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Sample records for linear equations ax

  1. Three Interpretations of the Matrix Equation Ax = b

    Science.gov (United States)

    Larson, Christine; Zandieh, Michelle

    2013-01-01

    Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…

  2. A Solution to the Fundamental Linear Fractional Order Differential Equation

    Science.gov (United States)

    Hartley, Tom T.; Lorenzo, Carl F.

    1998-01-01

    This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

  3. TOEPLITZ, Solution of Linear Equation System with Toeplitz or Circulant Matrix

    International Nuclear Information System (INIS)

    Garbow, B.

    1984-01-01

    Description of program or function: TOEPLITZ is a collection of FORTRAN subroutines for solving linear systems Ax=b, where A is a Toeplitz matrix, a Circulant matrix, or has one or several block structures based on Toeplitz or Circulant matrices. Such systems arise in problems of electrodynamics, acoustics, mathematical statistics, algebra, in the numerical solution of integral equations with a difference kernel, and in the theory of stationary time series and signals

  4. On Attainability of Optimal Solutions for Linear Elliptic Equations with Unbounded Coefficients

    Directory of Open Access Journals (Sweden)

    P. I. Kogut

    2011-12-01

    Full Text Available We study an optimal boundary control problem (OCP associated to a linear elliptic equation —div (Vj/ + A(xVy = f describing diffusion in a turbulent flow. The characteristic feature of this equation is the fact that, in applications, the stream matrix A(x = [a,ij(x]i,j=i,...,N is skew-symmetric, ац(х = —a,ji(x, measurable, and belongs to L -space (rather than L°°. An optimal solution to such problem can inherit a singular character of the original stream matrix A. We show that optimal solutions can be attainable by solutions of special optimal boundary control problems.

  5. Modifying a numerical algorithm for solving the matrix equation X + AX T B = C

    Science.gov (United States)

    Vorontsov, Yu. O.

    2013-06-01

    Certain modifications are proposed for a numerical algorithm solving the matrix equation X + AX T B = C. By keeping the intermediate results in storage and repeatedly using them, it is possible to reduce the total complexity of the algorithm from O( n 4) to O( n 3) arithmetic operations.

  6. Stochastic models with power-law tails the equation X = AX + B

    CERN Document Server

    Buraczewski, Dariusz; Mikosch, Thomas

    2016-01-01

    In this monograph the authors give a systematic approach to the probabilistic properties of the fixed point equation X=AX+B. A probabilistic study of the stochastic recurrence equation X_t=A_tX_{t-1}+B_t for real- and matrix-valued random variables A_t, where (A_t,B_t) constitute an iid sequence, is provided. The classical theory for these equations, including the existence and uniqueness of a stationary solution, the tail behavior with special emphasis on power law behavior, moments and support, is presented. The authors collect recent asymptotic results on extremes, point processes, partial sums (central limit theory with special emphasis on infinite variance stable limit theory), large deviations, in the univariate and multivariate cases, and they further touch on the related topics of smoothing transforms, regularly varying sequences and random iterative systems. The text gives an introduction to the Kesten-Goldie theory for stochastic recurrence equations of the type X_t=A_tX_{t-1}+B_t. It provides the c...

  7. Fast solution of elliptic partial differential equations using linear combinations of plane waves.

    Science.gov (United States)

    Pérez-Jordá, José M

    2016-02-01

    Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

  8. Solving linear inequalities in a least squares sense

    Energy Technology Data Exchange (ETDEWEB)

    Bramley, R.; Winnicka, B. [Indiana Univ., Bloomington, IN (United States)

    1994-12-31

    Let A {element_of} {Re}{sup mxn} be an arbitrary real matrix, and let b {element_of} {Re}{sup m} a given vector. A familiar problem in computational linear algebra is to solve the system Ax = b in a least squares sense; that is, to find an x* minimizing {parallel}Ax {minus} b{parallel}, where {parallel} {center_dot} {parallel} refers to the vector two-norm. Such an x* solves the normal equations A{sup T}(Ax {minus} b) = 0, and the optimal residual r* = b {minus} Ax* is unique (although x* need not be). The least squares problem is usually interpreted as corresponding to multiple observations, represented by the rows of A and b, on a vector of data x. The observations may be inconsistent, and in this case a solution is sought that minimizes the norm of the residuals. A less familiar problem to numerical linear algebraists is the solution of systems of linear inequalities Ax {le} b in a least squares sense, but the motivation is similar: if a set of observations places upper or lower bounds on linear combinations of variables, the authors want to find x* minimizing {parallel} (Ax {minus} b){sub +} {parallel}, where the i{sup th} component of the vector v{sub +} is the maximum of zero and the i{sup th} component of v.

  9. Global behavior of the difference equation $x_{n+1}=\\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$

    Directory of Open Access Journals (Sweden)

    R. Abo-Zeid

    2013-11-01

    Full Text Available The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of all admissible solutions of the difference equation $x_{n+1}=\\frac{Ax_{n-1}} {B-Cx_{n}x_{n-2}}$, n=0,1,2,... where A, B, C are positive real numbers.

  10. Linear integral equations and soliton systems

    International Nuclear Information System (INIS)

    Quispel, G.R.W.

    1983-01-01

    A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

  11. Quantum linear Boltzmann equation

    International Nuclear Information System (INIS)

    Vacchini, Bassano; Hornberger, Klaus

    2009-01-01

    We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

  12. Linear superposition solutions to nonlinear wave equations

    International Nuclear Information System (INIS)

    Liu Yu

    2012-01-01

    The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed

  13. Linear and quasi-linear equations of parabolic type

    CERN Document Server

    Ladyženskaja, O A; Ural′ceva, N N; Uralceva, N N

    1968-01-01

    Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.

  14. Approximate Solution of LR Fuzzy Sylvester Matrix Equations

    Directory of Open Access Journals (Sweden)

    Xiaobin Guo

    2013-01-01

    Full Text Available The fuzzy Sylvester matrix equation AX~+X~B=C~ in which A,B are m×m and n×n crisp matrices, respectively, and C~ is an m×n LR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.

  15. Linear determining equations for differential constraints

    International Nuclear Information System (INIS)

    Kaptsov, O V

    1998-01-01

    A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical determining equations used in the search for admissible Lie operators. As applications of this approach equations of an ideal incompressible fluid and non-linear heat equations are discussed

  16. Isomorphism of Intransitive Linear Lie Equations

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    Jose Miguel Martins Veloso

    2009-11-01

    Full Text Available We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an intransitive Lie algebra with each intransitive linear Lie equation, and from the intransitive Lie algebra we recover the linear Lie equation, unless of formal isomorphism. The intransitive Lie algebra gives the structure functions introduced by É. Cartan.

  17. Students’ difficulties in solving linear equation problems

    Science.gov (United States)

    Wati, S.; Fitriana, L.; Mardiyana

    2018-03-01

    A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

  18. Computing with linear equations and matrices

    International Nuclear Information System (INIS)

    Churchhouse, R.F.

    1983-01-01

    Systems of linear equations and matrices arise in many disciplines. The equations may accurately represent conditions satisfied by a system or, more likely, provide an approximation to a more complex system of non-linear or differential equations. The system may involve a few or many thousand unknowns and each individual equation may involve few or many of them. Over the past 50 years a vast literature on methods for solving systems of linear equations and the associated problems of finding the inverse or eigenvalues of a matrix has been produced. These lectures cover those methods which have been found to be most useful for dealing with such types of problem. References are given where appropriate and attention is drawn to the possibility of improved methods for use on vector and parallel processors. (orig.)

  19. Correct Linearization of Einstein's Equations

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    Rabounski D.

    2006-06-01

    Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.

  20. Diffusive limits for linear transport equations

    International Nuclear Information System (INIS)

    Pomraning, G.C.

    1992-01-01

    The authors show that the Hibert and Chapman-Enskog asymptotic treatments that reduce the nonlinear Boltzmann equation to the Euler and Navier-Stokes fluid equations have analogs in linear transport theory. In this linear setting, these fluid limits are described by diffusion equations, involving familiar and less familiar diffusion coefficients. Because of the linearity extant, one can carry out explicitly the initial and boundary layer analyses required to obtain asymptotically consistent initial and boundary conditions for the diffusion equations. In particular, the effects of boundary curvature and boundary condition variation along the surface can be included in the boundary layer analysis. A brief review of heuristic (nonasymptotic) diffusion description derivations is also included in our discussion

  1. Spectral theories for linear differential equations

    International Nuclear Information System (INIS)

    Sell, G.R.

    1976-01-01

    The use of spectral analysis in the study of linear differential equations with constant coefficients is not only a fundamental technique but also leads to far-reaching consequences in describing the qualitative behaviour of the solutions. The spectral analysis, via the Jordan canonical form, will not only lead to a representation theorem for a basis of solutions, but will also give a rather precise statement of the (exponential) growth rates of various solutions. Various attempts have been made to extend this analysis to linear differential equations with time-varying coefficients. The most complete such extensions is the Floquet theory for equations with periodic coefficients. For time-varying linear differential equations with aperiodic coefficients several authors have attempted to ''extend'' the Foquet theory. The precise meaning of such an extension is itself a problem, and we present here several attempts in this direction that are related to the general problem of extending the spectral analysis of equations with constant coefficients. The main purpose of this paper is to introduce some problems of current research. The primary problem we shall examine occurs in the context of linear differential equations with almost periodic coefficients. We call it ''the Floquet problem''. (author)

  2. Explicit solutions to the generalized Sylvester matrix equation AX- XF = BY%广义Sylvester矩阵方程AX-XF=BY的显式解

    Institute of Scientific and Technical Information of China (English)

    周彬; 段广仁

    2006-01-01

    A complete, general and explicit solution to the generalized Sylvester matrix equation AX-XF = BY, with F being an arbitrary square matrix, is investigated. The proposed solution is in an extremely neat form represented by a controllability matrix of the matrix pair (A,B), a symmetric operator and an observability matrix of the matrix pair (Z,F), where Z is an arbitrary matrix used to denote the degree of freedom in the solution. Furthermore, based on the Faddeev - Leverrier algorithm, an equivalent form of the proposed solution is established. At the same time, an equivalent form of the solutions proposed in [ 13 ] is also induced. These results provide great convenience to the analysis and design problems in control systems. The results proposed in this note is a further discussion of the results proposed in [ 13 ].%给出了广义Sylvester矩阵方程AX-XF=BY当F为任意矩阵时的一种完全的解析通解.该通解由矩阵对(A,B)构成的能控性矩阵,一个对称算子矩阵和矩阵对(Z,F)构成的能观性矩阵组成,这里Z是一个任意的参数矩阵,用来表征该方程的解的自由度.利用著名的Levverrier算法,该解析解的一个等价形式被给出.给出的结果是参考文献[13]的推广,在[13]中F被假设为友矩阵.

  3. Lie algebras and linear differential equations.

    Science.gov (United States)

    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.

  4. Induction and Persistence of Large γH2AX Foci by High Linear Energy Transfer Radiation in DNA-Dependent protein kinase–Deficient Cells

    Energy Technology Data Exchange (ETDEWEB)

    Bracalente, Candelaria; Ibañez, Irene L. [Departamento de Micro y Nanotecnología, Comisión Nacional de Energía Atómica, San Martín, Buenos Aires (Argentina); Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires (Argentina); Molinari, Beatriz [Departamento de Radiobiología, Comisión Nacional de Energía Atómica, San Martín, Buenos Aires (Argentina); Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires (Argentina); Palmieri, Mónica [Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires (Argentina); Kreiner, Andrés [Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires (Argentina); Gerencia de Investigación y Aplicaciones, Comisión Nacional de Energía Atómica, San Martín, Buenos Aires (Argentina); Escuela de Ciencia y Tecnología, Universidad Nacional de San Martín, San Martín, Buenos Aires (Argentina); Valda, Alejandro [Escuela de Ciencia y Tecnología, Universidad Nacional de San Martín, San Martín, Buenos Aires (Argentina); and others

    2013-11-15

    Purpose: To evaluate the cell response to DNA double-strand breaks induced by low and high linear energy transfer (LET) radiations when the catalytic subunit of DNA-dependent protein kinase (DNA-PKcs), an essential protein of the nonhomologous end-joining repair pathway, lacks kinase activity. Methods and Materials: CHO10B2, a Chinese hamster ovary cell line, and its derived radiosensitive mutant cell line, irs-20, lacking DNA-PKcs activity, were evaluated after 0 to 3 Gy of γ-rays, plateau and Bragg peak protons, and lithium beams by clonogenic assay, and as a measurement of double-strand breaks, phosphorylated H2AX (γH2AX) foci number and size were quantified by immunocytofluorescence. Results: Irs-20 exhibited greater radiosensitivity and a higher amount of γH2AX foci than CHO10B2 at 6 hours after irradiation for all types of radiations. Remarkably, CHO10B2 and irs-20 maintained their difference in radiosensitivity after high-LET radiation. Six hours after low-LET radiations, irs-20 did not reach basal levels of γH2AX at high doses, whereas CHO10B2 recovered basal levels for all doses. After high-LET radiation, only CHO10B2 exhibited a reduction in γH2AX foci, but it never reached basal levels. Persistent foci in irs-20 confirmed a repair deficiency. Interestingly, after 30 minutes of high-LET radiation both cell lines exhibited large foci (size >0.9 μm{sup 2}) related to the damage nature, whereas at 6 hours irs-20 showed a higher amount of large foci than CHO10B2, with a 7-fold increase at 3 Gy, that could also be associated to radiosensitivity. Conclusions: We demonstrated, for the first time, an association between deficient DNA-PKcs activity and not only high levels of H2AX phosphorylation but also persistence and size increase of γH2AX foci after high-LET irradiation.

