NASA Astrophysics Data System (ADS)
Miao, Qian; Hu, Xiao-Rui; Chen, Yong
2014-02-01
We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core of this theory is viewing the Killing form of the Lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.
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…
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…
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.
Laplace transform approach for solving integral equations using computer algebra system
NASA Astrophysics Data System (ADS)
Paneva-Konovska, Jordanka; Nikolova, Yanka
2016-12-01
The Laplace transform method, along with Computer Algebra Systems (CAS) "Maple" v. 13, are extremely successfully applied for solving a class of integral equations with an arbitrary order, including fractional order integral equations. The combining of both powerful approaches allows students more quickly, enjoyable and thoroughly to master the material.
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...
An automated system for evaluation of the potential functionome: MAPLE version 2.1.0
Takami, Hideto; Taniguchi, Takeaki; Arai, Wataru; Takemoto, Kazuhiro; Moriya, Yuki; Goto, Susumu
2016-01-01
Metabolic and physiological potential evaluator (MAPLE) is an automatic system that can perform a series of steps used in the evaluation of potential comprehensive functions (functionome) harboured in the genome and metagenome. MAPLE first assigns KEGG Orthology (KO) to the query gene, maps the KO-assigned genes to the Kyoto Encyclopedia of Genes and Genomes (KEGG) functional modules, and then calculates the module completion ratio (MCR) of each functional module to characterize the potential functionome in the user’s own genomic and metagenomic data. In this study, we added two more useful functions to calculate module abundance and Q-value, which indicate the functional abundance and statistical significance of the MCR results, respectively, to the new version of MAPLE for more detailed comparative genomic and metagenomic analyses. Consequently, MAPLE version 2.1.0 reported significant differences in the potential functionome, functional abundance, and diversity of contributors to each function among four metagenomic datasets generated by the global ocean sampling expedition, one of the most popular environmental samples to use with this system. MAPLE version 2.1.0 is now available through the web interface (http://www.genome.jp/tools/maple/) 17 June 2016, date last accessed. PMID:27374611
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.
Quantum Q systems: from cluster algebras to quantum current algebras
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Kedem, Rinat
2017-02-01
This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the A_r quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593-2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra U_{√{q}}({n}[u,u^{-1}])subset U_{√{q}}(widehat{{sl}}_2), in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97-152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.
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…
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…
Using Algebraic Computing To Teach General Relativity And Cosmology
NASA Astrophysics Data System (ADS)
Vulcanov, Dumitru N.; Boată, Remus-Ştefan Ş.
2012-12-01
The article presents some new aspects and experience on the use of computer in teaching general relativity and cosmology for undergraduate students (and not only) with some experience in computer manipulation. Some years ago certain results were reported [1] using old fashioned computer algebra platforms but the growing popularity of graphical platforms as Maple and Mathematica forced us to adapt and reconsider our methods and programs. We will describe some simple algebraic programming procedures (in Maple with GrTensorII package) for obtaining and the study of some exact solutions of the Einstein equations in order to convince a dedicated student in general relativity about the utility of a computer algebra system.
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
Dynamical systems and quantum bicrossproduct algebras
NASA Astrophysics Data System (ADS)
Arratia, Oscar; del Olmo, Mariano A.
2002-06-01
We present a unified study of some aspects of quantum bicrossproduct algebras of inhomogeneous Lie algebras, such as Poincaré, Galilei and Euclidean in N dimensions. The action associated with the bicrossproduct structure allows us to obtain a nonlinear action over a new group linked to the translations. This new nonlinear action associates a dynamical system with each generator which is the object of our study.
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…
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…
ADA interpretative system for image algebra
NASA Astrophysics Data System (ADS)
Murillo, Juan J.; Wilson, Joseph N.
1992-06-01
An important research problem in image processing is to find appropriate tools to support algorithm development. There have been efforts to build algorithm development support systems for image algebra in several languages, but these systems still have the disadvantage of the time consuming algorithm development style associated with compilation-oriented programming. This paper starts with a description of the Run-Time Support Library (RTSL), which serves as the base for executing programs on both the Image Algebra Ada Translator (IAAT) and Image Algebra Ada Interpreter (IAAI). A presentation on the current status of IAAT and its capabilities is followed by a brief introduction to the utilization of the Image Display Manager (IDM) for image manipulation and analysis. We then discuss in detail the current development stage of IAAI and its relation with RTSL and IDM. The last section describes the design of a syntax-directed graphical user interface for IAAI. We close with an analysis of the current performance of IAAI, and future trends are discussed. Appendix A gives a brief introduction to Image Algebra (IA), and in Appendix B the reader is presented to the Image Algebra Ada (IAA) grammar.
Constraint algebra for interacting quantum systems
NASA Astrophysics Data System (ADS)
Fubini, S.; Roncadelli, M.
1988-04-01
We consider relativistic constrained systems interacting with external fields. We provide physical arguments to support the idea that the quantum constraint algebra should be the same as in the free quantum case. For systems with ordering ambiguities this principle is essential to obtain a unique quantization. This is shown explicitly in the case of a relativistic spinning particle, where our assumption about the constraint algebra plus invariance under general coordinate transformations leads to a unique S-matrix. On leave from Dipartimento di Fisica Nucleare e Teorica, Università di Pavia and INFN, I-27100 Pavia, Italy.
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
Static friction, differential algebraic systems and numerical stability
NASA Astrophysics Data System (ADS)
Chen, Jian; Schinner, Alexander; Matuttis, Hans-Georg
We show how Differential Algebraic Systems (Ordinary Differential Equations with algebraic constraints) in mechanics are affected by stability issues and we implement Lubich's projection method to reduce the error to practically zero. Then, we explain how the "numerically exact" implementation for static friction by Differential Algebraic Systems can be stabilized. We conclude by comparing the corresponding steps in the "Contact mechanics" introduced by Moreau.
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.
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.
The Application of a Computer Algebra System as a Tool in College Algebra.
ERIC Educational Resources Information Center
Mayes, Robert L.
1995-01-01
Students (n=61) in an experimental course stressing active student involvement and the use of a computer algebra system scored higher than students (n=76) in a traditional college algebra course on final measures of inductive reasoning, visualization, and problem solving while maintaining equivalent manipulation and computation skills. (Author/MLB)
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.…
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)
Unified algebraic method to non-Hermitian systems with Lie algebraic linear structure
NASA Astrophysics Data System (ADS)
Zhang, Hong-Biao; Jiang, Guang-Yuan; Wang, Gang-Cheng
2015-07-01
We suggest a generic algebraic method to solve non-Hermitian Hamiltonian systems with Lie algebraic linear structure. Such method can not only unify the non-Hermitian Hamiltonian and the Hermitian Hamiltonian with the same structure but also keep self-consistent between similarity transformation and unitary transformation. To clearly reveal the correctness and physical meaning of such algebraic method, we illustrate our method with two different types of non-Hermitian Hamiltonians: the non-Hermitian Hamiltonian with Heisenberg algebraic linear structure and the non-Hermitian Hamiltonian with su(1, 1) algebraic linear structure. We obtain energy eigenvalues and the corresponding eigenstates of non-Hermitian forced harmonic oscillator with Heisenberg algebra structure via a proper similarity transformation. We also calculate the eigen-problems of general non-Hermitian Hamiltonian with su(1, 1) structure in terms of the similarity transformation. As an application, we focus on studying the non-Hermitian single-mode squeezed and coherent harmonic oscillator system and find that such similarity transformation associated with this model is in fact gauge-like transformation for simple harmonic oscillator.
Decidability of classes of algebraic systems in polynomial time
Anokhin, M I
2002-02-28
For some classes of algebraic systems several kinds of polynomial-time decidability are considered, which use an oracle performing signature operations and computing predicates. Relationships between various kinds of decidability are studied. Several results on decidability and undecidability in polynomial time are proved for some finitely based varieties of universal algebras.
Lie symmetry algebra of one-dimensional nonconservative dynamical systems
NASA Astrophysics Data System (ADS)
Liu, Cui-Mei; Wu, Run-Heng; Fu, Jing-Li
2007-09-01
Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1-1 mapping, the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.
Quantum integrable systems related to lie algebras
NASA Astrophysics Data System (ADS)
Olshanetsky, M. A.; Perelomov, A. M.
1983-03-01
Some quantum integrable finite-dimensional systems related to Lie algebras are considered. This review continues the previous review of the same authors [83] devoted to the classical aspects of these systems. The dynamics of some of these systems is closely related to free motion in symmetric spaces. Using this connection with the theory of symmetric spaces some results such as the forms of spectra, wave functions, S-matrices, quantum integrals of motion are derived. In specific cases the considered systems describe the one-dimensional n-body systems interacting pairwise via potentials g2v( q) of the following 5 types: vI( q) = q-2, vII( q) = sinh-2q, vIII( q) = sin-2q, v IV(q) = P(q) , vV( q) = q-2 + ω2q2. Here P(q) is the Weierstrass function, so that the first three cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbour potential exp( qjqj+ 1 ) is moreover considered. This review presents from a general and universal point of view results obtained mainly over the past fifteen years. Besides, it contains some new results both of physical and mathematical interest.
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.
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.
Category-theoretic models of algebraic computer systems
NASA Astrophysics Data System (ADS)
Kovalyov, S. P.
2016-01-01
A computer system is said to be algebraic if it contains nodes that implement unconventional computation paradigms based on universal algebra. A category-based approach to modeling such systems that provides a theoretical basis for mapping tasks to these systems' architecture is proposed. The construction of algebraic models of general-purpose computations involving conditional statements and overflow control is formally described by a reflector in an appropriate category of algebras. It is proved that this reflector takes the modulo ring whose operations are implemented in the conventional arithmetic processors to the Łukasiewicz logic matrix. Enrichments of the set of ring operations that form bases in the Łukasiewicz logic matrix are found.
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,…
Mathematical Concepts and Maple Animations
NASA Astrophysics Data System (ADS)
Siddique, Mohammad; Mitchell, Kristy
2010-09-01
Maple is a mathematics software package, which contains graphic, computation, and programming tools. Maple animation is a powerful tool that can help in comprehending many fundamental concepts in mathematics and other sciences. This paper deals with the use of maple animation to demonstrate many fundamental concepts in mathematics that are difficult to explain verbally or through static figures. We show Maple animations effectively convey different concepts. We present problems taken from the literature to exemplify and explain Maple animation procedures. Using Maple in teaching mathematics facilitates the students with a tool to experiment and visualize complicated mathematical concepts and thus, strengthen their grasp of the subject.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 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...
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...
Code of Federal Regulations, 2014 CFR
2014-01-01
... 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...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 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.
Dynamical algebra of observables in dissipative quantum systems
NASA Astrophysics Data System (ADS)
Alipour, Sahar; Chruściński, Dariusz; Facchi, Paolo; Marmo, Giuseppe; Pascazio, Saverio; Rezakhani, Ali T.
2017-02-01
Dynamics and features of quantum systems can be drastically different from classical systems. Dissipation is understood as a general mechanism through which quantum systems may lose part or all of their quantum aspects. Here we discuss a method to analyze behaviors of dissipative quantum systems in an algebraic sense. This method employs a time-dependent product between system’s observables which is induced by the underlying dissipative dynamics. We argue that the long-time limit of the algebra of observables defined with this product yields a contractive algebra which reflects the loss of some quantum features of the dissipative system, and it bears relevant information about irreversibility. We illustrate this result through several examples of dissipation in various Markovian and non-Markovian systems.
Analysis of solar cell using the Lambert W function with Maple
NASA Astrophysics Data System (ADS)
Villegas, Daniel
2014-06-01
A study of solar cells took place by using Lambert W function based diode model. All calculations were made through computer algebra, having the software Maple a special place. Current vs. Voltage graph corresponding to cells was obtained as a main result, so as diode's parameters values such as the series, shunt resistances and its constant. Analytical results will be useful for cell manufacturing, either for home or industrial usage. As a future research line, Lambert W function utilization is suggested as a mean for multi-diode systems development.
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.
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…
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…
Computer Algebra Systems in Education Newsletter[s].
ERIC Educational Resources Information Center
Computer Algebra Systems in Education Newsletter, 1990
1990-01-01
Computer Algebra Systems (CAS) are computer systems for the exact solution of problems in symbolic form. The newspaper is designed to serve as a conduit for information and ideas on the use of CAS in education, especially in lower division college and university courses. Articles included are about CAS programs in several colleges, experiences…
Computing Matrix Representations of Filiform Lie Algebras
NASA Astrophysics Data System (ADS)
Ceballos, Manuel; Núñez, Juan; Tenorio, Ángel F.
In this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie algebras. To do it, we use the nilpotent Lie algebra, g_n, formed of n ×n strictly upper-triangular matrices. More concretely, we search the lowest natural number n such that the Lie algebra g_n contains a given filiform Lie algebra, also computing a representative of this algebra. All the computations in this paper have been done using MAPLE 9.5.
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.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 10 2012-01-01 2012-01-01 false Maple sap. 1437.107 Section 1437.107 Agriculture... Yield Coverage Using Actual Production History § 1437.107 Maple sap. (a) NAP assistance for maple sap is limited to maple sap produced on private property for sale as sap or syrup. Eligible maple sap must...
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'…
A new application of algebraic geometry to systems theory
NASA Technical Reports Server (NTRS)
Martin, C. F.; Hermann, R.
1976-01-01
Following an introduction to algebraic geometry, the dominant morphism theorem is stated, and the application of this theorem to systems-theoretic problems, such as the feedback problem, is discussed. The Gaussian elimination method used for solving linear equations is shown to be an example of a dominant morphism.
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 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…
Models of quadratic quantum algebras and their relation to classical superintegrable systems
Kalnins, E. G.; Miller, W.; Post, S.
2009-05-15
We show how to construct realizations (models) of quadratic algebras for 2D second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.
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.)
Martin, Mark A.
2002-04-16
Vegetation Management along the Rocky Reach – Maple Valley No. 1 Transmission Line ROW from structure 98/2 to structure 110/1. The transmission line is a 500 kV line. BPA proposes to clear targeted vegetation along access roads and around tower structures that may impede the operation and maintenance of the subject transmission line. BPA plans to conduct vegetation management along existing access road and around structure landings for the purpose of maintaining access to structures site. All work will be in accordance with the National Electrical Safety Code and BPA standards.
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)
ERIC Educational Resources Information Center
van Herwaarden, Onno A.; Gielen, Joseph L. W.
2002-01-01
Focuses on students showing a lack of conceptual insight while using computer algebra systems (CAS) in the setting of an elementary calculus and linear algebra course for first year university students in social sciences. The use of a computer algebra environment has been incorporated into a more traditional course but with special attention on…
Identification of the Roessler system: algebraic approach and genetic algorithms
NASA Astrophysics Data System (ADS)
Ibanez, C. A.; Sanchez, J. H.; Suarez, M. S. C.; Flores, F. A.; Garrido, R. M.; Martinez, R. G.
2005-10-01
This article presents a method to determine the parameters of Rossler's attractor in a very approximated way, by means of observations of an available variable. It is shown that the system is observable and identifiable algebraically with respect to the chosen output. This fact allows to construct a differential parametrization of the output and its derivatives. Using this parametrization an identification scheme based on least mean squares is established and the solution is found with a genetic algorithm.
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)
NASA Astrophysics Data System (ADS)
Mikhalev, A. V.; Pinchuk, I. A.
2005-06-01
The structure of Steinberg conformal algebras is studied; these are analogues of Steinberg groups (algebras, superalgebras).A Steinberg conformal algebra is defined as an abstract algebra by a system of generators and relations between the generators. It is proved that a Steinberg conformal algebra is the universal central extension of the corresponding conformal Lie algebra; the kernel of this extension is calculated.
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…
TRIP: General computer algebra system for celestial mechanics
NASA Astrophysics Data System (ADS)
Laskar, J.; Gastineau, M.
2012-10-01
TRIP is an interactive computer algebra system that is devoted to perturbation series computations, and specially adapted to celestial mechanics. Its development started in 1988, as an upgrade of the special purpose FORTRAN routines elaborated by J. Laskar for the demonstration of the chaotic behavior of the Solar System. TRIP is a mature and efficient tool for handling multivariate generalized power series, and embeds two kernels, a symbolic and a numerical kernel. This numerical kernel communicates with Gnuplot or Grace to plot the graphics and allows one to plot the numerical evaluation of symbolic objects.
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.
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)
Analytical solutions for systems of partial differential-algebraic equations.
Benhammouda, Brahim; Vazquez-Leal, Hector
2014-01-01
This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.
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.
Robust algebraic image enhancement for intelligent control systems
NASA Technical Reports Server (NTRS)
Lerner, Bao-Ting; Morrelli, Michael
1993-01-01
Robust vision capability for intelligent control systems has been an elusive goal in image processing. The computationally intensive techniques a necessary for conventional image processing make real-time applications, such as object tracking and collision avoidance difficult. In order to endow an intelligent control system with the needed vision robustness, an adequate image enhancement subsystem capable of compensating for the wide variety of real-world degradations, must exist between the image capturing and the object recognition subsystems. This enhancement stage must be adaptive and must operate with consistency in the presence of both statistical and shape-based noise. To deal with this problem, we have developed an innovative algebraic approach which provides a sound mathematical framework for image representation and manipulation. Our image model provides a natural platform from which to pursue dynamic scene analysis, and its incorporation into a vision system would serve as the front-end to an intelligent control system. We have developed a unique polynomial representation of gray level imagery and applied this representation to develop polynomial operators on complex gray level scenes. This approach is highly advantageous since polynomials can be manipulated very easily, and are readily understood, thus providing a very convenient environment for image processing. Our model presents a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets.
Generalized MICZ-Kepler system, duality, polynomial, and deformed oscillator algebras
Marquette, Ian
2010-10-15
We present the quadratic algebra of the generalized MICZ-Kepler system in three-dimensional Euclidean space E{sub 3} and its dual, the four-dimensional singular oscillator, in four-dimensional Euclidean space E{sub 4}. We present their realization in terms of a deformed oscillator algebra using the Daskaloyannis construction. The structure constants are, in these cases, functions not only of the Hamiltonian but also of other integrals commuting with all generators of the quadratic algebra. We also present a new algebraic derivation of the energy spectrum of the MICZ-Kepler system on the three sphere S{sup 3} using a quadratic algebra. These results point out also that results and explicit formula for structure functions obtained for quadratic, cubic, and higher order polynomial algebras in the context of two-dimensional superintegrable systems may be applied to superintegrable systems in higher dimensions with and without monopoles.
Generalized MICZ-Kepler system, duality, polynomial, and deformed oscillator algebras
NASA Astrophysics Data System (ADS)
Marquette, Ian
2010-10-01
We present the quadratic algebra of the generalized MICZ-Kepler system in three-dimensional Euclidean space E3 and its dual, the four-dimensional singular oscillator, in four-dimensional Euclidean space E4. We present their realization in terms of a deformed oscillator algebra using the Daskaloyannis construction. The structure constants are, in these cases, functions not only of the Hamiltonian but also of other integrals commuting with all generators of the quadratic algebra. We also present a new algebraic derivation of the energy spectrum of the MICZ-Kepler system on the three sphere S3 using a quadratic algebra. These results point out also that results and explicit formula for structure functions obtained for quadratic, cubic, and higher order polynomial algebras in the context of two-dimensional superintegrable systems may be applied to superintegrable systems in higher dimensions with and without monopoles.
Classical integrable finite-dimensional systems related to Lie algebras
NASA Astrophysics Data System (ADS)
Olshanetsky, M. A.; Perelomov, A. M.
1981-05-01
During the last few years many dynamical systems have been identified, that are completely integrable or even such to allow an explicit solution of the equations of motion. Some of these systems have the form of classical one-dimensional many-body problems with pair interactions; others are more general. All of them are related to Lie algebras, and in all known cases the property of integrability results from the presence of higher (hidden) symmetries. This review presents from a general and universal viewpoint the results obtained in this field during the last few years. Besides it contains some new results both of physical and mathematical interest. The main focus is on the one-dimensional models of n particles interacting pairwise via potentials V( q) = g2ν( q) of the following 5 types: ν I(q)=q -2, ν II(q)=a -2sinh2(aq), ν III(q)=a 2/ sin2(aq), ν IV=a 2P(aq), , ν V(q)=q -2+ω 2q 2. Here P( q) is the Weierstrass function, so that the first 3 cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbor potential, gj2exp[- a( qj- qj+1 )], is moreover considered. Various generalizations of these models, naturally suggested by their association with Lie algebras, are also treated.
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)
Code of Federal Regulations, 2011 CFR
2011-04-01
... the sap of the maple tree (Acer) or by solution in water of maple sugar (mapel concrete) made from such sap. It contains not less than 66 percent by weight of soluble solids derived solely from such...
