; Banerjee, Rakhi
2004-01-01
A teaching intervention study was conducted with sixth grade students to explore the interconnections between students' growing understanding of arithmetic expressions and beginning algebra. Three groups of students were chosen, with two groups receiving instruction in arithmetic and algebra, and one group in algebra without arithmetic. Students…
Spinors in the hyperbolic algebra
NASA Astrophysics Data System (ADS)
Ulrych, S.
2006-01-01
The three-dimensional universal complex Clifford algebra Cbar3,0 is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.
Students' Understanding of Algebraic Notation: 11-15.
ERIC Educational Resources Information Center
MacGregor, Mollie; Stacey, Kaye
1997-01-01
Investigates the cognitive and linguistic demands of learning algebra and explores students' understanding of algebraic notation. Findings indicate specific origins of misinterpretation that include intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in…
Intertextuality and Sense Production in the Learning of Algebraic Methods
ERIC Educational Resources Information Center
Rojano, Teresa; Filloy, Eugenio; Puig, Luis
2014-01-01
In studies carried out in the 1980s the algebraic symbols and expressions are revealed through prealgebraic readers as non-independent texts, as texts that relate to other texts that in some cases belong to the reader's native language or to the arithmetic sign system. Such outcomes suggest that the act of reading algebraic texts submerges…
Symmetry algebra of a generalized anisotropic harmonic oscillator
NASA Technical Reports Server (NTRS)
Castanos, O.; Lopez-Pena, R.
1993-01-01
It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.
Factors Influencing Student Academic Performance in Online High School Algebra
ERIC Educational Resources Information Center
Liu, Feng; Cavanaugh, Cathy
2012-01-01
This paper describes the effect of teacher comments, students' demographic information and learning management system utilisation on student final scores in algebra courses in a K-12 virtual learning environment. Students taking algebra courses in a state virtual school in the Midwestern US region during 2007-2008 participated in this study.…
Introduction to Matrix Algebra, Student's Text, Unit 23.
ERIC Educational Resources Information Center
Allen, Frank B.; And Others
Unit 23 in the SMSG secondary school mathematics series is a student text covering the following topics in matrix algebra: matrix operations, the algebra of 2 X 2 matrices, matrices and linear systems, representation of column matrices as geometric vectors, and transformations of the plane. Listed in the appendix are four research exercises in…
From geometry to algebra: the Euclidean way with technology
NASA Astrophysics Data System (ADS)
Ferrarello, Daniela; Flavia Mammana, Maria; Pennisi, Mario
2016-05-01
In this paper, we present the results of an experimental classroom activity, history-based with a phylogenetic approach, to achieve algebra properties through geometry. In particular, we used Euclidean propositions, processed them by a dynamic geometry system and translate them into algebraic special products.
Response of sugar maple to calcium addition to northern hardwood forest.
Juice, Stephanie M; Fahey, Timothy J; Siccama, Thomas G; Driscoll, Charles T; Denny, Ellen G; Eagar, Christopher; Cleavitt, Natalie L; Minocha, Rakesh; Richardson, Andrew D
2006-05-01
Watershed budget studies at the Hubbard Brook Experimental Forest (HBEF), New Hampshire, USA, have demonstrated high calcium depletion of soil during the 20th century due, in part, to acid deposition. Over the past 25 years, tree growth (especially for sugar maple) has declined on the experimental watersheds at the HBEF. In October 1999, 0.85 Mg Ca/ha was added to Watershed 1 (W1) at the HBEF in the form of wollastonite (CaSiO3), a treatment that, by summer 2002, had raised the pH in the Oie horizon from 3.8 to 5.0 and, in the Oa horizon, from 3.9 to 4.2. We measured the response of sugar maple to the calcium fertilization treatment on W1. Foliar calcium concentration of canopy sugar maples in W1 increased markedly beginning the second year after treatment, and foliar manganese declined in years four and five. By 2005, the crown condition of sugar maple was much healthier in the treated watershed as compared with the untreated reference watershed (W6). Following high seed production in 2000 and 2002, the density of sugar maple seedlings increased significantly on W1 in comparison with W6 in 2001 and 2003. Survivorship of the 2003 cohort through July 2005 was much higher on W1 (36.6%) than W6 (10.2%). In 2003, sugar maple germinants on W1 were approximately 50% larger than those in reference plots, and foliar chlorophyll concentrations were significantly greater (0.27 g/m2 vs. 0.23 g/m2 leaf area). Foliage and fine-root calcium concentrations were roughly twice as high, and manganese concentrations twice as low in the treated than the reference seedlings in 2003 and 2004. Mycorrhizal colonization of seedlings was also much greater in the treated (22.4% of root length) than the reference sites (4.4%). A similar, though less dramatic, difference was observed for mycorrhizal colonization of mature sugar maples (56% vs. 35%). These results reinforce and extend other regional observations that sugar maple decline in the northeastern United States and southern Canada is
ERIC Educational Resources Information Center
Glick, David
1995-01-01
Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)
Computer Algebra versus Manipulation
ERIC Educational Resources Information Center
Zand, Hossein; Crowe, David
2004-01-01
In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…
ERIC Educational Resources Information Center
Boiteau, Denise; Stansfield, David
This document describes mathematical programs on the basic concepts of algebra produced by Louisiana Public Broadcasting. Programs included are: (1) "Inverse Operations"; (2) "The Order of Operations"; (3) "Basic Properties" (addition and multiplication of numbers and variables); (4) "The Positive and Negative Numbers"; and (5) "Using Positive…
Thinking Visually about Algebra
ERIC Educational Resources Information Center
Baroudi, Ziad
2015-01-01
Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…
ERIC Educational Resources Information Center
Kennedy, John
This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…
ERIC Educational Resources Information Center
Nwabueze, Kenneth K.
2004-01-01
The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…
NASA Astrophysics Data System (ADS)
Zhang, Ming; Yao, JingTao
2004-04-01
The XML is a new standard for data representation and exchange on the Internet. There are studies on XML query languages as well as XML algebras in literature. However, attention has not been paid to research on XML algebras for data mining due to partially the fact that there is no widely accepted definition of XML mining tasks. This paper tries to examine the XML mining tasks and provide guidelines to design XML algebras for data mining. Some summarization and comparison have been done to existing XML algebras. We argue that by adding additional operators for mining tasks, XML algebras may work well for data mining with XML documents.
Simulation of n-qubit quantum systems. II. Separability and entanglement
NASA Astrophysics Data System (ADS)
Radtke, T.; Fritzsche, S.
2006-07-01
Studies on the entanglement of n-qubit quantum systems have attracted a lot of interest during recent years. Despite the central role of entanglement in quantum information theory, however, there are still a number of open problems in the theoretical characterization of entangled systems that make symbolic and numerical simulation on n-qubit quantum registers indispensable for present-day research. To facilitate the investigation of the separability and entanglement properties of n-qubit quantum registers, here we present a revised version of the FEYNMAN program in the framework of the computer algebra system MAPLE. In addition to all previous capabilities of this MAPLE code for defining and manipulating quantum registers, the program now provides various tools which are necessary for the qualitative and quantitative analysis of entanglement in n-qubit quantum registers. A simple access, in particular, is given to several algebraic separability criteria as well as a number of entanglement measures and related quantities. As in the previous version, symbolic and numeric computations are equally supported. Program summaryTitle of program:FEYNMAN Catalogue identifier:ADWE_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v2_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:None Computers for which the program is designed: All computers with a license of the computer algebra system MAPLE [Maple is a registered trademark of Waterloo Maple Inc.] Operating systems under which the program has been tested: Linux, MS Windows XP Programming language used:MAPLE 10 Typical time and memory requirements:Most commands acting on quantum registers with five or less qubits take ⩽10 seconds of processor time (on a Pentium 4 with ⩾2 GHz or equivalent) and 5-20 MB of memory. However, storage and time requirements critically depend on the number of qubits, n, in the quantum registers due to the exponential
Not Available
1981-03-01
The objective of the research program is to determine the feasibility of converting existing pole-size maple stands to biomass/energy plantations using black locust as an interplanted species. Toward this end, progress has been made in quantifying sprout biomass. Significant differences have been identified in productivity by site, species, time of fertilizer application, and diameter and damage of stumps. Rhizobium strains for black locust have been identified which are tolerant of low pH and phosphorous and high aluminum levels. Frost-hardy black locust seed sources have been identified for future work. Methods for sampling and equations for young natural stands of maple have been developed. Detailed characterization of sugar and red maple sprouts by physical, chemical and thermal analysis were compared to those of old, mature trees. The results are discussed in terms of seasonal moisture content variation, effects of tree age on specific gravity, extractive contents, ash content, major cell wall components, heating values and thermal behavior. 7 references, 5 figures, 17 tables.
On Dunkl angular momenta algebra
NASA Astrophysics Data System (ADS)
Feigin, Misha; Hakobyan, Tigran
2015-11-01
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
Algebraic connectivity and graph robustness.
Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.
2009-07-01
Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.
SLAPP: A systolic linear algebra parallel processor
Drake, B.L.; Luk, F.T.; Speiser, J.M.; Symanski, J.J.
1987-07-01
Systolic array computer architectures provide a means for fast computation of the linear algebra algorithms that form the building blocks of many signal-processing algorithms, facilitating their real-time computation. For applications to signal processing, the systolic array operates on matrices, an inherently parallel view of the data, using numerical linear algebra algorithms that have been suitably parallelized to efficiently utilize the available hardware. This article describes work currently underway at the Naval Ocean Systems Center, San Diego, California, to build a two-dimensional systolic array, SLAPP, demonstrating efficient and modular parallelization of key matric computations for real-time signal- and image-processing problems.
Shapes and stability of algebraic nuclear models
NASA Technical Reports Server (NTRS)
Lopez-Moreno, Enrique; Castanos, Octavio
1995-01-01
A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.
NASA Astrophysics Data System (ADS)
Li, Zhi-Bin; Liu, Yin-Ping
2004-11-01
In Maple 8, by taking advantage of the package RIF contained in DEtools, we developed a package RAEEM which is a comprehensive and complete implementation of such methods as the tanh-method, the extended tanh-method, the Jacobi elliptic function method and the elliptic equation method. RAEEM can entirely automatically output a series of exact traveling wave solutions, including those of polynomial, exponential, triangular, hyperbolic, rational, Jacobi elliptic, Weierstrass elliptic type. The effectiveness of the package is illustrated by applying it to a large variety of equations. In addition to recovering previously known solutions, we also obtain more general forms of some solutions and new solutions. Program summaryTitle of program: RAEEM Catalogue identifier: ADUP Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUP Program obtained from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers: PC Pentium IV Installations: Copy Operating systems: Windows 98/2000/XP Program language used: Maple 8 Memory required to execute with typical data: depends on the problem, minimum about 8M words No. of bits in a word: 8 No. of lines in distributed program, including test data, etc.: 3163 No. of bytes in distributed program, including the test data, etc.: 26 720 Distribution format: tar.gz Nature of physical problem: Our program provides exact traveling wave solutions, which describe various phenomena in nature, and thus can give more insight into the physical aspects of problems. These solutions may be easily used in further applications. Restriction on the complexity of the problem: The program can handle system of nonlinear evolution equations with any number of independent and dependent variables, in which each equation is a polynomial (or can be converted to a polynomial) in the dependent variables and their derivatives. Typical running time: It depends on the input equations as well as the degrees of the desired polynomial solutions. For
MICROBIAL COLONIZATION, RESPIRATION AND BREAKDOWN OF MAPLE LEAVES ALONG A STREAM-MARSH CONTINUUM
Breakdown rates, macroinvertebrate and bacterial colonization, and microbial respiration were measured on decaying maple leaves at three sites along a stream-marsh continuum. Breakdown rates were 0.0284+/-0.0045 d-1 for leaves in a high-gradient, non-tidal stream; 0.0112 +/- 0.0...
Computer-Aided Assessment Questions in Engineering Mathematics Using "MapleTA"[R
ERIC Educational Resources Information Center
Jones, I. S.
2008-01-01
The use of "MapleTA"[R] in the assessment of engineering mathematics at Liverpool John Moores University (JMU) is discussed with particular reference to the design of questions. Key aspects in the formulation and coding of questions are considered. Problems associated with the submission of symbolic answers, the use of randomly generated numbers…
MICROBIAL COLONIZATION, RESPIRATION, AND BREAKDOWN OF MAPLE LEAVES ALONG A STREAM-MARSH CONTINUUM
Breakdown rates, macroinvertebrate and bacterial colonization, and microbial respiration were measured on decaying maple (Acer saccharum) leaves at three sites along a stream-marsh continuum. Breakdown rates (-k+-SE) were 0.0284+-0.0045 d-1 for leaves in a high-gradient, non-tida...