  5. Induction and Persistence of Large γH2AX Foci by High Linear Energy Transfer Radiation in DNA-Dependent protein kinase–Deficient Cells

    International Nuclear Information System (INIS)

    Bracalente, Candelaria; Ibañez, Irene L.; Molinari, Beatriz; Palmieri, Mónica; Kreiner, Andrés; Valda, Alejandro

    2013-01-01

    Purpose: To evaluate the cell response to DNA double-strand breaks induced by low and high linear energy transfer (LET) radiations when the catalytic subunit of DNA-dependent protein kinase (DNA-PKcs), an essential protein of the nonhomologous end-joining repair pathway, lacks kinase activity. Methods and Materials: CHO10B2, a Chinese hamster ovary cell line, and its derived radiosensitive mutant cell line, irs-20, lacking DNA-PKcs activity, were evaluated after 0 to 3 Gy of γ-rays, plateau and Bragg peak protons, and lithium beams by clonogenic assay, and as a measurement of double-strand breaks, phosphorylated H2AX (γH2AX) foci number and size were quantified by immunocytofluorescence. Results: Irs-20 exhibited greater radiosensitivity and a higher amount of γH2AX foci than CHO10B2 at 6 hours after irradiation for all types of radiations. Remarkably, CHO10B2 and irs-20 maintained their difference in radiosensitivity after high-LET radiation. Six hours after low-LET radiations, irs-20 did not reach basal levels of γH2AX at high doses, whereas CHO10B2 recovered basal levels for all doses. After high-LET radiation, only CHO10B2 exhibited a reduction in γH2AX foci, but it never reached basal levels. Persistent foci in irs-20 confirmed a repair deficiency. Interestingly, after 30 minutes of high-LET radiation both cell lines exhibited large foci (size >0.9 μm 2 ) related to the damage nature, whereas at 6 hours irs-20 showed a higher amount of large foci than CHO10B2, with a 7-fold increase at 3 Gy, that could also be associated to radiosensitivity. Conclusions: We demonstrated, for the first time, an association between deficient DNA-PKcs activity and not only high levels of H2AX phosphorylation but also persistence and size increase of γH2AX foci after high-LET irradiation

  6. Linear q-nonuniform difference equations

    International Nuclear Information System (INIS)

    Bangerezako, Gaspard

    2010-01-01

    We introduce basic concepts of q-nonuniform differentiation and integration and study linear q-nonuniform difference equations and systems, as well as their application in q-nonuniform difference linear control systems. (author)

  7. On Optimal Feedback Control for Stationary Linear Systems

    International Nuclear Information System (INIS)

    Russell, David L.

    2010-01-01

    We study linear-quadratic optimal control problems for finite dimensional stationary linear systems AX+BU=Z with output Y=CX+DU from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.

  8. Schwarz maps of algebraic linear ordinary differential equations

    Science.gov (United States)

    Sanabria Malagón, Camilo

    2017-12-01

    A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

  9. Basic linear partial differential equations

    CERN Document Server

    Treves, Francois

    1975-01-01

    Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their

  10. Non-local quasi-linear parabolic equations

    International Nuclear Information System (INIS)

    Amann, H

    2005-01-01

    This is a survey of the most common approaches to quasi-linear parabolic evolution equations, a discussion of their advantages and drawbacks, and a presentation of an entirely new approach based on maximal L p regularity. The general results here apply, above all, to parabolic initial-boundary value problems that are non-local in time. This is illustrated by indicating their relevance for quasi-linear parabolic equations with memory and, in particular, for time-regularized versions of the Perona-Malik equation of image processing

  11. The Cauchy problem for non-linear Klein-Gordon equations

    International Nuclear Information System (INIS)

    Simon, J.C.H.; Taflin, E.

    1993-01-01

    We consider in R n+1 , n≥2, the non-linear Klein-Gordon equation. We prove for such an equation that there is neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare-Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the wave operator. The Hilbert space is, in both cases, the closure of the space of the differentiable vectors for the linear representation of the Poincare group, associated with the Klein-Gordon equation, with respect to a norm defined by the representation of the enveloping algebra. (orig.)

  12. A non-linear detection of phospho-histone H2AX in EA.hy926 endothelial cells following low-dose X-irradiation is modulated by reactive oxygen species

    International Nuclear Information System (INIS)

    Large, Martin; Reichert, Sebastian; Hehlgans, Stephanie; Fournier, Claudia; Rödel, Claus; Rödel, Franz

    2014-01-01

    A discontinuous dose response relationship is a major characteristic of the anti-inflammatory effects of low-dose X-irradiation therapy. Although recent data indicate an involvement of a variety of molecular mechanisms in these characteristics, the impact of reactive oxygen species (ROS) production to give rise or contribute to these phenomena in endothelial cells (EC) remains elusive. HUVEC derived immortalized EA.hy926 cells were stimulated by tumor necrosis factor-α (TNF-α, 20 ng/ml) 4 h before irradiation with doses ranging from 0.3 to 1 Gy. To analyse DNA repair capacity, phospho-histone H2AX foci were assayed at 1 h, 4 h and 24 h after irradiation. ROS production and superoxide dismutase (SOD) activity were analysed by fluorometric 2′,7′-dichlorodihydrofluorescein-diacetate (H2DCFDA) and colorimetric assays. A functional impact of ROS on γH2AX production was analysed by treatment with the scavenger N-acetyl-L-cysteine (NAC). Irrespective of stimulation by TNF-α, EA.hy926 cells revealed a linear dose response characteristic of γH2AX foci detection at 1 h and 4 h after irradiation. By contrast, we observed a discontinuity in residual γH2AX foci detection at 24 h after irradiation with locally elevated values following a 0.5 Gy exposure that was abolished by inhibition of ROS by NAC. Moreover, SOD protein expression was significantly decreased at doses of 0.5 Gy and 0.7 Gy concomitant with a reduced SOD activity. These data implicate a non-linear regulation of ROS production and SOD activity in EA.hy926 EC following irradiation with doses < 1 Gy that may contribute to a discontinuous dose-response relationship of residual γH2AX foci detection

  13. Hamiltonian structures of some non-linear evolution equations

    International Nuclear Information System (INIS)

    Tu, G.Z.

    1983-06-01

    The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)

  14. Solving polynomial differential equations by transforming them to linear functional-differential equations

    OpenAIRE

    Nahay, John Michael

    2008-01-01

    We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

  15. Linear differential equations to solve nonlinear mechanical problems: A novel approach

    OpenAIRE

    Nair, C. Radhakrishnan

    2004-01-01

    Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...

  16. Linear measure functional differential equations with infinite delay

    OpenAIRE

    Monteiro, G. (Giselle Antunes); Slavík, A.

    2014-01-01

    We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.

  17. Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.

    Science.gov (United States)

    Sloss, J. M.; Kranzler, S. K.

    1972-01-01

    The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.

  18. The {P,Q,k+1}-Reflexive Solution to System of Matrix Equations AX=C, XB=D

    Directory of Open Access Journals (Sweden)

    Chang-Zhou Dong

    2015-01-01

    Full Text Available Let P∈Cm×m and Q∈Cn×n be Hermitian and {k+1}-potent matrices; that is, Pk+1=P=P⁎ and Qk+1=Q=Q⁎, where ·⁎ stands for the conjugate transpose of a matrix. A matrix X∈Cm×n is called {P,Q,k+1}-reflexive (antireflexive if PXQ=X (PXQ=-X. In this paper, the system of matrix equations AX=C and XB=D subject to {P,Q,k+1}-reflexive and antireflexive constraints is studied by converting into two simpler cases: k=1 and k=2. We give the solvability conditions and the general solution to this system; in addition, the least squares solution is derived; finally, the associated optimal approximation problem for a given matrix is considered.

  19. Saturation and linear transport equation

    International Nuclear Information System (INIS)

    Kutak, K.

    2009-03-01

    We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term. (orig.)

  20. Linearized pseudo-Einstein equations on the Heisenberg group

    Science.gov (United States)

    Barletta, Elisabetta; Dragomir, Sorin; Jacobowitz, Howard

    2017-02-01

    We study the pseudo-Einstein equation R11bar = 0 on the Heisenberg group H1 = C × R. We consider first order perturbations θɛ =θ0 + ɛ θ and linearize the pseudo-Einstein equation about θ0 (the canonical Tanaka-Webster flat contact form on H1 thought of as a strictly pseudoconvex CR manifold). If θ =e2uθ0 the linearized pseudo-Einstein equation is Δb u - 4 | Lu|2 = 0 where Δb is the sublaplacian of (H1 ,θ0) and L bar is the Lewy operator. We solve the linearized pseudo-Einstein equation on a bounded domain Ω ⊂H1 by applying subelliptic theory i.e. existence and regularity results for weak subelliptic harmonic maps. We determine a solution u to the linearized pseudo-Einstein equation, possessing Heisenberg spherical symmetry, and such that u(x) → - ∞ as | x | → + ∞.

  1. Tank 241-AX-101, grab samples, 1AX-97-1 through 1AX-97-3 analytical results for the final report

    International Nuclear Information System (INIS)

    Esch, R.A.

    1997-01-01

    This document is the final report for tank 241-AX-101 grab samples. Four grab samples were collected from riser 5B on July 29, 1997. Analyses were performed on samples 1AX-97-1, 1AX-97-2 and 1AX-97-3 in accordance with the Compatibility Grab Sampling and Analysis Plan (TSAP) and the Data Quality Objectives for Tank Farms Waste Compatibility Program (DQO) (Rev. 1: Fowler, 1995; Rev. 2: Mulkey and Miller, 1997). The analytical results are presented in Table 1. No notification limits were exceeded. All four samples contained settled solids that appeared to be large salt crystals that precipitated upon cooling to ambient temperature. Less than 25 % settled solids were present in the first three samples, therefore only the supernate was sampled and analyzed. Sample 1AX-97-4 contained approximately 25.3 % settled solids. Compatibility analyses were not performed on this sample. Attachment 1 is provided as a cross-reference for relating the tank farm customer identification numbers with the 222-S Laboratory sample numbers and the portion of sample analyzed. Table 2 provides the appearance information. All four samples contained settled solids that appeared to be large salt crystal that precipitated upon cooling to ambient temperature. The settled solids in samples 1AX-97-1, 1AX-97-2 and 1AX-97-3 were less than 25% by volume. Therefore, for these three samples, two 15-mL subsamples were pipetted to the surface of the liquid and submitted to the laboratory for analysis. In addition, a portion of the liquid was taken from each of the these three samples to perform an acidified ammonia analysis. No analysis was performed on the settled solid portion of the samples. Sample 1AX-97-4 was reserved for the Process Chemistry group to perform boil down and dissolution testing in accordance with Letter of Instruction for Non-Routine Analysis of Single-Shell Tank 241-AX-101 Grab Samples (Field, 1997) (Correspondence 1). However, prior to the analysis, the sample was inadvertently

  2. Tank 241-AX-101 grab samples 1AX-97-1 through 1AX-97-3 analytical results for the final report

    Energy Technology Data Exchange (ETDEWEB)

    Esch, R.A.

    1997-11-13

    This document is the final report for tank 241-AX-101 grab samples. Four grab samples were collected from riser 5B on July 29, 1997. Analyses were performed on samples 1AX-97-1, 1AX-97-2 and 1AX-97-3 in accordance with the Compatibility Grab Sampling and Analysis Plan (TSAP) and the Data Quality Objectives for Tank Farms Waste Compatibility Program (DQO) (Rev. 1: Fowler, 1995; Rev. 2: Mulkey and Miller, 1997). The analytical results are presented in Table 1. No notification limits were exceeded. All four samples contained settled solids that appeared to be large salt crystals that precipitated upon cooling to ambient temperature. Less than 25 % settled solids were present in the first three samples, therefore only the supernate was sampled and analyzed. Sample 1AX-97-4 contained approximately 25.3 % settled solids. Compatibility analyses were not performed on this sample. Attachment 1 is provided as a cross-reference for relating the tank farm customer identification numbers with the 222-S Laboratory sample numbers and the portion of sample analyzed. Table 2 provides the appearance information. All four samples contained settled solids that appeared to be large salt crystal that precipitated upon cooling to ambient temperature. The settled solids in samples 1AX-97-1, 1AX-97-2 and 1AX-97-3 were less than 25% by volume. Therefore, for these three samples, two 15-mL subsamples were pipetted to the surface of the liquid and submitted to the laboratory for analysis. In addition, a portion of the liquid was taken from each of the these three samples to perform an acidified ammonia analysis. No analysis was performed on the settled solid portion of the samples. Sample 1AX-97-4 was reserved for the Process Chemistry group to perform boil down and dissolution testing in accordance with Letter of Instruction for Non-Routine Analysis of Single-Shell Tank 241-AX-101 Grab Samples (Field, 1997) (Correspondence 1). However, prior to the analysis, the sample was inadvertently

  3. Linear causal modeling with structural equations

    CERN Document Server

    Mulaik, Stanley A

    2009-01-01

    Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal

  4. Some applications of the notion of duality in the research of support functions of the solutions of linear equations; Quelques applications de la notion de dualite a la recherche de fonctions d'appui de solutions d'equations lineaires

    Energy Technology Data Exchange (ETDEWEB)

    Martinet, B [Commissariat a l' Energie Atomique, Grenoble (France). Centre d' Etudes Nucleaires

    1969-07-01

    Let us consider the linear equation: Ax = b where A is a linear continue application of E in F (E and F are Banach spaces), b is an element of F approximately known x the unknown: a priori x belongs to C (C is a convex set of E). The set of solutions for this problem is defined by: D =[x belongs to C| ||Ax - b|| {<=}{epsilon}] {epsilon} given positive number. D is described by the set of values that takes when x belongs to D (c is a fixed element of the dual of E). The convex optimisation problems must be solved: (1) inf (sup) ( | x belongs to D). We find that the dual problems of (1) are very interesting intermediaries for the theoretic study (existence) as well as for the search of approximate solutions algorithms. The following example (which is by itself interesting: moment problem) is carefully studied:D= [{mu}: RADON non negative measures on [0,1] | {sigma} i = 1 to n [{integral}0 to 1 ai(t)d{mu}-bi]{sup 2} {<=} {epsilon}{sup 2}] inf (sup)[{integral}0 to 1 c(t)d{mu} | x belongs to D]. (author) [French] Soit l'equation lineaire: Ax = b ou A est une application lineaire continue de E dans F (E,F sont des espaces de Banach), b un element de F connu approximativement, x l'inconnue: on sait a priori que x appartient a C (C partie convexe de E). On definit l'ensemble des solutions de ce probleme par: D =[x appartient a C| ||Ax - b|| {<=}{epsilon}] {epsilon} nombre positif donne. On decrit D par l'ensemble des valeurs que peut prendre lorsque x parcourt D (c element fixe du dual de E), On doit resoudre les problemes d'optimisation convexe: (1) inf (sup) ( | x appartient a D). Les problemes duaux de (1) apparaissent comme des intermediaires tres interessants tant pour l'etude theorique (existence) que pour la recherche d'algorithmes de resolution approchee. On etudie tout particulierement l'exemple suivant (qui presente un interet propre: probleme des moments): D[{mu}: mesures de RADON non negatives sur [0,1] | {sigma} i = 1 to n [{integral}0 to

  5. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

    Directory of Open Access Journals (Sweden)

    Hamidreza Rezazadeh

    2014-05-01

    Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

  6. Adapting the γ-H2AX assay for automated processing in human lymphocytes. 1. Technological aspects.

    Science.gov (United States)

    Turner, Helen C; Brenner, David J; Chen, Youhua; Bertucci, Antonella; Zhang, Jian; Wang, Hongliang; Lyulko, Oleksandra V; Xu, Yanping; Shuryak, Igor; Schaefer, Julia; Simaan, Nabil; Randers-Pehrson, Gerhard; Yao, Y Lawrence; Amundson, Sally A; Garty, Guy

    2011-03-01

    The immunofluorescence-based detection of γ-H2AX is a reliable and sensitive method for quantitatively measuring DNA double-strand breaks (DSBs) in irradiated samples. Since H2AX phosphorylation is highly linear with radiation dose, this well-established biomarker is in current use in radiation biodosimetry. At the Center for High-Throughput Minimally Invasive Radiation Biodosimetry, we have developed a fully automated high-throughput system, the RABIT (Rapid Automated Biodosimetry Tool), that can be used to measure γ-H2AX yields from fingerstick-derived samples of blood. The RABIT workstation has been designed to fully automate the γ-H2AX immunocytochemical protocol, from the isolation of human blood lymphocytes in heparin-coated PVC capillaries to the immunolabeling of γ-H2AX protein and image acquisition to determine fluorescence yield. High throughput is achieved through the use of purpose-built robotics, lymphocyte handling in 96-well filter-bottomed plates, and high-speed imaging. The goal of the present study was to optimize and validate the performance of the RABIT system for the reproducible and quantitative detection of γ-H2AX total fluorescence in lymphocytes in a multiwell format. Validation of our biodosimetry platform was achieved by the linear detection of a dose-dependent increase in γ-H2AX fluorescence in peripheral blood samples irradiated ex vivo with γ rays over the range 0 to 8 Gy. This study demonstrates for the first time the optimization and use of our robotically based biodosimetry workstation to successfully quantify γ-H2AX total fluorescence in irradiated peripheral lymphocytes.