Code of Federal Regulations, 2013 CFR
2013-04-01
... the sap of the maple tree (Acer) or by solution in water of maple sugar (mapel concrete) made from such sap. It contains not less than 66 percent by weight of soluble solids derived solely from such...
Code of Federal Regulations, 2012 CFR
2012-04-01
... the sap of the maple tree (Acer) or by solution in water of maple sugar (mapel concrete) made from such sap. It contains not less than 66 percent by weight of soluble solids derived solely from such...
Code of Federal Regulations, 2010 CFR
2010-04-01
... the sap of the maple tree (Acer) or by solution in water of maple sugar (mapel concrete) made from such sap. It contains not less than 66 percent by weight of soluble solids derived solely from such...
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]).
Mastering algebra retrains the visual system to perceive hierarchical structure in equations.
Marghetis, Tyler; Landy, David; Goldstone, Robert L
2016-01-01
Formal mathematics is a paragon of abstractness. It thus seems natural to assume that the mathematical expert should rely more on symbolic or conceptual processes, and less on perception and action. We argue instead that mathematical proficiency relies on perceptual systems that have been retrained to implement mathematical skills. Specifically, we investigated whether the visual system-in particular, object-based attention-is retrained so that parsing algebraic expressions and evaluating algebraic validity are accomplished by visual processing. Object-based attention occurs when the visual system organizes the world into discrete objects, which then guide the deployment of attention. One classic signature of object-based attention is better perceptual discrimination within, rather than between, visual objects. The current study reports that object-based attention occurs not only for simple shapes but also for symbolic mathematical elements within algebraic expressions-but only among individuals who have mastered the hierarchical syntax of algebra. Moreover, among these individuals, increased object-based attention within algebraic expressions is associated with a better ability to evaluate algebraic validity. These results suggest that, in mastering the rules of algebra, people retrain their visual system to represent and evaluate abstract mathematical structure. We thus argue that algebraic expertise involves the regimentation and reuse of evolutionarily ancient perceptual processes. Our findings implicate the visual system as central to learning and reasoning in mathematics, leading us to favor educational approaches to mathematics and related STEM fields that encourage students to adapt, not abandon, their use of perception.
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.
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
Martin, Mark A.
2002-04-15
Vegetation Management along the Rocky Reach – Maple Valley No. 1 Transmission Line ROW from structure 110/1 to the Maple Valley Substation. The transmission line is a 500 kV line. BPA proposes to clear targeted vegetation along access roads and around tower structures that may impede the operation and maintenance of the subject transmission line. BPA plans to conduct vegetation management along existing access road and around structure landings for the purpose of maintaining access to structures site. All work will be in accordance with the National Electrical Safety Code and BPA standards.
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.…
Zhao, Shouwei
2011-06-01
A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.
NASA Astrophysics Data System (ADS)
Zhao, Shouwei
2011-06-01
A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.
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)
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
Quadratic algebra for superintegrable monopole system in a Taub-NUT space
NASA Astrophysics Data System (ADS)
Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong
2016-09-01
We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the corresponding Schrödinger equation of the Hamiltonian is separable in both spherical and parabolic coordinates. We obtain the integrals of motion of this superintegrable model and construct the quadratic algebra and Casimir operator. This algebra can be realized in terms of a deformed oscillator algebra and has finite dimensional unitary representations (unirreps) which provide energy spectra of the system. This result coincides with the physical spectra obtained from the separation of variables.
Using computer algebra and SMT-solvers to analyze a mathematical model of cholera propagation
NASA Astrophysics Data System (ADS)
Trujillo Arredondo, Mariana
2014-06-01
We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 < 1. Using Maple it is possible to prove that the endemic equilibrium state is locally stable when it exists, it is to say when R0 > 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.
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.
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.
Refined algebraic quantisation in a system with nonconstant gauge invariant structure functions
NASA Astrophysics Data System (ADS)
Martínez-Pascual, Eric
2013-08-01
In a previous work [J. Louko and E. Martínez-Pascual, "Constraint rescaling in refined algebraic quantisation: Momentum constraint," J. Math. Phys. 52, 123504 (2011)], 10.1063/1.3664336, 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.
Finding higher symmetries of differential equations using the MAPLE package DESOLVII
NASA Astrophysics Data System (ADS)
Vu, K. T.; Jefferson, G. F.; Carminati, J.
2012-04-01
We present and describe, with illustrative examples, the MAPLE computer algebra package DESOLVII, which is a major upgrade of DESOLV. DESOLVII now includes new routines allowing the determination of higher symmetries (contact and Lie-Bäcklund) for systems of both ordinary and partial differential equations. Catalogue identifier: ADYZ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYZ_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.: 10 858 No. of bytes in distributed program, including test data, etc.: 112 515 Distribution format: tar.gz Programming language: MAPLE internal language Computer: PCs and workstations Operating system: Linux, Windows XP and Windows 7 RAM: Depends on the type of problem and the complexity of the system (small ≈ MB, large ≈ GB) Classification: 4.3, 5 Catalogue identifier of previous version: ADYZ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 176 (2007) 682 Does the new version supersede the previous version?: Yes Nature of problem: There are a number of approaches one may use to find solutions to systems of differential equations. These include numerical, perturbative, and algebraic methods. Unfortunately, approximate or numerical solution methods may be inappropriate in many cases or even impossible due to the nature of the system and hence exact methods are important. In their own right, exact solutions are valuable not only as a yardstick for approximate/numerical solutions but also as a means of elucidating the physical meaning of fundamental quantities in systems. One particular method of finding special exact solutions is afforded by the work of Sophus Lie and the use of continuous transformation groups. The power of Lie's group theoretic method lies in its ability to unify a number of ad hoc
SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System
NASA Astrophysics Data System (ADS)
Choi, J. R.; Nahm, I. H.
2007-01-01
Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola-Kanai oscillator. The probability density of these coherent states for the Caldirola-Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed.
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.
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
Algebraic and adaptive learning in neural control systems
NASA Astrophysics Data System (ADS)
Ferrari, Silvia
A systematic approach is developed for designing adaptive and reconfigurable nonlinear control systems that are applicable to plants modeled by ordinary differential equations. The nonlinear controller comprising a network of neural networks is taught using a two-phase learning procedure realized through novel techniques for initialization, on-line training, and adaptive critic design. A critical observation is that the gradients of the functions defined by the neural networks must equal corresponding linear gain matrices at chosen operating points. On-line training is based on a dual heuristic adaptive critic architecture that improves control for large, coupled motions by accounting for actual plant dynamics and nonlinear effects. An action network computes the optimal control law; a critic network predicts the derivative of the cost-to-go with respect to the state. Both networks are algebraically initialized based on prior knowledge of satisfactory pointwise linear controllers and continue to adapt on line during full-scale simulations of the plant. On-line training takes place sequentially over discrete periods of time and involves several numerical procedures. A backpropagating algorithm called Resilient Backpropagation is modified and successfully implemented to meet these objectives, without excessive computational expense. This adaptive controller is as conservative as the linear designs and as effective as a global nonlinear controller. The method is successfully implemented for the full-envelope control of a six-degree-of-freedom aircraft simulation. The results show that the on-line adaptation brings about improved performance with respect to the initialization phase during aircraft maneuvers that involve large-angle and coupled dynamics, and parameter variations.
Shurtliff, Aaron
2003-02-18
Vegetation Management for portion of the Echo Lake – Maple Valley #1 500 kV transmission line located from tower structure 1/1 to 9/2. BPA proposes to clear targeted vegetation within the Right-of-Ways along access roads and around towers that may impede the operation and maintenance of the subject transmission lines. See Section 1.4 of the attached checklists for a complete description of the proposed action.
Shurtliff, Aaron
2003-02-18
Vegetation Management for portion of the Echo Lake – Maple Valley #1 500 kV transmission line located from tower structure 9/2 to 16/5. BPA proposes to clear targeted vegetation within the Right-of-Ways along access roads and around towers that may impede the operation and maintenance of the subject transmission lines. See Section 1.4 of the attached checklists for a complete description of the proposed action.
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…
Algebraic coarsening methods for linear and nonlinear PDE and systems
McWilliams, J C
2000-11-06
-grid variables. Once a coarse grid is chosen for which compatible relaxation converges fast, it follows that the dependence of the coarse-grid variables on each other decays exponentially or faster with the distance between them, measured in mesh-sizes. This implies that highly accurate coarse-grid equations can be constructed locally. A method for doing this by solving local constrained minimization problems is described in [1]. It is also shown how this approach can be applied to devise prolongation operators, which can be used for Galerkin coarsening in the usual way. In the present research we studied and developed methods based, in part, on these ideas. We developed and implemented an AMG approach which employs compatible relaxation to define the prolongation operator (hut is otherwise similar in its structure to classical AMG); we introduced a novel method for direct (i.e., non-Galerkin) algebraic coarsening, which is in the spirit of the approach originally proposed by Brandt in [1], hut is more efficient and well-defined; we investigated an approach for treating systems of equations and other problems where there is no unambiguous correspondence between equations and unknowns.
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,…
An algebraic criterion for the onset of chaos in nonlinear dynamic systems
NASA Technical Reports Server (NTRS)
Unal, A.; Tobak, M.
1987-01-01
The correspondence between iterated integrals and a noncommutative algebra is used to recast the given dynamical system from the time domain to the Laplace-Borel transform domain. It is then shown that the following algebraic criterion has to be satisfied for the outset of chaos: the limit (as tau approaches infinity and x sub 0 approaches infinity) of ((sigma(k=0) (tau sup k) / (k* x sub 0 sup k)) G II G = 0, where G is the generating power series of the trajectories, the symbol II is the shuffle product (le melange) of the noncommutative algebra, x sub 0 is a noncommutative variable, and tau is the correlation parameter. In the given equation, symbolic forms for both G and II can be obtained by use of one of the currently available symbolic languages such as PLI, REDUCE, and MACSYMA. Hence, the criterion is a computer-algebraic one.
Geary, David C.; Hoard, Mary K.; Nugent, Lara; Rouder, Jeffrey N.
2015-01-01
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 (92 girls) 9th graders, controlling 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 schema memory. Frequency of fact-retrieval errors was related to schema memory but not coordinate plane or expression evaluation accuracy. The results suggest the ANS may contribute to or is 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 different brain and cognitive systems are engaged during the learning of different components of algebraic competence, controlling demographic and domain general abilities. PMID:26255604
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.
Derive Workshop Matrix Algebra and Linear Algebra.
ERIC Educational Resources Information Center
Townsley Kulich, Lisa; Victor, Barbara
This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…
Lie algebraic structures of (1+1)-dimensional Lax integrable systems
Chen, D.; Zhang, D.
1996-11-01
An approach of constructing isospectral flows {ital K}{sub {ital l}}, nonisospectral flows {sigma}{sub {ital k}} and their implicit representations of a general Lax integrable system is proposed. By introducing product function matrices, it is shown that the two sets of flows and of related symmetries both constitute infinite-dimensional Lie algebras with respect to the commutator [{center_dot},{center_dot}] given in this paper. Algebraic properties for some well-known integrable systems such as the AKNS system, the generalized Harry Dym system, and the {ital n}-wave interaction system are obtained as particular examples. {copyright} {ital 1996 American Institute of Physics.}
Processing of medical images using Maple
NASA Astrophysics Data System (ADS)
Toro Betancur, V.
2013-05-01
Maple's Image Tools package was used to process medical images. The results showed clearer images and records of its intensities and entropy. The medical images of a rhinocerebral mucormycosis patient, who was not early diagnosed, were processed and analyzed using Maple's tools, which showed, in a clearer way, the affected parts in the perinasal cavities.
NASA Astrophysics Data System (ADS)
Hu, Hui; Ning, Zhe
2016-11-01
Due to the auto-rotating trait of maple seeds during falling down process, flow characteristics of rotating maple seeds have been studied by many researchers in recent years. In the present study, an experimental investigation was performed to explore maple-seed-inspired UAV propellers for improved aerodynamic and aeroacoustic performances. Inspired by the auto-rotating trait of maple seeds, the shape of a maple seed is leveraged for the planform design of UAV propellers. The aerodynamic and aeroacoustic performances of the maple-seed-inspired propellers are examined in great details, in comparison with a commercially available UAV propeller purchased on the market (i.e., a baseline propeller). During the experiments, in addition to measuring the aerodynamic forces generated by the maple-seed-inspired propellers and the baseline propeller, a high-resolution Particle Image Velocimetry (PIV) system was used to quantify the unsteady flow structures in the wakes of the propellers. The aeroacoustic characteristics of the propellers are also evaluated by leveraging an anechoic chamber available at the Aerospace Engineering Department of Iowa State University. The research work is supported by National Science Foundation under Award Numbers of OSIE-1064235.
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.
On Development of a Problem Based Learning System for Linear Algebra with Simple Input Method
NASA Astrophysics Data System (ADS)
Yokota, Hisashi
2011-08-01
Learning how to express a matrix using a keyboard inputs requires a lot of time for most of college students. Therefore, for a problem based learning system for linear algebra to be accessible for college students, it is inevitable to develop a simple method for expressing matrices. Studying the two most widely used input methods for expressing matrices, a simpler input method for expressing matrices is obtained. Furthermore, using this input method and educator's knowledge structure as a concept map, a problem based learning system for linear algebra which is capable of assessing students' knowledge structure and skill is developed.
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…
NASA Technical Reports Server (NTRS)
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.
MAPLE deposition of biomaterial multilayers
NASA Astrophysics Data System (ADS)
Califano, Valeria; Bloisi, Francesco; Vicari, Luciano R. M.; Colombi, Paolo; Bontempi, Elza; Depero, Laura E.
2008-09-01
Double layers of polyethylene glycol (PEG) and 3-(3,4-dihydroxyphenyl)-2-methyl- L-alanine (m-DOPA) thin films were obtained by matrix assisted pulsed laser evaporation (MAPLE) technique, by depositing a first layer of m-DOPA on Si substrate and a second layer of PEG on top of it. The films were characterized by low angle X-ray diffraction (LAXRD), X-ray reflectivity (XRR), atomic force microscopy (AFM), and micro-Raman spectroscopy. From these analyses it resulted that PEG was deposited without any relevant damage both in terms of chemical structure and molecular weight. Furthermore, PEG chains were mostly in the extended conformation, although PEG micelles appeared.
Discrete Integrable Systems and Poisson Algebras From Cluster Maps
NASA Astrophysics Data System (ADS)
Fordy, Allan P.; Hone, Andrew
2014-01-01
We consider nonlinear recurrences generated from cluster mutations applied to quivers that have the property of being cluster mutation-periodic with period 1. Such quivers were completely classified by Fordy and Marsh, who characterised them in terms of the skew-symmetric matrix that defines the quiver. The associated nonlinear recurrences are equivalent to birational maps, and we explain how these maps can be endowed with an invariant Poisson bracket and/or presymplectic structure. Upon applying the algebraic entropy test, we are led to a series of conjectures which imply that the entropy of the cluster maps can be determined from their tropical analogues, which leads to a sharp classification result. Only four special families of these maps should have zero entropy. These families are examined in detail, with many explicit examples given, and we show how they lead to discrete dynamics that is integrable in the Liouville-Arnold sense.
On a modification of minimal iteration methods for solving systems of linear algebraic equations
NASA Astrophysics Data System (ADS)
Yukhno, L. F.
2010-04-01
Modifications of certain minimal iteration methods for solving systems of linear algebraic equations are proposed and examined. The modified methods are shown to be superior to the original versions with respect to the round-off error accumulation, which makes them applicable to solving ill-conditioned problems. Numerical results demonstrating the efficiency of the proposed modifications are given.
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…
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
Hrubik-Vulanovic, Tatjana
2013-01-01
The purpose of this study was to investigate how intelligent tutoring system ALEKS, which was implemented in remedial Basic Algebra courses, affected students' success in subsequent lecture courses and how former ALEKS students and instructors in lecture courses perceived ALEKS learning environment. ALEKS courses were delivered in emporium style:…
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…
CENTER CONDITIONS AND CYCLICITY FOR A FAMILY OF CUBIC SYSTEMS: COMPUTER ALGEBRA APPROACH.
Ferčec, Brigita; Mahdi, Adam
2013-01-01
Using methods of computational algebra we obtain an upper bound for the cyclicity of a family of cubic systems. We overcame the problem of nonradicality of the associated Bautin ideal by moving from the ring of polynomials to a coordinate ring. Finally, we determine the number of limit cycles bifurcating from each component of the center variety.
CENTER CONDITIONS AND CYCLICITY FOR A FAMILY OF CUBIC SYSTEMS: COMPUTER ALGEBRA APPROACH
Ferčec, Brigita; Mahdi, Adam
2013-01-01
Using methods of computational algebra we obtain an upper bound for the cyclicity of a family of cubic systems. We overcame the problem of nonradicality of the associated Bautin ideal by moving from the ring of polynomials to a coordinate ring. Finally, we determine the number of limit cycles bifurcating from each component of the center variety. PMID:24223469
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…
ERIC Educational Resources Information Center
Buteau, Chantal; Marshall, Neil; Jarvis, Daniel; Lavicza, Zsolt
2010-01-01
We present results of a literature review pilot study (326 papers) regarding the use of Computer Algebra Systems (CAS) in tertiary mathematics education. Several themes that have emerged from the review are discussed: diverse uses of CAS, benefits to student learning, issues of integration and mathematics learning, common and innovative usage of…
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…
Galitski, Victor
2011-07-15
We propose a Lie-algebraic duality approach to analyze nonequilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-Stratonovich dynamical systems). The first part of the paper utilizes a geometric Hilbert-space-invariant formulation of unitary time evolution, where a quantum Hamiltonian is viewed as a trajectory in an abstract Lie algebra, while the sought-after evolution operator is a trajectory in a dynamic group, generated by the algebra via exponentiation. The evolution operator is uniquely determined by the time-dependent dual generators that satisfy a system of differential equations, dubbed here dual Schroedinger-Bloch equations, which represent a viable alternative to the conventional Schroedinger formulation. These dual Schroedinger-Bloch equations are derived and analyzed on a number of specific examples. It is shown that deterministic dynamics of a closed classical dynamical system occurs as action of a symmetry group on a classical manifold and is driven by the same dual generators as in the corresponding quantum problem. This represents quantum-to-classical correspondence. In the second part of the paper, we further extend the Lie-algebraic approach to a wide class of interacting many-particle lattice models. A generalized Hubbard-Stratonovich transform is proposed and it is used to show that the thermodynamic partition function of a generic many-body quantum lattice model can be expressed in terms of traces of single-particle evolution operators governed by the dynamic Hubbard-Stratonovich fields. The corresponding Hubbard-Stratonovich dynamical systems are generally nonunitary, which yields a number of notable complications, including breakdown of the global exponential representation. Finally, we derive Hubbard-Stratonovich dynamical systems for the Bose-Hubbard model and a quantum spin model and use the Lie-algebraic approach to obtain new nonperturbative dual
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.
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…
ERIC Educational Resources Information Center
Capani, Antonio; De Dominicis, Gabriel
This paper proposes a model for a general interface between people and Computer Algebra Systems (CAS). The main features in the CAS interface are data navigation and the possibility of accessing powerful remote machines. This model is based on the idea of session management, in which the main engine of the tool enables interactions with the…
a Logic-Algebraic Framework for Contextuality and Modality in Quantum Systems
NASA Astrophysics Data System (ADS)
Freytes, Hector
2014-03-01
In this work we develop a modal structure for the simultaneous treatment of actual and possible properties of quantum systems. A logical system based on orthomodular lattices enriched with a modal operator is given, obtaining algebraic completeness and completeness with respect to a Kripke-style semantic. We show that, in spite of the fact that, the language is enriched with the addition of a modal operator, contextuality remains a central feature of quantum systems.
NASA Astrophysics Data System (ADS)
Foerster, A.; Leymann, H. A. M.; Wiersig, J.
2017-03-01
We introduce an equation of motion approach that allows for an approximate evaluation of the time evolution of a quantum system, where the algebraic work to derive the equations of motion is done by the computer. The introduced procedures offer a variety of different types of approximations applicable for finite systems with strong coupling as well as for arbitrary large systems where augmented mean-field theories like the cluster expansion can be applied.
Control of Linear Systems Over Commutative Normed Algebras with Applications.
1987-02-01
Identify by block number) System Theory, Linear Systems, Control, Systems with Time Delays, Time - Varying Systems, State- Space Models, Pole...modes for the class of linear time -varying systems. These concepts are defined in terms of a noncommutative factorization of opera- tor polynomials...classes of complex linear systems, including systems with time delays, systems with unknown parameters and time -varying systems. In the work on
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.
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.)
Mishra, Bud
2009-07-06
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.