2015-01-01
Maple syrup has nutraceutical potential given the macronutrients (carbohydrates, primarily sucrose), micronutrients (minerals and vitamins), and phytochemicals (primarily phenolics) found in this natural sweetener. We conducted compositional (ash, fiber, carbohydrates, minerals, amino acids, organic acids, vitamins, phytochemicals), in vitro biological, and in vivo safety (animal toxicity) studies on maple syrup extracts (MSX-1 and MSX-2) derived from two declassified maple syrup samples. Along with macronutrient and micronutrient quantification, thirty-three phytochemicals were identified (by HPLC-DAD), and nine phytochemicals, including two new compounds, were isolated and identified (by NMR) from MSX. At doses of up to 1000 mg/kg/day, MSX was well tolerated with no signs of overt toxicity in rats. MSX showed antioxidant (2,2-diphenyl-1-picrylhydrazyl (DPPH) assay) and anti-inflammatory (in RAW 264.7 macrophages) effects and inhibited glucose consumption (by HepG2 cells) in vitro. Thus, MSX should be further investigated for potential nutraceutical applications given its similarity in chemical composition to pure maple syrup. PMID:24983789
ERIC Educational Resources Information Center
Salleh, Tuan Salwani; Zakaria, Effandi
2016-01-01
The objective of this research is to investigate the effectiveness of a learning strategy using Maple in integral calculus. This research was conducted using a quasi-experimental nonequivalent control group design. One hundred engineering technology students at a technical university were chosen at random. The effectiveness of the learning…
A controlled-environment experiment was initiated to evaluate the influence of CO2 enrichment on the growth and ontogeny of bigleaf maple (Acer macrophyllum). evelopment of seedlings was monitored from seed germination through the first five months of ontogeny in growth chambers ...
Zhang, Yan; Yuan, Tao; Li, Liya; Nahar, Pragati; Slitt, Angela; Seeram, Navindra P
2014-07-16
Maple syrup has nutraceutical potential given the macronutrients (carbohydrates, primarily sucrose), micronutrients (minerals and vitamins), and phytochemicals (primarily phenolics) found in this natural sweetener. We conducted compositional (ash, fiber, carbohydrates, minerals, amino acids, organic acids, vitamins, phytochemicals), in vitro biological, and in vivo safety (animal toxicity) studies on maple syrup extracts (MSX-1 and MSX-2) derived from two declassified maple syrup samples. Along with macronutrient and micronutrient quantification, thirty-three phytochemicals were identified (by HPLC-DAD), and nine phytochemicals, including two new compounds, were isolated and identified (by NMR) from MSX. At doses of up to 1000 mg/kg/day, MSX was well tolerated with no signs of overt toxicity in rats. MSX showed antioxidant (2,2-diphenyl-1-picrylhydrazyl (DPPH) assay) and anti-inflammatory (in RAW 264.7 macrophages) effects and inhibited glucose consumption (by HepG2 cells) in vitro. Thus, MSX should be further investigated for potential nutraceutical applications given its similarity in chemical composition to pure maple syrup. PMID:24983789
Student Organizations in Canada and Quebec's "Maple Spring"
ERIC Educational Resources Information Center
Bégin-Caouette, Olivier; Jones, Glen A.
2014-01-01
This article has two major objectives: to describe the structure of the student movement in Canada and the formal role of students in higher education governance, and to describe and analyze the "Maple Spring," the dramatic mobilization of students in opposition to proposed tuition fee increases in Quebec that eventually led to a…
The Minnesota Maple Series: Community-Generated Knowledge Delivered through an Extension Website
ERIC Educational Resources Information Center
Wilsey, David S.; Miedtke, Juile A.; Sagor, Eli
2012-01-01
Extension continuously seeks novel and effective approaches to outreach and education. The recent retirement of a longtime content specialist catalyzed members of University of Minnesota Extension's Forestry team to reflect on our instructional capacity (internal and external) and educational design in the realm of maple syrup production. We…
Dual Mechanism of Brain Injury and Novel Treatment Strategy in Maple Syrup Urine Disease
ERIC Educational Resources Information Center
Zinnanti, William J.; Lazovic, Jelena; Griffin, Kathleen; Skvorak, Kristen J.; Paul, Harbhajan S.; Homanics, Gregg E.; Bewley, Maria C.; Cheng, Keith C.; LaNoue, Kathryn F.; Flanagan, John M.
2009-01-01
Maple syrup urine disease (MSUD) is an inherited disorder of branched-chain amino acid metabolism presenting with life-threatening cerebral oedema and dysmyelination in affected individuals. Treatment requires life-long dietary restriction and monitoring of branched-chain amino acids to avoid brain injury. Despite careful management, children…
Hammami, Riadh; Ben Abdallah, Nour; Barbeau, Julie; Fliss, Ismail
2015-01-01
This study was undertaken to evaluate the in vivo impact of new symbiotic products based on liquid maple sap or its concentrate. Sap and concentrate, with or without inulin (2%), were inoculated with Bifidobacterium lactis Bb12 and Lactobacillus rhamnosus GG valio at initial counts of 2-4 × 10(8) cfu mL(-1). The experiments started with intra-gastric administration of antibiotic (kanamycin 40 mg in 0.1 cc) (to induce microbiota disturbance and/or diarrhea) to 3-to-5-week-old C57BL/6 female mice followed by a combination of prebiotic and probiotics included in the maple sap or its concentrate for a week. The combination inulin and probiotics in maple sap and concentrate appeared to minimize the antibiotic-induced breakdown of mice microbiota with a marked effect on bifidobacterium and bacteroides levels, thus permitting a more rapid re-establishment of the baseline microbiota levels. Results suggest that maple sap and its concentrate represent good candidates for the production of non-dairy functional foods. PMID:26218660
Carbon content variation in boles of mature sugar maple and giant sequoia.
Lamlom, Sabah H; Savidge, Rodney A
2006-04-01
At present, a carbon (C) content of 50% (w/w) in dry wood is widely accepted as a generic value; however, few wood C measurements have been reported. We used elemental analysis to investigate C content per unit of dry matter and observed that it varied both radially and vertically in boles of two old-growth tree species: sugar maple (Acer saccharum Marsh.) and giant sequoia (Sequoiadendron giganteum (Lindl.) Bucholz). In sugar maple there was considerable variation in tree ring widths among four radii for particular annual layers of xylem, revealing that the annual rate of C assimilation differs around the circumference and from the base of each tree to its top, but the observed variation in C content was unrelated to diameter growth rate and strongly related to the calendar year when the wood was formed. Carbon content in sugar maple wood increased in an approximately linear fashion, from < 50 to 51% from pith to cambium, at both the base and top of the boles. In giant sequoia, C was essentially constant at > 55% across many hundreds of years of heartwood, but it declined abruptly at the sapwood-heartwood boundary and remained lower in all sapwood samples, an indication that heartwood formation involves anabolic metabolism. Factors that may be responsible for the different C contents and trends with age between sugar maple and sequoia trees are considered. Tree-ring data from this study do not support some of the key assumptions made by dendrochronology. PMID:16414925
Invariant algebraic surfaces for a virus dynamics
NASA Astrophysics Data System (ADS)
Valls, Claudia
2015-08-01
In this paper, we provide a complete classification of the invariant algebraic surfaces and of the rational first integrals for a well-known virus system. In the proofs, we use the weight-homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations.
Lie algebras and linear differential equations.
NASA Technical Reports Server (NTRS)
Brockett, R. W.; Rahimi, A.
1972-01-01
Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.
Learning Activity Package, Pre-Algebra.
ERIC Educational Resources Information Center
Evans, Diane
A set of ten teacher-prepared Learning Activity Packages (LAPs) for individualized instruction in topics in pre-algebra, the units cover the decimal numeration system; number theory; fractions and decimals; ratio, proportion, and percent; sets; properties of operations; rational numbers; real numbers; open expressions; and open rational…
Algebra 1Q, Mathematics: 5215.12.
ERIC Educational Resources Information Center
Hirigoyen, Hector
This is the second of the six guidebooks on minimum course content for first-year algebra; it includes the ordered field properties of the real number system, solution of linear equations and inequalities, verbal problems, exponents and operations with polynomials. Overall goals for the course are stated; performance objectives for each unit, a…
Algebra 1p, Mathematics: 5215.11.
ERIC Educational Resources Information Center
Strachan, Florence; Hirigoyen, Hector
This is the first of six guidebooks on minimum course content for first-year algebra; it introduces the language of sets, the fundamental operations and properties of the real number system, the use of variables, and the solution of simple linear equations and inequalities. Overall goals for the course are stated; then performance objectives, a…
Pre-Algebra Groups. Concepts & Applications.
ERIC Educational Resources Information Center
Montgomery County Public Schools, Rockville, MD.
Discussion material and exercises related to pre-algebra groups are provided in this five chapter manual. Chapter 1 (mappings) focuses on restricted domains, order of operations (parentheses and exponents), rules of assignment, and computer extensions. Chapter 2 considers finite number systems, including binary operations, clock arithmetic,…
Using geometric algebra to study optical aberrations
Hanlon, J.; Ziock, H.
1997-05-01
This paper uses Geometric Algebra (GA) to study vector aberrations in optical systems with square and round pupils. GA is a new way to produce the classical optical aberration spot diagrams on the Gaussian image plane and surfaces near the Gaussian image plane. Spot diagrams of the third, fifth and seventh order aberrations for square and round pupils are developed to illustrate the theory.
An Application of Boolean Algebra to Biology
ERIC Educational Resources Information Center
McConnell, John W.
1971-01-01
Examines the model of interacting nerve systems based on a switching theory, which uses a mathematical structure familiar to many high school students and requires little knowledge of biology. Reviews the basic operation of nerves, and demonstrates how Boolean algebraic statements are applied to synaptic interactions. (PR)
Pauli spinors and Hestenes' geometric algebra
NASA Astrophysics Data System (ADS)
Hamilton, J. Dwayne
1984-01-01
Hestenes' geometric algebra and Pauli's two-component spinors are reviewed and are united into a simple mathematical system. The resulting formalism is used to develop a new method for spin 1/2 projection calculations and is also applied to a spin 1/2 electron magnetic resonance problem.
Hincapié, Doracelly; Ospina, Juan
2011-01-01
Algebraic analysis of social networks exhibited by SARS-Beijing-2003 and AH1N1 flu-México-2009 was realized. The main tools were the Tutte polynomials and Maple package Graph-Theory. The topological structures like graphs and networks were represented by invariant polynomials. The evolution of a given social network was represented like an evolution of the algebraic complexity of the corresponding Tutte polynomial. The reduction of a given social network was described like an involution of the algebraic complexity of the associated Tutte polynomial. The outbreaks of SARS and AH1N1 Flu were considered like represented by a reduction of previously existing contact networks via the control measures executed by health authorities. From Tutte polynomials were derived numerical indicators about efficiency of control measures. PMID:21431617
Sheaf-theoretic representation of quantum measure algebras
Zafiris, Elias
2006-09-15
We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras. The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet axiomatization at the level of events, to the sheaf-theoretic gluing conditions at the level of Boolean localization systems.
ERIC Educational Resources Information Center
Beigie, Darin
2014-01-01
Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…
Vertex Algebras, Kac-Moody Algebras, and the Monster
NASA Astrophysics Data System (ADS)
Borcherds, Richard E.
1986-05-01
It is known that the adjoint representation of any Kac-Moody algebra A can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of A. I define a product on the whole of the Fock space that restricts to the Lie algebra product on this subquotient. This product (together with a infinite number of other products) is constructed using a generalization of vertex operators. I also construct an integral form for the universal enveloping algebra of any Kac-Moody algebra that can be used to define Kac-Moody groups over finite fields, some new irreducible integrable representations, and a sort of affinization of any Kac-Moody algebra. The ``Moonshine'' representation of the Monster constructed by Frenkel and others also has products like the ones constructed for Kac-Moody algebras, one of which extends the Griess product on the 196884-dimensional piece to the whole representation.
NASA Astrophysics Data System (ADS)
Palmkvist, Jakob
2014-01-01
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D - 2 - p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
Palmkvist, Jakob
2014-01-15
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
MODEL IDENTIFICATION AND COMPUTER ALGEBRA.
Bollen, Kenneth A; Bauldry, Shawn
2010-10-01
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods. PMID:21769158
Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
NASA Astrophysics Data System (ADS)
Paseka, Jan; Riečanová, Zdenka
2010-12-01
We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.
Using computer algebra in quantum computation and quantum games
NASA Astrophysics Data System (ADS)
Bolívar, David A.