  7. Systems of Inhomogeneous Linear Equations

    Science.gov (United States)

    Scherer, Philipp O. J.

    Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.

  8. Diffusion phenomenon for linear dissipative wave equations

    KAUST Repository

    Said-Houari, Belkacem

    2012-01-01

    In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.

  9. A new linearized equation for servo valve in hydraulic control systems

    International Nuclear Information System (INIS)

    Kim, Tae Hyung; Lee, Ill Yeong

    2002-01-01

    In the procedure of the hydraulic control system analysis, a linearized approximate equation described by the first order term of Taylor's series has been widely used. Such a linearized equation is effective just near the operating point. And, as of now, there are no general standards on how to determine the operating point of a servo valve in the process of applying the linearized equation. So, in this study, a new linearized equation for valve characteristics is proposed as a modified form of the existing linearized equation. And, a method for selecting an optimal operating point is proposed for the new linearized equation. The effectiveness of the new linearized equation is confirmed through numerical simulations and experiments for a model hydraulic control system

  10. Hypocoercivity for linear kinetic equations conserving mass

    KAUST Repository

    Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian

    2015-01-01

    We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

  11. Hypocoercivity for linear kinetic equations conserving mass

    KAUST Repository

    Dolbeault, Jean

    2015-02-03

    We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

  12. General solutions of second-order linear difference equations of Euler type

    Directory of Open Access Journals (Sweden)

    Akane Hongyo

    2017-01-01

    Full Text Available The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \\(y^{\\prime\\prime}+(\\lambda/t^2y=0\\ or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.

  13. Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

    OpenAIRE

    Nakamura, Gen; Vashisth, Manmohan

    2017-01-01

    In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...

  14. The numerical solution of linear multi-term fractional differential equations: systems of equations

    Science.gov (United States)

    Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

    2002-11-01

    In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

  15. Infinite sets of conservation laws for linear and non-linear field equations

    International Nuclear Information System (INIS)

    Niederle, J.

    1984-01-01

    The work was motivated by a desire to understand group theoretically the existence of an infinite set of conservation laws for non-interacting fields and to carry over these conservation laws to the case of interacting fields. The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of its space-time symmetry group was established. It is shown that in the case of the Korteweg-de Vries (KdV) equation to each symmetry of the corresponding linear equation delta sub(o)uxxx=u sub() determined by an element of the enveloping algebra of the space translation algebra, there corresponds a symmetry of the full KdV equation

  16. Invariant imbedding equations for linear scattering problems

    International Nuclear Information System (INIS)

    Apresyan, L.

    1988-01-01

    A general form of the invariant imbedding equations is investigated for the linear problem of scattering by a bounded scattering volume. The conditions for the derivability of such equations are described. It is noted that the possibility of the explicit representation of these equations for a sphere and for a layer involves the separation of variables in the unperturbed wave equation

  17. Linear Einstein equations and Kerr-Schild maps

    International Nuclear Information System (INIS)

    Gergely, Laszlo A

    2002-01-01

    We prove that given a solution of the Einstein equations g ab for the matter field T ab , an autoparallel null vector field l a and a solution (l a l c , T ac ) of the linearized Einstein equation on the given background, the Kerr-Schild metric g ac + λl a l c (λ arbitrary constant) is an exact solution of the Einstein equation for the energy-momentum tensor T ac + λT ac + λ 2 l (a T c)b l b . The mixed form of the Einstein equation for Kerr-Schild metrics with autoparallel null congruence is also linear. Some more technical conditions hold when the null congruence is not autoparallel. These results generalize previous theorems for vacuum due to Xanthopoulos and for flat seed spacetime due to Guerses and Guersey

  18. Analytical exact solution of the non-linear Schroedinger equation

    International Nuclear Information System (INIS)

    Martins, Alisson Xavier; Rocha Filho, Tarcisio Marciano da

    2011-01-01

    Full text: In this work we present how to classify and obtain analytical solutions of the Schroedinger equation with a generic non-linearity in 1+1 dimensions. Our approach is based on the determination of Lie symmetry transformation mapping solutions into solutions, and non-classical symmetry transformations, mapping a given solution into itself. From these symmetries it is then possible to reduce the equation to a system of ordinary differential equations which can then be solved using standard methods. The generic non-linearity is handled by considering it as an additional unknown in the determining equations for the symmetry transformations. This results in an over-determined system of non-linear partial differential equations. Its solution can then be determined in some cases by reducing it to the so called involutive (triangular) form, and then solved. This reduction is very tedious and can only performed using a computer algebra system. Once the determining system is solved, we obtain the explicit form for the non-linearity admitting a Lie or non-classical symmetry. The analytical solutions are then derived by solving the reduced ordinary differential equations. The non-linear determining system for the non-classical symmetry transformations and Lie symmetry generators are obtaining using the computer algebra package SADE (symmetry analysis of differential equations), developed at our group. (author)

  19. A preliminary study to detect CT radiation doses by using the γH2AX focus formation assay

    International Nuclear Information System (INIS)

    Zhang Bo; Gong Jianping; Zhang Wei; Yu Zeyang; Zhou Liying; Zhang Hong; Fu Jinxiang

    2010-01-01

    To prospectively determine if γH2AX (phosphorylated form of H2AX histone variant)-based visualization and quantification of DNA damage induced in peripheral blood mononuclear cells (PBMCs) can be used to estimate the radiation dose received after multi-detector computed tomography (CT) by the in vitro study, comprehend the correlation between the dose and the induced γH2AX foci, and explore its prospect. The result showed that, DNA damage first presented as γH2AX foci after CT, which can be detected by fluorescence microscope. The γH2AX focus yields linearly depend on the radiation dose after CT. γH2AX focus yield in blood cells may be a useful quantitative biomarker of human radiation exposure by CT scans. (authors)

  20. Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

    Science.gov (United States)

    Freund, Roland W.

    1991-01-01

    We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

  1. Non-linear wave equations:Mathematical techniques

    International Nuclear Information System (INIS)

    1978-01-01

    An account of certain well-established mathematical methods, which prove useful to deal with non-linear partial differential equations is presented. Within the strict framework of Functional Analysis, it describes Semigroup Techniques in Banach Spaces as well as variational approaches towards critical points. Detailed proofs are given of the existence of local and global solutions of the Cauchy problem and of the stability of stationary solutions. The formal approach based upon invariance under Lie transformations deserves attention due to its wide range of applicability, even if the explicit solutions thus obtained do not allow for a deep analysis of the equations. A compre ensive introduction to the inverse scattering approach and to the solution concept for certain non-linear equations of physical interest are also presented. A detailed discussion is made about certain convergence and stability problems which arise in importance need not be emphasized. (author) [es

  2. Sensitivity theory for general non-linear algebraic equations with constraints

    International Nuclear Information System (INIS)

    Oblow, E.M.

    1977-04-01

    Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

  3. Developing SSRS reports for dynamics AX

    CERN Document Server

    Hirwani, Mukesh

    2013-01-01

    Written as a step-by-step tutorial, covering all technical aspects of AX 2012 reporting to enable you to quickly learn to and develop reports.This book is ideal for developers and administrators, who deal with Microsoft Dynamics AX 2012 reporting in day-to-day scenarios. No prior exposure to Dynamics AX 2012 reporting is assumed. Readers must know about AX architecture, about the AOT, basic X++ skills, and the basics of SSRS.

  4. Test Results for Caustic Demand Measurements on Tank 241-AX-101 and Tank 241-AX-103 Archive Samples

    International Nuclear Information System (INIS)

    Doll, Stephanie R.; Bolling, Stacie D.

    2016-01-01

    Caustic demand testing is used to determine the necessary amount of caustic required to neutralize species present in the Hanford tank waste and obtain a target molarity of free hydroxide for tank corrosion control. The presence and quantity of hydroxide-consuming analytes are just as important in determining the caustic demand as is the amount of free hydroxide present. No single data point can accurately predict whether a satisfactory hydroxide level is being met, as it is dependent on multiple factors (e.g., free hydroxide, buffers, amphoteric metal hydroxides, bicarbonate, etc.). This enclosure contains the caustic demand, scanning electron microscopy (SEM), polarized light microscopy (PLM), and X-ray diffraction (XRD) analysis for the tank 241-AX-101 (AX-101) and 241-AX-103 (AX-103) samples. The work was completed to fulfill a customer request outlined in the test plan, WRPS-1505529, ''Test Plan and Procedure for Caustic Demand Testing on Tank 241-AX-101 and Tank 241-AX-103 Archive Samples.'' The work results will provide a baseline to support planned retrieval of AX-101 and AX-103.

  5. Test Results for Caustic Demand Measurements on Tank 241-AX-101 and Tank 241-AX-103 Archive Samples

    Energy Technology Data Exchange (ETDEWEB)

    Doll, Stephanie R. [Washington River Protection Solutions, Richland, WA (United States); Bolling, Stacie D. [Washington River Protection Solutions, Richland, WA (United States)

    2016-07-14

    Caustic demand testing is used to determine the necessary amount of caustic required to neutralize species present in the Hanford tank waste and obtain a target molarity of free hydroxide for tank corrosion control. The presence and quantity of hydroxide-consuming analytes are just as important in determining the caustic demand as is the amount of free hydroxide present. No single data point can accurately predict whether a satisfactory hydroxide level is being met, as it is dependent on multiple factors (e.g., free hydroxide, buffers, amphoteric metal hydroxides, bicarbonate, etc.). This enclosure contains the caustic demand, scanning electron microscopy (SEM), polarized light microscopy (PLM), and X-ray diffraction (XRD) analysis for the tank 241-AX-101 (AX-101) and 241-AX-103 (AX-103) samples. The work was completed to fulfill a customer request outlined in the test plan, WRPS-1505529, “Test Plan and Procedure for Caustic Demand Testing on Tank 241-AX-101 and Tank 241-AX-103 Archive Samples.” The work results will provide a baseline to support planned retrieval of AX-101 and AX-103.

  6. Dynamical symmetries of semi-linear Schrodinger and diffusion equations

    International Nuclear Information System (INIS)

    Stoimenov, Stoimen; Henkel, Malte

    2005-01-01

    Conditional and Lie symmetries of semi-linear 1D Schrodinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrodinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf 3 ) C . We consider non-hermitian representations and also include a dimensionful coupling constant of the non-linearity. The corresponding representations of the parabolic and almost-parabolic subalgebras of (conf 3 ) C are classified and the complete list of conditionally invariant semi-linear Schrodinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed

  7. Half-trek criterion for generic identifiability of linear structural equation models

    NARCIS (Netherlands)

    Foygel, R.; Draisma, J.; Drton, M.

    2012-01-01

    A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations

  8. Half-trek criterion for generic identifiability of linear structural equation models

    NARCIS (Netherlands)

    Foygel, R.; Draisma, J.; Drton, M.

    2011-01-01

    A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations

  9. Introduction to linear systems of differential equations

    CERN Document Server

    Adrianova, L Ya

    1995-01-01

    The theory of linear systems of differential equations is one of the cornerstones of the whole theory of differential equations. At its root is the concept of the Lyapunov characteristic exponent. In this book, Adrianova presents introductory material and further detailed discussions of Lyapunov exponents. She also discusses the structure of the space of solutions of linear systems. Classes of linear systems examined are from the narrowest to widest: 1)�autonomous, 2)�periodic, 3)�reducible to autonomous, 4)�nearly reducible to autonomous, 5)�regular. In addition, Adrianova considers the following: stability of linear systems and the influence of perturbations of the coefficients on the stability the criteria of uniform stability and of uniform asymptotic stability in terms of properties of the solutions several estimates of the growth rate of solutions of a linear system in terms of its coefficients How perturbations of the coefficients change all the elements of the spectrum of the system is defin...

  10. GLOBAL LINEARIZATION OF DIFFERENTIAL EQUATIONS WITH SPECIAL STRUCTURES

    Institute of Scientific and Technical Information of China (English)

    2011-01-01

    This paper introduces the global linearization of the differential equations with special structures.The function in the differential equation is unbounded.We prove that the differential equation with unbounded function can be topologically linearlized if it has a special structure.

  11. Geometric Insight into Scalar Combination of Linear Equations

    Indian Academy of Sciences (India)

    ... Journals; Resonance – Journal of Science Education; Volume 14; Issue 11. Geometric Insight into Scalar Combination of Linear Equations. Ranjit Konkar. Classroom Volume 14 Issue 11 November 2009 pp 1092-1097 ... Keywords. Linear algebra; linear dependence; linear combination; family of lines; family of planes.