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
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.
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.
Fang, Hao; Wei, Yue; Chen, Jie; Xin, Bin
2017-04-01
The problem of flocking of second-order multiagent systems with connectivity preservation is investigated in this paper. First, for estimating the algebraic connectivity as well as the corresponding eigenvector, a new decentralized inverse power iteration scheme is formulated. Then, based on the estimation of the algebraic connectivity, a set of distributed gradient-based flocking control protocols is built with a new class of generalized hybrid potential fields which could guarantee collision avoidance, desired distance stabilization, and the connectivity of the underlying communication network simultaneously. What is important is that the proposed control scheme allows the existing edges to be broken without violation of connectivity constraints, and thus yields more flexibility of motions and reduces the communication cost for the multiagent system. In the end, nontrivial comparative simulations and experimental results are performed to demonstrate the effectiveness of the theoretical results and highlight the advantages of the proposed estimation scheme and control algorithm.
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.
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)
MAPLE: reflected light from exoplanets with a 50-cm diameter stratospheric balloon telescope
NASA Astrophysics Data System (ADS)
Marois, Christian; Bradley, Colin; Pazder, John; Nash, Reston; Metchev, Stanimir; Grandmont, Frédéric; Maire, Anne-Lise; Belikov, Ruslan; Macintosh, Bruce; Currie, Thayne; Galicher, Raphaël.; Marchis, Franck; Mawet, Dimitri; Serabyn, Eugene; Steinbring, Eric
2014-08-01
Detecting light reflected from exoplanets by direct imaging is the next major milestone in the search for, and characterization of, an Earth twin. Due to the high-risk and cost associated with satellites and limitations imposed by the atmosphere for ground-based instruments, we propose a bottom-up approach to reach that ultimate goal with an endeavor named MAPLE. MAPLE first project is a stratospheric balloon experiment called MAPLE-50. MAPLE-50 consists of a 50 cm diameter off-axis telescope working in the near-UV. The advantages of the near-UV are a small inner working angle and an improved contrast for blue planets. Along with the sophisticated tracking system to mitigate balloon pointing errors, MAPLE-50 will have a deformable mirror, a vortex coronograph, and a self-coherent camera as a focal plane wavefront-sensor which employs an Electron Multiplying CCD (EMCCD) as the science detector. The EMCCD will allow photon counting at kHz rates, thereby closely tracking telescope and instrument-bench-induced aberrations as they evolve with time. In addition, the EMCCD will acquire the science data with almost no read noise penalty. To mitigate risk and lower costs, MAPLE-50 will at first have a single optical channel with a minimum of moving parts. The goal is to reach a few times 109 contrast in 25 h worth of flying time, allowing direct detection of Jovians around the nearest stars. Once the 50 cm infrastructure has been validated, the telescope diameter will then be increased to a 1.5 m diameter (MAPLE-150) to reach 1010 contrast and have the capability to image another Earth.
Lie algebras for systems with mixed spectra. I. The scattering Pöschl-Teller potential
NASA Astrophysics Data System (ADS)
Frank, Alejandro; Wolf, Kurt Bernardo
1985-05-01
Starting from an N-body quantum space, we consider the Lie-algebraic framework where the Pöschl-Teller Hamiltonian, - 1/2 ∂2χ +c sech2 χ+s csch2 χ, is the single sp(2,R) Casimir operator. The spectrum of this system is mixed: it contains a finite number of negative-energy bound states and a positive-energy continuum of free states; it is identified with the Clebsch-Gordan series of the D+×D- representation coupling. The wave functions are the sp(2,R) Clebsch-Gordan coefficients of that coupling in the parabolic basis. Using only Lie-algebraic techniques, we find the asymptotic behavior of these wave functions; for the special pure-trough potential (s=0) we derive thus the transmission and reflection amplitudes of the scattering matrix.
Coherent population transfer in multilevel systems with magnetic sublevels. II. Algebraic analysis
NASA Astrophysics Data System (ADS)
Martin, J.; Shore, B. W.; Bergmann, K.
1995-07-01
We extend previous theoretical work on coherent population transfer by stimulated Raman adiabatic passage for states involving nonzero angular momentum. The pump and Stokes fields are either copropagating or counterpropagating with the corresponding linearly polarized electric-field vectors lying in a common plane with the magnetic-field direction. Zeeman splitting lifts the magnetic sublevel degeneracy. We present an algebraic analysis of dressed-state properties to explain the behavior noted in numerical studies. In particular, we discuss conditions which are likely to lead to a failure of complete population transfer. The applied strategy, based on simple methods of linear algebra, will also be successful for other types of discrete multilevel systems, provided the rotating-wave and adiabatic approximation are valid.
NASA Astrophysics Data System (ADS)
Hermann, Robert
1982-07-01
It is known that many of the Special Functions of mathematical physics appear as matrix elements of Lie group representations. This paper is concerned with a beginning attack on the converse problem, i.e., finding conditions that a given function be a matrix element. The methods used are based on a combination of ideas from system theory, functional analysis, Lie theory, differential algebra, and linear ordinary differential equation theory. A key idea is to attach a symbol as an element of a commutative algebra. In favorable cases, this symbol defines a Riemann surface, and a meromorphic differential form on that surface. The topological and analytical invariants attached to this form play a key role in system theory. The Lie algebras of the groups appear as linear differential operators on this Riemann surface. Finally, it is shown how the Picard-Vessiot-Infeld-Hull theory of factorization of linear differential operators leads to realization of many Special Functions as matrix representations of group representations.
Egri-Nagy, Attila; Nehaniv, Chrystopher L
2008-01-01
Biochemical and genetic regulatory networks are often modeled by Petri nets. We study the algebraic structure of the computations carried out by Petri nets from the viewpoint of algebraic automata theory. Petri nets comprise a formalized graphical modeling language, often used to describe computation occurring within biochemical and genetic regulatory networks, but the semantics may be interpreted in different ways in the realm of automata. Therefore, there are several different ways to turn a Petri net into a state-transition automaton. Here, we systematically investigate different conversion methods and describe cases where they may yield radically different algebraic structures. We focus on the existence of group components of the corresponding transformation semigroups, as these reflect symmetries of the computation occurring within the biological system under study. Results are illustrated by applications to the Petri net modelling of intermediary metabolism. Petri nets with inhibition are shown to be computationally rich, regardless of the particular interpretation method. Along these lines we provide a mathematical argument suggesting a reason for the apparent all-pervasiveness of inhibitory connections in living systems.
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
Preconditioning projection methods for solving algebraic linear systems
NASA Astrophysics Data System (ADS)
García-Palomares, Ubaldo
1999-09-01
Numerical experiments have shown that projection methods are robust for solving the problem of finding a point satisfying a linear system of n variables and m equations; however, their qualities of convergence depend on certain parameters: an n n symmetric positive definite matrix M, and a vector u with m components. We are concerned here with the choice of M. Through a link with Conjugate Gradient methods we determine an expedient M. Preliminary numerical results on a hard 3D partial differential equation are highly promising. We solve a discretized system that could not be solved by conventional methods. We also give hints on how to adapt our findings to the solution of a linear system of inequalities. This is the first stage of a forthcoming research.
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.
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.
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)
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 Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) FOOD FOR HUMAN CONSUMPTION SWEETENERS AND TABLE SIRUPS Requirements for Specific Standardized Sweeteners and Table...
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
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.
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
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.
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
2011-01-01
Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on
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.
NASA Astrophysics Data System (ADS)
Bolaños, Marduk; Barberis-Blostein, Pablo
2015-11-01
We consider the Lindblad equation for a collection of multilevel systems coupled to independent environments. The equation is symmetric under the exchange of the labels associated with each system and thus the open-system dynamics takes place in the permutation-symmetric subspace of the operator space. The dimension of this space grows polynomially with the number of systems. We construct a basis of this space and a set of superoperators whose action on this basis is easily specified. For a given number of levels, M, these superoperators are written in terms of a bosonic realization of the generators of the Lie algebra {sl}({M}2). In some cases, these results enable finding an analytic solution of the master equation using known Lie-algebraic methods. To demonstrate this, we obtain an analytic expression for the state operator of a collection of three-level atoms coupled to independent radiation baths. When analytic solutions are difficult to find, the basis and the superoperators can be used to considerably reduce the computational resources required for simulations.
Petzold, L.R.; Rosen, J.B.
1997-12-30
Differential-algebraic equations arise in a wide variety of engineering and scientific problems. Relatively little work has been done regarding sensitivity analysis and model reduction for this class of problems. Efficient methods for sensitivity analysis are required in model development and as an intermediate step in design optimization of engineering processes. Reduced order models are needed for modelling complex physical phenomena like turbulent reacting flows, where it is not feasible to use a fully-detailed model. The objective of this work has been to develop numerical methods and software for sensitivity analysis and model reduction of nonlinear differential-algebraic systems, including large-scale systems. In collaboration with Peter Brown and Alan Hindmarsh of LLNL, the authors developed an algorithm for finding consistent initial conditions for several widely occurring classes of differential-algebraic equations (DAEs). The new algorithm is much more robust than the previous algorithm. It is also very easy to use, having been designed to require almost no information about the differential equation, Jacobian matrix, etc. in addition to what is already needed to take the subsequent time steps. The new algorithm has been implemented in a version of the software for solution of large-scale DAEs, DASPK, which has been made available on the internet. The new methods and software have been used to solve a Tokamak edge plasma problem at LLNL which could not be solved with the previous methods and software because of difficulties in finding consistent initial conditions. The capability of finding consistent initial values is also needed for the sensitivity and optimization efforts described in this paper.
Kim, Joshua; Guan, Huaiqun; Gersten, David; Zhang, Tiezhi
2013-01-01
Tetrahedron beam computed tomography (TBCT) performs volumetric imaging using a stack of fan beams generated by a multiple pixel X-ray source. While the TBCT system was designed to overcome the scatter and detector issues faced by cone beam computed tomography (CBCT), it still suffers the same large cone angle artifacts as CBCT due to the use of approximate reconstruction algorithms. It has been shown that iterative reconstruction algorithms are better able to model irregular system geometries and that algebraic iterative algorithms in particular have been able to reduce cone artifacts appearing at large cone angles. In this paper, the SART algorithm is modified for the use with the different TBCT geometries and is tested using both simulated projection data and data acquired using the TBCT benchtop system. The modified SART reconstruction algorithms were able to mitigate the effects of using data generated at large cone angles and were also able to reconstruct CT images without the introduction of artifacts due to either the longitudinal or transverse truncation in the data sets. Algebraic iterative reconstruction can be especially useful for dual-source dual-detector TBCT, wherein the cone angle is the largest in the center of the field of view.
NASA Astrophysics Data System (ADS)
Zhang, Shunli; Zhang, Dinghua; Gong, Hao; Ghasemalizadeh, Omid; Wang, Ge; Cao, Guohua
2014-11-01
Iterative algorithms, such as the algebraic reconstruction technique (ART), are popular for image reconstruction. For iterative reconstruction, the area integral model (AIM) is more accurate for better reconstruction quality than the line integral model (LIM). However, the computation of the system matrix for AIM is more complex and time-consuming than that for LIM. Here, we propose a fast and accurate method to compute the system matrix for AIM. First, we calculate the intersection of each boundary line of a narrow fan-beam with pixels in a recursive and efficient manner. Then, by grouping the beam-pixel intersection area into six types according to the slopes of the two boundary lines, we analytically compute the intersection area of the narrow fan-beam with the pixels in a simple algebraic fashion. Overall, experimental results show that our method is about three times faster than the Siddon algorithm and about two times faster than the distance-driven model (DDM) in computation of the system matrix. The reconstruction speed of our AIM-based ART is also faster than the LIM-based ART that uses the Siddon algorithm and DDM-based ART, for one iteration. The fast reconstruction speed of our method was accomplished without compromising the image quality.
Soil acidity and manganese in declining and nondeclining sugar maple stands in Pennsylvania.
Kogelmann, Wilhelm J; Sharpe, William E
2006-01-01
For decades, the hardwood forests of northern Pennsylvania have been subjected to chronic atmospheric loading of acidifying agents. On marginal, high-elevation, unglaciated sites, sugar maples (Acer saccharum Marsh.) have experienced severe decline symptoms and mortality. Accelerated soil acidification, base cation leaching, and increased availability of toxic metals have been suggested as predisposing factors contributing to this decline. Manganese, an essential micronutrient, is also a potentially phytotoxic metal that may be a factor associated with poor sugar maple health on soils vulnerable to acidification from anthropogenic sources. We measured Mn levels in four compartments of the soil-tree system (soil, foliage, xylem wood, and sap) on three sugar maple stands in northern Pennsylvania. Two stands were classified as declining and one was in good health. Negative correlations were found between soil pH and Mn levels in the soil, foliage, sap, and xylem wood. Levels of Mn in these pools were consistently higher on declining sites, which correspondingly exhibited lower levels of Ca and Mg. Species differences between red maple (Acer rubrum L.) and sugar maple at the two declining sites suggested different tolerances to excessive Mn. Molar ratios of Mg/Mn and Ca/Mn were different among sites and showed potential as indicators of soil acidification. Significant correlations among soil, sap, foliage, and xylem wood Mn were also noted. These results show clear Mn differences among sites and, when viewed with recent Mn toxicity experiments and other observational studies, suggest that excessive Mn may play a role in the observed decline and mortality of sugar maple.
Learning Activity Package, Algebra.
ERIC Educational Resources Information Center
Evans, Diane
A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…
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 dissertation,…
Modelling and temporal performances evaluation of networked control systems using (max, +) algebra
NASA Astrophysics Data System (ADS)
Ammour, R.; Amari, S.
2015-01-01
In this paper, we address the problem of temporal performances evaluation of producer/consumer networked control systems. The aim is to develop a formal method for evaluating the response time of this type of control systems. Our approach consists on modelling, using Petri nets classes, the behaviour of the whole architecture including the switches that support multicast communications used by this protocol. (max, +) algebra formalism is then exploited to obtain analytical formulas of the response time and the maximal and minimal bounds. The main novelty is that our approach takes into account all delays experienced at the different stages of networked automation systems. Finally, we show how to apply the obtained results through an example of networked control system.
Algebraic approach for the reconstruction of Rossler system from the x(3)- variable
NASA Astrophysics Data System (ADS)
Ibanez, C. A.
2006-02-01
In this paper we propose a simple method to identify the unknown parameters and to estimate the underlying variables from a given chaotic time series {x(3)(t(k)) (k=n)(0) of the three-dimensional Rossler system (RS). The reconstruction of the RS from its x(3-) variable is known to be considerably more difficult than reconstruction from its two other variables. We show that the system is observable and algebraically identifiable with respect to the auxiliary output In(x(3)), hence, a differential parameterization of the output and its time derivatives can be obtained. Based on these facts, we proceed to form an extended re-parameterized system (linear-in-the -parameters), which turns out to be invertible, allowing us to estimate the variables and missing parameters.
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.
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)
Coherent states for a polynomial su(1, 1) algebra and a conditionally solvable system
NASA Astrophysics Data System (ADS)
Sadiq, Muhammad; Inomata, Akira; Junker, Georg
2009-09-01
In a previous paper (2007 J. Phys. A: Math. Theor. 40 11105), we constructed a class of coherent states for a polynomially deformed su(2) algebra. In this paper, we first prepare the discrete representations of the nonlinearly deformed su(1, 1) algebra. Then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su(1, 1) algebra which contains the Barut-Girardello set and the Perelomov set of the SU(1, 1) coherent states as special cases. We also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem.
Maple procedures for the coupling of angular momenta II. Sum rule evaluation
NASA Astrophysics Data System (ADS)
Fritzsche, S.; Varga, S.; Geschke, D.; Fricke, B.
1998-06-01
In a previous paper (S. Fritzsche, Comput. Phys. Commun. 103 (1997) 51), we defined data structures to deal with typical expressions from Racah algebra within the framework of Maple. Such expressions arise very frequently in various fields, for instance, by treating composite wave functions and tensor operators in many-particle physics. Often, these Racah expressions are written in terms of Clebsch-Gordan coefficients and Wigner n-j symbols. Our previous set of Maple procedures mainly concerned numerical computations on such symbols, the simplification by special values as well as the use of recursion relations. The full elegance of applying Racah algebra techniques in daily research work is, however, only revealed by the analytic simplification of more complex expressions. In practise, this even requires the major effort in dealing with these techniques. Its success closely depends on the knowledge of sum rules which typically include a number of dummy summation indices. The application of these sum rules is a rather straightforward task but may become very tedious for more difficult expressions due to the large number of symmetries of the Clebsch-Gordan coefficients and Wigner n-j symbols. We therefore extended the Racah program to facilitate sum rule evaluations in the given framework. A set of new and revised procedures now supports the evaluation of Racah algebra expressions by applying the orthogonality properties of the Wigner symbols and a variety of sum rules. More than 40 sum rules known from the literature and involving products of up to six Wigner n-j symbols have been implemented and are available for interactive use. The applicability of this new tool will be demonstrated by three examples from many-particle physics.
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.
Application of the Cramer rule in the solution of sparse systems of linear algebraic equations
NASA Astrophysics Data System (ADS)
Mittal, R. C.; Al-Kurdi, Ahmad
2001-11-01
In this work, the solution of a sparse system of linear algebraic equations is obtained by using the Cramer rule. The determinants are computed with the help of the numerical structure approach defined in Suchkov (Graphs of Gearing Machines, Leningrad, Quebec, 1983) in which only the non-zero elements are used. Cramer rule produces the solution directly without creating fill-in problem encountered in other direct methods. Moreover, the solution can be expressed exactly if all the entries, including the right-hand side, are integers and if all products do not exceed the size of the largest integer that can be represented in the arithmetic of the computer used. The usefulness of Suchkov numerical structure approach is shown by applying on seven examples. Obtained results are also compared with digraph approach described in Mittal and Kurdi (J. Comput. Math., to appear). It is shown that the performance of the numerical structure approach is better than that of digraph approach.
Abstract algebraic-delay differential systems and age structured population dynamics
NASA Astrophysics Data System (ADS)
Kosovalić, N.; Magpantay, F. M. G.; Chen, Y.; Wu, J.
We consider the abstract algebraic-delay differential system, x'(t)=Ax(t)+F(x(t),a(t)), a(t)=H(xt,at). Here A is a linear operator on D(A)⊂X satisfying the Hille-Yosida conditions, x(t)∈D(A)¯⊂X, and a(t)∈Rn, where X is a real Banach space. With a global Lipschitz condition on F and an appropriate hypothesis on the function H, we show that the corresponding initial value problem gives rise to a continuous semiflow in a subset of the space of continuous functions. We establish the positivity of the x-component and give some examples arising from age structured population dynamics. The examples come from situations where the age of maturity of an individual at a given time is determined by whether or not the resource concentration density, which depends on the immature population, reaches a prescribed threshold within that time.
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
Exley, I. Sheck
The high percentage of high school pre-algebra students having difficulty learning the abstract concept of graphing ordered pairs on the Cartesian rectangular coordinate system was addressed by the creation and implementation of a computer-managed instructional program. Modules consisted of a pretest, instruction, two practice sessions, and a…
ERIC Educational Resources Information Center
Leng, Ng Wee; Choo, Kwee Tiow; Soon, Lau Hock; Yi-Huak, Koh; Sun, Yap Yew
2005-01-01
This study examines the effects of using Texas Instruments' Voyage 200 calculator (V200), a graphing calculator with a built-in computer algebra system (CAS), on attitudes towards CAS and achievement in mathematics of junior college students (17 year olds). Students' attitudes towards CAS were examined using a 40-item Likert-type instrument…
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…
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…
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.
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.
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
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.
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.
Jordan Algebraic Quantum Categories
NASA Astrophysics Data System (ADS)
Graydon, Matthew; Barnum, Howard; Ududec, Cozmin; Wilce, Alexander
2015-03-01
State cones in orthodox quantum theory over finite dimensional complex Hilbert spaces enjoy two particularly essential features: homogeneity and self-duality. Orthodox quantum theory is not, however, unique in that regard. Indeed, all finite dimensional formally real Jordan algebras -- arenas for generalized quantum theories with close algebraic kinship to the orthodox theory -- admit homogeneous self-dual positive cones. We construct categories wherein these theories are unified. The structure of composite systems is cast from universal tensor products of the universal C*-algebras enveloping ambient spaces for the constituent state cones. We develop, in particular, a notion of composition that preserves the local distinction of constituent systems in quaternionic quantum theory. More generally, we explicitly derive the structure of hybrid quantum composites with subsystems of arbitrary Jordan algebraic type.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Choi, Jeong Ryeol; Choi, Seong Soo
We realized SU(1,1) Lie algebra in terms of the appropriate SU(1,1) generators for the time-dependent quadratic Hamiltonian system perturbed by a singularity. Exact quantum states of the system are investigated using SU(1,1) Lie algebra. Various expectation values in two kinds of the generalized SU(1,1) coherent states, that is, BG coherent states and Perelomov coherent states are derived. We applied our study to the CKOPS (Caldirola-Kanai oscillator perturbed by a singularity). Due to the damping constant γ, the probability density of the SU(1,1) coherent states for the CKOPS converged to the center with time. The time evolution of the probability density in SU(1,1) coherent states for the CKOPS are very similar to the classical trajectory.