2011-05-01
Research in contemporary physics is emphasizing the development and evolution of computer systems to facilitate the calculations. Quantum computing is a branch of modern physics is believed promising results for the future, Thanks to the ability of qubits to store more information than a bit. The work of this paper focuses on the simulation of certain quantum algorithms such as the prisoner's dilemma in its quantum version using the MATHEMATICA® software and implementing stochastic version of the software MAPLE ® and the Grover search algorithm that simulates finding a needle in a haystack.
Locally finite dimensional Lie algebras
NASA Astrophysics Data System (ADS)
Hennig, Johanna
We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L. Then we prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form [K(R, *), K( R, *)] / (Z(R) ∩ [ K(R, *), K(R, *)]) for a simple, locally finite dimensional associative algebra R with involution *. Lastly, we explore the noncommutative geometry of locally simple representations of the diagonal locally finite Lie algebras sl(ninfinity), o( ninfinity), and sp(n infinity).
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075
On the cohomology of Leibniz conformal algebras
NASA Astrophysics Data System (ADS)
Zhang, Jiao
2015-04-01
We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.
Assessing Algebraic Solving Ability: A Theoretical Framework
ERIC Educational Resources Information Center
Lian, Lim Hooi; Yew, Wun Thiam
2012-01-01
Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…
Hesse, Cedar N.; Mueller, Rebecca C.; Vuyisich, Momchilo; Gallegos-Graves, La Verne; Gleasner, Cheryl D.; Zak, Donald R.; Kuske, Cheryl R.
2015-01-01
Anthropogenic N deposition alters patterns of C and N cycling in temperate forests, where forest floor litter decomposition is a key process mediated by a diverse community of bacteria and fungi. To track forest floor decomposer activity we generated metatranscriptomes that simultaneously surveyed the actively expressed bacterial and eukaryote genes in the forest floor, to compare the impact of N deposition on the decomposers in two natural maple forests in Michigan, USA, where replicate field plots had been amended with N for 16 years. Site and N amendment responses were compared using about 74,000 carbohydrate active enzyme transcript sequences (CAZymes) in each metatranscriptome. Parallel ribosomal RNA (rRNA) surveys of bacterial and fungal biomass and taxonomic composition showed no significant differences in either biomass or OTU richness between the two sites or in response to N. Site and N amendment were not significant variables defining bacterial taxonomic composition, but they were significant for fungal community composition, explaining 17 and 14% of the variability, respectively. The relative abundance of expressed bacterial and fungal CAZymes changed significantly with N amendment in one of the forests, and N-response trends were also identified in the second forest. Although the two ambient forests were similar in community biomass, taxonomic structure and active CAZyme profile, the shifts in active CAZyme profiles in response to N-amendment differed between the sites. One site responded with an over-expression of bacterial CAZymes, and the other site responded with an over-expression of both fungal and different bacterial CAZymes. Both sites showed reduced representation of fungal lignocellulose degrading enzymes in N-amendment plots. The metatranscriptome approach provided a holistic assessment of eukaryote and bacterial gene expression and is applicable to other systems where eukaryotes and bacteria interact. PMID:25954263
Hesse, Cedar N.; Mueller, Rebecca C.; Vuyisich, Momchilo; Gallegos-Graves, La Verne; Gleasner, Cheryl D.; Zak, Donald R.; Kuske, Cheryl R.
2015-04-23
Anthropogenic N deposition alters patterns of C and N cycling in temperate forests, where forest floor litter decomposition is a key process mediated by a diverse community of bacteria and fungi. To track forest floor decomposer activity we generated metatranscriptomes that simultaneously surveyed the actively expressed bacterial and eukaryote genes in the forest floor, to compare the impact of N deposition on the decomposers in two natural maple forests in Michigan, USA, where replicate field plots had been amended with N for 16 years. Site and N amendment responses were compared using about 74,000 carbohydrate active enzyme transcript sequences (CAZymes) in each metatranscriptome. Parallel ribosomal RNA (rRNA) surveys of bacterial and fungal biomass and taxonomic composition showed no significant differences in either biomass or OTU richness between the two sites or in response to N. Site and N amendment were not significant variables defining bacterial taxonomic composition, but they were significant for fungal community composition, explaining 17 and 14% of the variability, respectively. The relative abundance of expressed bacterial and fungal CAZymes changed significantly with N amendment in one of the forests, and N-response trends were also identified in the second forest. Although the two ambient forests were similar in community biomass, taxonomic structure and active CAZyme profile, the shifts in active CAZyme profiles in response to N-amendment differed between the sites. One site responded with an over-expression of bacterial CAZymes, and the other site responded with an over-expression of both fungal and different bacterial CAZymes. Both sites showed reduced representation of fungal lignocellulose degrading enzymes in N-amendment plots. The metatranscriptome approach provided a holistic assessment of eukaryote and bacterial gene expression and is applicable to other systems where eukaryotes and bacteria interact.
Hesse, Cedar N.; Mueller, Rebecca C.; Vuyisich, Momchilo; Gallegos-Graves, La Verne; Gleasner, Cheryl D.; Zak, Donald R.; Kuske, Cheryl R.
2015-04-23
Anthropogenic N deposition alters patterns of C and N cycling in temperate forests, where forest floor litter decomposition is a key process mediated by a diverse community of bacteria and fungi. To track forest floor decomposer activity we generated metatranscriptomes that simultaneously surveyed the actively expressed bacterial and eukaryote genes in the forest floor, to compare the impact of N deposition on the decomposers in two natural maple forests in Michigan, USA, where replicate field plots had been amended with N for 16 years. Site and N amendment responses were compared using about 74,000 carbohydrate active enzyme transcript sequences (CAZymes)more » in each metatranscriptome. Parallel ribosomal RNA (rRNA) surveys of bacterial and fungal biomass and taxonomic composition showed no significant differences in either biomass or OTU richness between the two sites or in response to N. Site and N amendment were not significant variables defining bacterial taxonomic composition, but they were significant for fungal community composition, explaining 17 and 14% of the variability, respectively. The relative abundance of expressed bacterial and fungal CAZymes changed significantly with N amendment in one of the forests, and N-response trends were also identified in the second forest. Although the two ambient forests were similar in community biomass, taxonomic structure and active CAZyme profile, the shifts in active CAZyme profiles in response to N-amendment differed between the sites. One site responded with an over-expression of bacterial CAZymes, and the other site responded with an over-expression of both fungal and different bacterial CAZymes. Both sites showed reduced representation of fungal lignocellulose degrading enzymes in N-amendment plots. The metatranscriptome approach provided a holistic assessment of eukaryote and bacterial gene expression and is applicable to other systems where eukaryotes and bacteria interact.« less
Hesse, Cedar N; Mueller, Rebecca C; Vuyisich, Momchilo; Gallegos-Graves, La Verne; Gleasner, Cheryl D; Zak, Donald R; Kuske, Cheryl R
2015-01-01
Anthropogenic N deposition alters patterns of C and N cycling in temperate forests, where forest floor litter decomposition is a key process mediated by a diverse community of bacteria and fungi. To track forest floor decomposer activity we generated metatranscriptomes that simultaneously surveyed the actively expressed bacterial and eukaryote genes in the forest floor, to compare the impact of N deposition on the decomposers in two natural maple forests in Michigan, USA, where replicate field plots had been amended with N for 16 years. Site and N amendment responses were compared using about 74,000 carbohydrate active enzyme transcript sequences (CAZymes) in each metatranscriptome. Parallel ribosomal RNA (rRNA) surveys of bacterial and fungal biomass and taxonomic composition showed no significant differences in either biomass or OTU richness between the two sites or in response to N. Site and N amendment were not significant variables defining bacterial taxonomic composition, but they were significant for fungal community composition, explaining 17 and 14% of the variability, respectively. The relative abundance of expressed bacterial and fungal CAZymes changed significantly with N amendment in one of the forests, and N-response trends were also identified in the second forest. Although the two ambient forests were similar in community biomass, taxonomic structure and active CAZyme profile, the shifts in active CAZyme profiles in response to N-amendment differed between the sites. One site responded with an over-expression of bacterial CAZymes, and the other site responded with an over-expression of both fungal and different bacterial CAZymes. Both sites showed reduced representation of fungal lignocellulose degrading enzymes in N-amendment plots. The metatranscriptome approach provided a holistic assessment of eukaryote and bacterial gene expression and is applicable to other systems where eukaryotes and bacteria interact. PMID:25954263
ERIC Educational Resources Information Center
Novotna, Jarmila; Hoch, Maureen
2008-01-01
Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…
NASA Astrophysics Data System (ADS)
Farnell, D. J. J.; Darradi, R.; Schmidt, R.; Richter, J.
2011-09-01
We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized J-J' model interpolating between both systems by varying J'/J from J'/J=0 (bounce limit) to J'/J=1 (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the “pure” bounce (J'/J=0) and maple-leaf (J'/J=1) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range 0⩽J'/J≲Jc'/J and that the magnetic order parameter varies only weakly with J'/J. At Jc'≈1.45J, a transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place that is probably of first-order type, although we cannot rule out that this transition is second order. The orthogonal-dimer state is the exact ground state in this large-J' regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We find a 1/3 magnetization plateau for J'/J≳1.07 and another one at 2/3 of saturation emerging only at large J'/J≳3.
Biogeochemical features of maple and dandelion in Eastern Administrative District of Moscow
NASA Astrophysics Data System (ADS)
Vlasov, Dmitry
2014-05-01
Today more than half of world population and 73% of population in Russia live in cities. Moscow is the only one megacity in Russia with the population more than 11 million. The main source of technogenic impact in Moscow is transport. Plants can be used as indicators of urban environment heavy metals and metalloids (HM) pollution. Large scale biogeochemical research was done in Eastern Administrative District of Moscow. Apart from transport there are many industrial sources of pollution: metalworking, mechanical engineering, chemical, energetic and incinerator. This study focuses on detection of HM composition of woody plant leaves (maple - Acer platanoides) and herbaceous species leaves (dandelion - Taraxacum officinale). Plant material was collected on a regular greed with a step of 500-700 m. Background plants were sampled at 40 km west away from the city. Determination of Fe, Mn, Mo, Cd, Pb, Zn, Cu, As, Sb in plants was done using atomic absorption spectrometry after washing, drying and digestion with HNO3+H2O2. It was revealed that dandelion accumulates (index - concentration factors CF relatively background) Mo13Fe6Pb5Cd4.5As4Sb3, while maple Sb13As5.5Fe3Mo2Pb,Zn1.5. Geochemical specialization of plants in functional zones (industrial, transport, recreational, agricultural, residential areas with high-, middle- and low-rise buildings) was identified. The highest CF were determined for Mo in dandelion of all zones except industrial. In which the most accumulated elements are Fe and Mo, as well as Pb10As6Sb5Cu2. Arsenic is accumulated by dandelion in all zones. Copper is not concentrated by herbaceous species because of antagonism between Mo and Cu. The highest CF were determined for HM in maple of industrial zone. There trees concentrate Sb and As9Fe7Mo6Pb3Zn2. In the other zones levels of CF are lower in 2-5 times. Dandelion and maple don't accumulate Mn because of antagonism between Zn, Mo and Mn. Urban plants condition is estimated by the ratio between
Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators
NASA Astrophysics Data System (ADS)
Marquette, Ian
2011-06-01
We present a generalized Kaluza-Klein monopole system. We solve this quantum superintegrable system on a Euclidean Taub Nut manifold using the separation of variables of the corresponding Schrödinger equation in spherical and parabolic coordinates. We present the integrals of motion of this system, the quadratic algebra generated by these integrals, the realization in terms of a deformed oscillator algebra using the Daskaloyannis construction and the energy spectrum. The structure constants and the Casimir operator are functions not only of the Hamiltonian but also of other two integrals commuting with all generators of the quadratic algebra and forming an Abelian subalgebra. We present another algebraic derivation of the energy spectrum of this system using the factorization method and ladder operators.