  12. Study of the dose-effect relationship of γ-H2AX radiation

    International Nuclear Information System (INIS)

    Cui Shuangshuang; Fan Yaguang; Gun Zhijuan; Wang Jixian; Zhao Yongcheng; Sun Yuping

    2010-01-01

    Objective: By using laser scanning confocal microscopy (LSCM) to test the dose-effects relationship between ionizing radiation intensity and quantity of the γ-H2AX in vivo and in vitro respectively, and the consistency relationship between the vivo and vitro retrial. Methods: To irradiate the peripheral blood from Wister female rats by 137 Cs at 7 with different doses (0, 0.5, 1, 2, 2.54, 4, 6, 8 Gy) extract the lymphocytes from the peripheral blood and detect the dose-effects relationship between irradiation intensity and number of γ-H2AX foci. Results: There are good dose-effects relationships between the irradiation and foci number both in vivo and in vitro, which are linear, Y vivo =0.096+0.13X; Y vitro =0.040+0.21X. And there is good consistency (R=0.98) between the γ-H2AX in vivo and in vitro. Conclusions: γ-H2AX has the possibility for clinical trial as an indicator, and we can use vitro trials in place of the vivo trails to evaluate the dose people received. (authors)

  13. What happens to linear properties as we move from the Klein-Gordon equation to the sine-Gordon equation

    International Nuclear Information System (INIS)

    Kovalyov, Mikhail

    2010-01-01

    In this article the sets of solutions of the sine-Gordon equation and its linearization the Klein-Gordon equation are discussed and compared. It is shown that the set of solutions of the sine-Gordon equation possesses a richer structure which partly disappears during linearization. Just like the solutions of the Klein-Gordon equation satisfy the linear superposition principle, the solutions of the sine-Gordon equation satisfy a nonlinear superposition principle.

  14. Emmy Noether and Linear Evolution Equations

    Directory of Open Access Journals (Sweden)

    P. G. L. Leach

    2013-01-01

    Full Text Available Noether’s Theorem relates the Action Integral of a Lagrangian with symmetries which leave it invariant and the first integrals consequent upon the variational principle and the existence of the symmetries. These each have an equivalent in the Schrödinger Equation corresponding to the Lagrangian and by extension to linear evolution equations in general. The implications of these connections are investigated.

  15. Simplified Linear Equation Solvers users manual

    Energy Technology Data Exchange (ETDEWEB)

    Gropp, W. [Argonne National Lab., IL (United States); Smith, B. [California Univ., Los Angeles, CA (United States)

    1993-02-01

    The solution of large sparse systems of linear equations is at the heart of many algorithms in scientific computing. The SLES package is a set of easy-to-use yet powerful and extensible routines for solving large sparse linear systems. The design of the package allows new techniques to be used in existing applications without any source code changes in the applications.

  16. A linearizing transformation for the Korteweg-de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations

    NARCIS (Netherlands)

    Dorren, H.J.S.

    1998-01-01

    It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of

  17. Construction of a Roe linearization for the ideal MHD equations

    International Nuclear Information System (INIS)

    Cargo, P.; Gallice, G.; Raviart, P.A.

    1996-01-01

    In [3], Munz has constructed a Roe linearization for the equations of gas dynamics in Lagrangian coordinates. We extend this construction to the case of the ideal magnetohydrodynamics equations again in Lagrangian coordinates. As a consequence we obtain a Roe linearization for the MHD equations in Eulerian coordinates. (author)

  18. Variational linear algebraic equations method

    International Nuclear Information System (INIS)

    Moiseiwitsch, B.L.

    1982-01-01

    A modification of the linear algebraic equations method is described which ensures a variational bound on the phaseshifts for potentials having a definite sign at all points. The method is illustrated by the elastic scattering of s-wave electrons by the static field of atomic hydrogen. (author)

  19. Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

    Science.gov (United States)

    Freund, Roland

    1989-01-01

    We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

  20. Rational approximations to solutions of linear differential equations.

    Science.gov (United States)

    Chudnovsky, D V; Chudnovsky, G V

    1983-08-01

    Rational approximations of Padé and Padé type to solutions of differential equations are considered. One of the main results is a theorem stating that a simultaneous approximation to arbitrary solutions of linear differential equations over C(x) cannot be "better" than trivial ones implied by the Dirichlet box principle. This constitutes, in particular, the solution in the linear case of Kolchin's problem that the "Roth's theorem" holds for arbitrary solutions of algebraic differential equations. Complete effective proofs for several valuations are presented based on the Wronskian methods and graded subrings of Picard-Vessiot extensions.

  1. Non-linear effects in the Boltzmann equation

    International Nuclear Information System (INIS)

    Barrachina, R.O.

    1985-01-01

    The Boltzmann equation is studied by defining an integral transformation of the energy distribution function for an isotropic and homogeneous gas. This transformation may be interpreted as a linear superposition of equilibrium states with variable temperatures. It is shown that the temporal evolution features of the distribution function are determined by the singularities of said transformation. This method is applied to Maxwell and Very Hard Particle interaction models. For the latter, the solution of the Boltzmann equation with the solution of its linearized version is compared, finding out many basic discrepancies and non-linear effects. This gives a hint to propose a new rational approximation method with a clear physical meaning. Applying this technique, the relaxation features of the BKW (Bobylev, Krook anf Wu) mode is analyzed, finding a conclusive counter-example for the Krook and Wu conjecture. The anisotropic Boltzmann equation for Maxwell models is solved as an expansion in terms of the eigenfunctions of the corresponding linearized collision operator, finding interesting transient overpopulation and underpopulation effects at thermal energies as well as a new preferential spreading effect. By analyzing the initial collision, a criterion is established to deduce the general features of the final approach to equilibrium. Finally, it is shown how to improve the convergence of the eigenfunction expansion for high energy underpopulated distribution functions. As an application of this theory, the linear cascade model for sputtering is analyzed, thus finding out that many differences experimentally observed are due to non-linear effects. (M.E.L.) [es

  2. Asymptotic properties for half-linear difference equations

    Czech Academy of Sciences Publication Activity Database

    Cecchi, M.; Došlá, Z.; Marini, M.; Vrkoč, Ivo

    2006-01-01

    Roč. 131, č. 4 (2006), s. 347-363 ISSN 0862-7959 R&D Projects: GA ČR(CZ) GA201/04/0580 Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear second order difference equation * nonoscillatory solutions * Riccati difference equation Subject RIV: BA - General Mathematics

  3. Students' errors in solving linear equation word problems: Case ...

    African Journals Online (AJOL)

    The study examined errors students make in solving linear equation word problems with a view to expose the nature of these errors and to make suggestions for classroom teaching. A diagnostic test comprising 10 linear equation word problems, was administered to a sample (n=130) of senior high school first year Home ...

  4. New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

    Science.gov (United States)

    Chen, Haiwen; Holland, Paul

    2010-01-01

    In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

  5. Age-related disease association of endogenous γ-H2AX foci in mononuclear cells derived from leukapheresis.

    Directory of Open Access Journals (Sweden)

    Shepherd H Schurman

    Full Text Available The phosphorylated form of histone H2AX (γ-H2AX forms immunohistochemically detectable foci at DNA double strand breaks. In peripheral blood mononuclear cells (PBMCs derived from leukapheresis from patients enrolled in the Baltimore Longitudinal Study of Aging, γ-H2AX foci increased in a linear fashion with regards to age, peaking at ~57 years. The relationship between the frequency of γ-H2AX foci and age-related pathologies was assessed. We found a statistically significant (p = 0.023 50% increase in foci in PBMCs derived from patients with a known history of vitamin D deficiency. In addition, there were trends toward increased γ-H2AX foci in patients with cataracts (34% increase, p<0.10 and in sleep apnea patients (44%, p<0.10. Among patients ≥57 y/o, we found a significant (p = 0.037 36% increase in the number of γ-H2AX foci/cell for patients with hypertension compared to non-hypertensive patients. Our results support a role for increased DNA damage in the morbidity of age-related diseases. γ -H2AX may be a biomarker for human morbidity in age-related diseases.

  6. High-order quantum algorithm for solving linear differential equations

    International Nuclear Information System (INIS)

    Berry, Dominic W

    2014-01-01

    Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms to general inhomogeneous sparse linear differential equations, which describe many classical physical systems. We examine the use of high-order methods (where the error over a time step is a high power of the size of the time step) to improve the efficiency. These provide scaling close to Δt 2 in the evolution time Δt. As with other algorithms of this type, the solution is encoded in amplitudes of the quantum state, and it is possible to extract global features of the solution. (paper)

  7. Periodic feedback stabilization for linear periodic evolution equations

    CERN Document Server

    Wang, Gengsheng

    2016-01-01

    This book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.

  8. Non-resonant oscillations for some third-order differential equations II

    International Nuclear Information System (INIS)

    Ezeilo, J.O.C.; Omari, P.

    1987-11-01

    The existence of 2π-periodic solutions to the equation x'''+ax''+g(t,x')+cx=p(t) is proved, under certain non-resonance conditions on the non-linear function g(t,y). Here a,c are constants, but the case where a,c are not necessarily constants is also discussed, subject to some rather special non-resonance conditions on g. The uniqueness of the solutions is also examined. (author). 12 refs

  9. Infinite sets of conservation laws for linear and nonlinear field equations

    International Nuclear Information System (INIS)

    Mickelsson, J.

    1984-01-01

    The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of the space-time symmetry group is established. It is shown that each symmetric element of the enveloping algebra of the space-time symmetry group of a linear field equation generates a one-parameter group of symmetries of the field equation. The cases of the Maxwell and Dirac equations are studied in detail. Then it is shown that (at least in the sense of a power series in the 'coupling constant') the conservation laws of the linear case can be deformed to conservation laws of a nonlinear field equation which is obtained from the linear one by adding a nonlinear term invariant under the group of space-time symmetries. As an example, our method is applied to the Korteweg-de Vries equation and to the massless Thirring model. (orig.)

  10. A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

    Science.gov (United States)

    Chen, Haiwen

    2012-01-01

    In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

  11. Dual exponential polynomials and linear differential equations

    Science.gov (United States)

    Wen, Zhi-Tao; Gundersen, Gary G.; Heittokangas, Janne

    2018-01-01

    We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.

  12. Exact non-linear equations for cosmological perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Gong, Jinn-Ouk [Asia Pacific Center for Theoretical Physics, Pohang 37673 (Korea, Republic of); Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 41566 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 34055 (Korea, Republic of); Wu, David Chan Lon; Yoo, Jaiyul, E-mail: jinn-ouk.gong@apctp.org, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: clwu@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch [Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, Universität Zürich, CH-8057 Zürich (Switzerland)

    2017-10-01

    We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations—scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.

  13. Spatiotemporal kinetics of γ-H2AX protein on charged particles induced DNA damage

    Energy Technology Data Exchange (ETDEWEB)

    Niu, H., E-mail: hniu@mx.nthu.edu.tw [Nuclear Science and Technology Development Center, National Tsing Hua University, Hsinchu, Taiwan (China); Chang, H.C. [Department of Biomedical Engineering and Environmental Sciences, National Tsing Hua University, Hsinchu, Taiwan (China); Cho, I.C. [Institute for Radiological Research, Chang Gung University and Chang Gung Memorial Hospital, Taoyuan, Taiwan (China); Chen, C.H. [Nuclear Science and Technology Development Center, National Tsing Hua University, Hsinchu, Taiwan (China); Liu, C.S. [Cancer Center of Taipei Veterans General Hospital, Taipei, Taiwan (China); Chou, W.T. [Department of Biomedical Engineering and Environmental Sciences, National Tsing Hua University, Hsinchu, Taiwan (China)

    2014-08-15

    Highlights: • Charged particles can induce more complex DNA damages, and these complex damages have higher ability to cause the cell death or cell carcinogenesis. • In this study, we used γ-H2AX protein to investigate the spatiotemporal kinetics of DNA double strand breaks in particle irradiated HeLa cells. • The HeLa cells were irradiated by 400 keV alpha-particles in four different dosages. • The result shows that a good linear relationship can be observed between foci number and radiation dose. • The data shows that the dissolution rate of γ-H2AX foci agree with the two components DNA repairing model, and it was decreasing as the radiation dose increased. • These results suggest that charged particles can induce more complex DNA damages and causing the retardation of DNA repair. - Abstract: In several researches, it has been demonstrated that charged particles can induce more complex DNA damages. These complex damages have higher ability to cause the cell death or cell carcinogenesis. For this reason, clarifying the DNA repair mechanism after charged particle irradiation plays an important role in the development of charged particle therapy and space exploration. Unfortunately, the detail spatiotemporal kinetic of DNA damage repair is still unclear. In this study, we used γ-H2AX protein to investigate the spatiotemporal kinetics of DNA double strand breaks in alpha-particle irradiated HeLa cells. The result shows that the intensity of γ-H2AX foci increased gradually, and reached to its maximum at 30 min after irradiation. A good linear relationship can be observed between foci intensity and radiation dose. After 30 min, the γ-H2AX foci intensity was decreased with time passed, but remained a large portion (∼50%) at 48 h passed. The data show that the dissolution rate of γ-H2AX foci agreed with two components DNA repairing model. These results suggest that charged particles can induce more complex DNA damages and causing the retardation of DNA

  14. Inverse scattering solution of non-linear evolution equations in one space dimension: an introduction

    International Nuclear Information System (INIS)

    Alvarez-Estrada, R.F.

    1979-01-01

    A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly

  15. HESS Opinions: Linking Darcy's equation to the linear reservoir

    Science.gov (United States)

    Savenije, Hubert H. G.

    2018-03-01

    In groundwater hydrology, two simple linear equations exist describing the relation between groundwater flow and the gradient driving it: Darcy's equation and the linear reservoir. Both equations are empirical and straightforward, but work at different scales: Darcy's equation at the laboratory scale and the linear reservoir at the watershed scale. Although at first sight they appear similar, it is not trivial to upscale Darcy's equation to the watershed scale without detailed knowledge of the structure or shape of the underlying aquifers. This paper shows that these two equations, combined by the water balance, are indeed identical provided there is equal resistance in space for water entering the subsurface network. This implies that groundwater systems make use of an efficient drainage network, a mostly invisible pattern that has evolved over geological timescales. This drainage network provides equally distributed resistance for water to access the system, connecting the active groundwater body to the stream, much like a leaf is organized to provide all stomata access to moisture at equal resistance. As a result, the timescale of the linear reservoir appears to be inversely proportional to Darcy's conductance, the proportionality being the product of the porosity and the resistance to entering the drainage network. The main question remaining is which physical law lies behind pattern formation in groundwater systems, evolving in a way that resistance to drainage is constant in space. But that is a fundamental question that is equally relevant for understanding the hydraulic properties of leaf veins in plants or of blood veins in animals.

  16. ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

    Science.gov (United States)

    Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

    2018-04-01

    In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

  17. MAIA, Eigenvalues for MHD Equation of Tokamak Plasma Stability Problems

    International Nuclear Information System (INIS)

    Tanaka, Y.; Azumi, M.; Kurita, G.; Tsunematsu, T.; Takeda, T.