NASA Astrophysics Data System (ADS)
Yukhno, L. F.
2007-12-01
The use of modifications of certain well-known methods of the conjugate direction type for solving systems of linear algebraic equations with rectangular matrices is examined. The modified methods are shown to be superior to the original versions with respect to the round-off accumulation; the advantage is especially large for ill-conditioned matrices. Examples are given of the efficient use of the modified methods for solving certain fairly large ill-conditioned problems.
Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras
NASA Astrophysics Data System (ADS)
Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent; Kato La, V.
2016-10-01
We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.
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.
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.
Chemical distinctions between Stradivari’s maple and modern tonewood
Li, Guo-Chian; Huang, Shing-Jong; Jhu, Chang-Ruei; Chung, Jen-Hsuan; Wang, Bo Y.; Hsu, Chia-Shuo; Brandmair, Brigitte; Chung, Dai-Ting; Chen, Hao Ming; Chan, Jerry Chun Chung
2017-01-01
Violins made by Antonio Stradivari are renowned for having been the preferred instruments of many leading violinists for over two centuries. There have been long-standing questions about whether wood used by Stradivari possessed unique properties compared with modern tonewood for violin making. Analyses of maple samples removed from four Stradivari and a Guarneri instrument revealed highly distinct organic and inorganic compositions compared with modern maples. By solid-state 13C NMR spectroscopy, we observed that about one-third of hemicellulose had decomposed after three centuries, accompanied by signs of lignin oxidation. No apparent changes in cellulose were detected by NMR and synchrotron X-ray diffraction. By thermogravimetric analysis, historical maples exhibited reduced equilibrium moisture content. In differential scanning calorimetry measurements, only maples from Stradivari violins, but not his cellos, exhibited unusual thermooxidation patterns distinct from natural wood. Elemental analyses by inductively coupled plasma mass spectrometry suggested that Stradivari’s maples were treated with complex mineral preservatives containing Al, Ca, Cu, Na, K, and Zn. This type of chemical seasoning was an unusual practice, unknown to later generations of violin makers. In their current state, maples in Stradivari violins have very different chemical properties compared with their modern counterparts, likely due to the combined effects of aging, chemical treatments, and vibrations. These findings may inspire further chemical experimentation with tonewood processing for instrument making in the 21st century. PMID:27994135
A computer algorithm for performing interactive algebraic computation on the GE Image-100 system
NASA Technical Reports Server (NTRS)
Hart, W. D.; Kim, H. H.
1979-01-01
A subroutine which performs specialized algebraic computations upon ocean color scanner multispectral data is presented. The computed results are displayed on a video display. The subroutine exists as a component of the aircraft sensor analysis package. The user specifies the parameters of the computations by directly interacting with the computer. A description of the conversational options is also given.
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.…
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.
Building food safety into the company culture: a look at Maple Leaf Foods.
Lone, Jespersen; Huffman, Randy
2014-07-01
Maple Leaf Foods learned a hard lesson following its tragic 2008 Listeria outbreak that ended up taking the lives of 23 Canadians. The organization has since 2008 transformed its commitment to food safety with a strong drive and manifest in embedding sustainable food safety behaviours into the existing company culture. Its focus on combining technical risk analysis with behavioural sciences has led to the development and deployment of a food safety strategy deeply rooted in the company values and management commitment. Using five tactics described in this article the organization has been on a journey towards food safety transformation through adoption of best practices for people and systems. The approach to food safety has been one where food safety is treated as a non-competitive issue and Maple Leaf Foods have been open to sharing learning about what happened and how the organization will continue to take a leadership position in food safety to continuously raise the bar for food safety across the industry. Maple Leaf Foods has benefited tremendously by learning about best practice from numerous companies in North America and around the world. The authors believe this brief story will bring value to others as we continue to learn and improve.
RIR-MAPLE deposition of plasmonic silver nanoparticles
NASA Astrophysics Data System (ADS)
Ge, Wangyao; Hoang, Thang B.; Mikkelsen, Maiken H.; Stiff-Roberts, Adrienne D.
2016-09-01
Nanoparticles are being explored in many different applications due to the unique properties offered by quantum effects. To broaden the scope of these applications, the deposition of nanoparticles onto substrates in a simple and controlled way is highly desired. In this study, we use resonant infrared matrix-assisted pulsed laser evaporation (RIR-MAPLE) for the deposition of metallic, silver nanoparticles for plasmonic applications. We find that RIR-MAPLE, a simple and versatile approach, is able to deposit silver nanoparticles as large as 80 nm onto different substrates with good adhesion, regardless of substrate properties. In addition, the nanoparticle surface coverage of the substrates, which result from the random distribution of nanoparticles across the substrate per laser pulse, can be simply and precisely controlled by RIR-MAPLE. Polymer films of poly(3-hexylthiophene-2,5-diyl) (P3HT) are also deposited by RIR-MAPLE on top of the deposited silver nanoparticles in order to demonstrate enhanced absorption due to the localized surface plasmon resonance effect. The reported features of RIR-MAPLE nanoparticle deposition indicate that this tool can enable efficient processing of nanoparticle thin films for applications that require specific substrates or configurations that are not easily achieved using solution-based approaches.
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.
Richards' Equation and its Constitutive Relations as a System of Differential-Algebraic Equations
NASA Astrophysics Data System (ADS)
Murray, S. K.; Mead, J. L.
2007-12-01
Richards' Equation is commonly used to understand how water flows in unsaturated soils. We present a new formulation of Richards' Equation which will allow us to incorporate model and observation errors. In addition, we can address spatial and temporal inconsistencies existing between the model and observations. There are two basic formulations for Richards' Equation: the pressure head form and the mixed form, the latter of which explicitly incorporates soil moisture content. The mixed form is typically solved using HYDRUS, a freely available program that uses finite elements with Picard iteration to handle the nonlinearities. However, recent results suggest considering Richards' Equation as a differential-algebraic equation (DAE), where the algebraic models for soil moisture content (van Genuchten's equation) is solved simultaneously with Richards' Equation (Kees, et. al., 2002). This formulation can give more accurate forward model solutions, however, we note that it also allows us to consider the uncertainties in the pressure head ψ and the soil moister content θ during the inversion process. We extend the DAE formulation to include the algebraic constraint for hydraulic conductivity K, so that its uncertainty can also be considered in an inversion. This poster focuses on the efficiency and accuracy of the forward numerical solution of this particular DAE formulation of Richards' Equation and how it compares to other forward solutions, such as HYDRUS.
NASA Astrophysics Data System (ADS)
Akhunov, R. R.; Gazizov, T. R.; Kuksenko, S. P.
2016-08-01
The mean time needed to solve a series of systems of linear algebraic equations (SLAEs) as a function of the number of SLAEs is investigated. It is proved that this function has an extremum point. An algorithm for adaptively determining the time when the preconditioner matrix should be recalculated when a series of SLAEs is solved is developed. A numerical experiment with multiply solving a series of SLAEs using the proposed algorithm for computing 100 capacitance matrices with two different structures—microstrip when its thickness varies and a modal filter as the gap between the conductors varies—is carried out. The speedups turned out to be close to the optimal ones.
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…
[SADE] a Maple package for the symmetry analysis of differential equations
NASA Astrophysics Data System (ADS)
Rocha Filho, Tarcísio M.; Figueiredo, Annibal
2011-02-01
We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, nonclassical, Lie-Bäcklund and potential symmetries, invariant solutions, first-integrals, Nöther theorem for both discrete and continuous systems, solution of ordinary differential equations, order and dimension reductions using Lie symmetries, classification of differential equations, Casimir invariants, and the quasi-polynomial formalism for ODE's (previously implemented by the authors in the package QPSI) for the determination of quasi-polynomial first-integrals, Lie symmetries and invariant surfaces. Examples of use of the package are given. Program summaryProgram title: SADE Catalogue identifier: AEHL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 27 704 No. of bytes in distributed program, including test data, etc.: 346 954 Distribution format: tar.gz Programming language: MAPLE 13 and MAPLE 14 Computer: PCs and workstations Operating system: UNIX/LINUX systems and WINDOWS Classification: 4.3 Nature of problem: Determination of analytical properties of systems of differential equations, including symmetry transformations, analytical solutions and conservation laws. Solution method: The package implements in MAPLE some algorithms (discussed in the text) for the study of systems of differential equations. Restrictions: Depends strongly on the system and on the algorithm required. Typical restrictions are related to the solution of a large over-determined system of linear or non-linear differential equations. Running time: Depends strongly on the order, the complexity of the differential
Red maple (Acer rubrum) inhibits feeding by beaver (Castor canadensis).
Müller-Schwarze, D; Schulte, B A; Sun, L; Müller-Schwarze, A; Müller-Schwarze, C
1994-08-01
At many beaver (Castor canadensis) sites at Allegany State Park in New York State, red maple (Acer rubrum) is the only or one of the few tree species left standing at the ponds' edges. The relative palatability of red maple (RM) was studied in three ways. (1) At seven beaver sites, the available and utilized trees were recorded and an electivity index (E) computed. Of 15 tree species, RM ranked second or fourth lowest. (2) In experiment I, RM, sugar maple (A. saccharum, SM), and quaking aspen (Populus tremuloides) logs were presented cafeteria style at 10 colonies. RM was the least preferred. (3) Bark of RM was extracted with solvents. Aspen logs were painted (experiment II) or soaked (experiment III) with this RM extract and presented to beaver cafeteria-style, along with aspen and RM controls. This treatment rendered aspen logs less palatable, indicating that a chemical factor had been transferred.
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...
Chang, P
2004-09-15
A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3-D magnetic field are then obtained through slice-by-slice symplectic integration. The particle phase-space coordinates are advanced by using the integrable polynomial procedure. This algorithm is a powerful tool to attain nonlinear maps for insertion devices in synchrotron light source or complicated magnetic field in the interaction region in high energy colliders.
Abhyankar, Shrirang; Anitescu, Mihai; Constantinescu, Emil; Zhang, Hong
2016-03-31
Sensitivity analysis is an important tool to describe power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this work, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating trajectory sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as DC exciters, by deriving and implementing the adjoint jump conditions that arise from state and time-dependent discontinuities. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach.
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.
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 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…
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…
NASA Astrophysics Data System (ADS)
Fabijonas, Bruce R.
2002-09-01
We examine a Maple implementation of two distinct approaches to Laplace's method used to obtain asymptotic expansions of Laplace-type integrals. One algorithm uses power series reversion, whereas the other expands all quantities in Taylor or Puiseux series. These algorithms are used to derive asymptotic expansions for the real valued modified Bessel functions of pure imaginary order and real argument that mimic the well-known corresponding expansions for the unmodified Bessel functions.
NASA Astrophysics Data System (ADS)
Vaninsky, Alexander
2011-04-01
This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.
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.
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.
Using MapleSim to model a six-strut kinematic mount for aligning optical components
NASA Astrophysics Data System (ADS)
Duffy, Alan; Yates, Brian; Hu, Yongfeng
2011-09-01
Ray tracing simulations are often performed for an ideal situation of perfect alignment, but it is usually necessary to move optical components for various reasons. The mounts that hold these components can be complicated and modeling their motion is vital to understanding how they affect the performance of the system. This paper examines the behaviour of a six-strut kinematic mount using MapleSim to investigate and understand precisely how a mirror pole moves with its mount and quantify any cross-coupled motion that may occur during actuator adjustments. This positional information can be used to mitigate errors, improve ray tracing results, and assist in alignment.
NASA Astrophysics Data System (ADS)
Borzykh, A. N.
2017-01-01
The Seidel method for solving a system of linear algebraic equations and an estimate of its convergence rate are considered. It is proposed to change the order of equations. It is shown that the method described in Faddeevs' book Computational Methods of Linear Algebra can deteriorate the convergence rate estimate rather than improve it. An algorithm for establishing the optimal order of equations is proposed, and its validity is proved. It is shown that the computational complexity of the reordering is 2 n 2 additions and (12) n 2 divisions. Numerical results for random matrices of order 100 are presented that confirm the proposed improvement.
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)
Krasnikov, S. D.; Kuznetsov, E. B.
2016-09-01
Numerical continuation of solution through certain singular points of the curve of the set of solutions to a system of nonlinear algebraic or transcendental equations with a parameter is considered. Bifurcation points of codimension two and three are investigated. Algorithms and computer programs are developed that implement the procedure of discrete parametric continuation of the solution and find all branches at simple bifurcation points of codimension two and three. Corresponding theorems are proved, and each algorithm is rigorously justified. A novel algorithm for the estimation of errors of tangential vectors at simple bifurcation points of a finite codimension m is proposed. The operation of the computer programs is demonstrated by test examples, which allows one to estimate their efficiency and confirm the theoretical results.
NASA Astrophysics Data System (ADS)
Trell, Erik; Edeagu, Samuel; Animalu, Alexander
2017-01-01
From a brief recapitulation of the foundational works of Marius Sophus Lie and Herrmann Günther Grassmann, and including missing African links, a rhapsodic survey is made of the straight line of extension and existence that runs as the very fibre of generation and creation throughout Nature's all utterances, which must therefore ultimately be the web of Reality itself of which the Arts and Sciences are interpreters on equal explorer terms. Assuming their direct approach, the straight line and its archaic and algebraic and artistic bearings and convolutions have been followed towards their inner reaches, which earlier resulted in a retrieval of the baryon and meson elementary particles and now equally straightforward the electron geodesics and the organic build of the periodic system of the elements.
NASA Astrophysics Data System (ADS)
Letellier, Christophe; Amaral, Gleison F. V.; Aguirre, Luis A.
2007-06-01
The characterization of chaotic attractors has been a widely addressed problem and there are now many different techniques to define their nature in a rather accurate way, at least in the case of a three-dimensional system. Nevertheless, the link between the structure of the ordinary differential equations and the topology of their solutions is still missing and only a few necessary conditions on the algebraic structure are known today. By using a feedback circuit analysis, it is shown that it is possible to identify the relevant terms of the equations, that is, the terms that really contribute to the structure of the phase portrait. Such analysis also provides some guidelines for constructing piecewise affine models. Moreover, equivalence classes can be defined on the basis of the active feedback circuits involved.
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.
NASA Astrophysics Data System (ADS)
Průša, Vít; Řehoř, Martin; Tůma, Karel
2017-02-01
The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its response is governed by a system of linear ordinary differential equations. In the linear case, the mathematical method of choice for the analysis of the response is the classical theory of distributions. However, if the system contains nonlinear elements, then the classical theory of distributions is of no use, since it is strictly limited to the linear setting. Consequently, a question arises whether it is even possible or reasonable to study the response of nonlinear systems to step inputs. The answer is positive. A mathematical theory that can handle the challenge is the so-called Colombeau algebra. Building on the abstract result by Průša and Rajagopal (Int J Non-Linear Mech 81:207-221, 2016), we show how to use the theory in the analysis of response of nonlinear spring-dashpot and spring-dashpot-mass systems.
MAPLE deposited polymeric blends coatings for controlled drug delivery
NASA Astrophysics Data System (ADS)
Paun, Irina Alexandra; Ion, Valentin; Moldovan, Antoniu; Dinescu, Maria
2012-07-01
We report on the use of Matrix Assisted Pulsed Laser Evaporation (MAPLE) for producing coatings of polymer blends for controlled drug delivery. The coatings consisting of blends of polyethylene glycol: poly(lactide-co-glycolide) (PEG: PLGA blends) are compared with those consisting of individual polymers (PEG, PLGA) in terms of chemical composition, morphology, hydrophilicity and optical constants. The release kinetics of an anti-inflammatory drug (indomethacin) through the polymeric coatings is monitored and possible mechanisms of the drug release are discussed. Furthermore, the compatibility of the polymeric coatings with blood constituents is investigated. Finally, the perspectives for employing MAPLE for producing coatings of polymer blends to be used in implants that deliver drugs in a controlled manner, along with the routes to be followed for elucidating the mechanism of drug release, are revealed.
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.
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.
Cerebral computed tomography in maple syrup urine disease.
Romero, F J; Ibarra, B; Rovira, M; Natal, A; Herrera, M; Segarra, A
1984-06-01
Maple syrup urine disease (MSUD) is an inherited metabolic disorder due to decreased decarboxylation of branched chain keto acids triggering an accumulation of leucine, isoleucine, and valine. We describe two infants with biochemically confirmed MSUD in whom computed tomography (CT) revealed cerebral edema. In one of these cases repeat CT 40 days after institution of appropriate therapy revealed that the edema had disappeared and the ventricles had enlarged.
Numerical linear algebra algorithms and software
NASA Astrophysics Data System (ADS)
Dongarra, Jack J.; Eijkhout, Victor
2000-11-01
The increasing availability of advanced-architecture computers has a significant effect on all spheres of scientific computation, including algorithm research and software development in numerical linear algebra. Linear algebra - in particular, the solution of linear systems of equations - lies at the heart of most calculations in scientific computing. This paper discusses some of the recent developments in linear algebra designed to exploit these advanced-architecture computers. We discuss two broad classes of algorithms: those for dense, and those for sparse matrices.
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
Limitations in the use of ozone to disinfect maple sap.
Labbe, R G; Kinsley, M; Wu, J
2001-01-01
The sap of the maple sugar tree (Acer saccharum) contains 2 to 3% sucrose and is traditionally collected early in the year and concentrated by boiling to produce maple syrup. High levels of microorganisms in the sap occur during holding, leading to a darker syrup with lower economic value. We investigated the use of dissolved ozone as a method to reduce the microbial population in sap. After 40 min of ozone treatment, concentrations of up to 0.30 mg/liter were achieved but were ineffective in reducing the aerobic plate count. Three predominant colonies on nutrient agar were selected for isolation and identification from sap. These included one mucoid and one nonmucoid yeast, both identified as Candida, and Pseudomonas fluorescens. When suspended in buffer, each was readily inactivated by ozone. Addition of 3% sucrose to the buffer markedly reduced the effectiveness of ozone. With the use of an ozone generator with a larger ozone output, saturating ozone concentrations (1 mg/liter) were achieved within 5 min but were accompanied by only a 1-log reduction in aerobic plate count of maple sap. After 40 min of ozone treatment, a less than 3-log reduction occurred. The results indicate that, because of the presence of sucrose, ozone may be of limited use in reducing the microbial population in sap.
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.
Chlorophyll content monitoring in sugar maple (Acer saccharum).
Cate, Thomas M; Perkins, T D
2003-10-01
We conducted two experiments to determine the usefulness of a chlorophyll content meter (CCM) for the measurement of foliar chlorophyll concentration in sugar maple (Acer saccharum Marsh.) in the fall color period. In Experiment 1, four sugar maple trees were visually assigned to each of four fall foliage color categories in October 1998. On four dates in the fall of 1999, leaves were taken from the trees and analyzed for chlorophyll concentration by absorbance of pigment extracts and by determination of the chlorophyll content index (CCI) with a CCM. The two measures of chlorophyll concentration were strongly correlated (P < 0.001, r2 = 0.72). In Experiment 2, the CCI of leaves from sugar maple trees subjected to one of four fertilization treatments (lime, lime + manure, lime + 10:10:10 N,P,K fertilizer and an untreated control) were determined with a CCM. Treatment effects were distinguishable between all pairwise comparisons (P < 0.001), except for the lime versus lime + NPK fertilizer treatments.
MaPLE: A MapReduce Pipeline for Lattice-based Evaluation and Its Application to SNOMED CT.
Zhang, Guo-Qiang; Zhu, Wei; Sun, Mengmeng; Tao, Shiqiang; Bodenreider, Olivier; Cui, Licong
2014-10-01
Non-lattice fragments are often indicative of structural anomalies in ontological systems and, as such, represent possible areas of focus for subsequent quality assurance work. However, extracting the non-lattice fragments in large ontological systems is computationally expensive if not prohibitive, using a traditional sequential approach. In this paper we present a general MapReduce pipeline, called MaPLE (MapReduce Pipeline for Lattice-based Evaluation), for extracting non-lattice fragments in large partially ordered sets and demonstrate its applicability in ontology quality assurance. Using MaPLE in a 30-node Hadoop local cloud, we systematically extracted non-lattice fragments in 8 SNOMED CT versions from 2009 to 2014 (each containing over 300k concepts), with an average total computing time of less than 3 hours per version. With dramatically reduced time, MaPLE makes it feasible not only to perform exhaustive structural analysis of large ontological hierarchies, but also to systematically track structural changes between versions. Our change analysis showed that the average change rates on the non-lattice pairs are up to 38.6 times higher than the change rates of the background structure (concept nodes). This demonstrates that fragments around non-lattice pairs exhibit significantly higher rates of change in the process of ontological evolution.