Liu, Yongqiang; Ma, Hang; Seeram, Navindra P
2016-05-01
The phenolic contents of plant foods are commonly quantified by the Folin-Ciocalteu assay based on gallic acid equivalents (GAEs). However, this may lead to inaccuracies because gallic acid is not always representative of the structural heterogeneity of plant phenolics. Therefore, product-specific standards have been developed for the phenolic quantification of several foods. Currently, maple-derived foods (syrup, sugar, sap/water, and extracts) are quantified for phenolic contents based on GAEs. Because lignans are the predominant phenolics present in maple, herein, a maple phenolic lignan-enriched standard (MaPLES) was purified (by chromatography) and characterized (by UFLC-MS/MS with lignans previously isolated from maple syrup). Using MaPLES and secoisolariciresinol (a commercially available lignan), the phenolic contents of the maple-derived foods increased 3-fold compared to GAEs. Therefore, lignan-based standards are more appropriate for phenolic quantification of maple-derived foods versus GAEs. Also, MaPLES can be utilized for the authentication and detection of fake label claims on maple products. PMID:27101225
NASA Astrophysics Data System (ADS)
Stiff-Roberts, Adrienne D.; McCormick, Ryan D.; Ge, Wangyao
2015-03-01
Resonant-infrared, matrix-assisted pulsed laser evaporation (RIR-MAPLE) has been used to deposit blended, organic thin-films with nanoscale domain sizes of constituent polymers, small molecules, or colloidal nanoparticles. In the emulsion-based RIR-MAPLE process, the target contains a nonpolar, organic solvent phase and a polar, water phase. The emulsion properties have a direct impact on the nanoscale morphology of single-component organic thin films, while the morphology of blended, organic thin films also depends on the RIR-MAPLE deposition mode. In addition to these fundamental aspects, applications of blended organic films (organic solar cells, anti-reflection coatings, and multi-functional surfaces) deposited by emulsion-based RIR-MAPLE are presented. Importantly, domain sizes in the blended films are critical to thin-film functionality.
The algebra of supertraces for (2 + 1) super de Sitter gravity
Urrutia, L.F. ); Waelbroeck, H. ); Zertuche, F. )
1992-09-21
In this paper, the authors calculate the algebra of the observables for 2 + 1 super de Sitter gravity, for one genus of the spatial surface. The algebra turns out to be an infinite Lie algebra subject to nonlinear constraints. The authors solve the constraints explicitly in terms of five independent complex supertraces. These variables are the true degrees of freedom of the system and their quantized algebra generates a new structure which we refer to as a central extension of the quantum algebra SU(2)[sub q].
The algebra of supertraces for 2+1 super de Sitter gravity
NASA Technical Reports Server (NTRS)
Urrutia, L. F.; Waelbroeck, H.; Zertuche, F.
1993-01-01
The algebra of the observables for 2+1 super de Sitter gravity, for one genus of the spatial surface is calculated. The algebra turns out to be an infinite Lie algebra subject to non-linear constraints. The constraints are solved explicitly in terms of five independent complex supertraces. These variables are the true degrees of freedom of the system and their quantized algebra generates a new structure which is referred to as a 'central extension' of the quantum algebra SU(2)q.
Abstract Algebra to Secondary School Algebra: Building Bridges
ERIC Educational Resources Information Center
Christy, Donna; Sparks, Rebecca
2015-01-01
The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…
Algebra and Algebraic Thinking in School Math: 70th YB
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, 2008
2008-01-01
Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…
A Cohomology Theory of Grading-Restricted Vertex Algebras
NASA Astrophysics Data System (ADS)
Huang, Yi-Zhi
2014-04-01
We introduce a cohomology theory of grading-restricted vertex algebras. To construct the correct cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the algebraic completion of a module for the algebra," instead of linear maps from tensor powers of the algebra to a module for the algebra. One subtle complication arising from such functions is that we have to carefully address the issue of convergence when we compose these linear maps with vertex operators. In particular, for each , we have an inverse system of nth cohomologies and an additional nth cohomology of a grading-restricted vertex algebra V with coefficients in a V-module W such that is isomorphic to the inverse limit of the inverse system . In the case of n = 2, there is an additional second cohomology denoted by which will be shown in a sequel to the present paper to correspond to what we call square-zero extensions of V and to first order deformations of V when W = V.
NASA Astrophysics Data System (ADS)
Latini, Danilo; Ragnisco, Orlando
2015-05-01
The formalism of SUperSYmmetric quantum mechanics (SUSYQM) is properly modified in such a way to be suitable for the description and the solution of a classical maximally superintegrable Hamiltonian system, the so-called Taub-Nut system, associated with the Hamiltonian: In full agreement with the results recently derived by Ballesteros et al for the quantum case, we show that the classical Taub-Nut system shares a number of essential features with the Kepler system, that is just its Euclidean version arising in the limit η \\to 0, and for which a ‘SUSYQM’ approach has been recently introduced by Kuru and Negro. In particular, for positive η and negative energy the motion is always periodic; it turns out that the period depends upon η and goes to the Euclidean value as η \\to 0. Moreover, the maximal superintegrability is preserved by the η-deformation, due to the existence of a larger symmetry group related to an η-deformed Runge-Lenz vector, which ensures that in {{{R}}3} closed orbits are again ellipses. In this context, a deformed version of the third Kepler’s law is also recovered. The closing section is devoted to a discussion of the η \\lt 0 case, where new and partly unexpected features arise.
Kimball, Briant A.; Johnson, Kevin K.; Runkel, Robert L.; Steiger, Judy I.
2004-01-01
The Silver Maple Claims area along Silver Creek, near Park City, Utah, is administered by the Bureau of Land Management. To quantify possible sources of elevated zinc concentrations in Silver Creek that exceed water-quality standards, the U.S. Geological Survey conducted a mass-loading study in May 2002 along a 1,400-meter reach of Silver Creek that included the Silver Maple Claims area. Additional samples were collected upstream and downstream from the injection reach to investigate other possible sources of zinc and other metals to the stream. Many metals were investigated in the study, but zinc is of particular concern for water-quality standards. The total loading of zinc along the study reach from Park City to Wanship, Utah, was about 49 kilograms per day. The Silver Maple Claims area contributed about 38 percent of this load. The Silver Creek tailings discharge pipe, which empties just inside the Silver Maple Claims area, contributed more than half the load of the Silver Maple Claims area. Substantial zinc loads also were added to Silver Creek downstream from the Silver Maple Claims area. Ground-water discharge upstream from the waste-water treatment plant contributed 20 percent of the total zinc load, and another 17 percent was contributed near the waste-water treatment plant. By identifying the specific areas where zinc and other metal loads are contributed to Silver Creek, it is possible to assess the needs of a remediation plan. For example, removing the tailings from the Silver Maple Claims area could contribute to lowering the zinc concentration in Silver Creek, but without also addressing the loading from the Silver Creek tailings discharge pipe and the ground-water discharge farther downstream, the zinc concentration could not be lowered enough to meet water-quality standards. Additional existing sources of zinc loading downstream from the Silver Maple Claims area could complicate the process of lowering zinc concentration to meet water
Panzuto, M; Lorenzetti, F; Mauffette, Y; Albert, P J
2001-10-01
We investigated the behavioral feeding preference and the chemoreception of leaf polar extracts from trembling aspen, Populus tremuloides, and from sun and shade sugar maple, Acer saccharum, by larvae of the polyphagous forest tent caterpillar, Malacosoma disstria, a defoliator of deciduous forests in the Northern Hemisphere. Three polar extracts were obtained from each tree species: a total extract, a water fraction, and a methanol fraction. M. disstria larvae were allowed ad libitum access to an artificial diet from eclosion to the fifth instar. Two-choice cafeteria tests were performed comparing the mean (+/-SE) surface area eaten of the total extracts, and the following order of preference was obtained: aspen > sun maple > shade maple. Tests with the other fractions showed that M. disstria larvae preferred the total aspen extract to its water fraction, and the latter to its methanol fraction. The response to sun maple was similar to aspen. However, for the shade maple experiment, there was no difference between the total extract and its water fraction. Electrophysiological recordings for aspen showed that the sugar-sensitive cell elicited more spikes to the water fraction, followed by the total extract, and finally the methanol fraction. Spike activity to stimulations of sun and shade maple extracts revealed a similar trend, where methanol fraction > water fraction > total extract. Our findings are discussed in light of previously known information about this insect's performance on these host plants. PMID:11710605
NASA Astrophysics Data System (ADS)
Piqué, A.; Wu, P.; Ringeisen, B. R.; Bubb, D. M.; Melinger, J. S.; McGill, R. A.; Chrisey, D. B.
2002-01-01
The matrix-assisted pulsed laser evaporation (MAPLE) technique has been successfully used to deposit highly uniform thin films of various functional materials such as non-linear optical (NLO) organic materials, conductive polymers, luminescent organic molecules and several types of proteinaceous compounds. MAPLE is a laser evaporation technique for growing thin films of organic and polymeric materials which involves directing a pulsed laser beam (λ=193 nm; fluence=0.01-0.5 J cm -2) onto a frozen target (-40 to -160 °C) consisting of a solute polymeric or organic compound dissolved in a solvent matrix. Using MAPLE, thin films of N-(4-nitrophenyl)-( L)-prolinol or NPP, an NLO material; polypyrrole, a conductive polymer; and tris-(8-hydroxyquinoline) aluminum or Alq3, a luminescent organic compound, have been separately deposited with minor (in the case of Alq3) or no degradation (for the NPP and polypyrrole) to their optical and electrical properties. The MAPLE process has also been used to deposit discrete thin film micro-arrays of biotinylated bovine serum albumin (BSA). The deposited BSA films, after washing with a blocking protein and fluorescently tagged streptavidin, fluoresce when exposed to UV. This fluorescence indicates that the biochemical specificity of the transferred biotinylated protein is unaffected by the MAPLE process. These results demonstrate that the MAPLE technique can be used for growing thin films of functional polymer and active biomaterials.
The Propositional Logic Induced by Means of Basic Algebras
NASA Astrophysics Data System (ADS)
Chajda, I.
2015-12-01
A propositional logic induced by means of commutative basic algebras was already described by M. Botur and R. Halaš. It turns out that this is a kind of non-associative fuzzy logic which can be used e.g. in expert systems. Unfortunately, there are other important classes of basic algebras which are not commutative, e.g. orthomodular lattices which are used as an axiomatization of the logic of quantum mechanics. This motivated us to develop another axioms and derivation rules which form a propositional logic induced by basic algebras in general. We show that this logic is algebraizable in the sense of W. J. Blok and D. Pigozzi.
The Algebra of Complex Numbers.
ERIC Educational Resources Information Center
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
Algebraic Squares: Complete and Incomplete.
ERIC Educational Resources Information Center
Gardella, Francis J.
2000-01-01
Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)
ERIC Educational Resources Information Center
Buerman, Margaret
2007-01-01
Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…
Online Algebraic Tools for Teaching
ERIC Educational Resources Information Center
Kurz, Terri L.
2011-01-01
Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)
Condensing Algebra for Technical Mathematics.
ERIC Educational Resources Information Center
Greenfield, Donald R.
Twenty Algebra-Packets (A-PAKS) were developed by the investigator for technical education students at the community college level. Each packet contained a statement of rationale, learning objectives, performance activities, performance test, and performance test answer key. The A-PAKS condensed the usual sixteen weeks of algebra into a six-week…
Algebraic Thinking in Adult Education
ERIC Educational Resources Information Center
Manly, Myrna; Ginsburg, Lynda
2010-01-01
In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic…
Linear Algebra and Image Processing
ERIC Educational Resources Information Center
Allali, Mohamed
2010-01-01
We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)
ERIC Educational Resources Information Center
Instructional Objectives Exchange, Los Angeles, CA.
A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…
Exploring Algebraic Patterns through Literature.
ERIC Educational Resources Information Center
Austin, Richard A.; Thompson, Denisse R.
1997-01-01
Presents methods for using literature to develop algebraic thinking in an environment that connects algebra to various situations. Activities are based on the book "Anno's Magic Seeds" with additional resources listed. Students express a constant function, exponential function, and a recursive function in their own words as well as writing about…
Learning Algebra from Worked Examples
ERIC Educational Resources Information Center
Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.
2014-01-01
For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is…
Asymptotics of bivariate generating functions with algebraic singularities
NASA Astrophysics Data System (ADS)
Greenwood, Torin
Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.
Dosimetry aspects of the new Canadian MAPLE-X10 reactor
Lidstone, R.F.; Wilkin, G.B.
1994-12-31
Atomic Energy of Canada Limited is building the 10-MW{sub t} MAPLE-X10 reactor facility as a dedicated producer of medical and industrial radioisotopes. Dosimetry aspects of the MAPLE-X10 nuclear design include the calculated thermal and fast neutron flux distributions throughout the reactor assembly and the rate of heat generation in reactor materials and components. Examples of the resolution of design issues are also presented, such as the use of fission counters and ion chambers to provide diverse methods of detecting neutron flux levels and the use of the difference between photon and neutron signals to guard against the effects of downgrading of the heavy-water reflector. Computer codes employed in the calculations include MCNP, ONEDANT, WIMS-AECL, and 3DDT.