    1986-01-01

    1 - Description of program or function: This program solves an eigenvalue problem zBx=Ax where A and B are real block tri-diagonal matrices. This eigenvalue problem is derived from a reduced set of linear resistive MHD equations which is often employed to study tokamak plasma stability problem. 2 - Method of solution: Both the determinant and inverse iteration methods are employed. 3 - Restrictions on the complexity of the problem: The eigenvalue z must be real

  18. Integration of differential equations by the pseudo-linear (PL) approximation

    International Nuclear Information System (INIS)

    Bonalumi, Riccardo A.

    1998-01-01

    A new method of integrating differential equations was originated with the technique of approximately calculating the integrals called the pseudo-linear (PL) procedure: this method is A-stable. This article contains the following examples: 1st order ordinary differential equations (ODEs), 2nd order linear ODEs, stiff system of ODEs (neutron kinetics), one-dimensional parabolic (diffusion) partial differential equations. In this latter case, this PL method coincides with the Crank-Nicholson method

  19. Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

    Science.gov (United States)

    El-Gebeily, M.; Yushau, B.

    2008-01-01

    In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

  20. On Positive Solutions for the Rational Difference Equation Systems x n+1 = A/x n y n (2), and y n+1 = By n /x n-1 y n-1.

    Science.gov (United States)

    Ma, Hui-Li; Feng, Hui

    2014-01-01

    Our aim in this paper is to investigate the behavior of positive solutions for the following systems of rational difference equations: x n+1 = A/x n y n (2), and y n+1 = By n /x n-1 y n-1, n = 0,1,…, where x -1, x 0, y -1, and y 0 are positive real numbers and A and B are positive constants.

  1. Linear matrix differential equations of higher-order and applications

    Directory of Open Access Journals (Sweden)

    Mustapha Rachidi

    2008-07-01

    Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.

  2. Equations of motion for a (non-linear) scalar field model as derived from the field equations

    International Nuclear Information System (INIS)

    Kaniel, S.; Itin, Y.

    2006-01-01

    The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  3. Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations

    International Nuclear Information System (INIS)

    Kaikina, Elena I; Naumkin, Pavel I; Shishmarev, Il'ya A

    2009-01-01

    The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.

  4. A General Linear Method for Equating with Small Samples

    Science.gov (United States)

    Albano, Anthony D.

    2015-01-01

    Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…

  5. A local-global problem for linear differential equations

    NARCIS (Netherlands)

    Put, Marius van der; Reversat, Marc

    An inhomogeneous linear differential equation Ly = f over a global differential field can have a formal solution for each place without having a global solution. The vector space lgl(L) measures this phenomenon. This space is interpreted in terms of cohomology of linear algebraic groups and is

  6. A local-global problem for linear differential equations

    NARCIS (Netherlands)

    Put, Marius van der; Reversat, Marc

    2008-01-01

    An inhomogeneous linear differential equation Ly = f over a global differential field can have a formal solution for each place without having a global solution. The vector space lgl(L) measures this phenomenon. This space is interpreted in terms of cohomology of linear algebraic groups and is

  7. Iterative solution of linear equations in ODE codes. [Krylov subspaces

    Energy Technology Data Exchange (ETDEWEB)

    Gear, C. W.; Saad, Y.

    1981-01-01

    Each integration step of a stiff equation involves the solution of a nonlinear equation, usually by a quasi-Newton method that leads to a set of linear problems. Iterative methods for these linear equations are studied. Of particular interest are methods that do not require an explicit Jacobian, but can work directly with differences of function values using J congruent to f(x + delta) - f(x). Some numerical experiments using a modification of LSODE are reported. 1 figure, 2 tables.

  8. Runge-Kutta Methods for Linear Ordinary Differential Equations

    Science.gov (United States)

    Zingg, David W.; Chisholm, Todd T.

    1997-01-01

    Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

  9. Dicentric chromosomes and γ-H2AX foci formation in lymphocytes of human blood samples exposed to a CT scanner: A direct comparison of dose response relationships

    International Nuclear Information System (INIS)

    Golfier, S.; Jost, G.; Pietsch, H.; Lengsfeld, P.; Eckardt-Schupp, F.; Schmid, E.; Voth, M.

    2009-01-01

    Experiments using the induction of dicentric chromosomes (dicentrics) as well as the γ-H2AX foci formation in lymphocytes of blood samples from a healthy donor were performed to directly evaluate the radiation sensitivity of both biological endpoints. For computed tomography scans at dose levels from 0.025 to 1 Gy, a linear-quadratic dose - response relationship for dicentrics and a linear dose - response relationship for γ-H2AX foci were obtained. The coefficients of the dose - response relationship for dicentrics are α = (3.76 ± 0.29) x 10 -2 Gy -1 and β = (5.54 ± 0.45) x 10 -2 Gy -2 , the linear coefficient for γ-H2AX foci is (7.38 ± 0.11) Gy -1 . The findings indicate that scoring of dicentrics as well as microscopic analysis of γ-H2AX foci are sensitive methods to quantify a radiation-induced biological damage at low doses. However, since γ-H2AX foci can be partially repaired within a few hours, biological damages present for days or even months, which constitute the clinically relevant endpoints, can only be quantified reliably by scoring of chromosome aberrations. Thus currently the quantification of dicentrics or reciprocal translocations remains the recommended method for estimating the effect of exposures to low dose levels of radiation ('biological dosimetry'). However, owing to the high radiation sensitivity of the γ-H2AX foci assay observed in the present study, further investigations on the effectiveness of low-linear energy transfer radiation qualities in producing γ-H2AX foci in lymphocytes from healthy donors should be performed. (authors)

  10. Dissipative behavior of some fully non-linear KdV-type equations

    Science.gov (United States)

    Brenier, Yann; Levy, Doron

    2000-03-01

    The KdV equation can be considered as a special case of the general equation u t+f(u) x-δg(u xx) x=0, δ>0, where f is non-linear and g is linear, namely f( u)= u2/2 and g( v)= v. As the parameter δ tends to 0, the dispersive behavior of the KdV equation has been throughly investigated (see, e.g., [P.G. Drazin, Solitons, London Math. Soc. Lect. Note Ser. 85, Cambridge University Press, Cambridge, 1983; P.D. Lax, C.D. Levermore, The small dispersion limit of the Korteweg-de Vries equation, III, Commun. Pure Appl. Math. 36 (1983) 809-829; G.B. Whitham, Linear and Nonlinear Waves, Wiley/Interscience, New York, 1974] and the references therein). We show through numerical evidence that a completely different, dissipative behavior occurs when g is non-linear, namely when g is an even concave function such as g( v)=-∣ v∣ or g( v)=- v2. In particular, our numerical results hint that as δ→0 the solutions strongly converge to the unique entropy solution of the formal limit equation, in total contrast with the solutions of the KdV equation.

  11. Darboux transformations and linear parabolic partial differential equations

    International Nuclear Information System (INIS)

    Arrigo, Daniel J.; Hickling, Fred

    2002-01-01

    Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (n+1) nonlinear partial differential equations. This system arises as the coefficients of a Darboux transformation and is equivalent to a matrix Burgers' equation. This matrix equation is solved using a generalized Hopf-Cole transformation. The solutions for the original equation are given in terms of solutions of the heat equation. These results are applied to the (1+1)-dimensional Schroedinger equation where all bound state solutions are obtained for a 2n-parameter family of potentials. As a special case, the solutions for integral members of the regular and modified Poeschl-Teller potentials are recovered. (author). Letter-to-the-editor

  12. Piecewise-linear and bilinear approaches to nonlinear differential equations approximation problem of computational structural mechanics

    OpenAIRE

    Leibov Roman

    2017-01-01

    This paper presents a bilinear approach to nonlinear differential equations system approximation problem. Sometimes the nonlinear differential equations right-hand sides linearization is extremely difficult or even impossible. Then piecewise-linear approximation of nonlinear differential equations can be used. The bilinear differential equations allow to improve piecewise-linear differential equations behavior and reduce errors on the border of different linear differential equations systems ...

  13. Solvable linear potentials in the Dirac equation

    International Nuclear Information System (INIS)

    Dominguez-Adame, F.; Gonzalez, M.A.

    1990-01-01

    The Dirac equation for some linear potentials leading to Schroedinger-like oscillator equations for the upper and lower components of the Dirac spinor have been solved. Energy levels for the bound states appear in pairs, so that both particles and antiparticles may be bound with the same energy. For weak coupling, the spacing between levels is proportional to the coupling constant while in the strong limit those levels are depressed compared to the nonrelativistic ones

  14. Human lymphocyte damage and phosphorylation of H2AX and ATM induced by γ-rays

    International Nuclear Information System (INIS)

    Tian Mei; Pan Yan; Liu Jianxiang; Ruan Jianlei; Su Xu

    2011-01-01

    Objective: To investigate 60 Co γ-ray induced damage in lymphocytes and the relationship between doses of 60 Co γ-ray irradiation and the levels of phosphorylated H2AX and ATM. Methods: Cells were irradiated with 60 Co γ-rays in the range of 0-8 Gy. The levels of phosphorylated H2AX and ATM were detected by Western blot and FACScan,respectively. The micronucleus(MN)was analyzed by CB method to evaluate DNA damage. Results: FACScan results showed the dose-effect relationship of γ-H2AX expression were linear.square at 0.5 h post-irradiation to different doses, and the fitting curve was shown as Y=3.96+11.29D-0.45D 2 . The level of phosphorylated ATM (p-ATM) was not changed significantly by using the same method. Western blot showed that p-ATM protein expression was significantly increased after irradiation compared with sham, irradiated group. The MN assay which represented DNA damage was sensitive to different doses. Conclusions: γ-ray irradiation could induce the phosphorylation of H2AX and ATM, which may play an important role in indicating DNA damage. Both of H2AX and ATM have the potential as sensitive biomarker and biodosimeter for radiation damage. (authors)

  15. Technological pedagogical content knowledge of junior high school mathematics teachers in teaching linear equation

    Science.gov (United States)

    Wati, S.; Fitriana, L.; Mardiyana

    2018-04-01

    Linear equation is one of the topics in mathematics that are considered difficult. Student difficulties of understanding linear equation can be caused by lack of understanding this concept and the way of teachers teach. TPACK is a way to understand the complex relationships between teaching and content taught through the use of specific teaching approaches and supported by the right technology tools. This study aims to identify TPACK of junior high school mathematics teachers in teaching linear equation. The method used in the study was descriptive. In the first phase, a survey using a questionnaire was carried out on 45 junior high school mathematics teachers in teaching linear equation. While in the second phase, the interview involved three teachers. The analysis of data used were quantitative and qualitative technique. The result PCK revealed teachers emphasized developing procedural and conceptual knowledge through reliance on traditional in teaching linear equation. The result of TPK revealed teachers’ lower capacity to deal with the general information and communications technologies goals across the curriculum in teaching linear equation. The result indicated that PowerPoint constitutes TCK modal technological capability in teaching linear equation. The result of TPACK seems to suggest a low standard in teachers’ technological skills across a variety of mathematics education goals in teaching linear equation. This means that the ability of teachers’ TPACK in teaching linear equation still needs to be improved.

  16. On some perturbation techniques for quasi-linear parabolic equations

    Directory of Open Access Journals (Sweden)

    Igor Malyshev

    1990-01-01

    Full Text Available We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in “explicit” form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.

  17. Linearized gyro-kinetic equation

    International Nuclear Information System (INIS)

    Catto, P.J.; Tsang, K.T.

    1976-01-01

    An ordering of the linearized Fokker-Planck equation is performed in which gyroradius corrections are retained to lowest order and the radial dependence appropriate for sheared magnetic fields is treated without resorting to a WKB technique. This description is shown to be necessary to obtain the proper radial dependence when the product of the poloidal wavenumber and the gyroradius is large (k rho much greater than 1). A like particle collision operator valid for arbitrary k rho also has been derived. In addition, neoclassical, drift, finite β (plasma pressure/magnetic pressure), and unperturbed toroidal electric field modifications are treated

  18. Study on characteristic differences of wheat 1Ax1 and 1Ax2* NILS obtained by transgenic HMW-GS 1Dx5 + 1Dy10 gene

    International Nuclear Information System (INIS)

    Sun Yan; Zhang Hongji; Liu Dongjun; Qi Qianqian; Yang Shuping; Guo Yipan; Ma Shumei; Liu Wenlin; Wang Guangjin; Zhao Wei

    2012-01-01

    Use wheat 1Ax1 and 1Ax2* NILS obtained by transgenic HMW-GS 1Dx5 + 1Dy10 gene, characteristics differences have been studied. The two-year results showed that the statistical differences in seed quality parameters, farinogram parameters, extensigram parameters, botany characters and main agricultural characters between 1Ax1 and 1Ax2* were not significant. We considered that 08K860 and 08K871 are similar in hereditary background, 1Ax1 and 1Ax2* have identical contribute on quality. Breeder should attach to 1Ax1 and 1Ax2* identically on wheat breeding. (authors)

  19. Study on characteristic differences of wheat 1Ax1 and 1Ax2* NILS obtained by transgenic HMW-GS 1Dx5+1Dy10 gene

    International Nuclear Information System (INIS)

    Sun Yan; Zhang Hongji; Liu Dongjun; Qi Qianqian; Yang Shuping; Guo Yifan; Ma Shumei; Liu Wenlin; Wang Guangjin; Zhao Wei

    2011-01-01

    Use wheat 1Ax1 and 1Ax2 * NILS obtained by transgenic HMW-GS 1Dx5+1Dy10 gene, characteristics differences have been studied. The two-year results showed that the statistical differences in seed quality parameters, farinogram parameters, extensigram parameters, botany characters and main agricultural characters between 1Ax1 and 1Ax2 * were not significant. We considered that 08K860 and 08K871 are similar in hereditary background, 1Ax1 and 1Ax2 * have identical contribute on quality. Breeder should atlach to 1Ax1 and 1Ax2 * identically on wheat breeding. (authors)

  20. Experimental quantum computing to solve systems of linear equations.

    Science.gov (United States)

    Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

    2013-06-07

    Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

  1. Oscillation and non-oscillation criterion for Riemann–Weber type half-linear differential equations

    Directory of Open Access Journals (Sweden)

    Petr Hasil

    2016-08-01

    Full Text Available By the combination of the modified half-linear Prüfer method and the Riccati technique, we study oscillatory properties of half-linear differential equations. Taking into account the transformation theory of half-linear equations and using some known results, we show that the analysed equations in the Riemann–Weber form with perturbations in both terms are conditionally oscillatory. Within the process, we identify the critical oscillation values of their coefficients and, consequently, we decide when the considered equations are oscillatory and when they are non-oscillatory. As a direct corollary of our main result, we solve the so-called critical case for a certain type of half-linear non-perturbed equations.