MaPLE: A MapReduce Pipeline for Lattice-based Evaluation and Its Application to SNOMED CT
Zhang, Guo-Qiang; Zhu, Wei; Sun, Mengmeng; Tao, Shiqiang; Bodenreider, Olivier; Cui, Licong
2015-01-01
Non-lattice fragments are often indicative of structural anomalies in ontological systems and, as such, represent possible areas of focus for subsequent quality assurance work. However, extracting the non-lattice fragments in large ontological systems is computationally expensive if not prohibitive, using a traditional sequential approach. In this paper we present a general MapReduce pipeline, called MaPLE (MapReduce Pipeline for Lattice-based Evaluation), for extracting non-lattice fragments in large partially ordered sets and demonstrate its applicability in ontology quality assurance. Using MaPLE in a 30-node Hadoop local cloud, we systematically extracted non-lattice fragments in 8 SNOMED CT versions from 2009 to 2014 (each containing over 300k concepts), with an average total computing time of less than 3 hours per version. With dramatically reduced time, MaPLE makes it feasible not only to perform exhaustive structural analysis of large ontological hierarchies, but also to systematically track structural changes between versions. Our change analysis showed that the average change rates on the non-lattice pairs are up to 38.6 times higher than the change rates of the background structure (concept nodes). This demonstrates that fragments around non-lattice pairs exhibit significantly higher rates of change in the process of ontological evolution. PMID:25705725
Methyl gallate is a natural constituent of maple (Genus Acer) leaves.
Abou-Zaid, Mamdouh M; Lombardo, Domenic A; Nozzolillo, Constance
2009-01-01
Methyl gallate was found in ethanolic extracts of red maple (Acer rubrum L.), silver maple (A. saccharinum L.) and sugar maple (A. saccharum Marsh) leaves, but more was present in methanolic extracts. The increased amount of methyl gallate in methanolic extracts was accompanied by a disappearance of m-digallate. It is concluded that only some of the methyl gallate detected in methanolic extracts is an artefact as a result of methanolysis of m-digallate. Its presence in ethanolic extracts is evidence that it is also a natural constituent of maple leaves.
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.
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
2015-01-01
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
NASA Technical Reports Server (NTRS)
Ghosh, Bijoy K.
1988-01-01
This paper studies structured uncertainty problems in feedback system design, considers a compact parameterization of the space of linear dynamical systems and introduces 'base points' and 'critical points' as two algebraic-geometric objects that have significance in sensitivity and robustness studies, respectively. Using the Nevanlinna-Pick interpolation theory, the author obtains a necessary and sufficient condition for simultaneous stabilization of a structured one-parameter family of plants. A recent result due to Kharitonov, on the simultaneous stability of a parameterized family of polynomials, leads to a sufficiency condition for simultaneous stabilization of a structured multiparameter family of plants. Furthermore, the author considers 'simultaneous pole placement' of an r-tuple of plants as a means to arbitrarily tune the natural frequencies of a multimode linear dynamical system. The concept of 'nondegenerate' and 'twisted' r-tuples of plants is introduced as the pole placement problem is studied via Schubert enumerative geometry as an intersection problem on the associated Grassmannian. Various other design problems, viz., the strong stabilization problem and the dead beat control problem, are also considered.
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
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.
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.
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…
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.
Zhang, Yi; Sun, Weiguo; Fu, Jia; Fan, Qunchao; Ma, Jie; Xiao, Liantuan; Jia, Suotang; Feng, Hao; Li, Huidong
2014-01-03
The algebraic method (AM) proposed by Sun et al. is improved to be a variational AM (VAM) to offset the possible experimental errors and to adapt to the individual energy expansion nature of different molecular systems. The VAM is used to study the full vibrational spectra {Eυ} and the dissociation energies De of (4)HeH(+)-X(1)Σ(+), (7)Li2-1(3)Δg,Na2-C(1)Πu,NaK-7(1)Π, Cs2-B(1)Πu and (79)Br2-β1g((3)P2) diatomic electronic states. The results not only precisely reproduce all known experimental vibrational energies, but also predict correct dissociation energies and all unknown high-lying levels that may not be given by the original AM or other numerical methods or experimental methods. The analyses and the skill suggested here might be useful for other numerical simulations and theoretical fittings using known data that may carry inevitable errors.
A new algebra core for the minimal form' problem
Purtill, M.R. . Center for Communications Research); Oliveira, J.S.; Cook, G.O. Jr. )
1991-12-20
The demands of large-scale algebraic computation have led to the development of many new algorithms for manipulating algebraic objects in computer algebra systems. For instance, parallel versions of many important algorithms have been discovered. Simultaneously, more effective symbolic representations of algebraic objects have been sought. Also, while some clever techniques have been found for improving the speed of the algebraic simplification process, little attention has been given to the issue of restructuring expressions, or transforming them into minimal forms.'' By minimal form,'' we mean that form of an expression that involves a minimum number of operations. In a companion paper, we introduce some new algorithms that are very effective at finding minimal forms of expressions. These algorithms require algebraic and combinatorial machinery that is not readily available in most algebra systems. In this paper we describe a new algebra core that begins to provide the necessary capabilities.
Upper bound for the length of commutative algebras
NASA Astrophysics Data System (ADS)
Markova, Ol'ga V.
2009-12-01
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.
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…
ERIC Educational Resources Information Center
Miller, L. Diane; England, David A.
1989-01-01
Describes a study in a large metropolitan high school to ascertain what influence the use of regular writing in algebra classes would have on students' attitudes towards algebra and their skills in algebra. Reports the simpler and more direct the writing topics the better. (MVL)
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.
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…
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…
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.
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.
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 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)
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.
Shapiro, Bruce E; Levchenko, Andre; Meyerowitz, Elliot M; Wold, Barbara J; Mjolsness, Eric D
2003-03-22
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.
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.
Discrete Minimal Surface Algebras
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Hoppe, Jens
2010-05-01
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
NASA Astrophysics Data System (ADS)
Saldarriaga Vargas, Clarita
When there are diseases affecting large populations where the social, economic and cultural diversity is significant within the same region, the biological parameters that determine the behavior of the dispersion disease analysis are affected by the selection of different individuals. Therefore and because of the variety and magnitude of the communities at risk of contracting dengue disease around all over the world, suggest defining differentiated populations with individual contributions in the results of the dispersion dengue disease analysis. In this paper those conditions were taken in account when several epidemiologic models were analyzed. Initially a stability analysis was done for a SEIR mathematical model of Dengue disease without differential susceptibility. Both free disease and endemic equilibrium states were found in terms of the basic reproduction number and were defined in the Theorem (3.1). Then a DSEIR model was solved when a new susceptible group was introduced to consider the effects of important biological parameters of non-homogeneous populations in the spreading analysis. The results were compiled in the Theorem (3.2). Finally Theorems (3.3) and (3.4) resumed the basic reproduction numbers for three and n different susceptible groups respectively, giving an idea of how differential susceptibility affects the equilibrium states. The computations were done using an algorithmic method implemented in Maple 11, a general-purpose computer algebra system.
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.
Dynamics of a freely-falling maple seed
NASA Astrophysics Data System (ADS)
Lee, Injae; Choi, Haecheon
2016-11-01
We conduct numerical simulations of a freely-falling maple seed using an immersed boundary method in a non-inertial reference frame. A three-dimensional seed model is obtained by scanning a maple seed. The seed reaches a steady autorotation after a transient period, and a stable leading-edge vortex is attached on the surface of the rotating seed, which increases the drag force during autorotation. In addition, two different approaches are considered to obtain scaling laws describing the relation among the seed weight and geometry, and descending and rotating velocities. The first uses the conservations of mass, linear and angular momentum, and energy. In this approach, a model constant to be determined, called axial induction factor, is obtained from the result of present simulation. The second approach employs a classical steady wing theory in which the vortical strength is scaled with the circulation around a wing and the lift force is modeled by the time derivative of vortical impulse. Available data on various seeds well fall on these scaling laws. Supported by NRF-2014M3C1B1033848.
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.
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…
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 contemporary…
[GENETIC AND METABOLIC URGENCIES IN THE NEONATAL INTENSIVE CARE UNIT: MAPLE SYRUP URINE DISEASE].
Páez Rojas, Paola Liliana; Suarez Obando, Fernando
2015-07-01
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.
Hydraulic Analysis of Water Flow through Leaves of Sugar Maple and Red Oak1
Sack, Lawren; Streeter, Christopher M.; Holbrook, N. Michele
2004-01-01
Leaves constitute a substantial fraction of the total resistance to water flow through plants. A key question is how hydraulic resistance within the leaf is distributed among petiole, major veins, minor veins, and the pathways downstream of the veins. We partitioned the leaf hydraulic resistance (Rleaf) for sugar maple (Acer saccharum) and red oak (Quercus rubra) by measuring the resistance to water flow through leaves before and after cutting specific vein orders. Simulations using an electronic circuit analog with resistors arranged in a hierarchical reticulate network justified the partitioning of total Rleaf into component additive resistances. On average 64% and 74% of the Rleaf was situated within the leaf xylem for sugar maple and red oak, respectively. Substantial resistance—32% and 49%— was in the minor venation, 18% and 21% in the major venation, and 14% and 4% in the petiole. The large number of parallel paths (i.e. a large transfer surface) for water leaving the minor veins through the bundle sheath and out of the leaf resulted in the pathways outside the venation comprising only 36% and 26% of Rleaf. Changing leaf temperature during measurement of Rleaf for intact leaves resulted in a temperature response beyond that expected from changes in viscosity. The extra response was not found for leaves with veins cut, indicating that water crosses cell membranes after it leaves the xylem. The large proportion of resistance in the venation can explain why stomata respond to leaf xylem damage and cavitation. The hydraulic importance of the leaf vein system suggests that the diversity of vein system architectures observed in angiosperms may reflect variation in whole-leaf hydraulic capacity. PMID:15064368
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.
Downie, J D; Goodman, J W
1989-10-15
A ground-based adaptive optics imaging telescope system attempts to improve image quality by measuring and correcting for atmospherically induced wavefront aberrations. The necessary control computations during each cycle will take a finite amount of time, which adds to the residual error variance since the atmosphere continues to change during that time. Thus an optical processor may be well-suited for this task. This paper investigates this possibility by studying the accuracy requirements in a general optical processor that will make it competitive with, or superior to, a conventional digital computer for adaptive optics use.
Symmetric hyperbolic systems in algebras of generalized functions and distributional limits
Hörmann, Günther; Spreitzer, Christian
2012-01-01
We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial differential equations with Colombeau generalized functions as coefficients and data. The proofs of solvability are based on refined energy estimates on lens-shaped regions with spacelike boundaries. We obtain several variants and also partial extensions of previous results in Oberguggenberger (1989), Lafon and Oberguggenberger (1991), and Hörmann (2004) [26,23,16] and provide aspects accompanying related recent work in Oberguggenberger (2009), Garetto and Oberguggenberger (2011) [28,10,9]. PMID:22511813
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.
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.
Superintegrability in Two Dimensions and the Racah-Wilson Algebra
NASA Astrophysics Data System (ADS)
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
2014-08-01
The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere is cast in the framework of the Racah problem for the algebra. The Hamiltonian of the 3-parameter system and the generators of its quadratic symmetry algebra are seen to correspond to the total and intermediate Casimir operators of the combination of three algebras, respectively. The construction makes explicit the isomorphism between the Racah-Wilson algebra, which is the fundamental algebraic structure behind the Racah problem for , and the invariance algebra of the generic 3-parameter system. It also provides an explanation for the occurrence of the Racah polynomials as overlap coefficients in this context. The irreducible representations of the Racah-Wilson algebra are reviewed as well as their connection with the Askey scheme of classical orthogonal polynomials.
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.
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
Prediction of Algebraic Instabilities
NASA Astrophysics Data System (ADS)
Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael
2016-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.
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.
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)
Bernardini, A. E.; Rocha, R. da
2007-03-15
We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the corresponding deformed symmetries are presented with particular emphasis on deformed dilatation transformations. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided in order to preserve the Lorentz algebra. Two distinct cases are considered: a deformed dilatation transformation with a spacelike preferred direction and a very special relativity embedding with a lightlike preferred direction. In both analysis we consider the possibility of introducing quantum deformations of the corresponding symmetries such that the spacetime coordinates can be reconstructed and the particular form of the real space-momentum commutator remains covariant. Eventually feasible experiments, for which the nonlinear Lorentz dilatation effects here pointed out may be detectable, are suggested.
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Tam, Honwah; Wu, Lixin
2015-10-01
We deduce a set of integrable equations under the framework of zero curvature equations and obtain two sets of integrable soliton equations, which can be reduced to some new integrable equations including the generalised nonlinear Schrödinger (NLS) equation. Under the case where the isospectral functions are one-order polynomials in the parameter λ, we generate a set of rational integrable equations, which are reduced to the loop soliton equation. Under the case where the derivative λt of the spectral parameter λ is a quadratic algebraic curve in λ, we derive a set of variable-coefficient integrable equations. In addition, we discretise a pair of isospectral problems introduced through the Lie algebra given by us for which a set of new semi-discrete nonlinear equations are available; furthermore, the semi-discrete MKdV equation and the Hirota lattice equation are followed to produce, respectively. Finally, we apply the Lie algebra to introduce a set of operator Lax pairs with an operator, and then through the Tu scheme and the binomial-residue representation method proposed by us, we generate a 2+1-dimensional integrable hierarchy of evolution equations, which reduces to a generalised 2+1-dimensional Davey-Stewartson (DS) equation.
NASA Astrophysics Data System (ADS)
Gou, Li-Dan; Xue, Kang; Wang, Gang-Cheng
2011-02-01
We present a 9 × 9 S-matrix and E-matrix. A representation of specialized Birman—Wenzl—Murakami algebra is obtained. Starting from the given braid group representation S-matrix, we obtain the trigonometric solution of Yang-Baxter equation. A unitary matrix Ř(x, ϕ1,ϕ2) is generated via the Yang—Baxterization approach. Then we construct a Yang—Baxter Hamiltonian through the unitary matrix Ř(x, ϕ1,ϕ2). Berry phase of this Yang—Baxter system is investigated in detail.
Generalized conformal realizations of Kac-Moody algebras
NASA Astrophysics Data System (ADS)
Palmkvist, Jakob
2009-01-01
We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n =1, this reduces to the well known Kantor-Koecher-Tits construction. Our generalization utilizes a new relation between different generalized Jordan triple systems, together with their known connections to Jordan and Lie algebras. Applied to the Jordan algebra of Hermitian 3×3 matrices over the division algebras R, C, H, O, the construction gives the exceptional Lie algebras f4, e6, e7, e8 for n =2. Moreover, we obtain their infinite-dimensional extensions for n ≥3. In the case of 2×2 matrices, the resulting Lie algebras are of the form so(p +n,q+n) and the concomitant nonlinear realization generalizes the conformal transformations in a spacetime of signature (p,q).
Bicovariant quantum algebras and quantum Lie algebras
NASA Astrophysics Data System (ADS)
Schupp, Peter; Watts, Paul; Zumino, Bruno
1993-10-01
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(mathfrak{G}_q ) to U q g, given by elements of the pure braid group. These operators—the “reflection matrix” Y≡L + SL - being a special case—generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N).
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
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…
Parastatistics Algebras and Combinatorics
NASA Astrophysics Data System (ADS)
Popov, T.
2005-03-01
We consider the algebras spanned by the creation parafermionic and parabosonic operators which give rise to generalized parastatistics Fock spaces. The basis of such a generalized Fock space can be labelled by Young tableaux which are combinatorial objects. By means of quantum deformations a nice combinatorial structure of the algebra of the plactic monoid that lies behind the parastatistics is revealed.
Algebraic Reasoning through Patterns
ERIC Educational Resources Information Center
Rivera, F. D.; Becker, Joanne Rossi
2009-01-01
This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…
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
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…
Legault, Jean; Girard-Lalancette, Karl; Grenon, Carole; Dussault, Catherine; Pichette, André
2010-04-01
Antioxidant activity, inhibition of nitric oxide (NO) overproduction, and antiproliferative effect of ethyl acetate extracts of maple sap and syrup from 30 producers were evaluated in regard to the period of harvest in three different regions of Québec, Canada. Oxygen radical absorbance capacity (ORAC) values of maple sap and syrup extracts are, respectively, 12 +/- 6 and 15 +/- 5 micromol of Trolox equivalents (TE)/mg. The antioxidant activity was also confirmed by a cell-based assay. The period of harvest has no statistically significant incidence on the antioxidant activity of both extracts. The antioxidant activity of pure maple syrup was also determined using the ORAC assay. Results indicate that the ORAC value of pure maple syrup (8 +/- 2 micromol of TE/mL) is lower than the ORAC value of blueberry juice (24 +/- 1 micromol of TE/mL) but comparable to the ORAC values of strawberry (10.7 +/- 0.4 micromol of TE/mL) and orange (10.8 +/- 0.5 micromol of TE/mL) juices. Maple sap and syrup extracts showed to significantly inhibit lipopolysaccharide-induced NO overproduction in RAW264.7 murine macrophages. Maple syrup extract was significantly more active than maple sap extract, suggesting that the transformation of maple sap into syrup increases NO inhibition activity. The highest NO inhibition induced by the maple syrup extracts was observed at the end of the season. Moreover, darker maple syrup was found to be more active than clear maple syrup, suggesting that some colored oxidized compounds could be responsible in part for the activity. Finally, maple syrup extracts (50% inhibitory concentration = 42 +/- 6 microg/mL) and pure maple syrup possess a selective in vitro antiproliferative activity against cancer cells.
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.
Bouchet, Freddy; Dauxois, Thierry
2005-10-01
We explain the ubiquity and extremely slow evolution of non-Gaussian out-of-equilibrium distributions for the Hamiltonian mean-field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one also unambiguously explains and predicts striking slow algebraic relaxation of the momenta autocorrelation, previously found in numerical simulations. Finally, angular anomalous diffusion are predicted for a large class of initial distributions. Non-extensive statistical mechanics is shown to be unnecessary for the interpretation of these phenomena.
Algebraic Nonlinear Collective Motion
NASA Astrophysics Data System (ADS)
Troupe, J.; Rosensteel, G.
1998-11-01
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).
Algebraic invariants for homotopy types
NASA Astrophysics Data System (ADS)
Blanc, David
1999-11-01
We define a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the [Pi]-algebra [pi][low asterisk]X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract [Pi]-algebra can be realized as the homotopy [Pi]-algebra of a space.
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,…
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.
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.
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.
Pseudo-Riemannian Novikov algebras
NASA Astrophysics Data System (ADS)
Chen, Zhiqi; Zhu, Fuhai
2008-08-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.
Minimax Techniques For Optimizing Non-Linear Image Algebra Transforms
NASA Astrophysics Data System (ADS)
Davidson, Jennifer L.
1989-08-01
It has been well established that the Air Force Armament Technical Laboratory (AFATL) image algebra is capable of expressing all linear transformations [7]. The embedding of the linear algebra in the image algebra makes this possible. In this paper we show a relation of the image algebra to another algebraic system called the minimax algebra. This system is used extensively in economics and operations research, but until now has not been investigated for applications to image processing. The relationship is exploited to develop new optimization methods for a class of non-linear image processing transforms. In particular, a general decomposition technique for templates in this non-linear domain is presented. Template decomposition techniques are an important tool in mapping algorithms efficiently to both sequential and massively parallel architectures.
Serum Markers of Neurodegeneration in Maple Syrup Urine Disease.