NASA Astrophysics Data System (ADS)
Grumezescu, Valentina; Andronescu, Ecaterina; Holban, Alina Maria; Mogoantă, Laurenţiu; Mogoşanu, George Dan; Grumezescu, Alexandru Mihai; Stănculescu, Anca; Socol, Gabriel; Iordache, Florin; Maniu, Horia; Chifiriuc, Mariana Carmen
2015-05-01
In this study we aimed to evaluate the biocompatibility and antimicrobial activity of kanamycin functionalized 5 nm-magnetite (Fe3O4@KAN) nanoparticles thin films deposited by Matrix Assisted Pulsed Laser Evaporation (MAPLE) technique. A laser deposition regime was established in order to stoichiometrically transfer Fe3O4@KAN thin films on silicone and glass substrates. Morphological and physico-chemical properties of powders and coatings were characterized by XRD, TEM, SEM, AFM and IR microscopy (IRM). Our nanostructured thin films have proved efficiency in the prevention of microbial adhesion and mature biofilms development as a result of antibiotic release in its active form. Furthermore, kanamycin functionalized nanostructures exhibit a good biocompatibility, both in vivo and in vitro, demonstrating their potential for implants application. This is the first study reporting the assessment of the in vivo biocompatibility of a magnetite-antimicrobial thin films produced by MAPLE technique.
Variation in mineral content of red maple sap across an atmospheric deposition gradient
McCormick, L.H.
1997-11-01
Xylem sap was collected from red maple (Acer rubrum L.) trees during the spring of 1988 and 1989 at seven forest sites along an atmospheric deposition gradient in north central Pennsylvania and analyzed for pH and twelve mineral constituents. The objectives of the study were to examine the sources and patterns of variation in red maple sap chemistry across an atmospheric deposition gradient and to assess the feasibility of using sap analysis as an indicator of nutrient bioavailability. For most sap constituents, there was considerable spatial and temporal variation in concentration. Sources of variation included within and between site variation, date, and year of collection. The nature and extent of variation varied for different constituents. Site differences were similar in 1988 and 1989 for most sap constituents and for some constituents corresponded with differences in soil levels.
Aaron, Catherine; Beaudry, Gabrielle; Parker, J Alex; Therrien, Martine
2016-05-01
Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease causing death of the motor neurons. Proteotoxicity caused by TDP-43 protein is an important aspect of ALS pathogenesis, with TDP-43 being the main constituent of the aggregates found in patients. We have previously tested the effect of different sugars on the proteotoxicity caused by the expression of mutant TDP-43 in Caenorhabditis elegans. Here we tested maple syrup, a natural compound containing many active molecules including sugars and phenols, for neuroprotective activity. Maple syrup decreased several age-dependent phenotypes caused by the expression of TDP-43(A315T) in C. elegans motor neurons and requires the FOXO transcription factor DAF-16 to be effective. PMID:27071850
Invariants of triangular Lie algebras
NASA Astrophysics Data System (ADS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-07-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated.
Application of polynomial su(1, 1) algebra to Pöschl-Teller potentials
Zhang, Hong-Biao Lu, Lu
2013-12-15
Two novel polynomial su(1, 1) algebras for the physical systems with the first and second Pöschl-Teller (PT) potentials are constructed, and their specific representations are presented. Meanwhile, these polynomial su(1, 1) algebras are used as an algebraic technique to solve eigenvalues and eigenfunctions of the Hamiltonians associated with the first and second PT potentials. The algebraic approach explores an appropriate new pair of raising and lowing operators K-circumflex{sub ±} of polynomial su(1, 1) algebra as a pair of shift operators of our Hamiltonians. In addition, two usual su(1, 1) algebras associated with the first and second PT potentials are derived naturally from the polynomial su(1, 1) algebras built by us.
Parametric Decay of Pump Waves into two Linear Modes in SINP MaPLE Device
Biswas, Subir; Pal, Rabindranath
2010-11-23
Parametric decay of incident waves of ion cyclotron frequency range into linear modes is observed in experiment performed in the SINP MaPLE device where nitrogen plasma produced by ECR discharge. Along with a mode in drift wave frequency range, sideband of the incident waves are observed when amplitude of the exciter signal goes above a threshold value. Sideband of the second harmonic is also seen. Preliminary studies point towards excitation of ion Bernstein wave. Details of the experimental results are presented.
Parametric Decay of Pump Waves into two Linear Modes in SINP MaPLE Device
NASA Astrophysics Data System (ADS)
Biswas, Subir; Pal, Rabindranath
2010-11-01
Parametric decay of incident waves of ion cyclotron frequency range into linear modes is observed in experiment performed in the SINP MaPLE device where nitrogen plasma produced by ECR discharge. Along with a mode in drift wave frequency range, sideband of the incident waves are observed when amplitude of the exciter signal goes above a threshold value. Sideband of the second harmonic is also seen. Preliminary studies point towards excitation of ion Bernstein wave. Details of the experimental results are presented.
Atwal, P.S.; Macmurdo, C.; Grimm, P.C.
2015-01-01
Acute metabolic decompensation in maple syrup urine disease can occur during intercurrent illness and is a medical emergency. A handful of reports in the medical literature describe the use of peritoneal dialysis and haemodialysis as therapeutic inventions. We report the only patient from our centre to have haemodialysis performed in this setting. Combined with dietary BCAA restriction and calorific support, haemodialysis allows rapid reduction in plasma leucine concentrations considerably faster than conservative methods. PMID:26937409
Atwal, P S; Macmurdo, C; Grimm, P C
2015-09-01
Acute metabolic decompensation in maple syrup urine disease can occur during intercurrent illness and is a medical emergency. A handful of reports in the medical literature describe the use of peritoneal dialysis and haemodialysis as therapeutic inventions. We report the only patient from our centre to have haemodialysis performed in this setting. Combined with dietary BCAA restriction and calorific support, haemodialysis allows rapid reduction in plasma leucine concentrations considerably faster than conservative methods. PMID:26937409
Fuel values of stems and branches in post oak and red maple
Harris, R.A.
1985-01-01
In red maple (Acer rubrum), there was n.s.d. in higher heating value (HHV) between stem wood and branch wood or between stem bark and branch bark. In post oak (Quercus stellata) the HHV of stem bark was significantly higher than that of branch bark, but there was n.s.d. between stem wood and branch wood. For both species the wood had a significantly higher HHV than the bark. 1 reference.
Maisuria, Vimal B; Hosseinidoust, Zeinab; Tufenkji, Nathalie
2015-06-01
Phenolic compounds are believed to be promising candidates as complementary therapeutics. Maple syrup, prepared by concentrating the sap from the North American maple tree, is a rich source of natural and process-derived phenolic compounds. In this work, we report the antimicrobial activity of a phenolic-rich maple syrup extract (PRMSE). PRMSE exhibited antimicrobial activity as well as strong synergistic interaction with selected antibiotics against Gram-negative clinical strains of Escherichia coli, Proteus mirabilis, and Pseudomonas aeruginosa. Among the phenolic constituents of PRMSE, catechol exhibited strong synergy with antibiotics as well as with other phenolic components of PRMSE against bacterial growth. At sublethal concentrations, PRMSE and catechol efficiently reduced biofilm formation and increased the susceptibility of bacterial biofilms to antibiotics. In an effort to elucidate the mechanism for the observed synergy with antibiotics, PRMSE was found to increase outer membrane permeability of all bacterial strains and effectively inhibit efflux pump activity. Furthermore, transcriptome analysis revealed that PRMSE significantly repressed multiple-drug resistance genes as well as genes associated with motility, adhesion, biofilm formation, and virulence. Overall, this study provides a proof of concept and starting point for investigating the molecular mechanism of the reported increase in bacterial antibiotic susceptibility in the presence of PRMSE. PMID:25819960
Fungi in Ontario maple syrup & some factors that determine the presence of mold damage.
Frasz, Samantha L; Miller, J David
2015-08-17
Maple syrup is a high value artisanal product produced mainly in Canada and a number of States primarily in the northeast USA. Mold growth (Wallemia sebi) on commercial product was first reported in syrup in 1908. Since then, few data have been published. We conducted a systematic examination for fungi in maple syrup from 68 producers from all of the syrup-producing areas of Ontario, Canada. The mean pH of the samples was pH 6.82, sugar content averaged 68.0±0.89 °Brix and aw averaged 0.841±0.011. Some 23 species of fungi were isolated based on morphology and molecular techniques. The most common fungus in the maple syrup samples was Eurotium herbariorum, followed by Penicillium chrysogenum, Aspergillus penicillioides, Aspergillus restrictus, Aspergillus versicolor and two species of Wallemia. Cladosporium cladosporioides was also common but only recovered when fungi known from high sugar substrates were also present in the mold damaged sample. The rarely reported yeast Citeromyces matrinsis was found in samples from three producers. There appear to be three potential causes for mold damage observed. High aw was associated with about one third of the mold damage. Independently, cold packing (bottling at ~25 °C) was a risk factor. However, syrup of good quality and quite low aw values was contaminated. We hypothesize that sanitation in the bottling line and other aspects of the bottling process may be partial explanations. Clarifying this requires further study. PMID:26001061
Anderson, Rachel; Ryser, Peter
2015-01-01
Several theories exist about the role of anthocyanins in senescing leaves. To elucidate factors contributing to variation in autumn leaf anthocyanin contents among individual trees, we analysed anthocyanins and other leaf traits in 27 individuals of red maple (Acer rubrum L.) over two growing seasons in the context of timing of leaf senescence. Red maple usually turns bright red in the autumn, but there is considerable variation among the trees. Leaf autumn anthocyanin contents were consistent between the two years of investigation. Autumn anthocyanin content strongly correlated with degree of chlorophyll degradation mid to late September, early senescing leaves having the highest concentrations of anthocyanins. It also correlated positively with leaf summer chlorophyll content and dry matter content, and negatively with specific leaf area. Time of leaf senescence and anthocyanin contents correlated with soil pH and with canopy openness. We conclude that the importance of anthocyanins in protection of leaf processes during senescence depends on the time of senescence. Rather than prolonging the growing season by enabling a delayed senescence, autumn anthocyanins in red maple in Ontario are important when senescence happens early, possibly due to the higher irradiance and greater danger of oxidative damage early in the season. PMID:27135339
New Gallotannin and other Phytochemicals from Sycamore Maple (Acer pseudoplatanus) Leaves.
Zhang, Lu; Tu, Zong-cai; Yuan, Tao; Ma, Hang; Niesen, Daniel B; Wang, Hui; Seeram, Navindra P
2015-11-01
The maple (Acer) genus is a reported source of bioactive (poly)phenols, including gallotannins, but several of its members, such as the sycamore maple (A. pseudoplatanus), remain uninvestigated. Herein, thirty-nine compounds, including a new gallotannin, 1,2,3-tri-O-galloyl-6-O-(p-hydroxybenzoyl)-β-D- glucopyranoside (1), and thirty-eight (2-39) known compounds, consisting of four gallotannins, one ellagitannin, thirteen flavonoids, eight hydroxycinnamic acids, ten benzoic acid derivatives, and two sesquiterpenoids, were isolated from sycamore maple leaves. Their structures were determined based on NMR and mass spectral analyses. The isolates were evaluated for α-glucosidase inhibitory and antioxidant activities. Among the isolates, the gallotannins were the most potent α-glucosidase inhibitors with thirteen-fold more potent activity compared with the clinical drug, acarbose (IC50 = 16-31 vs. 218 µM). Similarly, the gallotannins showed the highest antioxidant activities, followed by the other phenolic sub-classes, while the sesquiterpenoids were inactive. PMID:26749841
Insects attracted to Maple Sap: Observations from Prince Edward Island, Canada
Majka, Christopher G.
2010-01-01
Abstract The collection of maple sap for the production of maple syrup is a large commercial enterprise in Canada and the United States. In Canada, which produces 85% of the world’s supply, it has an annual value of over $168 million CAD. Over 38 million trees are tapped annually, 6.5% of which use traditional buckets for sap collection. These buckets attract significant numbers of insects. Despite this, there has been very little investigation of the scale of this phenomenon and the composition of insects that are attracted to this nutrient source. The present paper reports the results of a preliminary study conducted on Prince Edward Island, Canada. Twenty-eight species of Coleoptera, Lepidoptera, and Trichoptera were found in maple sap buckets, 19 of which are known to be attracted to saps and nectars. The physiological role of sap feeding is discussed with reference to moths of the tribe Xylenini, which are active throughout the winter, and are well documented as species that feed on sap flows. Additionally, 18 of the 28 species found in this study are newly recorded in Prince Edward Island. PMID:21594122
Maisuria, Vimal B.; Hosseinidoust, Zeinab
2015-01-01
Phenolic compounds are believed to be promising candidates as complementary therapeutics. Maple syrup, prepared by concentrating the sap from the North American maple tree, is a rich source of natural and process-derived phenolic compounds. In this work, we report the antimicrobial activity of a phenolic-rich maple syrup extract (PRMSE). PRMSE exhibited antimicrobial activity as well as strong synergistic interaction with selected antibiotics against Gram-negative clinical strains of Escherichia coli, Proteus mirabilis, and Pseudomonas aeruginosa. Among the phenolic constituents of PRMSE, catechol exhibited strong synergy with antibiotics as well as with other phenolic components of PRMSE against bacterial growth. At sublethal concentrations, PRMSE and catechol efficiently reduced biofilm formation and increased the susceptibility of bacterial biofilms to antibiotics. In an effort to elucidate the mechanism for the observed synergy with antibiotics, PRMSE was found to increase outer membrane permeability of all bacterial strains and effectively inhibit efflux pump activity. Furthermore, transcriptome analysis revealed that PRMSE significantly repressed multiple-drug resistance genes as well as genes associated with motility, adhesion, biofilm formation, and virulence. Overall, this study provides a proof of concept and starting point for investigating the molecular mechanism of the reported increase in bacterial antibiotic susceptibility in the presence of PRMSE. PMID:25819960
The complete Heyting algebra of subsystems and contextuality
Vourdas, A.