  2. Solution methods for large systems of linear equations in BACCHUS

    International Nuclear Information System (INIS)

    Homann, C.; Dorr, B.

    1993-05-01

    The computer programme BACCHUS is used to describe steady state and transient thermal-hydraulic behaviour of a coolant in a fuel element with intact geometry in a fast breeder reactor. In such computer programmes generally large systems of linear equations with sparse matrices of coefficients, resulting from discretization of coolant conservation equations, must be solved thousands of times giving rise to large demands of main storage and CPU time. Direct and iterative solution methods of the systems of linear equations, available in BACCHUS, are described, giving theoretical details and experience with their use in the programme. Besides use of a method of lines, a Runge-Kutta-method, for solution of the partial differential equation is outlined. (orig.) [de

  3. Perturbations of linear delay differential equations at the verge of instability.

    Science.gov (United States)

    Lingala, N; Namachchivaya, N Sri

    2016-06-01

    The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

  4. Local energy decay for linear wave equations with variable coefficients

    Science.gov (United States)

    Ikehata, Ryo

    2005-06-01

    A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

  5. Constructive Development of the Solutions of Linear Equations in Introductory Ordinary Differential Equations

    Science.gov (United States)

    Mallet, D. G.; McCue, S. W.

    2009-01-01

    The solution of linear ordinary differential equations (ODEs) is commonly taught in first-year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognizing what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to…

  6. Linear orbit parameters for the exact equations of motion

    International Nuclear Information System (INIS)

    Parzen, G.

    1995-01-01

    This paper defines the beta function and other linear orbit parameters using the exact equations of motion. The β, α and ψ functions are redefined using the exact equations. Expressions are found for the transfer matrix and the emittance. The differential equations for η = x/β 1/2 is found. New relationships between α, β, ψ and ν are derived

  7. Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

    Directory of Open Access Journals (Sweden)

    S. Narayanamoorthy

    2015-01-01

    Full Text Available We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

  8. A canonical form of the equation of motion of linear dynamical systems

    Science.gov (United States)

    Kawano, Daniel T.; Salsa, Rubens Goncalves; Ma, Fai; Morzfeld, Matthias

    2018-03-01

    The equation of motion of a discrete linear system has the form of a second-order ordinary differential equation with three real and square coefficient matrices. It is shown that, for almost all linear systems, such an equation can always be converted by an invertible transformation into a canonical form specified by two diagonal coefficient matrices associated with the generalized acceleration and displacement. This canonical form of the equation of motion is unique up to an equivalence class for non-defective systems. As an important by-product, a damped linear system that possesses three symmetric and positive definite coefficients can always be recast as an undamped and decoupled system.

  9. An implicit spectral formula for generalized linear Schroedinger equations

    International Nuclear Information System (INIS)

    Schulze-Halberg, A.; Garcia-Ravelo, J.; Pena Gil, Jose Juan

    2009-01-01

    We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schroedinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schroedinger equation or the Schroedinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form. (author)

  10. Linear Equating for the NEAT Design: Parameter Substitution Models and Chained Linear Relationship Models

    Science.gov (United States)

    Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

    2009-01-01

    This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…

  11. An Evaluation of Five Linear Equating Methods for the NEAT Design

    Science.gov (United States)

    Mroch, Andrew A.; Suh, Youngsuk; Kane, Michael T.; Ripkey, Douglas R.

    2009-01-01

    This study uses the results of two previous papers (Kane, Mroch, Suh, & Ripkey, this issue; Suh, Mroch, Kane, & Ripkey, this issue) and the literature on linear equating to evaluate five linear equating methods along several dimensions, including the plausibility of their assumptions and their levels of bias and root mean squared difference…

  12. SUPPORTING STUDENTS’ UNDERSTANDING OF LINEAR EQUATIONS WITH ONE VARIABLE USING ALGEBRA TILES

    Directory of Open Access Journals (Sweden)

    Sari Saraswati

    2016-01-01

    Full Text Available This research aimed to describe how algebra tiles can support students’ understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students use the algebra tiles to find a method to solve linear equations with one variable. Design research was used as an approach in this study. It consists of three phases, namely preliminary design, teaching experiment and retrospective analysis. Video registrations, students’ written works, pre-test, post-test, field notes, and interview are technic to collect data. The data were analyzed by comparing the hypothetical learning trajectory (HLT and the actual learning process. The result shows that algebra tiles could supports students’ understanding to find the formal solution of linear equation with one variable.Keywords: linear equation with one variable, algebra tiles, design research, balancing method, HLT DOI: http://dx.doi.org/10.22342/jme.7.1.2814.19-30

  13. New approach to solve fully fuzzy system of linear equations using ...

    Indian Academy of Sciences (India)

    This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and applied ...

  14. Growth of meromorphic solutions of higher-order linear differential equations

    Directory of Open Access Journals (Sweden)

    Wenjuan Chen

    2009-01-01

    Full Text Available In this paper, we investigate the higher-order linear differential equations with meromorphic coefficients. We improve and extend a result of M.S. Liu and C.L. Yuan, by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen, and the extended Winman-Valiron theory which proved by J. Wang and H.X. Yi. In addition, we also consider the nonhomogeneous linear differential equations.

  15. Microsoft Dynamics AX 2012 R3 development cookbook

    CERN Document Server

    Pocius, Mindaugas

    2015-01-01

    If you are a Dynamics AX developer who is primarily focused on delivering time-proven applications, then this book is for you. This book is focused more on people who are willing to raise their programming skills above the beginner level, and at the same time learn the functional aspects of Dynamics AX. Some Dynamics AX coding experience is expected.

  16. Q{sub {gamma}-H2AX}, an analysis method for partial-body radiation exposure using {gamma}-H2AX in non-human primate lymphocytes

    Energy Technology Data Exchange (ETDEWEB)

    Redon, Christophe E., E-mail: redonc@mail.nih.gov [NIH, NCI, CCR, Laboratory of Molecular Pharmacology, Bethesda, MD 20892 (United States); Nakamura, Asako J.; Gouliaeva, Ksenia [NIH, NCI, CCR, Laboratory of Molecular Pharmacology, Bethesda, MD 20892 (United States); Rahman, Arifur; Blakely, William F. [Armed Forces Radiobiology Research Institute, Uniformed Services University, Bethesda, MD 20889-5603 (United States); Bonner, William M. [NIH, NCI, CCR, Laboratory of Molecular Pharmacology, Bethesda, MD 20892 (United States)

    2011-09-15

    We previously used the {gamma}-H2AX assay as a biodosimeter for total-body irradiation (TBI) exposure ({gamma}-rays) in a rhesus macaque (Macaca mulatta) model. Utilizing peripheral blood lymphocytes and plucked hairs, we obtained statistically significant {gamma}-H2AX responses days after total-body exposure to 1-8.5 Gy ({sup 60}Co {gamma}-rays at 55 cGy min{sup -1}). Here, we introduce a partial-body exposure analysis method, Q{sub {gamma}-H2AX}, which is based on the number of {gamma}-H2AX foci per damaged cells as evident by having one or more {gamma}-H2AX foci per cell. Results from the rhesus monkey - TBI study were used to establish Q{sub {gamma}-H2AX} dose-response calibration curves to assess acute partial-body exposures. {gamma}-H2AX foci were detected in plucked hairs for several days after in vivo irradiation demonstrating this assay's utility for dose assessment in various body regions. The quantitation of {gamma}-H2AX may provide a robust biodosimeter for analyzing partial-body exposures to ionizing radiation in humans.

  17. SUPPORTING STUDENTS’ UNDERSTANDING OF LINEAR EQUATIONS WITH ONE VARIABLE USING ALGEBRA TILES

    Directory of Open Access Journals (Sweden)

    Sari Saraswati

    2016-01-01

    Full Text Available This research aimed to describe how algebra tiles can support students’ understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students use the algebra tiles to find a method to solve linear equations with one variable. Design research was used as an approach in this study. It consists of three phases, namely preliminary design, teaching experiment and retrospective analysis. Video registrations, students’ written works, pre-test, post-test, field notes, and interview are technic to collect data. The data were analyzed by comparing the hypothetical learning trajectory (HLT and the actual learning process. The result shows that algebra tiles could supports students’ understanding to find the formal solution of linear equation with one variable.

  18. Histone H2AX in DNA repair

    International Nuclear Information System (INIS)

    Lewandowska, H.; Szumiel, I.

    2002-01-01

    The paper reviews the recent reports on the role of the phosphorylated histone H2AX (γ-H2AX). The modification of this histone is an important part of the cellular response to the induction of DNA double strand brakes (DSB) by ionising radiation and other DSB-generating factors. In irradiated cells the modification is carried out mainly by ATM (ataxia-telangiectasia mutated) kinase, the enzyme that starts the alarm signalling upon induction of DSB.γ-H2AX molecules are formed within 1-3 min after irradiation and form foci at the sites of DSB. This seems to be necessary for the recruitment of repair factors that are later present in foci of damaged nuclei. Modification of a constant percentage of H2AX molecules per DSB takes place, corresponding to chromatin domains of megabase of DNA. (author)

  19. Biochemical Kinetics Model of DSB Repair and GammaH2AX FOCI by Non-homologous End Joining

    Science.gov (United States)

    Cucinotta, Francis, A.; Pluth, Janice M.; Anderson, Jennifer A.; Harper, Jane V.; O'Neill, Peter

    2007-01-01

    We developed a biochemical kinetics approach to describe the repair of double strand breaks (DSB) produced by low LET radiation by modeling molecular events associated with the mechanisms of non-homologous end-joining (NHEJ). A system of coupled non-linear ordinary differential equations describes the induction of DSB and activation pathways for major NHEJ components including Ku(sub 70/80), DNA-PK(sub cs), and the Ligase IV-XRCC4 hetero-dimer. The autophosphorylation of DNA-PK(sub cs and subsequent induction of gamma-H2AX foci observed after ionizing radiation exposure were modeled. A two-step model of DNA-PK(sub cs) regulation of repair was developed with the initial step allowing access of other NHEJ components to breaks, and a second step limiting access to Ligase IV-XRCC4. Our model assumes that the transition from the first to second-step depends on DSB complexity, with a much slower-rate for complex DSB. The model faithfully reproduced several experimental data sets, including DSB rejoining as measured by pulsed-field electrophoresis (PFGE), quantification of the induction of gamma-H2AX foci, and live cell imaging of the induction of Ku(sub 70/80). Predictions are made for the behaviors of NHEJ components at low doses and dose-rates, where a steady-state is found at dose-rates of 0.1 Gy/hr or lower.

  20. New non-linear modified massless Klein-Gordon equation

    Energy Technology Data Exchange (ETDEWEB)

    Asenjo, Felipe A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Facultad de Ingenieria y Ciencias, Santiago (Chile); Hojman, Sergio A. [Universidad Adolfo Ibanez, UAI Physics Center, Santiago (Chile); Universidad Adolfo Ibanez, Departamento de Ciencias, Facultad de Artes Liberales, Santiago (Chile); Universidad de Chile, Departamento de Fisica, Facultad de Ciencias, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)

    2017-11-15

    The massless Klein-Gordon equation on arbitrary curved backgrounds allows for solutions which develop ''tails'' inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost 60 years ago. A modification of the massless Klein-Gordon equation is presented, which always exhibits null geodesic propagation of waves on arbitrary curved spacetimes. This new equation is derived from a Lagrangian which exhibits current-current interaction. Its non-linearity is due to a self-coupling term which is related to the quantum mechanical Bohm potential. (orig.)

  1. A discrete homotopy perturbation method for non-linear Schrodinger equation

    Directory of Open Access Journals (Sweden)

    H. A. Wahab

    2015-12-01

    Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.

  2. On index-2 linear implicit difference equations

    NARCIS (Netherlands)

    Nguyen Huu Du, [No Value; Le Cong Loi, [No Value; Trinh Khanh Duy, [No Value; Vu Tien Viet, [No Value

    2011-01-01

    This paper deals with an index-2 notion for linear implicit difference equations (LIDEs) and with the solvability of initial value problems (IVPs) for index-2 LIDEs. Besides, the cocycle property as well as the multiplicative ergodic theorem of Oseledets type are also proved. (C) 2010 Elsevier Inc.

  3. Singular Linear Differential Equations in Two Variables

    NARCIS (Netherlands)

    Braaksma, B.L.J.; Put, M. van der

    2008-01-01

    The formal and analytic classification of integrable singular linear differential equations has been studied among others by R. Gerard and Y. Sibuya. We provide a simple proof of their main result, namely: For certain irregular systems in two variables there is no Stokes phenomenon, i.e. there is no

  4. Visual construction of characteristic equations of linear electric circuits

    Directory of Open Access Journals (Sweden)

    V.V. Kostyukov

    2013-12-01

    Full Text Available A visual identification method with application of partial circuits is developed for characteristic equation coefficients of transients in linear electric circuits. The method is based on interrelationship between the roots of algebraic polynomial and its coefficients. The method is illustrated with an example of a third-order linear electric circuit.

  5. Numerical method for solving linear Fredholm fuzzy integral equations of the second kind

    Energy Technology Data Exchange (ETDEWEB)

    Abbasbandy, S. [Department of Mathematics, Imam Khomeini International University, P.O. Box 288, Ghazvin 34194 (Iran, Islamic Republic of)]. E-mail: saeid@abbasbandy.com; Babolian, E. [Faculty of Mathematical Sciences and Computer Engineering, Teacher Training University, Tehran 15618 (Iran, Islamic Republic of); Alavi, M. [Department of Mathematics, Arak Branch, Islamic Azad University, Arak 38135 (Iran, Islamic Republic of)

    2007-01-15

    In this paper we use parametric form of fuzzy number and convert a linear fuzzy Fredholm integral equation to two linear system of integral equation of the second kind in crisp case. We can use one of the numerical method such as Nystrom and find the approximation solution of the system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equations of the second kind. The proposed method is illustrated by solving some numerical examples.

  6. Nonoscillation of half-linear dynamic equations

    Czech Academy of Sciences Publication Activity Database

    Matucci, S.; Řehák, Pavel

    2010-01-01

    Roč. 60, č. 5 (2010), s. 1421-1429 ISSN 0898-1221 R&D Projects: GA AV ČR KJB100190701 Grant - others:GA ČR(CZ) GA201/07/0145 Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear dynamic equation * time scale * (non)oscillation * Riccati technique Subject RIV: BA - General Mathematics Impact factor: 1.472, year: 2010 http://www.sciencedirect.com/science/article/pii/S0898122110004384

  7. Subroutine for series solutions of linear differential equations

    International Nuclear Information System (INIS)

    Tasso, H.; Steuerwald, J.