Scaini, Giselli; Tonon, Tássia; de Souza, Carolina F Moura; Schuk, Patricia F; Ferreira, Gustavo C; Neto, Joao Seda; Amorin, Tatiana; Schwartz, Ida Vanessa D; Streck, Emilio L
2016-09-22
Maple syrup urine disease (MSUD) is an inherited disorder caused by deficient activity of the branched-chain α-keto acid dehydrogenase complex involved in the degradation pathway of branched-chain amino acids (BCAAs) and their respective α-keto-acids. Patients affected by MSUD present severe neurological symptoms and brain abnormalities, whose pathophysiology is poorly known. However, preclinical studies have suggested alterations in markers involved with neurodegeneration. Because there are no studies in the literature that report the neurodegenerative markers in MSUD patients, the present study evaluated neurodegenerative markers (brain-derived neurotrophic factor (BDNF), cathepsin D, neural cell adhesion molecule (NCAM), plasminogen activator inhibitor-1 total (PAI-1 (total)), platelet-derived growth factor AA (PDGF-AA), PDGF-AB/BB) in plasma from 10 MSUD patients during dietary treatment. Our results showed a significant decrease in BDNF and PDGF-AA levels in MSUD patients. On the other hand, NCAM and cathepsin D levels were significantly greater in MSUD patients compared to the control group, while no significant changes were observed in the levels of PAI-1 (total) and PDGF-AB/BB between the control and MSUD groups. Our data show that MSUD patients present alterations in proteins involved in the neurodegenerative process. Thus, the present findings corroborate previous studies that demonstrated that neurotrophic factors and lysosomal proteases may contribute, along with other mechanisms, to the intellectual deficit and neurodegeneration observed in MSUD.
Biocompatible polymeric implants for controlled drug delivery produced by MAPLE
NASA Astrophysics Data System (ADS)
Paun, Irina Alexandra; Moldovan, Antoniu; Luculescu, Catalin Romeo; Dinescu, Maria
2011-10-01
Implants consisting of drug cores coated with polymeric films were developed for delivering drugs in a controlled manner. The polymeric films were produced using matrix assisted pulsed laser evaporation (MAPLE) and consist of poly(lactide-co-glycolide) (PLGA), used individually as well as blended with polyethylene glycol (PEG). Indomethacin (INC) was used as model drug. The implants were tested in vitro (i.e. in conditions similar with those encountered inside the body), for predicting their behavior after implantation at the site of action. To this end, they were immersed in physiological media (i.e. phosphate buffered saline PBS pH 7.4 and blood). At various intervals of PBS immersion (and respectively in blood), the polymeric films coating the drug cores were studied in terms of morphology, chemistry, wettability and blood compatibility. PEG:PLGA film exhibited superior properties as compared to PLGA film, the corresponding implant being thus more suitable for internal use in the human body. In addition, the implant containing PEG:PLGA film provided an efficient and sustained release of the drug. The kinetics of the drug release was consistent with a diffusion mediated mechanism (as revealed by fitting the data with Higuchi's model); the drug was gradually released through the pores formed during PBS immersion. In contrast, the implant containing PLGA film showed poor drug delivery rates and mechanical failure. In this case, fitting the data with Hixson-Crowell model indicated a release mechanism dominated by polymer erosion.
NASA Astrophysics Data System (ADS)
Markarian, Nikita
2017-03-01
We introduce Weyl n-algebras and show how their factorization complex may be used to define invariants of manifolds. In the appendix, we heuristically explain why these invariants must be perturbative Chern-Simons invariants.
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)
Accounting Equals Applied Algebra.
ERIC Educational Resources Information Center
Roberts, Sondra
1997-01-01
Argues that students should be given mathematics credits for completing accounting classes. Demonstrates that, although the terminology is different, the mathematical concepts are the same as those used in an introductory algebra class. (JOW)
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…
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.
Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations
2014-07-01
non- linear hybrid systems by linear algebraic methods. In Radhia Cousot and Matthieu Martel, editors, SAS, volume 6337 of LNCS, pages 373–389. Springer...Tarski. A decision method for elementary algebra and geometry. Bulletin of the American Mathematical Society, 59, 1951. [36] Wolfgang Walter. Ordinary...Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations Khalil Ghorbal1 Andrew Sogokon2 André Platzer1 July 2014
Twisted vertex algebras, bicharacter construction and boson-fermion correspondences
NASA Astrophysics Data System (ADS)
Anguelova, Iana I.
2013-12-01
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.
Doiron, Karine; Goyon, Vanessa; Coyaud, Etienne; Rajapakse, Sanjeeva; Raught, Brian; McBride, Heidi M
2017-12-01
Activation of the innate immune response triggered by dsRNA viruses occurs through the assembly of the Mitochondrial Anti-Viral Signaling (MAVS) complex. Upon recognition of viral dsRNA, the cytosolic receptor RIG-I is activated and recruited to MAVS to activate the immune signaling response. We here demonstrate a strict requirement for a mitochondrial anchored protein ligase, MAPL (also called MUL1) in the signaling events that drive the transcriptional activation of antiviral genes downstream of Sendai virus infection, both in vivo and in vitro. A biotin environment scan of MAPL interacting polypeptides identified a series of proteins specific to Sendai virus infection; including RIG-I, IFIT1, IFIT2, HERC5 and others. Upon infection, RIG-I is SUMOylated in a MAPL-dependent manner, a conjugation step that is required for its activation. Consistent with this, MAPL was not required for signaling downstream of a constitutively activated form of RIG-I. These data highlight a critical role for MAPL and mitochondrial SUMOylation in the early steps of antiviral signaling.
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.
Ambient ozone effects on the ecophysiology of sugar maple (Acer saccharum)
Scherzer, A.J.; Boerner, R.E.J. )
1990-01-01
Sugar maple is among the most widespread and abundant canopy tree species in eastern North America, and is increasing in abundance in the American midwest; yet recent surveys indicate it is declining throughout much of eastern Canada. A number of factors have been cited as causing or contributing to this decline, including both gaseous air pollutants and acidic deposition. The authors hypothesized that ozone has the potential to act as a predisposing factor for sugar maple decline by affecting net carbon gain, carbon allocation, and carbohydrate reserves, resulting in reduced growth and vigor of sugar maple trees. To test this, 1 yr old sugar maple seedlings were fumigated in open top chambers with charcoal-filtered (ozone free) air, ambient ozone, or ambient ozone {plus minus} 15%. Leaf area, biomass, root:shoot ratio, and instantaneous photosynthetic rate, all potential indicators of short term ozone damage, were not significantly affected by a five month exposure to these ozone levels. Ozone may reduce levels of carbohydrate storage in roots, or alter transport of photosynthate from leaves to root, thereby increasing overwintering mortality or reducing spring growth; results of experiments to test these hypotheses will be presented. The genotype of an individual may also affect its response to ozone, and the relative sensitivity of populations may vary among geographic sites. They will also present preliminary data related to geographic patterns of susceptibility to ozone among sugar maple populations.
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.
Calcium and aluminum impacts on sugar maple physiology in a northern hardwood forest.
Halman, Joshua M; Schaberg, Paul G; Hawley, Gary J; Pardo, Linda H; Fahey, Timothy J
2013-11-01
Forests of northeastern North America have been exposed to anthropogenic acidic inputs for decades, resulting in altered cation relations and disruptions to associated physiological processes in multiple tree species, including sugar maple (Acer saccharum Marsh.). In the current study, the impacts of calcium (Ca) and aluminum (Al) additions on mature sugar maple physiology were evaluated at the Hubbard Brook Experimental Forest (Thornton, NH, USA) to assess remediation (Ca addition) or exacerbation (Al addition) of current acidified conditions. Fine root cation concentrations and membrane integrity, carbon (C) allocation, foliar cation concentrations and antioxidant activity, foliar response to a spring freezing event and reproductive ability (flowering, seed quantity, filled seed and seed germination) were evaluated for dominant sugar maple trees in a replicated plot study. Root damage and foliar antioxidant activity were highest in Al-treated trees, while growth-associated C, foliar re-flush following a spring frost and reproductive ability were highest in Ca-treated trees. In general, we found that trees on Ca-treated plots preferentially used C resources for growth and reproductive processes, whereas Al-treated trees devoted C to defense-based processes. Similarities between Al-treated and control trees were observed for foliar cation concentrations, C partitioning and seed production, suggesting that sugar maples growing in native forests may be more stressed than previously perceived. Our experiment suggests that disruption of the balance of Ca and Al in sugar maples by acid deposition continues to be an important driver of tree health.
Algebraic mesh quality metrics
KNUPP,PATRICK
2000-04-24
Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. Condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Combined metrics for shape and volume, shape-volume-orientation are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to non-simplical elements. A series of numerical tests verify the theoretical properties of the metrics defined.
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.
Red Maple (Acer rubrum) Aerial Parts as a Source of Bioactive Phenolics.
Zhang, Yan; Ma, Hang; Yuan, Tao; Seeram, Navindra P
2015-08-01
The bark and stems of red maple (Acer rubrum) are reported to contain bioactive phenolics but its aerial parts, namely, flowers and leaves, remain largely unexplored. This is unfortunate considering that various parts of the red maple were used for traditional medicinal purposes by the indigenous peoples of eastern North America, where this species is found. Herein, we report the identification of twenty-five (1-25) phenolics, including two new galloyl derivatives (1 and 2), from red maple flowers and leaves. Of these, ten compounds (1-10), including the new compounds, were isolated and identified by NMR and HRESIMS data while the remaining fifteen compounds (11-25) were identified by HPLC-DAD analyses (by comparison with chemical standards). The isolates (1-10), along with the clinical drug, acarbose, were evaluated for their alpha-glucosidase enzyme inhibitory activities.
Characterization of MAPLE deposited WO3 thin films for electrochromic applications
NASA Astrophysics Data System (ADS)
Boyadjiev, S. I.; Stefan, N.; Szilágyi, I. M.; Mihailescu, N.; Visan, A.; Mihailescu, I. N.; Stan, G. E.; Besleaga, C.; Iliev, M. T.; Gesheva, K. A.
2017-01-01
Tungsten trioxide (WO3) is a widely studied material for electrochromic applications. The structure, morphology and optical properties of WO3 thin films, grown by matrix assisted pulsed laser evaporation (MAPLE) from monoclinic WO3 nano-sized particles, were investigated for their possible application as electrochromic layers. A KrF* excimer (λ=248 nm, ζFWHM=25 ns) laser source was used in all experiments. The MAPLE deposited WO3 thin films were studied by atomic force microscopy (AFM), grazing incidence X-ray diffraction (GIXRD) and Fourier transform infrared spectroscopy (FTIR). Cyclic voltammetry measurements were also performed, and the coloring and bleaching were observed. The morpho-structural investigations disclosed the synthesis of single-phase monoclinic WO3 films consisting of crystalline nano-grains embedded in an amorphous matrix. All thin films showed good electrochromic properties, thus validating application of the MAPLE deposition technique for the further development of electrochromic devices.
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.
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…
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…
Federal Register 2010, 2011, 2012, 2013, 2014
2010-09-17
... 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 rate... Reference Room in Washington, DC. There is an eSubscription link on the Web site that enables subscribers...
William R. Maples, forensic historian: four men, four centuries, four countries.
Goza, W M
1999-07-01
Prior to 1984, William R. Maples, Ph.D. worked primarily with Medical Examiners in the State of Florida in investigation of and testimony in criminal cases. In 1984 the Republic of Peru requested him to identify skeletal remains thought to be those of Francisco Pizarro, conqueror of Peru and the Incas in the early 16th Century. Dr. Maples made a positive identification of those remains as Pizarro, resulting in their substitution in a glass-sided coffin in the Cathedral of Lima, where other remains had been displayed as those of Pizarro for a hundred years. In addition, it was proved that the remains removed could not have been those of Pizarro. In 1988, Dr. Maples examined the skeletal remains of Joseph Merrick ("The Elephant Man") at Royal London Hospital, Whitechapel, and made photographic studies of them for comparison with death casts of limbs and skull to ascertain depth of tissue by video-superimposition. In 1991, Dr. Maples, headed a team which removed President Zachary Taylor (1779-1842) from his tomb in Louisville, Kentucky. The purpose was to determine if he had been poisoned, as had been proposed by some at the time. Test results showed that he had not been. In 1992, Dr. Maples and a team of forensic specialists went by invitation to Ekaterinburg, Russia to study skeletal remains which the Russians had tentatively identified as the Russian Royal Family, and entourage, murdered in 1918. The American team identified them as Tsar Nicholas II, his wife, three of his children, his physician, and three of his servants. William Ross Maples died in Gainesville, Florida, 27 February 1997.
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…
NASA Astrophysics Data System (ADS)
Durka, R.
2017-04-01
The S-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition, and associating the Lorentz generator with the semigroup identity element, leads to a wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type {{B}m} , {{C}m} , and the recently introduced {{D}m} . The additional new examples complete the resulting generalization of the bosonic enlargements for an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.
Sugar maple growth in relation to nutrition and stress in the northeastern United States.
Long, Robert P; Horsley, Stephen B; Hallett, Richard A; Bailey, Scott W
2009-09-01
Sugar maple, Acer saccharum, decline disease is incited by multiple disturbance factors when imbalanced calcium (Ca), magnesium (Mg), and manganese (Mn) act as predisposing stressors. Our objective in this study was to determine whether factors affecting sugar maple health also affect growth as estimated by basal area increment (BAI). We used 76 northern hardwood stands in northern Pennsylvania, New York, Vermont, and New Hampshire, USA, and found that sugar maple growth was positively related to foliar concentrations of Ca and Mg and stand level estimates of sugar maple crown health during a high stress period from 1987 to 1996. Foliar nutrient threshold values for Ca, Mg, and Mn were used to analyze long-term BAI trends from 1937 to 1996. Significant (P < or = 0.05) nutrient threshold-by-time interactions indicate changing growth in relation to nutrition during this period. Healthy sugar maples sampled in the 1990s had decreased growth in the 1970s, 10-20 years in advance of the 1980s and 1990s decline episode in Pennsylvania. Even apparently healthy stands that had no defoliation, but had below-threshold amounts of Ca or Mg and above-threshold Mn (from foliage samples taken in the mid 1990s), had decreasing growth by the 1970s. Co-occurring black cherry, Prunus serotina, in a subset of the Pennsylvania and New York stands, showed opposite growth responses with greater growth in stands with below-threshold Ca and Mg compared with above-threshold stands. Sugar maple growing on sites with the highest concentrations of foliar Ca and Mg show a general increase in growth from 1937 to 1996 while other stands with lower Ca and Mg concentrations show a stable or decreasing growth trend. We conclude that acid deposition induced changes in soil nutrient status that crossed a threshold necessary to sustain sugar maple growth during the 1970s on some sites. While nutrition of these elements has not been considered in forest management decisions, our research shows species
Janowiak, J.J.; Manbeck, H.B.; Hernandez, R.; Moody, R.C.; Blankenhorn, P.R.
1995-09-01
The feasibility of utilizing cant-sawn hardwood lumber, which would not usually be desired for furniture manufacture, was studied for the manufacture of structural glue-laminated (glulam) timber. Two red maple beam combinations were evaluated. Test results of 42 red maple glulam beams showed that it was feasible to develop structural glulam timber from cant-swan lumber. The glulam combinations made from E-rated lumber exceeded the target design bending stress of 2,400 lb/in 2 and met the target modulus of elasticity (MOE) of 1.8 x 106 lb/in 2.
NASA Astrophysics Data System (ADS)
Roytenberg, Dmitry
2007-11-01
A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between Lie 2-algebras can also be defined, yielding a 2-category. Passing to the normalized chain complex gives an equivalence of 2-categories between Lie 2-algebras and certain "up to homotopy" structures on the complex; for strictly skew-symmetric Lie 2-algebras these are L∞-algebras, by a result of Baez and Crans. Lie 2-algebras appear naturally as infinitesimal symmetries of solutions of the Maurer-Cartan equation in some differential graded Lie algebras and L∞-algebras. In particular, (quasi-) Poisson manifolds, (quasi-) Lie bialgebroids and Courant algebroids provide large classes of examples.
Algebra for Gifted Third Graders.
ERIC Educational Resources Information Center
Borenson, Henry
1987-01-01
Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)
A Holistic Approach to Algebra.
ERIC Educational Resources Information Center
Barbeau, Edward J.
1991-01-01
Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)
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.
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.
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…
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…
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.
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.…
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…
Operator algebra in logarithmic conformal field theory
Nagi, Jasbir
2005-10-15
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the extensions of this machinery to the logarithmic case are studied and used. More precisely, from Moebius symmetry constraints, the generic three- and four-point functions of logarithmic quasiprimary fields are calculated in closed form for arbitrary Jordan rank. As an example, c=0 disordered systems with nondegenerate vacua are studied. With the aid of two-, three-, and four-point functions, the operator algebra is obtained and associativity of the algebra studied.
Direct determination of the underlying Lie algebra in nonlinear optics
NASA Astrophysics Data System (ADS)
Arnold, J. M.
1991-01-01
It is shown that the equations of resonant nonlinear optics can be studied entirely within the framework of an underlying Lie algebra, in which the 2x2 su(2) Hamiltonian and density matrices of the quantum mechanical description of the atomic system transform directly to the 2x2 sl(2,R) matrices of the Ablowitz-Kaup-Newell-Segur (AKNS) scheme, and the AKNS eigenvalue is introduced naturally as a free parameter. The Lie algebra sl(2,R) is also the symmetry algebra of transformations between equivalence classes of AKNS systems under SL(2,R) gauge transformations. The Lie algebra formalism condenses much algebraic manipulation, and provides a natural basis for the perturbation theory of "nearly integrable" nonlinear wave systems.
NASA Astrophysics Data System (ADS)
Liu, Yin-Ping; Li, Zhi-Bin
2003-03-01
Based on a type of elliptic equation, a new algebraic method to construct a series of exact solutions for nonlinear evolution equations is proposed, meanwhile, its complete implementation TRWS in Maple is presented. The TRWS can output a series of travelling wave solutions entirely automatically, which include polynomial solutions, exponential function solutions, triangular function solutions, hyperbolic function solutions, rational function solutions, Jacobi elliptic function solutions, and Weierstrass elliptic function solutions. The effectiveness of the package is illustrated by applying it to a variety of equations. Not only are previously known solutions recovered but also new solutions and more general form of solutions are obtained.
Cartan-Weyl 3-algebras and the BLG theory. I: classification of Cartan-Weyl 3-algebras
NASA Astrophysics Data System (ADS)
Chu, Chong-Sun
2010-10-01
As Lie algebras of compact connected Lie groups, semisimple Lie algebras have wide applications in the description of continuous symmetries of physical systems. Mathematically, semisimple Lie algebra admits a Cartan-Weyl basis of generators which consists of a Cartan subalgebra of mutually commuting generators H I and a number of step generators E α that are characterized by a root space of non-degenerate one-forms α. This simple decomposition in terms of the root space allows for a complete classification of semisimple Lie algebras. In this paper, we introduce the analogous concept of a Cartan-Weyl Lie 3-algebra. We analyze their structure and obtain a complete classification of them. Many known examples of metric Lie 3-algebras (e.g. the Lorentzian 3-algebras) are special cases of the Cartan-Weyl 3-algebras. Due to their elegant and simple structure, we speculate that Cartan-Weyl 3-algebras may be useful for describing some kinds of generalized symmetries. As an application, we consider their use in the Bagger-Lambert-Gustavsson (BLG) theory.
An algebra of reversible computation.
Wang, Yong
2016-01-01
We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.
Age and Availability of Nonstructural Carbohydrates in Red Maple
NASA Astrophysics Data System (ADS)
Carbone, M. S.; Keenan, T. F.; Czimczik, C. I.; Murakami, P.; O'Keefe, J.; Schaberg, P.; Xu, X.; Richardson, A. D.