2013-08-15
The finite set of subsystems of a finite quantum system with variables in Z(n), is studied as a Heyting algebra. The physical meaning of the logical connectives is discussed. It is shown that disjunction of subsystems is more general concept than superposition. Consequently, the quantum probabilities related to commuting projectors in the subsystems, are incompatible with associativity of the join in the Heyting algebra, unless if the variables belong to the same chain. This leads to contextuality, which in the present formalism has as contexts, the chains in the Heyting algebra. Logical Bell inequalities, which contain “Heyting factors,” are discussed. The formalism is also applied to the infinite set of all finite quantum systems, which is appropriately enlarged in order to become a complete Heyting algebra.
Dynamics of gelling liquids: algebraic relaxation.
Srivastava, Sunita; Kumar, C N; Tankeshwar, K
2009-08-19
The sol-gel system which is known, experimentally, to exhibit a power law decay of stress autocorrelation function has been studied theoretically. A second-order nonlinear differential equation obtained from Mori's integro-differential equation is derived which provides the algebraic decay of a time correlation function. Involved parameters in the expression obtained are related to exact properties of the corresponding correlation function. The algebraic model has been applied to Lennard-Jones and sol-gel systems. The model shows the behaviour of viscosity as has been observed in computer simulation and theoretical studies. The expression obtained for the viscosity predicts a logarithmic divergence at a critical value of the parameter in agreement with the prediction of other theories. PMID:21828600
Algebraic parameters identification of DC motors: methodology and analysis
NASA Astrophysics Data System (ADS)
Becedas, J.; Mamani, G.; Feliu, V.
2010-10-01
A fast, non-asymptotic, algebraic parameter identification method is applied to an uncertain DC motor to estimate the uncertain parameters: viscous friction coefficient and inertia. In this work, the methodology is developed and analysed, its convergence, a comparative study between the traditional recursive least square method and the algebraic identification method is carried out, and an analysis of the estimator in a noisy system is presented. Computer simulations were carried out to validate the suitability of the identification algorithm.
Chen, J.; Safro, I.
2011-01-01
Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.
Constraint algebra in bigravity
Soloviev, V. O.
2015-07-15
The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.
Projective Connections and the Algebra of Densities
George, Jacob
2008-11-18
Projective connections first appeared in Cartan's papers in the 1920's. Since then they have resurfaced periodically in, for example, integrable systems and perhaps most recently in the context of so called projectively equivariant quantisation. We recall the notion of projective connection and describe its relation with the algebra of densities on a manifold. In particular, we construct a Laplace-type operator on functions using a Thomas projective connection and a symmetric contravariant tensor of rank 2 ('upper metric')
Using Homemade Algebra Tiles To Develop Algebra and Prealgebra Concepts.
ERIC Educational Resources Information Center
Leitze, Annette Ricks; Kitt, Nancy A.
2000-01-01
Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)
Distance geometry and geometric algebra
NASA Astrophysics Data System (ADS)
Dress, Andreas W. M.; Havel, Timothy F.
1993-10-01
As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)
Loop Virasoro Lie conformal algebra
Wu, Henan Chen, Qiufan; Yue, Xiaoqing
2014-01-15
The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.
Hopf algebras and Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Weinzierl, Stefan
2016-06-01
In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.
A spatial operator algebra for manipulator modeling and control
NASA Technical Reports Server (NTRS)
Rodriguez, G.; Kreutz, K.; Milman, M.
1988-01-01
A powerful new spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed along with its implementation in the Ada programming language. Applications of this algebra to robotics include an operator representation of the manipulator Jacobian matrix; the robot dynamical equations formulated in terms of the spatial algebra, showing the complete equivalence between the recursive Newton-Euler formulations to robot dynamics; the operator factorization and inversion of the manipulator mass matrix which immediately results in O(N) recursive forward dynamics algorithms; the joint accelerations of a manipulator due to a tip contact force; the recursive computation of the equivalent mass matrix as seen at the tip of a manipulator; and recursive forward dynamics of a closed chain system. Finally, additional applications and current research involving the use of the spatial operator algebra are discussed in general terms.
Strauss, Kevin A; Wardley, Bridget; Robinson, Donna; Hendrickson, Christine; Rider, Nicholas L; Puffenberger, Erik G; Shellmer, Diana; Shelmer, Diana; Moser, Ann B; Morton, D Holmes
2010-04-01
Branched-chain ketoacid dehydrogenase deficiency results in complex and volatile metabolic derangements that threaten brain development. Treatment for classical maple syrup urine disease (MSUD) should address this underlying physiology while also protecting children from nutrient deficiencies. Based on a 20-year experience managing 79 patients, we designed a study formula to (1) optimize transport of seven amino acids (Tyr, Trp, His, Met, Thr, Gln, Phe) that compete with branched-chain amino acids (BCAAs) for entry into the brain via a common transporter (LAT1), (2) compensate for episodic depletions of glutamine, glutamate, and alanine caused by reverse transamination, and (3) correct deficiencies of omega-3 essential fatty acids, zinc, and selenium widespread among MSUD patients. The formula was enriched with LAT1 amino acid substrates, glutamine, alanine, zinc, selenium, and alpha-linolenic acid (18:3n-3). Fifteen Old Order Mennonite children were started on study formula between birth and 34 months of age and seen at least monthly in the office. Amino acid levels were checked once weekly and more often during illnesses. All children grew and developed normally over a period of 14-33 months. Energy demand, leucine tolerance, and protein accretion were tightly linked during periods of normal growth. Rapid shifts to net protein degradation occurred during illnesses. At baseline, most LAT1 substrates varied inversely with plasma leucine, and their calculated rates of brain uptake were 20-68% below normal. Treatment with study formula increased plasma concentrations of LAT1 substrates and normalized their calculated uptakes into the nervous system. Red cell membrane omega-3 polyunsaturated fatty acids and serum zinc and selenium levels increased on study formula. However, selenium and docosahexaenoic acid (22:6n-3) levels remained below normal. During the study period, hospitalizations decreased from 0.35 to 0.14 per patient per year. There were 28 hospitalizations
Strauss, Kevin A.; Wardley, Bridget; Robinson, Donna; Hendrickson, Christine; Rider, Nicholas L.; Puffenberger, Erik G.; Shelmer, Diana; Moser, Ann B.; Morton, D. Holmes
2012-01-01
Branched-chain ketoacid dehydrogenase deficiency results in complex and volatile metabolic derangements that threaten brain development. Treatment for classical maple syrup urine disease (MSUD) should address this underlying physiology while also protecting children from nutrient deficiencies. Based on a 20-year experience managing 79 patients, we designed a study formula to (1) optimize transport of seven amino acids (Tyr, Trp, His, Met, Thr, Gln, Phe) that compete with branched-chain amino acids (BCAAs) for entry into the brain via a common transporter (LAT1), (2) compensate for episodic depletions of glutamine, glutamate, and alanine caused by reverse transamination, and (3) correct deficiencies of omega-3 essential fatty acids, zinc, and selenium widespread among MSUD patients. The formula was enriched with LAT1 amino acid substrates, glutamine, alanine, zinc, selenium, and alphalinolenic acid (18:3n – 3). Fifteen Old Order Mennonite children were started on study formula between birth and 34 months of age and seen at least monthly in the office. Amino acid levels were checked once weekly and more often during illnesses. All children grew and developed normally over a period of 14– 33 months. Energy demand, leucine tolerance, and protein accretion were tightly linked during periods of normal growth. Rapid shifts to net protein degradation occurred during illnesses. At baseline, most LAT1 substrates varied inversely with plasma leucine, and their calculated rates of brain uptake were 20–68% below normal. Treatment with study formula increased plasma concentrations of LAT1 substrates and normalized their calculated uptakes into the nervous system. Red cell membrane omega-3 polyunsaturated fatty acids and serum zinc and selenium levels increased on study formula. However, selenium and docosahexaenoic acid (22:6n – 3) levels remained below normal. During the study period, hospitalizations decreased from 0.35 to 0.14 per patient per year. There were 28
Implementing Computer Algebra Enabled Questions for the Assessment and Learning of Mathematics
ERIC Educational Resources Information Center
Sangwin, Christopher J.; Naismith, Laura
2008-01-01
We present principles for the design of an online system to support computer algebra enabled questions for use within the teaching and learning of mathematics in higher education. The introduction of a computer algebra system (CAS) into a computer aided assessment (CAA) system affords sophisticated response processing of student provided answers.…
Simulation of n-qubit quantum systems. I. Quantum registers and quantum gates
NASA Astrophysics Data System (ADS)
Radtke, T.; Fritzsche, S.
2005-12-01
During recent years, quantum computations and the study of n-qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing quantum computations, however, these investigations also revealed a great deal of difficulties which still need to be solved in practice. In quantum computing, unitary and non-unitary quantum operations act on a given set of qubits to form (entangled) states, in which the information is encoded by the overall system often referred to as quantum registers. To facilitate the simulation of such n-qubit quantum systems, we present the FEYNMAN program to provide all necessary tools in order to define and to deal with quantum registers and quantum operations. Although the present version of the program is restricted to unitary transformations, it equally supports—whenever possible—the representation of the quantum registers both, in terms of their state vectors and density matrices. In addition to the composition of two or more quantum registers, moreover, the program also supports their decomposition into various parts by applying the partial trace operation and the concept of the reduced density matrix. Using an interactive design within the framework of MAPLE, therefore, we expect the FEYNMAN program to be helpful not only for teaching the basic elements of quantum computing but also for studying their physical realization in the future. Program summaryTitle of program:FEYNMAN Catalogue number:ADWE Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:None Computers for which the program is designed:All computers with a license of the computer algebra system MAPLE [Maple is a registered trademark of Waterlo Maple Inc.] Operating systems or monitors under which the program has been tested:Linux, MS Windows XP Programming language used:MAPLE 9.5 (but should be compatible
Curvature calculations with spacetime algebra
Hestenes, D.
1986-06-01
A new method for calculating the curvature tensor is developed and applied to the Scharzschild case. The method employs Clifford algebra and has definite advantages over conventional methods using differential forms or tensor analysis.
GCD, LCM, and Boolean Algebra?
ERIC Educational Resources Information Center
Cohen, Martin P.; Juraschek, William A.
1976-01-01
This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)
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.
NASA Technical Reports Server (NTRS)
Klumpp, A. R.; Lawson, C. L.
1988-01-01
Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.
Hopf algebras and topological recursion
NASA Astrophysics Data System (ADS)
Esteves, João N.
2015-11-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).
2005-04-11
The ALGEBRA program allows the user to manipulate data from a finite element analysis before it is plotted. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database. The ALGEBRA program evaluates user-supplied functions of the data and writes the results to an output EXODUS II database that can be read by plot programs.
NASA Astrophysics Data System (ADS)
Caricato, A. P.; Anni, M.; Cesaria, M.; Lattante, S.; Leggieri, G.; Leo, C.; Martino, M.; Perulli, A.; Resta, V.
2015-06-01
The Matrix-Assisted Pulsed Laser Evaporation (MAPLE) technique is emerging as an alternative route to the conventional methods for depositing organic materials, although the MAPLE-deposited films very often present high surface roughness and characteristic morphological features. Films of the blue-emitting polymer, poly(9,9-dioctylfluorene)—PFO, have been deposited by MAPLE to investigate the influence of the laser fluence and repetition rate on both their topography and emission properties. The laser fluence has been changed from 150 up to 450 mJ/cm2, while laser repetition rates of 2 and 10 Hz have been considered. The interplay/relationship between the topography and the emission properties of the MAPLE-deposited films has been studied by confocal microscopy, photoluminescence spectrometry and atomic force microscopy. It has been found that under high irradiation (fluence of 450 mJ/cm2) conditions, the sample surface is characterized by bubbles presenting the intrinsic PFO blue emission. Instead, while improvements in the film morphology can be observed for lowered fluence and laser repetition rate, green emission becomes predominant in such conditions. Such result is very interesting to better understand the MAPLE ablation mechanism, which is discussed in this study.