    1976-02-01

    A subroutine for Taylor series solutions of systems of ordinary linear differential equations is descriebed. It uses the old idea of Lie series but allows simple implementation and is time-saving for symbolic manipulations. (orig.) [de

  8. ATM and SIRT6/SNF2H Mediate Transient H2AX Stabilization When DSBs Form by Blocking HUWE1 to Allow Efficient γH2AX Foci Formation

    Directory of Open Access Journals (Sweden)

    Yuko Atsumi

    2015-12-01

    Full Text Available In response to DNA double-strand breaks (DSBs, H2AX is rapidly phosphorylated at Ser139 to promote DSB repair. Here we show that H2AX is rapidly stabilized in response to DSBs to efficiently generate γH2AX foci. This mechanism operated even in quiescent cells that barely expressed H2AX. H2AX stabilization resulted from the inhibition of proteasome-mediated degradation. Synthesized H2AX ordinarily underwent degradation through poly-ubiquitination mediated by the E3 ligase HUWE1; however, H2AX ubiquitination was transiently halted upon DSB formation. Such rapid H2AX stabilization by DSBs was associated with chromatin incorporation of H2AX and halting of its poly-ubiquitination mediated by the ATM kinase, the sirtuin protein SIRT6, and the chromatin remodeler SNF2H. H2AX Ser139, the ATM phosphorylation site, was essential for H2AX stabilization upon DSB formation. Our results reveal a pathway controlled by ATM, SIRT6, and SNF2H to block HUWE1, which stabilizes H2AX and induces its incorporation into chromatin only when cells are damaged.

  9. A fast iterative scheme for the linearized Boltzmann equation

    Science.gov (United States)

    Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.

    2017-06-01

    Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference

  10. Performance of the fully automated progesterone assays on the Abbott AxSYM and the Technicon Immuno 1 Analyser compared with the radioimmunoassay progesterone MAIA

    International Nuclear Information System (INIS)

    Reinsberg, J.; Jost, E.; Van der Ven, H.

    1997-01-01

    Test performance of two automated progesterone assays available on the immunoassay analysers Abbott AxSYM and Technicon Immuno 1, respectively, was evaluated in comparison with the radioimmunoassay Progesterone MAIA. For assessment of test performance imprecision, functional sensitivity and linearity of dilution was examined. Correlation with the manual radioimmunoassay was assessed using 122 serum samples over the range 0-110 nmol/L. Imprecision studies revealed for the AxSYM Progesterone within-run CV's of 1.8-6.4% and day-to-day CV's of 3.5-9.7% (concentration range 2.3-75 nmol/L); Immuno 1 Progesterone: within-run CV's 1.0-7.3%, day-to-day CV's 2.3-7.7% (concentration range 1.2-60 nmol/L). The functional sensitivity was <1.7 nmol/L for the AxSYM Progesterone and <1.1 nmol/L for the Immuno 1 Progesterone. With the AxSYM Progesterone the mean recovery after dilution from five samples was 102% (89-107%), from one sample only 69-80% was recovered; with the Immuno 1 Progesterone the mean recovery was 95% (80-105%). Despite of a quite good overall correlation (coefficients 0.972 and 0.981) the relationship of both assays to the Progesterone MAIA significantly deviate from linearity with a considerably higher slope within the lower concentration range. The relationship between the automated assays was linear over the entire concentration range (Immuno = 1.207 * AxSYM + 1; r = 0.986). The time to first result was 20 min for the AxSYM Progesterone, 45 min for the Immuno 1 Progesterone and 90 min for the Progesterone MAIA. The evaluated progesterone assays both exhibit an excellent precision and a high degree of sensitivity. They offer a rapid and flexible method for progesterone determination which may be especially useful for the monitoring of ovarian stimulation during in-vitro fertilization. (author)

  11. Asymptotic solutions and spectral theory of linear wave equations

    International Nuclear Information System (INIS)

    Adam, J.A.

    1982-01-01

    This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)

  12. Appearance of eigen modes for the linearized Vlasov-Poisson equation

    International Nuclear Information System (INIS)

    Degond, P.

    1983-01-01

    In order to determine the asymptotic behaviour, when the time goes to infinity, of the solution of the linearized Vlasov-Poisson equation, we use eigen modes, associated to continuous linear functionals on a Banach space of analytic functions [fr

  13. Linear algebra a first course with applications to differential equations

    CERN Document Server

    Apostol, Tom M

    2014-01-01

    Developed from the author's successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization. To accommodate a variety of backgrounds, the text begins with a review of prerequisites divided into precalculus and calculus prerequisites. It continues to cover vector algebra, analytic geometry, linear spaces, determinants, linear differential equations and more.

  14. Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions

    International Nuclear Information System (INIS)

    Goreac, D.

    2009-01-01

    The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded operator acting on the Y-component of the solution there is still another one acting on the Z-component. With the help of this dual equation we then deduce the duality between approximate controllability and observability. Finally, under the assumption that the unbounded operator acting on the state process of the forward equation is an infinitesimal generator of an exponentially stable semigroup, we show that the generalized Hautus test provides a necessary condition for the approximate controllability. The paper generalizes former results by Buckdahn, Quincampoix and Tessitore (Stochastic Partial Differential Equations and Applications, Series of Lecture Notes in Pure and Appl. Math., vol. 245, pp. 253-260, Chapman and Hall, London, 2006) and Goreac (Applied Analysis and Differential Equations, pp. 153-164, World Scientific, Singapore, 2007) from the finite dimensional to the infinite dimensional case

  15. Spectrum of the linearized operator for the Ginzburg-Landau equation

    Directory of Open Access Journals (Sweden)

    Tai-Chia Lin

    2000-06-01

    Full Text Available We study the spectrum of the linearized operator for the Ginzburg-Landau equation about a symmetric vortex solution with degree one. We show that the smallest eigenvalue of the linearized operator has multiplicity two, and then we describe its behavior as a small parameter approaches zero. We also find a positive lower bound for all the other eigenvalues, and find estimates of the first eigenfunction. Then using these results, we give partial results on the dynamics of vortices in the nonlinear heat and Schrodinger equations.

  16. AX Tank Farm ancillary equipment study

    International Nuclear Information System (INIS)

    SKELLY, W.A.

    1999-01-01

    This report examines the feasibility of remediating ancillary equipment associated with the 241-AX Tank Farm at the Hanford Site. Ancillary equipment includes surface structures and equipment, process waste piping, ventilation components, wells, and pits, boxes, sumps, and tanks used to make waste transfers to/from the AX tanks and adjoining tank farms. Two remedial alternatives are considered: (1) excavation and removal of all ancillary equipment items, and (2) in-situ stabilization by grout filling, the 241-AX Tank Farm is being employed as a strawman in engineering studies evaluating clean and landfill closure options for Hanford single-shell tanks. This is one of several reports being prepared for use by the Hanford Tanks Initiative Project to explore potential closure options and to develop retrieval performance evaluation criteria for tank farms

  17. AX Tank Farm tank removal study

    Energy Technology Data Exchange (ETDEWEB)

    SKELLY, W.A.

    1999-02-24

    This report examines the feasibility of remediating ancillary equipment associated with the 241-AX Tank Farm at the Hanford Site. Ancillary equipment includes surface structures and equipment, process waste piping, ventilation components, wells, and pits, boxes, sumps, and tanks used to make waste transfers to/from the AX tanks and adjoining tank farms. Two remedial alternatives are considered: (1) excavation and removal of all ancillary equipment items, and (2) in-situ stabilization by grout filling, the 241-AX Tank Farm is being employed as a strawman in engineering studies evaluating clean and landfill closure options for Hanford single-shell tanks. This is one of several reports being prepared for use by the Hanford Tanks Initiative Project to explore potential closure options and to develop retrieval performance evaluation criteria for tank farms.

  18. Stability of numerical method for semi-linear stochastic pantograph differential equations

    Directory of Open Access Journals (Sweden)

    Yu Zhang

    2016-01-01

    Full Text Available Abstract As a particular expression of stochastic delay differential equations, stochastic pantograph differential equations have been widely used in nonlinear dynamics, quantum mechanics, and electrodynamics. In this paper, we mainly study the stability of analytical solutions and numerical solutions of semi-linear stochastic pantograph differential equations. Some suitable conditions for the mean-square stability of an analytical solution are obtained. Then we proved the general mean-square stability of the exponential Euler method for a numerical solution of semi-linear stochastic pantograph differential equations, that is, if an analytical solution is stable, then the exponential Euler method applied to the system is mean-square stable for arbitrary step-size h > 0 $h>0$ . Numerical examples further illustrate the obtained theoretical results.

  19. Quantum osp-invariant non-linear Schroedinger equation

    International Nuclear Information System (INIS)

    Kulish, P.P.

    1985-04-01

    The generalizations of the non-linear Schroedinger equation (NS) associated with the orthosymplectic superalgebras are formulated. The simplest osp(1/2)-NS model is solved by the quantum inverse scattering method on a finite interval under periodic boundary conditions as well as on the wholeline in the case of a finite number of excitations. (author)

  20. Supporting Students' Understanding of Linear Equations with One Variable Using Algebra Tiles

    Science.gov (United States)

    Saraswati, Sari; Putri, Ratu Ilma Indra; Somakim

    2016-01-01

    This research aimed to describe how algebra tiles can support students' understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students…

  1. Novel algorithm of large-scale simultaneous linear equations

    International Nuclear Information System (INIS)

    Fujiwara, T; Hoshi, T; Yamamoto, S; Sogabe, T; Zhang, S-L

    2010-01-01

    We review our recently developed methods of solving large-scale simultaneous linear equations and applications to electronic structure calculations both in one-electron theory and many-electron theory. This is the shifted COCG (conjugate orthogonal conjugate gradient) method based on the Krylov subspace, and the most important issue for applications is the shift equation and the seed switching method, which greatly reduce the computational cost. The applications to nano-scale Si crystals and the double orbital extended Hubbard model are presented.

  2. Dark energy cosmology with generalized linear equation of state

    International Nuclear Information System (INIS)

    Babichev, E; Dokuchaev, V; Eroshenko, Yu

    2005-01-01

    Dark energy with the usually used equation of state p = wρ, where w const 0 ), where the constants α and ρ 0 are free parameters. This non-homogeneous linear equation of state provides the description of both hydrodynamically stable (α > 0) and unstable (α < 0) fluids. In particular, the considered cosmological model describes the hydrodynamically stable dark (and phantom) energy. The possible types of cosmological scenarios in this model are determined and classified in terms of attractors and unstable points by using phase trajectories analysis. For the dark energy case, some distinctive types of cosmological scenarios are possible: (i) the universe with the de Sitter attractor at late times, (ii) the bouncing universe, (iii) the universe with the big rip and with the anti-big rip. In the framework of a linear equation of state the universe filled with a phantom energy, w < -1, may have either the de Sitter attractor or the big rip

  3. POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.

  4. Focal decompositions for linear differential equations of the second order

    Directory of Open Access Journals (Sweden)

    L. Birbrair

    2003-01-01

    two-points problems to itself such that the image of the focal decomposition associated to the first equation is a focal decomposition associated to the second one. In this paper, we present a complete classification for linear second-order equations with respect to this equivalence relation.

  5. Effect of prolonging radiation delivery time on retention of gammaH2AX

    International Nuclear Information System (INIS)

    Moiseenko, Vitali; Banáth, Judit P; Duzenli, Cheryl; Olive, Peggy L

    2008-01-01

    Compared to conventional external beam radiotherapy, IMRT requires significantly more time to deliver the dose. Prolonging dose delivery potentially increases DNA repair which would reduce the biological effect. We questioned whether retention of γH2AX, a measure of lack of repair of DNA damage, would decrease when dose delivery was protracted. Exponentially growing SiHa cervical carinoma cells were irradiated with 6 MV photons in a water tank using a VarianEX linear accelerator. Cells held at 37°C received 2 Gy in 0.5 min and 4 Gy in 1 min. To evaluate effect of dose delivery prolongation, 2 and 4 Gy were delivered in 30 and 60 min. After 24 h recovery, cells were analyzed for clonogenic survival and for residual γH2AX as measured using flow cytometry. Increasing the dose delivery time from 0.5 or 1 min to 30 or 60 min produced a signficant increase in cell survival from 0.45 to 0.48 after 2 Gy, and from 0.17 to 0.20 after 4 Gy. Expression of residual γH2AX decreased from 1.27 to 1.22 relative to background after 2 Gy and 1.46 to 1.39 relative to background after 4 Gy, but differences were not statistically significant. The relative differences in the slopes of residual γH2AX versus dose for acute versus prolonged irradiation bordered on significant (p = 0.055), and the magnitude of the change was consistent with the observed increase in surviving fraction. These results support the concept that DNA repair underlies the increase in survival observed when dose delivery is prolonged. They also help to establish the limits of sensitivity of residual γH2AX, as measured using flow cytometry, for detecting differences in response to irradiation

  6. Prolongation structure and linear eigenvalue equations for Einstein-Maxwell fields

    International Nuclear Information System (INIS)

    Kramer, D.; Neugebauer, G.

    1981-01-01

    The Einstein-Maxwell equations for stationary axisymmetric exterior fields are shown to be the integrability conditions of a set of linear eigenvalue equations for pseudopotentials. Using the method of Wahlquist and Estabrook (J. Math Phys.; 16:1 (1975)) it is shown that the prolongation structure of the Einstein-Maxwell equations contains the SU(2,1) Lie algebra. A new mapping of known solutions to other solutions has been found. (author)

  7. From the hypergeometric differential equation to a non-linear Schrödinger one

    International Nuclear Information System (INIS)

    Plastino, A.; Rocca, M.C.

    2015-01-01

    We show that the q-exponential function is a hypergeometric function. Accordingly, it obeys the hypergeometric differential equation. We demonstrate that this differential equation can be transformed into a non-linear Schrödinger equation (NLSE). This NLSE exhibits both similarities and differences vis-a-vis the Nobre–Rego-Monteiro–Tsallis one. - Highlights: • We show that the q-exponential is a hypergeometric function. • It thus obeys the hypergeometric differential equation (HDE). • We show that the HDE can be cast as a non-linear Schrödinger equation. • This is different from the Nobre, Rego-Monteiro, Tsallis one.

  8. Exact solution of some linear matrix equations using algebraic methods

    Science.gov (United States)

    Djaferis, T. E.; Mitter, S. K.