2012-12-01
Recent studies show that nonstructural carbohydrates (NSC) pools in mature trees can be quite large and on average a decade old. Yet, little is known about how older stored NSC reserves vs. recently-assimilated NSCs are used to support growth and metabolism, or how available these stored NSC reserves are to trees during stress or following disturbance. To better understand these aspects of NSC dynamics, we studied mature red maple (Acer rubrum) trees that ranged in size and age in two New England temperate forests, Harvard Forest (Massachusetts) and Bartlett Experimental Forest (New Hampshire). Applying the radiocarbon (14C) "bomb spike" approach, we estimated the age of carbon in stemwood NSCs, bole respiration, and stump sprouts regenerated following harvesting. These isotopic measurements along with stemwood NSC concentrations allowed us to compare the NSC used for metabolic demands and the NSC available for regrowth following disturbance to the NSC actually present in the stemwood. We found that the mean age of stemwood sugars was 9.8 ± 5.3 y. Trees with slower growth rates had older sugar reserves and lower concentrations of sugar, starch, and total NSC reserves. The age of NSCs used to support dormant season metabolism (bole respiration) was between 1-3.5 y, and thus much younger than the mean age of stemwood sugars, indicating preferential use of more recently-assimilated NSC. There were no relationships observed between tree age or size and 1) the age of sugars present in stemwood cores or 2) the age of NSCs used for bole respiration. Moreover, there was no relationship between the age of sugars in stemwood and the age of NSCs used for bole respiration. The stump sprouts were formed from NSCs 1-17 y old, (mean 5.8 ± 5.4 y), with older trees using older NSCs to produce stump sprouts. The stump sprout data indicate that some of these older NSCs reserves are available to the tree for use following major disturbance. However, the bole respiration data
Age, allocation, and availability of nonstructural carbohydrates in red maple
NASA Astrophysics Data System (ADS)
Carbone, Mariah; Keenan, Trevor; Czimczik, Claudia; Murakami, Paula; O'Keefe, John; Pederson, Neil; Schaberg, Paul; Xu, Xiaomei; Richardson, Andrew
2013-04-01
Nonstructural carbohydrates (NSC) are the primary products of photosynthesis, composed mostly of sugars and starch. Recent studies show that NSC pools in mature trees can be quite large and on average a decade old. Thus, NSC pools integrate years of carbon assimilation and represent significant ecological memory at the whole plant and ecosystem level. However, we know very little about how older stored NSC versus newly assimilated NSC are used to support growth and metabolism, or how available older NSC are to trees during stress or following disturbance. To better understand these potential lags in NSC allocation, we studied mature red maple (Acer rubrum) trees in New England temperate forests. Applying the radiocarbon (14C) "bomb spike" approach, we estimated the age of carbon in stemwood NSC, ring cellulose, bole respiration, and stump sprouts regenerated following harvesting. These measurements allowed us to compare the NSC used for metabolic demands, annual growth, and the NSC available for regrowth following disturbance to the NSC actually present in the stemwood. Finally, tree ring widths were analyzed to determine the annual autocorrelation in radial wood increment. We found that the mean age of stemwood sugars was 9.8 ± 5 y. The age of NSC used to support metabolism (bole respiration) was much younger than the mean age of stemwood sugars, indicating preferential use of more recently assimilated NSC. In the spring before leaves emerged, bole respiration was between 1-2 y, whereas it was composed of newly assimilated NSC in the late summer. The ring cellulose 14C age was on average 0.8 y older than direct ring counts (within error of 14C measurement) which may or may not indicate a stored NSC contribution. Tree ring width analyses indicate strong autocorrelation between ring growth in one year and in the following year, in agreement with ring cellulose 14C ages. However, autocorrelation weakened over the following 10 years, consistent with the measured mean
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.
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…
Algebraic Thinking through Origami.
ERIC Educational Resources Information Center
Higginson, William; Colgan, Lynda
2001-01-01
Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)
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…
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
Current algebra formulation of M-theory based on E11 Kac-Moody algebra
NASA Astrophysics Data System (ADS)
Sugawara, Hirotaka
2017-02-01
Quantum M-theory is formulated using the current algebra technique. The current algebra is based on a Kac-Moody algebra rather than usual finite dimensional Lie algebra. Specifically, I study the E11 Kac-Moody algebra that was shown recently1‑5 to contain all the ingredients of M-theory. Both the internal symmetry and the external Lorentz symmetry can be realized inside E11, so that, by constructing the current algebra of E11, I obtain both internal gauge theory and gravity theory. The energy-momentum tensor is constructed as the bilinear form of the currents, yielding a system of quantum equations of motion of the currents/fields. Supersymmetry is incorporated in a natural way. The so-called “field-current identity” is built in and, for example, the gravitino field is itself a conserved supercurrent. One unanticipated outcome is that the quantum gravity equation is not identical to the one obtained from the Einstein-Hilbert action.
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.
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…
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…
Interannual and spatial variability of maple syrup yield as related to climatic factors.
Duchesne, Louis; Houle, Daniel
2014-01-01
Sugar maple syrup production is an important economic activity for eastern Canada and the northeastern United States. Since annual variations in syrup yield have been related to climate, there are concerns about the impacts of climatic change on the industry in the upcoming decades. Although the temporal variability of syrup yield has been studied for specific sites on different time scales or for large regions, a model capable of accounting for both temporal and regional differences in yield is still lacking. In the present study, we studied the factors responsible for interregional and interannual variability in maple syrup yield over the 2001-2012 period, by combining the data from 8 Quebec regions (Canada) and 10 U.S. states. The resulting model explained 44.5% of the variability in yield. It includes the effect of climatic conditions that precede the sapflow season (variables from the previous growing season and winter), the effect of climatic conditions during the current sapflow season, and terms accounting for intercountry and temporal variability. Optimal conditions for maple syrup production appear to be spatially restricted by less favourable climate conditions occurring during the growing season in the north, and in the south, by the warmer winter and earlier spring conditions. This suggests that climate change may favor maple syrup production northwards, while southern regions are more likely to be negatively affected by adverse spring conditions.
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.
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.
Identification of protoxins and a microbial basis for red maple (Acer rubrum) toxicosis in equines.
Agrawal, Karan; Ebel, Joseph G; Altier, Craig; Bischoff, Karyn
2013-01-01
The leaves of Acer rubrum (red maple), especially when wilted in the fall, cause severe oxidative damage to equine erythrocytes, leading to potentially fatal methemoglobinemia and hemolytic anemia. Gallic acid and tannins from A. rubrum leaves have been implicated as the toxic compounds responsible for red maple toxicosis, but the mechanism of action and toxic principle(s) have not been elucidated to date. In order to investigate further how red maple toxicosis occurs, aqueous solutions of gallic acid, tannic acid, and ground dried A. rubrum leaves were incubated with contents of equine ileum, jejunum, cecum, colon, and liver, and then analyzed for the metabolite pyrogallol, as pyrogallol is a more potent oxidizing agent. Gallic acid was observed to be metabolized to pyrogallol maximally in equine ileum contents in the first 24 hr. Incubation of tannic acid and A. rubrum leaves, individually with ileum contents, produced gallic acid and, subsequently, pyrogallol. Ileum suspensions, when passed through a filter to exclude microbes but not enzymes, formed no pyrogallol, suggesting a microbial basis to the pathway. Bacteria isolated from ileum capable of pyrogallol formation were identified as Klebsiella pneumoniae and Enterobacter cloacae. Therefore, gallotannins and free gallic acid are present in A. rubrum leaves and can be metabolized by K. pneumoniae and E. cloacae found in the equine ileum to form pyrogallol either directly or through a gallic acid intermediate (gallotannins). Identification of these compounds and their physiological effects is necessary for the development of effective treatments for red maple toxicosis in equines.
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...
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...
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.
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…
Movement disorders in adult surviving patients with maple syrup urine disease.
Carecchio, Miryam; Schneider, Susanne A; Chan, Heidi; Lachmann, Robin; Lee, Philip J; Murphy, Elaine; Bhatia, Kailash P
2011-06-01
Maple syrup urine disease is a rare metabolic disorder caused by mutations in the branched-chain α-keto acid dehydrogenase complex gene. Patients generally present early in life with a toxic encephalopathy because of the accumulation of the branched-chain amino acids leucine, isoleucine, and valine and the corresponding ketoacids. Movement disorders in maple syrup urine disease have typically been described during decompensation episodes or at presentation in the context of a toxic encephalopathy, with complete resolution after appropriate dietary treatment. Movement disorders in patients surviving childhood are not well documented. We assessed 17 adult patients with maple syrup urine disease (mean age, 27.5 years) with a special focus on movement disorders. Twelve (70.6%) had a movement disorder on clinical examination, mainly tremor and dystonia or a combination of both. Parkinsonism and simple motor tics were also observed. Pyramidal signs were present in 11 patients (64.7%), and a spastic-dystonic gait was observed in 6 patients (35.2%). In summary, movement disorders are common in treated adult patients with maple syrup urine disease, and careful neurological examination is advisable to identify those who may benefit from specific therapy. © 2011 Movement Disorder Society.
Interannual and spatial variability of maple syrup yield as related to climatic factors
Houle, Daniel
2014-01-01
Sugar maple syrup production is an important economic activity for eastern Canada and the northeastern United States. Since annual variations in syrup yield have been related to climate, there are concerns about the impacts of climatic change on the industry in the upcoming decades. Although the temporal variability of syrup yield has been studied for specific sites on different time scales or for large regions, a model capable of accounting for both temporal and regional differences in yield is still lacking. In the present study, we studied the factors responsible for interregional and interannual variability in maple syrup yield over the 2001–2012 period, by combining the data from 8 Quebec regions (Canada) and 10 U.S. states. The resulting model explained 44.5% of the variability in yield. It includes the effect of climatic conditions that precede the sapflow season (variables from the previous growing season and winter), the effect of climatic conditions during the current sapflow season, and terms accounting for intercountry and temporal variability. Optimal conditions for maple syrup production appear to be spatially restricted by less favourable climate conditions occurring during the growing season in the north, and in the south, by the warmer winter and earlier spring conditions. This suggests that climate change may favor maple syrup production northwards, while southern regions are more likely to be negatively affected by adverse spring conditions. PMID:24949244
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
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.
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.
LINPACK. Simultaneous Linear Algebraic Equations
Miller, M.A.
1990-05-01
LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE General, GB General band, PO Positive definite, PP Positive definite packed, PB Positive definite band, SI Symmetric indefinite, SP Symmetric indefinite packed, HI Hermitian indefinite, HP Hermitian indefinite packed, TR Triangular, GT General tridiagonal, PT Positive definite tridiagonal, CH Cholesky decomposition, QR Orthogonal-triangular decomposition, SV Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA Factor, CO Factor and estimate condition, SL Solve, DI Determinant and/or inverse and/or inertia, DC Decompose, UD Update, DD Downdate, EX Exchange. The LINPACK package also includes a set of routines to perform basic vector operations called the Basic Linear Algebra Subprograms (BLAS).
LINPACK. Simultaneous Linear Algebraic Equations
Dongarra, J.J.
1982-05-02
LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE General, GB General band, PO Positive definite, PP Positive definite packed, PB Positive definite band, SI Symmetric indefinite, SP Symmetric indefinite packed, HI Hermitian indefinite, HP Hermitian indefinite packed, TR Triangular, GT General tridiagonal, PT Positive definite tridiagonal, CH Cholesky decomposition, QR Orthogonal-triangular decomposition, SV Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA Factor, CO Factor and estimate condition, SL Solve, DI Determinant and/or inverse and/or inertia, DC Decompose, UD Update, DD Downdate, EX Exchange. The LINPACK package also includes a set of routines to perform basic vector operations called the Basic Linear Algebra Subprograms (BLAS).
Simon, J; Waldhecker, P; Brüggemann, N; Rennenberg, H
2010-05-01
To investigate the short-term consequences of direct competition between beech and sycamore maple on root N uptake and N composition, mycorrhizal seedlings of both tree species were incubated for 4 days (i.e. beech only, sycamore maple only or both together) in an artificial nutrient solution with low N availability. On the fourth day, N uptake experiments were conducted to study the effects of competition on inorganic and organic N uptake. For this purpose, multiple N sources were applied with a single label. Furthermore, fine roots were sampled and analysed for total amino acids, soluble protein, total nitrogen, nitrate and ammonium content. Our results clearly show that both tree species were able to use inorganic and organic N sources. Uptake of inorganic and organic N by beech roots was negatively affected in the presence of the competing tree species. In contrast, the presence of beech stimulated inorganic N uptake by sycamore maple roots. Both the negative effect of sycamore maple on N uptake of beech and the positive effect of beech on N uptake of sycamore maple led to an increase in root soluble protein in beech, despite an overall decrease in total N concentration. Thus, beech compensated for the negative effects of the tree competitor on N uptake by incorporating less N into structural N components, but otherwise exhibited the same strategy as the competitor, namely, enhancing soluble protein levels in roots when grown under competition. It is speculated that enhanced enzyme activities of so far unknown nature are required in beech as a defence response to inter-specific competition.
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,…
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.
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.
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.
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.
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.
2015-01-01
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
2015-01-01
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.
Hesse, Cedar N.; Mueller, Rebecca C.; Vuyisich, Momchilo; ...
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
MODEL IDENTIFICATION AND COMPUTER ALGEBRA.
Bollen, Kenneth A; Bauldry, Shawn
2010-10-07
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.
Algebraic and geometric structures of analytic partial differential equations
NASA Astrophysics Data System (ADS)
Kaptsov, O. V.
2016-11-01
We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.
Lee, Jaehoon; Wilczek, Frank
2013-11-27
Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.
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®,…
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
Double conformal space-time algebra
NASA Astrophysics Data System (ADS)
Easter, Robert Benjamin; Hitzer, Eckhard
2017-01-01
contraction effect of special relativity. DCSTA is an algebra for computing with quadrics and their cyclide inversions in spacetime. For applications or testing, DCSTA G 4,8 can be computed using various software packages, such as Gaalop, the Clifford Multivector Toolbox (for MATLAB), or the symbolic computer algebra system SymPy with the G Algebra module.
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.
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…
Applications of algebraic grid generation
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Smith, Robert E.
1990-01-01
Techniques and applications of algebraic grid generation are described. The techniques are univariate interpolations and transfinite assemblies of univariate interpolations. Because algebraic grid generation is computationally efficient, the use of interactive graphics in conjunction with the techniques is advocated. A flexible approach, which works extremely well in an interactive environment, called the control point form of algebraic grid generation is described. The applications discussed are three-dimensional grids constructed about airplane and submarine configurations.
Liu, Yongqiang; Ma, Hang; Seeram, Navindra P
2016-05-04
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.
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.
The exotic conformal Galilei algebra and nonlinear partial differential equations
NASA Astrophysics Data System (ADS)
Cherniha, Roman; Henkel, Malte
2010-09-01
The conformal Galilei algebra (CGA) and the exotic conformal Galilei algebra (ECGA) are applied to construct partial differential equations (PDEs) and systems of PDEs, which admit these algebras. We show that there are no single second-order PDEs invariant under the CGA but systems of PDEs can admit this algebra. Moreover, a wide class of nonlinear PDEs exists, which are conditionally invariant under CGA. It is further shown that there are systems of non-linear PDEs admitting ECGA with the realisation obtained very recently in [D. Martelli and Y. Tachikawa, arXiv:0903.5184v2 [hep-th] (2009)]. Moreover, wide classes of non-linear systems, invariant under two different 10-dimensional subalgebras of ECGA are explicitly constructed and an example with possible physical interpretation is presented.
Comparative study of homotopy continuation methods for nonlinear algebraic equations
NASA Astrophysics Data System (ADS)
Nor, Hafizudin Mohamad; Ismail, Ahmad Izani Md.; Majid, Ahmad Abd.
2014-07-01
We compare some recent homotopy continuation methods to see which method has greater applicability and greater accuracy. We test the methods on systems of nonlinear algebraic equations. The results obtained indicate the superior accuracy of Newton Homotopy Continuation Method (NHCM).
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
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.
Beyond the Schwinger boson representation of the su(2)-algebra
NASA Astrophysics Data System (ADS)
Tsue, Yasuhiko; Providência, Constança; da Providência, João; Yamamura, Masatoshi
2015-04-01
With the use of two kinds of boson operators, a new boson representation of the su(2)-algebra is proposed. The basic idea comes from the pseudo su(1,1)-algebra recently given by the present authors [Y. Tsue et al., Prog. Theor. Exp. Phys. 2013, 103D04 (2013)]. It forms a striking contrast to the Schwinger boson representation of the su(2)-algebra, which is also based on two kinds of bosons. It is proved that this new boson representation obeys the su(2)-algebra in a certain subspace in the whole boson space constructed by the Schwinger boson representation of the su(1,1)-algebra. This representation may be suitable for describing the time dependence of the system interacting with the external environment in the framework of the thermo field dynamics formalism, i.e., phase space doubling. Further, several deformations related to the su(2)-algebra in this boson representation are discussed. On the basis of these deformed algebras, various types of time evolution of a simple boson system are investigated.
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.
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…
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…
A Topos for Algebraic Quantum Theory
NASA Astrophysics Data System (ADS)
Heunen, Chris; Landsman, Nicolaas P.; Spitters, Bas
2009-10-01
The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr’s idea that the empirical content of quantum physics is accessible only through classical physics, we show how a noncommutative C*-algebra of observables A induces a topos {mathcal{T}(A)} in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra {A} . According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum {\\underline{Σ}(A)} in {mathcal{T}(A)} , which in our approach plays the role of the quantum phase space of the system. Thus we associate a locale (which is the topos-theoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on {\\underline{Σ}} , and self-adjoint elements of A define continuous functions (more precisely, locale maps) from {\\underline{Σ}} to Scott’s interval domain. Noting that open subsets of {\\underline{Σ}(A)} correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos {mathcal{T}(A)}. These results were inspired by the topos-theoretic approach to quantum physics proposed by Butterfield and Isham, as recently generalized by Döring and Isham.
Aaron, Catherine; Beaudry, Gabrielle; Parker, J Alex; Therrien, Martine
2016-05-04
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.
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.
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.
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.
Almost split real forms for hyperbolic Kac Moody Lie algebras
NASA Astrophysics Data System (ADS)
Ben Messaoud, Hechmi
2006-11-01
A Borel Tits theory was developed for almost split forms of symmetrizable Kac Moody Lie algebras. In this paper, we look to almost split real forms and their restricted root systems for symmetrizable hyperbolic Kac Moody Lie algebras. We establish a complete list of these forms, in terms of their Satake Tits index, for the strictly hyperbolic ones and for those which are obtained as (hyperbolic) canonical Lorentzian extensions of affine Lie algebras. These forms are of particular interest in theoretical physics because of their connection to supergravity theories.
W∞-ALGEBRA for Fermions in the Lowest Landau Level
NASA Astrophysics Data System (ADS)
Myung, Yun Soo
We derive the W∞-algebra directly from the cocycle (translational) transformation of fermions in the lowest Landau level. This happens whenever the translational symmetry is unbroken in the ground state. Under the cocycle transformations, the lowest Landau level condition and fermion number are preserved. In the droplet approximation, the algebra of this system is reduced to the classical w∞-algebra (area-preserving deformations) and is related to condensed matter physics. This describes the edge modes of the fractional quantum Hall effect.
Three-dimensional polarization algebra.
R Sheppard, Colin J; Castello, Marco; Diaspro, Alberto
2016-10-01
If light is focused or collected with a high numerical aperture lens, as may occur in imaging and optical encryption applications, polarization should be considered in three dimensions (3D). The matrix algebra of polarization behavior in 3D is discussed. It is useful to convert between the Mueller matrix and two different Hermitian matrices, representing an optical material or system, which are in the literature. Explicit transformation matrices for converting the column vector form of these different matrices are extended to the 3D case, where they are large (81×81) but can be generated using simple rules. It is found that there is some advantage in using a generalization of the Chandrasekhar phase matrix treatment, rather than that based on Gell-Mann matrices, as the resultant matrices are of simpler form and reduce to the two-dimensional case more easily. Explicit expressions are given for 3D complex field components in terms of Chandrasekhar-Stokes parameters.
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.
Thirty-two years of change in an old-growth Ohio beech-maple forest.
Runkle, James R
2013-05-01
Old-growth forests dominated by understory-tolerant tree species are among forest types most likely to be in equilibrium. However, documentation of the degree to which they are in equilibrium over decades-long time periods is lacking. Changes in climate, pathogens, and land use all are likely to impact stand characteristics and species composition, even in these forests. Here, 32 years of vegetation changes in an old-growth beech (Fagus grandifolia)-sugar maple (Acer saccharum) forest in Hueston Woods, southwest Ohio, USA, are summarized. These changes involve canopy composition and structure, turnover in snags, and development of vegetation in treefall gaps. Stand basal area and canopy density have changed little in 32 years. However, beech has decreased in canopy importance (49% to 32%) while sugar maple has increased (32% to 47%). Annual mortality was about 1.3% throughout the study period. Mortality rates increased with stem size, but the fraction of larger stems increased due to ingrowth from smaller size classes. Beech was represented by more very large stems than small canopy stems: over time, death of those larger stems with inadequate replacement has caused the decrease in beech importance. Sugar maple was represented by more small canopy stems whose growth has increased its importance. The changes in beech and sugar maple relative importance are hypothesized to be due to forest fragmentation mostly from the early 1800s with some possible additional effects associated with the formation of the state park. Snag densities (12-16 snags/ha) and formation rates (1-3 snags.ha(-1).yr(-1)) remained consistent. The treefall gaps previously studied are closing, with a few, large stems remaining. Death of gap border trees occurs consistently enough to favor species able to combine growth in gaps and survival in the understory.
ERIC Educational Resources Information Center
Hauk, Shandy; Matlen, Bryan
2016-01-01
A variety of computerized interactive learning platforms exist. Most include instructional supports in the form of problem sets. Feedback to users ranges from a single word like "Correct!" to offers of hints and partially to fully worked examples. Behind-the-scenes design of such systems varies as well --from static dictionaries of…
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.
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
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
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
Anderson, Rachel; Ryser, Peter
2015-08-05
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.
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.
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.
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.