Tappeiner, J. C., II; Zasada, J.; Maxwell, B.
1996-01-01
In order to determine the effects of stump height, year of cutting, parent-tree size, logging damage, and deer browsing on bigleaf maple (Acer macrophyllum) sprout clump development, maple trees were cut to two stump heights at three different times. Stump height had the greatest impact on sprout clump size. Two years after clearcutting, the sprout clump volume for short stumps was significantly less than that for tall stumps. The sprout clump volume, area, and number of sprouts were significantly less for trees cut 1 and 2 yr before harvest than for trees cut at harvest. Sprout clump size was positively correlated with parent tree stem diameter and stump volume, and negatively correlated with the percentage of bark removed during logging. Browsing had no significant impact on average clump size. Uncut trees produced sprout clumps at their base and epicormic branches along the length of their stems; thus their crown volume averaged four to five times that of cut trees. Cutting maple in clearcuts to low stumps may reduce maple competition with Douglas-fir regeneration and still maintain maple in the next stand.
Diagonalization and Jordan Normal Form--Motivation through "Maple"[R
ERIC Educational Resources Information Center
Glaister, P.
2009-01-01
Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package…
Cirelli, Damián; Jagels, Richard; Tyree, Melvin T
2008-08-01
Two theories have been proposed to explain how high positive pressures are developed in sugar maple stems when temperatures fluctuate around freezing. The Milburn-O'Malley theory proposes that pressure development is purely physical and does not require living cells or sucrose. The osmotic theory invokes the involvement of living cells and sucrose to generate an osmotic pressure difference between fibers and vessels, which are assumed to be separated by an osmotic barrier. We analyzed wood of Acer saccharum Marsh., Juglans cinerea L. and Betula papyrifera Marsh. (all generate positive pressures) examining three critical components of the osmotic model: pits in cell walls, selectivity of the osmotic barrier and stability of air bubbles under positive xylem pressure. We examined the distribution and type of pits directly by light and scanning electron microscopy (SEM), and indirectly by perfusion of branch segments with fluorescent dyes with molecular masses similar to sucrose. The latter approach allowed us to use osmotic surrogates for sucrose that could be tracked by epifluorescence. Infusion experiments were used to assess the compartmentalization of sucrose and to determine the behavior of gas bubbles as predicted by Fick's and Henry's laws. The SEM images of sugar maple revealed a lack of pitting between fibers and vessels but connections between fiber-tracheids and vessels were present. Fluorescein-perfusion experiments demonstrated that large molecules do not diffuse into libriform fibers but are confined within the domain of vessels, parenchyma and fiber-tracheids. Results of the infusion experiments were in agreement with those of the fluorescein perfusions and further indicated the necessity of a compartmentalized osmolyte to drive stem pressure, as well as the inability of air bubbles to maintain such pressure because of instability. These results support the osmotic model and demonstrate that the secondary cell wall is an effective osmotic barrier for
ERIC Educational Resources Information Center
Yantz, Jennifer
2013-01-01
The attainment and retention of later algebra skills in high school has been identified as a factor significantly impacting the postsecondary success of students majoring in STEM fields. Researchers maintain that learners develop meaning for algebraic procedures by forming connections to the basic number system properties. The present study…
Multifractal vector fields and stochastic Clifford algebra
NASA Astrophysics Data System (ADS)
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Multifractal vector fields and stochastic Clifford algebra
Schertzer, Daniel Tchiguirinskaia, Ioulia
2015-12-15
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Multifractal vector fields and stochastic Clifford algebra.
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality. PMID:26723166
CULA: hybrid GPU accelerated linear algebra routines
NASA Astrophysics Data System (ADS)
Humphrey, John R.; Price, Daniel K.; Spagnoli, Kyle E.; Paolini, Aaron L.; Kelmelis, Eric J.
2010-04-01
The modern graphics processing unit (GPU) found in many standard personal computers is a highly parallel math processor capable of nearly 1 TFLOPS peak throughput at a cost similar to a high-end CPU and an excellent FLOPS/watt ratio. High-level linear algebra operations are computationally intense, often requiring O(N3) operations and would seem a natural fit for the processing power of the GPU. Our work is on CULA, a GPU accelerated implementation of linear algebra routines. We present results from factorizations such as LU decomposition, singular value decomposition and QR decomposition along with applications like system solution and least squares. The GPU execution model featured by NVIDIA GPUs based on CUDA demands very strong parallelism, requiring between hundreds and thousands of simultaneous operations to achieve high performance. Some constructs from linear algebra map extremely well to the GPU and others map poorly. CPUs, on the other hand, do well at smaller order parallelism and perform acceptably during low-parallelism code segments. Our work addresses this via hybrid a processing model, in which the CPU and GPU work simultaneously to produce results. In many cases, this is accomplished by allowing each platform to do the work it performs most naturally.
Invertible linear transformations and the Lie algebras
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Tam, Honwah; Guo, Fukui
2008-07-01
With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.
Management of a Woman With Maple Syrup Urine Disease During Pregnancy, Delivery, and Lactation.
Wessel, Ann E; Mogensen, Kris M; Rohr, Frances; Erick, Miriam; Neilan, Edward G; Chopra, Sameer; Levy, Harvey L; Gray, Kathryn J; Wilkins-Haug, Louise; Berry, Gerard T
2015-09-01
Maple syrup urine disease (MSUD) is an inherited disorder of metabolism of the branched-chain amino acids leucine, isoleucine, and valine. Complications of acute elevation in plasma leucine include ketoacidosis and risk of cerebral edema, which can be fatal. Individuals with MSUD are at risk of metabolic crisis throughout life, especially at times of physiological stress. We present a case of successful management of a woman with MSUD through pregnancy, delivery, postpartum, and lactation, including nutrition therapy using modified parenteral nutrition. PMID:24618664
ERIC Educational Resources Information Center
Crittenden, Barry D.
1991-01-01
A simple liquid-liquid equilibrium (LLE) system involving a constant partition coefficient based on solute ratios is used to develop an algebraic understanding of multistage contacting in a first-year separation processes course. This algebraic approach to the LLE system is shown to be operable for the introduction of graphical techniques…
The algebra of the quantum nondegenerate three-dimensional Kepler-Coulomb potential
Tanoudis, Y.; Daskaloyannis, C.
2011-07-15
The classical generalized Kepler-Coulomb potential, introduced by Verrier and Evans, corresponds to a quantum superintegrable system, with quadratic and quartic integrals of motion. In this paper we show that the algebra of the integrals is a quadratic ternary algebra, i.e a quadratic extension of a Lie triple system.
Generic, Type-Safe and Object Oriented Computer Algebra Software
NASA Astrophysics Data System (ADS)
Kredel, Heinz; Jolly, Raphael
Advances in computer science, in particular object oriented programming, and software engineering have had little practical impact on computer algebra systems in the last 30 years. The software design of existing systems is still dominated by ad-hoc memory management, weakly typed algorithm libraries and proprietary domain specific interactive expression interpreters. We discuss a modular approach to computer algebra software: usage of state-of-the-art memory management and run-time systems (e.g. JVM) usage of strongly typed, generic, object oriented programming languages (e.g. Java) and usage of general purpose, dynamic interactive expression interpreters (e.g. Python) To illustrate the workability of this approach, we have implemented and studied computer algebra systems in Java and Scala. In this paper we report on the current state of this work by presenting new examples.
NASA Technical Reports Server (NTRS)
Schwaller, M. R.; Schnetzler, C. C.; Marshall, P. E.
1983-01-01
The effects of heavy metal stress on leaf reflectance of sugar maple seedlings (Acer saccharum Marsh) are examined. It is found that sugar maple seedlings treated with anomalous amounts of heavy metals in the rooting medium exhibited an increased leaf reflectance over the entire range of investigated wavelengths, from 475 to 1650 nm. These results conform to those of a previous investigation in the wavelengths from 475 to 660 nm, but tend to contradict the previous study in the near infrared wavelengths from 1000 to 1650 nm. The differences may possibly be due to different water regimes in the two investigations. Previously announced in STAR as N81-29729
NASA Technical Reports Server (NTRS)
Schwaller, M. R.; Schnetzler, C. C.; Marshall, P. E.
1981-01-01
The effects of heavy metal stress on leaf reflectance of sugar maple seedlings (Acer saccharum Marsh) are examined. It is found that sugar maple seedlings treated with anomalous amounts of heavy metals in the rooting medium exhibited an increased leaf reflectance over the entire range of investigated wavelengths, from 475 to 1650 nm. These results conform to those of a previous investigation in the wavelengths from 475 to 660nm, but tend to contradict the previous study in the near infrared wavelengths from 1000 to 1650nm. The differences may possible be due to different water regimes in the two investigations.
Vector fields and nilpotent Lie algebras
NASA Technical Reports Server (NTRS)
Grayson, Matthew; Grossman, Robert
1987-01-01
An infinite-dimensional family of flows E is described with the property that the associated dynamical system: x(t) = E(x(t)), where x(0) is a member of the set R to the Nth power, is explicitly integrable in closed form. These flows E are of the form E = E1 + E2, where E1 and E2 are the generators of a nilpotent Lie algebra, which is either free, or satisfies some relations at a point. These flows can then be used to approximate the flows of more general types of dynamical systems.
Fast Modular Exponentiation and Elliptic Curve Group Operation in Maple
ERIC Educational Resources Information Center
Yan, S. Y.; James, G.
2006-01-01
The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…
Ternary generalization of Heisenberg's algebra
NASA Astrophysics Data System (ADS)
Kerner, Richard
2015-06-01
A concise study of ternary and cubic algebras with Z3 grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, S3, and its abelian subgroup Z3 may play an important role in quantum physics. We show then how most of important algebras with Z2 grading can be generalized with ternary composition laws combined with a Z3 grading. We investigate in particular a ternary, Z3-graded generalization of the Heisenberg algebra. It turns out that introducing a non-trivial cubic root of unity, , one can define two types of creation operators instead of one, accompanying the usual annihilation operator. The two creation operators are non-hermitian, but they are mutually conjugate. Together, the three operators form a ternary algebra, and some of their cubic combinations generate the usual Heisenberg algebra. An analogue of Hamiltonian operator is constructed by analogy with the usual harmonic oscillator, and some properties of its eigenfunctions are briefly discussed.
Beyond Dirac - a Unified Algebra
NASA Astrophysics Data System (ADS)
Lundberg, Wayne R.
2001-10-01
A introductory insight will be shared regarding a 'separation of variables' approach to understanding the relationship between QCD and the origins of cosmological and particle mass. The discussion will then build upon work presented at DFP 2000, focussing on the formal basis for using 3x3x3 matrix algebra as it underlies and extends Dirac notation. A set of restrictions are established which break the multiple symmetries of the 3x3x3 matrix algebra, yielding Standard Model QCD objects and interactions. It will be shown that the 3x3x3 matrix representation unifies the algebra of strong and weak (and by extension, electromagnetic) interactions. A direct correspondence to string theoretic objects is established by considering the string to be partitioned in thirds. Rubik's cube is used as a graphical means of handling algebraic manipulation of 3x3x3 algebra. Further, its potential utility for advancing pedagogical methods through active engagement is discussed. A simulated classroom exercize will be conducted.
Free-field realisations of the BMS3 algebra and its extensions
NASA Astrophysics Data System (ADS)
Banerjee, Nabamita; Jatkar, Dileep P.; Mukhi, Sunil; Neogi, Turmoli
2016-06-01
We construct an explicit realisation of the BMS3 algebra with nonzero central charges using holomorphic free fields. This can be extended by the addition of chiral matter to a realisation having arbitrary values for the two independent central charges. Via the introduction of additional free fields, we extend our construction to the minimally supersymmetric BMS3 algebra and to the nonlinear higher-spin BMS3-W3 algebra. We also describe an extended system that realises both the SU(2) current algebra as well as BMS3 via the Wakimoto representation, though in this case introducing a central extension also brings in new non-central operators.
A computer code for calculations in the algebraic collective model of the atomic nucleus
NASA Astrophysics Data System (ADS)
Welsh, T. A.; Rowe, D. J.
2016-03-01
A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1 , 1) × SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments qˆM and are at most quadratic in the corresponding conjugate momenta πˆN (- 2 ≤ M , N ≤ 2). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators [ π ˆ ⊗ q ˆ ⊗ π ˆ ] 0 and [ π ˆ ⊗ π ˆ ] LM. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5) ⊃ SO(3) Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.
Teaching Mathematics Using a Computer Algebra.
ERIC Educational Resources Information Center
Westermann, Thomas
2001-01-01
Demonstrates the principal concept and the application of MAPLE in mathematical education in various examples. Discusses lengthy and abstract topics like the convergence of Fourier series to a given function, performs the visualization of the wave equation in the case of a vibrating string, and computes the oscillations of an idealized skyscraper…
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-04-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
A Maple Program That Illustrates the Effect of pH on Peptide Charge
NASA Astrophysics Data System (ADS)
Sokolik, Charles W.
1998-11-01
One topic covered early in an introductory biochemistry course is acid-base chemistry and the Henderson-Hasselbalch equation (buffer equation). Using this equation a biochemistry student can determine the partial charges of amino acids in a peptide chain. This is an important concept to master for a student who is learning the structure-function relationship in proteins. The program described in this paper, written for Maple V, release 3 (Waterloo Maple Software, Waterloo, ON, Canada), uses the Henderson-Hasselbalch equation to calculate the partial charges of individual amino acids and the net charge of a peptide over the pH range 0 to 14. The amino acid sequence of a peptide is entered and an animated histogram is displayed illustrating the partial charge of the amino acids over the pH range. A graph showing the net charge of the peptide from pH 0 to 14 is also given. The program has been used with success in an introductory biochemistry course as an in-class demonstration as well as for individual homework assignments. The program is available through the Web page of the Journal of Chemical Education.
A numerical study of a freely-falling maple seed with autorotation
NASA Astrophysics Data System (ADS)
Lee, Injae; Choi, Haecheon
2015-11-01
Many single winged seeds such as those of maples exploit autorotation to decrease the descending velocity and increase the dispersal distance for the conservation of species. In this study, a numerical simulation is conducted for flow around a freely-falling maple seed (Acer palmatum) at the Reynolds number of 1186 (based on the mean chord length and characteristic terminal velocity). We use an immersed boundary method in a non-inertial reference frame (Kim & Choi, JCP, 2006) for the simulation. After a transient period, the seed reaches the steady autorotation with a stable leading edge vortex attached on the surface of the wing at which the descending velocity significantly decreases. At steady autorotation, the descending velocity is proportional to the square root of disc loading. We also study the effect of the initial position of the seeds on the timing of autorotation, and show that the autorotation occurs earlier when the wing leading edge or nut is initially positioned upward. Supported by NRF-2011-0028032.
Flexible heterostructures based on metal phthalocyanines thin films obtained by MAPLE
NASA Astrophysics Data System (ADS)
Socol, M.; Preda, N.; Rasoga, O.; Breazu, C.; Stavarache, I.; Stanculescu, F.; Socol, G.; Gherendi, F.; Grumezescu, V.; Popescu-Pelin, G.; Girtan, M.; Stefan, N.
2016-06-01
Heterostructures based on zinc phthalocyanine (ZnPc), magnesium phthalocyanine (MgPc) and 5,10,15,20-tetra(4-pyrydil)21H,23H-porphine (TPyP) were deposited on ITO flexible substrates by Matrix Assisted Pulsed Laser Evaporation (MAPLE) technique. Organic heterostructures containing (TPyP/ZnPc(MgPc)) stacked or (ZnPc(MgPc):TPyP) mixed layers were characterized by X-ray diffraction-XRD, photoluminescence-PL, UV-vis and FTIR spectroscopy. No chemical decomposition of the initial materials was observed. The investigated structures present a large spectral absorption in the visible range making them suitable for organic photovoltaics applications (OPV). Scanning electron microscopy-SEM and atomic force microscopy-AFM revealed morphologies typical for the films prepared by MAPLE. The current-voltage characteristics of the investigated structures, measured in dark and under light, present an improvement in the current value (∼3 order of magnitude larger) for the structure based on the mixed layer (Al/MgPc:TPyP/ITO) in comparison with the stacked layer (Al/MgPc//TPyP/ITO). A photogeneration process was evidenced in the case of structures Al/ZnPc:TPyP/ITO with mixed layers.
NASA Astrophysics Data System (ADS)
Stanculescu, F.; Rasoga, O.; Catargiu, A. M.; Vacareanu, L.; Socol, M.; Breazu, C.; Preda, N.; Socol, G.; Stanculescu, A.
2015-05-01
This paper presents some studies about the preparation by matrix-assisted pulsed laser evaporation (MAPLE) technique of heterostructures with single layer of arylene based polymer, poly[N-(2-ethylhexyl)2.7-carbazolyl vinylene]/AMC16 and poly[N-(2-ethylhexyl)2.7-carbazolyl 1.4-phenylene ethynylene]/AMC22, and with layers of these polymers mixed with Buckminsterfullerene/C60 in the weight ratio of 1:2 (AMC16:C60) and 1:3 (AMC22:C60). The deposited layers have been characterized by spectroscopic (UV-Vis-NIR, PL, FTIR) and microscopic (SEM, AFM) methods. The effect of the polymer particularities on the optical and electrical properties of the structures based on polymer and polymer:C60 mixed layer has been analyzed. The study of the electrical properties has revealed typical solar cell behavior for the heterostructure prepared by MAPLE on glass/ITO/PEDOT-PSS with AMC16, AMC22 and AMC22:C60 layer, confirming that this method is adequate for the preparation of polymeric and mixed active layers for solar cells applications. The highest photovoltaic effect was shown by the solar cell structure realized with single layer of AMC16 polymer: glass/ITO/PEDOT-PSS/AMC16/Al.
DNA damage in an animal model of maple syrup urine disease.
Scaini, Giselli; Jeremias, Isabela C; Morais, Meline O S; Borges, Gabriela D; Munhoz, Bruna P; Leffa, Daniela D; Andrade, Vanessa M; Schuck, Patrícia F; Ferreira, Gustavo C; Streck, Emilio L
2012-06-01
Maple syrup urine disease is an inborn error of metabolism caused by a severe deficiency of the branched chain alpha-ketoacid dehydrogenase complex. Neurological dysfunction is a common finding in patients with maple syrup urine disease. However, the mechanisms underlying the neuropathology of brain damage in this disorder are poorly understood. In this study, we investigated whether acute or chronic administration of a branched chain amino acid pool (leucine, isoleucine and valine) causes transient DNA damage, as determined by the alkaline comet assay, in the brain and blood of rats during development and whether antioxidant treatment prevented the alterations induced by branched chain amino acids. Our results showed that the acute administration of branched chain amino acids increased the DNA damage frequency and damage index in the hippocampus. However, the chronic administration of branched chain amino acids increased the DNA damage frequency and damage index in both the hippocampus and the striatum, and the antioxidant treatment was able to prevent DNA damage in the hippocampus and striatum. The present study demonstrated that metabolite accumulation in MSUD induces DNA damage in the hippocampus and striatum and that it may be implicated in the neuropathology observed in the affected patients. We demonstrated that the effect of antioxidant treatment (N-acetylcysteine plus deferoxamine) prevented DNA damage, suggesting the involvement of oxidative stress in DNA damage. PMID:22560665
Spring leaf phenology and the diurnal temperature range in a temperate maple forest
NASA Astrophysics Data System (ADS)
Hanes, Jonathan M.
2014-03-01
Spring leaf phenology in temperate climates is intricately related to numerous aspects of the lower atmosphere [e.g., surface energy balance, carbon flux, humidity, the diurnal temperature range (DTR)]. To further develop and improve the accuracy of ecosystem and climate models, additional investigations of the specific nature of the relationships between spring leaf phenology and various ecosystem and climate processes are required in different environments. This study used visual observations of maple leaf phenology, below-canopy light intensities, and micrometeorological data collected during the spring seasons of 2008, 2009, and 2010 to examine the potential influence of leaf phenology on a seasonal transition in the trend of the DTR. The timing of a reversal in the DTR trend occurred near the time when the leaves were unfolding and expanding. The results suggest that the spring decline in the DTR can be attributed primarily to the effect of canopy closure on daily maximum temperature. These findings improve our understanding of the relationship between leaf phenology and the diurnal temperature range in temperate maple forests during the spring. They also demonstrate the necessity of incorporating accurate phenological data into ecosystem and climate models and warrant a careful examination of the extent to which canopy phenology is currently incorporated into existing models.
NASA Astrophysics Data System (ADS)
Bloisi, Francesco; Califano, Valeria; Perretta, Giuseppe; Nasti, Libera; Aronne, Antonio; Di Girolamo, Rocco; Auriemma, Finizia; De Rosa, Claudio; Vicari, Luciano R. M.
2016-06-01
Lipases are enzymes used for catalyzing reactions of acylglycerides in biodiesel production from lipids, where enzyme immobilization on a substrate is required. Silica nanoparticles in different morphologies and configurations are currently used in conjunction with biological molecules for drug delivery and catalysis applications, but up to date their use for triglycerides has been limited by the large size of long-chain lipid molecules. Matrix assisted pulsed laser evaporation (MAPLE), a laser deposition technique using a frozen solution/suspension as a target, is widely used for deposition of biomaterials and other delicate molecules. We have carried out a MAPLE deposition starting from a frozen mixture containing fumed silica and lipase in water. Deposition parameters were chosen in order to increase surface roughness and to promote the formation of complex structures. Both the target (a frozen thickened mixture of nanoparticles/catalyst in water) and the deposition configuration (a small target to substrate distance) are unusual and have been adopted in order to increase surface contact of catalyst and to facilitate access to long-chain molecules. The resulting innovative film morphology (fumed silica/lipase cluster level aggregation) and the lipase functionality (for catalytic biodiesel production) have been studied by FESEM, FTIR and transesterification tests.
Effect of substrate temperature on MAPLE deposition of synthetic eumelanin films
NASA Astrophysics Data System (ADS)
Bloisi, F.; Pezzella, A.; Barra, M.; Alfè, M.; Chiarella, F.; Cassinese, A.; Vicari, L.
2011-11-01
Eumelanin is an important pigment almost ubiquitous in animals and plants exhibiting interesting charge transport capabilities. Its poor solubility in common solvents represents a severe limitation for preparing thin films. It was recently demonstrated that eumelanin films can be successfully deposited with the MAPLE (Matrix Assisted Pulsed Laser Evaporation) technique starting from a frozen water suspension, using infrared laser radiation. The low laser absorption of ice together with the high absorption of eumelanin suggests that the target ablation is due to laser energy absorbed by the eumelanin molecules, followed by thermal energy transfer, and ejection of ice/water/vapor containing undamaged eumelanin molecules and supramolecular structures. Here, we report on the deposition of eumelanin thin films on substrates at different temperatures eventually followed by in-situ annealing. Structural characterization (UV-VIS, FTIR, AP-MALDI) confirms that the deposited films maintain the characteristics of the eumelanin biopolymer. Morphological characterization (AFM) shows that surface roughness increases with increasing substrate temperature during MAPLE deposition, but is not influenced by annealing. Preliminary electrical characterization shows that eumelanin films seem to obey Ohm's law without evidence that charge injection from gold electrodes is affected by the presence of significant energy barriers. Moreover, charge transport is drastically reduced in vacuum, even if the phenomenon is at least partially reversible.
MAPLE deposition of polypyrrole-based composite layers for bone regeneration
NASA Astrophysics Data System (ADS)
Paun, Irina Alexandra; Acasandrei, Adriana Maria; Luculescu, Catalin Romeo; Mustaciosu, Cosmin Catalin; Ion, Valentin; Mihailescu, Mona; Vasile, Eugenia; Dinescu, Maria
2015-12-01
We report on biocompatible, electrically conductive layers of polypyrrole (PPy)-based composites obtained by Matrix Assisted Pulsed Laser Evaporation (MAPLE) for envisioned bone regeneration. In order to preserve the conductivity of the PPy while overcoming its lack of biodegradability and low mechanical resilience, conductive PPy nanograins were embedded in two biocompatible, insulating polymeric matrices, i.e. poly(lactic-co-glycolic)acid (PLGA) and polyurethane (PU). PLGA offers the advantage of full biodegradability into non-toxic products, while PU provides toughness and elasticity. The PPy nanograins formed micro-domains and networks within the PLGA and PU matrices, in a compact spatial arrangement favorable for electrical percolation. The proposed approach allowed us to obtain PPy-based composite layers with biologically meaningful conductivities up to 10-2 S/cm for PPy loadings as low as 1:10 weight ratios. Fluorescent staining and viability assays showed that the MG63 osteoblast-like cells cultured on the PPy-based layers deposited by MAPLE were viable and retained their capacity to proliferate. The performance of the proposed method was demonstrated by quantitative evaluation of the calcium phosphate deposits from the cultured cells, as indicative for cell mineralization. Electrical stimulation using 200 μA currents passing through the PPy-based layers, during a time interval of 4 h, enhanced the osteogenesis in the cultured cells. Despite their lowest conductivity, the PPy/PU layers showed the best biocompatibility and the highest osteogenic potential.