RIR MAPLE procedure for deposition of carbon rich Si/C/H films
NASA Astrophysics Data System (ADS)
Dřínek, Vladislav; Strašák, Tomáš; Novotný, Filip; Fajgar, Radek; Bastl, Zdeněk
2014-02-01
We applied the resonant infrared matrix assisted pulsed laser evaporation (RIR MAPLE) technique to demonstrate a new approach to a controlled deposition of carbon rich amorphous Si/C/H film. In absence of radicals and accelerated species commonly generated in PECVD and sputtering setups, the RIR MAPLE method does not decompose precursor molecules. Moreover, unlike the standard MAPLE procedure, in which solvent molecules absorb laser energy from excimer or near infrared lasers, we applied the pulsed TEA CO2 laser to excite the dendrimer precursor molecules in a frozen target. In this manner we achieved just cross-linking of the starting precursor on substrates and the deposition of carbon rich Si/C/H film. The film was analyzed by Fourier Transformed Infrared (FTIR), UV/VIS, Raman and X-ray Photoelectron (XPS) spectroscopy and Atomic Force Microscopy (AFM) technique. According to analyses the film retained the precursor elemental composition free of graphitic (sp2) clusters. In course of reaction only the peripheral allyl groups containing C=C bonds were opened to achieve cross-linking. Whereas annealing to 300 °C was necessary for the elimination of =C-H1, 2 bonds in the films prepared at 200 °C, those bonds vanished completely for the films prepared at substrate temperature 255 °C. The film posseses a smooth surface with root mean square (RMS) parameter up to 10 nm within scanned distance 2.5 μm.
Patterns to Develop Algebraic Reasoning
ERIC Educational Resources Information Center
Stump, Sheryl L.
2011-01-01
What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…
Viterbi/algebraic hybrid decoder
NASA Technical Reports Server (NTRS)
Boyd, R. W.; Ingels, F. M.; Mo, C.
1980-01-01
Decoder computer program is hybrid between optimal Viterbi and optimal algebraic decoders. Tests have shown that hybrid decoder outperforms any strictly Viterbi or strictly algebraic decoder and effectively handles compound channels. Algorithm developed uses syndrome-detecting logic to direct two decoders to assume decoding load alternately, depending on real-time channel characteristics.
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.)
ERIC Educational Resources Information Center
1997
Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…
Elementary maps on nest algebras
NASA Astrophysics Data System (ADS)
Li, Pengtong
2006-08-01
Let , be algebras and let , be maps. An elementary map of is an ordered pair (M,M*) such that for all , . In this paper, the general form of surjective elementary maps on standard subalgebras of nest algebras is described. In particular, such maps are automatically additive.
Linear algebra and image processing
NASA Astrophysics Data System (ADS)
Allali, Mohamed
2010-09-01
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.
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.)
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 the…
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…
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…
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.
The complete Heyting algebra of subsystems and contextuality
NASA Astrophysics Data System (ADS)
Vourdas, A.
2013-08-01
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.
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.
Symplectic Clifford Algebraic Field Theory.
NASA Astrophysics Data System (ADS)
Dixon, Geoffrey Moore
We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.
Quasi-Linear Algebras and Integrability (the Heisenberg Picture)
NASA Astrophysics Data System (ADS)
Vinet, Luc; Zhedanov, Alexei
2008-02-01
We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables (operators) as functions of ''time'' t. We show that many algebras with nonlinear commutation relations such as the Askey-Wilson, q-Dolan-Grady and others satisfy this property. This provides one more (explicit Heisenberg evolution) interpretation of the corresponding integrable systems.
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.
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.
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')
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.
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.
Investigating Teacher Noticing of Student Algebraic Thinking
ERIC Educational Resources Information Center
Walkoe, Janet Dawn Kim
2013-01-01
Learning algebra is critical for students in the U.S. today. Algebra concepts provide the foundation for much advanced mathematical content. In addition, algebra serves as a gatekeeper to opportunities such as admission to college. Yet many students in the U.S. struggle in algebra classes. Researchers claim that one reason for these difficulties…
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.…
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…
Central extensions of Lax operator algebras
NASA Astrophysics Data System (ADS)
Schlichenmaier, M.; Sheinman, O. K.
2008-08-01
Lax operator algebras were introduced by Krichever and Sheinman as a further development of Krichever's theory of Lax operators on algebraic curves. These are almost-graded Lie algebras of current type. In this paper local cocycles and associated almost-graded central extensions of Lax operator algebras are classified. It is shown that in the case when the corresponding finite-dimensional Lie algebra is simple the two-cohomology space is one-dimensional. An important role is played by the action of the Lie algebra of meromorphic vector fields on the Lax operator algebra via suitable covariant derivatives.
Simon, Judy; Li, Xiuyuan; Rennenberg, Heinz
2014-01-01
Plant species use different strategies for maximizing growth and fitness under changing environmental conditions. At the ecosystem level, seedlings in particular compete with other vegetation components for light and nitrogen (N), which often constitute growth-limiting resources. In this study, we investigated the effect of light availability on the competition for N between seedlings of European beech and sycamore maple and analysed the consequences of this competition for the composition of N metabolites in fine roots. Our results show different strategies in N acquisition between beech and sycamore maple. Both species responded to reduced light availability by adapting their morphological and physiological traits with a decrease in biomass and net assimilation rate and an increase in specific leaf area and leaf area ratio. For beech seedlings, competition with sycamore maple led to a reduction in organic N uptake capacity. Reduced light availability led to a decrease in ammonium, but an increase in glutamine-N uptake capacity in sycamore maple. However, this response was stronger compared with that of beech and was accompanied by reduced growth. Thus, our results suggest better adaptation of N acquisition to reduced light availability in beech compared with sycamore maple seedlings.
Tappeiner, J. C.; 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.
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
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
Asymptotic aspect of derivations in Banach algebras.
Roh, Jaiok; Chang, Ick-Soon
2017-01-01
We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.
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.
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)
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.
Li, Liya; Seeram, Navindra P
2011-07-27
Maple syrup is made by boiling the sap collected from certain maple ( Acer ) species. During this process, phytochemicals naturally present in tree sap are concentrated in maple syrup. Twenty-three phytochemicals from a butanol extract of Canadian maple syrup (MS-BuOH) had previously been reported; this paper reports the isolation and identification of 30 additional compounds (1-30) from its ethyl acetate extract (MS-EtOAc) not previously reported from MS-BuOH. Of these, 4 compounds are new (1-3, 18) and 20 compounds (4-7, 10-12, 14-17, 19, 20, 22-24, 26, and 28-30) are being reported from maple syrup for the first time. The new compounds include 3 lignans and 1 phenylpropanoid: 5-(3″,4″-dimethoxyphenyl)-3-hydroxy-3-(4'-hydroxy-3'-methoxybenzyl)-4-(hydroxymethyl)dihydrofuran-2-one (1), (erythro,erythro)-1-[4-[2-hydroxy-2-(4-hydroxy-3-methoxyphenyl)-1-(hydroxymethyl)ethoxy]-3,5-dimethoxyphenyl]-1,2,3-propanetriol (2), (erythro,threo)-1-[4-[2-hydroxy-2-(4-hydroxy-3-methoxyphenyl)-1-(hydroxymethyl)ethoxy]-3,5-dimethoxyphenyl]-1,2,3-propanetriol (3), and 2,3-dihydroxy-1-(3,4- dihydroxyphenyl)-1-propanone (18), respectively. In addition, 25 other phenolic compounds were isolated including (threo,erythro)-1-[4-[(2-hydroxy-2-(4-hydroxy-3-methoxyphenyl)-1-(hydroxymethyl)ethoxy]-3-methoxyphenyl]-1,2,3-propanetriol (4), (threo,threo)-1-[4-[(2-hydroxy-2-(4-hydroxy-3-methoxyphenyl)-1-(hydroxymethyl)ethoxy]-3-methoxyphenyl]-1,2,3-propanetriol (5), threo-guaiacylglycerol-β-O-4'-dihydroconiferyl alcohol (6), erythro-1-(4-hydroxy-3-methoxyphenyl)-2-[4-(3-hydroxypropyl)-2,6-dimethoxyphenoxy]-1,3-propanediol (7), 2-[4-[2,3-dihydro-3-(hydroxymethyl)-5-(3-hydroxypropyl)-7-methoxy-2-benzofuranyl]-2,6-dimethoxyphenoxy]-1-(4-hydroxy-3-methoxyphenyl)-1,3-propanediol (8), acernikol (9), leptolepisol D (10), buddlenol E (11), (1S,2R)-2-[2,6-dimethoxy-4-[(1S,3aR,4S,6aR)-tetrahydro-4-(4-hydroxy-3,5-dimethoxyphenyl)-1H,3H-furo[3,4-c]furan-1-yl]phenoxy]-1-(4-hydroxy-3-methoxyphenyl)-1
Coherent States for Hopf Algebras
NASA Astrophysics Data System (ADS)
Škoda, Zoran
2007-07-01
Families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras. A global geometric picture involving locally trivial noncommutative fibre bundles is involved in the construction. If, in addition, the Hopf algebra has a left Haar integral, then a formula for noncommutative resolution of identity in terms of the family of coherent states holds. Examples come from quantum groups.
Multiplier operator algebras and applications
Blecher, David P.; Zarikian, Vrej
2004-01-01
The one-sided multipliers of an operator space X are a key to “latent operator algebraic structure” in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals. PMID:14711990
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).
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…
Friedrich, Timo; Lambert, Aaron M; Masino, Mark A; Downes, Gerald B
2012-03-01
Analysis of zebrafish mutants that demonstrate abnormal locomotive behavior can elucidate the molecular requirements for neural network function and provide new models of human disease. Here, we show that zebrafish quetschkommode (que) mutant larvae exhibit a progressive locomotor defect that culminates in unusual nose-to-tail compressions and an inability to swim. Correspondingly, extracellular peripheral nerve recordings show that que mutants demonstrate abnormal locomotor output to the axial muscles used for swimming. Using positional cloning and candidate gene analysis, we reveal that a point mutation disrupts the gene encoding dihydrolipoamide branched-chain transacylase E2 (Dbt), a component of a mitochondrial enzyme complex, to generate the que phenotype. In humans, mutation of the DBT gene causes maple syrup urine disease (MSUD), a disorder of branched-chain amino acid metabolism that can result in mental retardation, severe dystonia, profound neurological damage and death. que mutants harbor abnormal amino acid levels, similar to MSUD patients and consistent with an error in branched-chain amino acid metabolism. que mutants also contain markedly reduced levels of the neurotransmitter glutamate within the brain and spinal cord, which probably contributes to their abnormal spinal cord locomotor output and aberrant motility behavior, a trait that probably represents severe dystonia in larval zebrafish. Taken together, these data illustrate how defects in branched-chain amino acid metabolism can disrupt nervous system development and/or function, and establish zebrafish que mutants as a model to better understand MSUD.
Tjoelker, M.G.; Volin, J.C.; Oleksyn, J.; Reich, P.B. )
1993-06-01
The impact of ozone on leaf gas exchange in a forest canopy as influenced by light environment was studied in a 35-year-old stand of sugar maple (Acer sacchharum) in southern Wisconsin. We developed a chamberless system to expose branches to elevated concentrations of ozone. Ten branches and ten paired controls in the upper canopy (14 to 16 m) were selected along a light gradient, ranging from sunlit (14.5 mol m[sup [minus]2] day[sup [minus]1] PPFD) to deeply shaded (0.6 mol m[sup [minus]2] day[sup [minus]1] PPFD). The branches were exposed for 8 hours each day to ozone concentrations averaging 95 nl 1[sup [minus]1](+/-13 SD), about twice the ambient levels between June and September. Among the branches, area-based rates of light-saturated photosynthesis and dark respiration were positively correlated with mean daily integrated PPFD. Light-saturated rates of photosynthesis and chlorophyll concentrations declined while dark respiration increased with increasing ozone dose. Over time stomatal conductance became uncoupled from light-saturated photosynthesis rates in exposed branches. Photosynthesis and quantum yield were reduced more in a shaded branch than in a sunlit branch in response to ozone treatment. In general, shaded branches were more sensitive to ozone than sunlit branches.
MAPLE: Multi-Agent Planning, Learning, and Execution
2004-02-01
generating cyclic maps of large-scale environments from raw laser range measure- ments. In Proceedings of the Conference on Intelligent Robots and Systems...Joint Conference on Artificial Intelligence (IJCAI), Acapulco, Mexico, 2003. IJCAI. [20] E. Nettleton , S. Thrun, and H. Durrant-Whyte. Decentralised
Universal Algebraic Varieties and Ideals in Physics:. Field Theory on Algebraic Varieties
NASA Astrophysics Data System (ADS)
Iguchi, Kazumoto
A class of universal algebraic varieties in physics is discussed herein using the concepts of determinant ideals in algebraic geometry. It is shown that these algebraic varieties arise with very different physical contexts in many branches of physics and mathematics from high energy physics theory to chaos theory. In these physical systems the models are constructed by using the fields on usual manifolds such as vector fields in a Euclidean space and a Minkowskian space. But there is a universal mathematical aspect of linear algebra for linear vector spaces, where the linear independency and dependency are described using the Gramians of the vectors. These Gramians form a class of hypersurfaces in a higher-dimensional mathematical space: If there exist g vectors vi in an n-dimensional Euclidean space, the Gramian Gg is given as a g × g determinant Gg=Det[xij] with the inner products xij=(vi,vj), and exists in a g(g-1)/2-[g(g+1)/2-] dimensional space if the vectors are (not) normalized, xii=1 (xii ≠ 1). It is also shown that the Gramians are invariant under automorphisms of the vectors. The mathematical structure of the Gramians is revealed to be equivalent to the concepts of determinant ideals Ig(v), each element of which is a g × g determinant constructed from components of an arbitrary N×N matrix with N>n and which have inclusion relation: R=I0(v)⊃ I1(v) ⊃···⊃ Ig(v) ⊃···, and Ig(v)=0 if g>n. In the various physical systems the ideals naturally emerge to give us dynamical flows on the hypersurfaces, and therefore, it is called the field theory on algebraic varieties. This viewpoint provides us a grand viewpoint in physics and mathematics.
Nagai, Noriaki; Ito, Yoshimasa; Taga, Atsushi
2013-01-01
Maple syrup is used as a premium natural sweeter, and is known for being good for human health. In the present study, we investigate whether maple syrup is suitable as a sweetener in the management of type 2 diabetes using Otsuka Long-Evans Tokushima Fatty (OLETF) rats, a model of type 2 diabetes mellitus. OLETF rats develop type 2 diabetes mellitus by 30 weeks of age, and 60-week-old OLETF rats show hyperglycemia and hypoinsulinemia via pancreatic β-cell dysfunction. The administration of sucrose or maple syrup following an OGT test increased plasma glucose (PG) levels in OLETF rats, but the enhancement in PG following the oral administration of maple syrup was lower than in the case of sucrose administration in both 30- and 60-week-old OLETF rats. Although, the insulin levels in 30-week-old OLETF rats also increased following the oral administration of sucrose or maple syrup, no increase in insulin levels was seen in 60-week-old OLETF rats following the oral administration of either sucrose or maple syrup. No significant differences were observed in insulin levels between sucrose- and maple syrup-administered OLETF rats at either 30 or 60 weeks of age. The present study strongly suggests that the maple syrup may have a lower glycemic index than sucrose, which may help in the prevention of type 2 diabetes.
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…
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.
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.
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.
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.
Novikov algebras with associative bilinear forms
NASA Astrophysics Data System (ADS)
Zhu, Fuhai; Chen, Zhiqi
2007-11-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.
The applications of a higher-dimensional Lie algebra and its decomposed subalgebras.
Yu, Zhang; Zhang, Yufeng
2009-01-15
With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 x 6 matrix Lie algebra smu(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra smu(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras smu(6) and E is used to directly construct integrable couplings.
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.
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
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.
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.
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.
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.
Lepeduš, Hrvoje; Gaća, Vlatka; Viljevac, Marija; Kovač, Spomenka; Fulgosi, Hrvoje; Simić, Domagoj; Jurković, Vlatka; Cesar, Vera
2011-04-01
Different structural and functional changes take place during leaf development. Since some of them are highly connected to oxidative metabolism, regulation of reactive oxygen species (ROS) abundance is required. Most of the reactive oxygen species ROS in plant cells are produced in chloroplasts as a result of highly energetic reactions of photosynthesis. The aim of our study was to examine the changes in concentration of oxidative stress parameters (TBARS - thiobarbituric acid-reacting substances and protein carbonyls) as well as antioxidative strategies during development of maple (Acer platanoides L.) leaves in the light of their enhanced photosynthetic performance. We reveal that biogenesis of the photosynthetic apparatus during maple leaf maturation corresponded with oxidative damage of lipids, but not proteins. In addition, antioxidative responses in young leaves differed from that in older leaves. Young leaves had high values of non-photochemical quenching (NPQ) and catalase (CAT, EC 1.11.1.6) activity which declined during the maturation process. Developing leaves were characterized by an increase in TBARS level, the content of non-enzymatic antioxidants as well as ascorbate peroxidase activity (APX, EC 1.11.1.11), while the content of protein carbonyls decreased with leaf maturation. Fully developed leaves had the highest lipid peroxidation level accompanied by a maximum in ascorbic acid content and superoxide dismutase activity (SOD, EC1.15.1.1). These observations imply completely different antioxidative strategies during leaf maturation enabling them to perform their basic function.
Sager, E P S; Hutchinson, T C; Croley, T R
2005-06-01
Tropospheric O3 has been implicated in the declining health of forest ecosystems in Europe and North America and has been shown to have negative consequences on human health. We have measured tropospheric ozone (O3) in the lower canopy through the use of passive monitors located in five woodlots along a 150 km urban-rural transect, originating in the large urban complex of Toronto, Canada. We also sampled foliage from 10 mature sugar maple trees in each woodlot and measured the concentration of a number of phenolic compounds and macronutrients. O3 concentrations were highest in the two rural woodlots, located approximately 150 km downwind of Toronto, when compared to the woodlots found within the Greater Toronto Area. Foliar concentrations of three flavonoids, avicularin, isoquercitrin, and quercitrin, were significantly greater and nitrogen concentrations significantly lower at these same rural woodlots, suggesting some physiological disruption is occurring in those sites where exposure to tropospheric O3 is greater. We suggest that foliar phenolics of sugar maple may be a biochemical indicator of tropospheric ozone exposure.
Genetic consequences of selection cutting on sugar maple (Acer saccharum Marshall).
Graignic, Noémie; Tremblay, Francine; Bergeron, Yves
2016-07-01
Selection cutting is a treatment that emulates tree-by-tree replacement for forests with uneven-age structures. It creates small openings in large areas and often generates a more homogenous forest structure (fewer large leaving trees and defective trees) that differs from old-growth forest. In this study, we evaluated whether this type of harvesting has an impact on genetic diversity of sugar maple (Acer saccharum Marshall). Genetic diversity among seedlings, saplings, and mature trees was compared between selection cut and old-growth forest stands in Québec, Canada. We found higher observed heterozygosity and a lower inbreeding coefficient in mature trees than in younger regeneration cohorts of both forest types. We detected a recent bottleneck in all stands undergoing selection cutting. Other genetic indices of diversity (allelic richness, observed and expected heterozygosity, and rare alleles) were similar between forest types. We concluded that the effect of selection cutting on the genetic diversity of sugar maple was recent and no evidence of genetic erosion was detectable in Québec stands after one harvest. However, the cumulative effect of recurring applications of selection cutting in bottlenecked stands could lead to fixation of deleterious alleles, and this highlights the need for adopting better forest management practices.
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.
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.
Antioxidant capacity, phenolic constituents and toxicity of hot water extract from red maple buds.
Meda, Naamwin R; Poubelle, Patrice E; Stevanovic, Tatjana
2017-03-11
The present study reports, for the first time, the results of the antioxidant capacity and the phenolic composition of a hot water extract from red maple buds (RMB), as well as its safety. In this regard and comparatively to antioxidant standards, this extract exhibits a significant antiradical capacity when tested by 2,2-diphenyl-1-picrylhydrazyl (DPPH•) and anion superoxide trapping assays. High-resolution mass spectrometric (HRMS) and Nuclear Magnetic Resonance (NMR) analyses permitted to determine for the first time, in red maple species, cyanidin-3-O-glucoside, quercetin-3-O-galactoside, quercetin-3-O-arabinoside and quercetin. Also, the quantification of individual phenolics by high-performance liquid chromatography (HPLC) method revealed that ginnalin A at 117.0 mg/g is the major compound of RMB hot water extract. Finally, using flow cytometry evaluation, the extract of RMB was determined to have no toxicity neither to cause significant modification of apoptosis process, up to concentration of 100 μg / mL, on human peripheral blood neutrophils. These results allow anticipating various fields of application of RMB water extract. This article is protected by copyright. All rights reserved.