    1977-01-01

    A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

  9. Staining Against Phospho-H2AX (gamma-H2AX) as a Marker for DNA Damage and Genomic Instability in Cancer Tissues and Cells

    NARCIS (Netherlands)

    Nagelkerke, A.P.; Span, P.N.

    2016-01-01

    Phospho-H2AX or gamma-H2AX- is a marker of DNA double-stranded breaks and can therefore be used to monitor DNA repair after, for example, irradiation. In addition, positive staining for phospho-H2AX may indicate genomic instability and telomere dysfunction in tumour cells and tissues. Here, we

  10. Construction of local and non-local conservation laws for non-linear field equations

    International Nuclear Information System (INIS)

    Vladimirov, V.S.; Volovich, I.V.

    1984-08-01

    A method of constructing conserved currents for non-linear field equations is presented. More explicitly for non-linear equations, which can be derived from compatibility conditions of some linear system with a parameter, a procedure of obtaining explicit expressions for local and non-local currents is developed. Some examples such as the classical Heisenberg spin chain and supersymmetric Yang-Mills theory are considered. (author)

  11. A Hamiltonian structure for the linearized Einstein vacuum field equations

    International Nuclear Information System (INIS)

    Torres del Castillo, G.F.

    1991-01-01

    By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained (Author)

  12. Analysis of transmission speed of AX.25 Protocol implemented in satellital earth station UPTC

    Directory of Open Access Journals (Sweden)

    Oscar Fernando Vera Cely

    2015-11-01

    Full Text Available One of the important parameters for the proper functioning of satellital ground station projected on Pedagogical and Technological University of Colombia (UPTC is the efficiency in transmission speed on communications protocol. This paper shows the results of analysis of the transmission speed of the AX.25 protocol implemented in the communication system of the satellital ground station UPTC. It begins with a brief description of the implemented hardware; the behavior of the transmission rate is evaluated using a theoretical analysis based on equations to estimate this parameter in the operation of the protocol, then tests are performed using the hardware that the satellital ground station UPTC has and finally, the conclusions are presented. Based on comparison of the theoretical analysis results obtained experimentally, it became apparent that AX.25 protocol efficiency is higher when increasing the number of frames.

  13. Collective spin by linearization of the Schrodinger equation for nuclear collective motion

    International Nuclear Information System (INIS)

    Greiner, M.; Scheid, W.; Herrmann, R.

    1988-01-01

    The free Schrodinger equation for multipole degrees of freedom is linearized so that energy and momentum operators appear only in first order. As an example, the authors demonstrate the linearization procedure for quadrupole degrees of freedom. The wave function solving this equation carries a spin. The authors derive the operator of the collective spin and its eigen values depending on multipolarity

  14. Two-dimensional differential transform method for solving linear and non-linear Schroedinger equations

    International Nuclear Information System (INIS)

    Ravi Kanth, A.S.V.; Aruna, K.

    2009-01-01

    In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.

  15. Solutions of the linearized Bach-Einstein equation in the static spherically symmetric case

    International Nuclear Information System (INIS)

    Schmidt, H.J.

    1985-01-01

    The Bach-Einstein equation linearized around Minkowski space-time is completely solved. The set of solutions depends on three parameters; a two-parameter subset of it becomes asymptotically flat. In that region the gravitational potential is of the type phi = -m/r + epsilon exp (-r/l). Because of the different asymptotic behaviour of both terms, it became necessary to linearize also around the Schwarzschild solution phi = -m/r. The linearized equation resulting in this case is discussed using qualitative methods. The result is that for m = 2l phi = -m/r + epsilon r -2 exp (-r/l) u, where u is some bounded function; m is arbitrary and epsilon again small. Further, the relation between the solution of the linearized and the full equation is discussed. (author)

  16. On a representation of linear differential equations

    Czech Academy of Sciences Publication Activity Database

    Neuman, František

    2010-01-01

    Roč. 52, 1-2 (2010), s. 355-360 ISSN 0895-7177 Grant - others:GA ČR(CZ) GA201/08/0469 Institutional research plan: CEZ:AV0Z10190503 Keywords : Brandt and Ehresmann groupoinds * transformations * canonical forms * linear differential equations Subject RIV: BA - General Mathematics Impact factor: 1.066, year: 2010 http://www.sciencedirect.com/science/article/pii/S0895717710001184

  17. CFORM- LINEAR CONTROL SYSTEM DESIGN AND ANALYSIS: CLOSED FORM SOLUTION AND TRANSIENT RESPONSE OF THE LINEAR DIFFERENTIAL EQUATION

    Science.gov (United States)

    Jamison, J. W.

    1994-01-01

    CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.

  18. The non-linear coupled spin 2-spin 3 Cotton equation in three dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Linander, Hampus; Nilsson, Bengt E.W. [Department of Physics, Theoretical PhysicsChalmers University of Technology, S-412 96 Göteborg (Sweden)

    2016-07-05

    In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F=0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 “translation”, “Lorentz” and “dilatation”) properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.

  19. GDTM-Padé technique for the non-linear differential-difference equation

    Directory of Open Access Journals (Sweden)

    Lu Jun-Feng

    2013-01-01

    Full Text Available This paper focuses on applying the GDTM-Padé technique to solve the non-linear differential-difference equation. The bell-shaped solitary wave solution of Belov-Chaltikian lattice equation is considered. Comparison between the approximate solutions and the exact ones shows that this technique is an efficient and attractive method for solving the differential-difference equations.

  20. Induction and Rejoining of DNA Double Strand Breaks Assessed by H2AX Phosphorylation in Melanoma Cells Irradiated with Proton and Lithium Beams

    International Nuclear Information System (INIS)

    Ibanez, Irene L.; Bracalente, Candelaria; Molinari, Beatriz L.; Palmieri, Monica A.; Policastro, Lucia; Kreiner, Andres J.; Burlon, Alejandro A.; Valda, Alejandro; Navalesi, Daniela; Davidson, Jorge; Davidson, Miguel; Vazquez, Monica; Ozafran, Mabel; Duran, Hebe

    2009-01-01

    Purpose: The aim of this study was to evaluate the induction and rejoining of DNA double strand breaks (DSBs) in melanoma cells exposed to low and high linear energy transfer (LET) radiation. Methods and Materials: DSBs and survival were determined as a function of dose in melanoma cells (B16-F0) irradiated with monoenergetic proton and lithium beams and with a gamma source. Survival curves were obtained by clonogenic assay and fitted to the linear-quadratic model. DSBs were evaluated by the detection of phosphorylated histone H2AX (γH2AX) foci at 30 min and 6 h post-irradiation. Results: Survival curves showed the increasing effectiveness of radiation as a function of LET. γH2AX labeling showed an increase in the number of foci vs. dose for all the radiations evaluated. A decrease in the number of foci was found at 6 h post-irradiation for low LET radiation, revealing the repair capacity of DSBs. An increase in the size of γH2AX foci in cells irradiated with lithium beams was found, as compared with gamma and proton irradiations, which could be attributed to the clusters of DSBs induced by high LET radiation. Foci size increased at 6 h post-irradiation for lithium and proton irradiations in relation with persistent DSBs, showing a correlation with surviving fraction. Conclusions: Our results showed the response of B16-F0 cells to charged particle beams evaluated by the detection of γH2AX foci. We conclude that γH2AX foci size is an accurate parameter to correlate the rejoining of DSBs induced by different LET radiations and radiosensitivity.

  1. On the Liouvillian solution of second-order linear differential equations and algebraic invariant curves

    International Nuclear Information System (INIS)

    Man, Yiu-Kwong

    2010-01-01

    In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided. (fast track communication)

  2. On the economical solution method for a system of linear algebraic equations

    Directory of Open Access Journals (Sweden)

    Jan Awrejcewicz

    2004-01-01

    Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O(hx12+hx22. The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.

  3. On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations

    International Nuclear Information System (INIS)

    Valat, J.

    1960-12-01

    Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [fr

  4. Inhomogeneous linear equation in Rota-Baxter algebra

    OpenAIRE

    Pietrzkowski, Gabriel

    2014-01-01

    We consider a complete filtered Rota-Baxter algebra of weight $\\lambda$ over a commutative ring. Finding the unique solution of a non-homogeneous linear algebraic equation in this algebra, we generalize Spitzer's identity in both commutative and non-commutative cases. As an application, considering the Rota-Baxter algebra of power series in one variable with q-integral as the Rota-Baxter operator, we show certain Eulerian identities.

  5. ITMETH, Iterative Routines for Linear System

    International Nuclear Information System (INIS)

    Greenbaum, A.

    1989-01-01

    1 - Description of program or function: ITMETH is a collection of iterative routines for solving large, sparse linear systems. 2 - Method of solution: ITMETH solves general linear systems of the form AX=B using a variety of methods: Jacobi iteration; Gauss-Seidel iteration; incomplete LU decomposition or matrix splitting with iterative refinement; diagonal scaling, matrix splitting, or incomplete LU decomposition with the conjugate gradient method for the problem AA'Y=B, X=A'Y; bi-conjugate gradient method with diagonal scaling, matrix splitting, or incomplete LU decomposition; and ortho-min method with diagonal scaling, matrix splitting, or incomplete LU decomposition. ITMETH also solves symmetric positive definite linear systems AX=B using the conjugate gradient method with diagonal scaling or matrix splitting, or the incomplete Cholesky conjugate gradient method

  6. Solution of systems of linear algebraic equations by the method of summation of divergent series

    International Nuclear Information System (INIS)

    Kirichenko, G.A.; Korovin, Ya.S.; Khisamutdinov, M.V.; Shmojlov, V.I.

    2015-01-01

    A method for solving systems of linear algebraic equations has been proposed on the basis on the summation of the corresponding continued fractions. The proposed algorithm for solving systems of linear algebraic equations is classified as direct algorithms providing an exact solution in a finite number of operations. Examples of solving systems of linear algebraic equations have been presented and the effectiveness of the algorithm has been estimated [ru

  7. Stability of the trivial solution for linear stochastic differential equations with Poisson white noise

    International Nuclear Information System (INIS)

    Grigoriu, Mircea; Samorodnitsky, Gennady

    2004-01-01

    Two methods are considered for assessing the asymptotic stability of the trivial solution of linear stochastic differential equations driven by Poisson white noise, interpreted as the formal derivative of a compound Poisson process. The first method attempts to extend a result for diffusion processes satisfying linear stochastic differential equations to the case of linear equations with Poisson white noise. The developments for the method are based on Ito's formula for semimartingales and Lyapunov exponents. The second method is based on a geometric ergodic theorem for Markov chains providing a criterion for the asymptotic stability of the solution of linear stochastic differential equations with Poisson white noise. Two examples are presented to illustrate the use and evaluate the potential of the two methods. The examples demonstrate limitations of the first method and the generality of the second method

  8. Tangent Lines without Derivatives for Quadratic and Cubic Equations

    Science.gov (United States)

    Carroll, William J.

    2009-01-01

    In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

  9. Factorization of a class of almost linear second-order differential equations

    International Nuclear Information System (INIS)

    Estevez, P G; Kuru, S; Negro, J; Nieto, L M

    2007-01-01

    A general type of almost linear second-order differential equations, which are directly related to several interesting physical problems, is characterized. The solutions of these equations are obtained using the factorization technique, and their non-autonomous invariants are also found by means of scale transformations

  10. Variations in the Solution of Linear First-Order Differential Equations. Classroom Notes

    Science.gov (United States)

    Seaman, Brian; Osler, Thomas J.

    2004-01-01

    A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…

  11. A Proposed Method for Solving Fuzzy System of Linear Equations

    Directory of Open Access Journals (Sweden)

    Reza Kargar

    2014-01-01

    Full Text Available This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m×n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.

  12. On a class of fourth order linear recurrence equations

    Directory of Open Access Journals (Sweden)

    Sui-Sun Cheng

    1984-01-01

    Full Text Available This paper is concerned with sequences that satisfy a class of fourth order linear recurrence equations. Basic properties of such sequences are derived. In addition, we discuss the oscillatory and nonoscillatory behavior of such sequences.

  13. Could solitons be adiabatic invariants attached to certain non linear equations

    International Nuclear Information System (INIS)

    Lochak, P.

    1984-01-01

    Arguments are given to support the claim that solitons should be the adiabatic invariants associated to certain non linear partial differential equations; a precise mathematical form of this conjecture is then stated. As a particular case of the conjecture, the Korteweg-de Vries equation is studied. (Auth.)

  14. On a Linear Equation Arising in Isometric Embedding of Torus-like Surface

    Institute of Scientific and Technical Information of China (English)

    Chunhe LI

    2009-01-01

    The solvability of a linear equation and the regularity of the solution are discussed.The equation is arising in a geometric problem which is concerned with the realization of Alexandroff's positive annul in R3.

  15. Stochastic modeling of mode interactions via linear parabolized stability equations

    Science.gov (United States)

    Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

    2017-11-01

    Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

  16. KAM for the non-linear Schroedinger equation

    CERN Document Server

    Eliasson, L H

    2006-01-01

    We consider the $d$-dimensional nonlinear Schr\\"o\\-dinger equation under periodic boundary conditions:-i\\dot u=\\Delta u+V(x)*u+\\ep|u|^2u;\\quad u=u(t,x),\\;x\\in\\T^dwhere $V(x)=\\sum \\hat V(a)e^{i\\sc{a,x}}$ is an analytic function with $\\hat V$ real. (This equation is a popular model for the `real' NLS equation, where instead of the convolution term $V*u$ we have the potential term $Vu$.) For $\\ep=0$ the equation is linear and has time--quasi-periodic solutions $u$,u(t,x)=\\sum_{s\\in \\AA}\\hat u_0(a)e^{i(|a|^2+\\hat V(a))t}e^{i\\sc{a,x}}, \\quad 0<|\\hat u_0(a)|\\le1,where $\\AA$ is any finite subset of $\\Z^d$. We shall treat $\\omega_a=|a|^2+\\hat V(a)$, $a\\in\\AA$, as free parameters in some domain $U\\subset\\R^{\\AA}$. This is a Hamiltonian system in infinite degrees of freedom, degenerate but with external parameters, and we shall describe a KAM-theory which, in particular, will have the following consequence: \\smallskip {\\it If $|\\ep|$ is sufficiently small, then there is a large subset $U'$ of $U$ such that for all $...

  17. Minimal solution of linear formed fuzzy matrix equations

    Directory of Open Access Journals (Sweden)

    Maryam Mosleh

    2012-10-01

    Full Text Available In this paper according to the structured element method, the $mimes n$ inconsistent fuzzy matrix equation $Ailde{X}=ilde{B},$ which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method.

  18. A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials

    Science.gov (United States)

    Li, Chen; Liao, Yufei

    2018-03-01

    Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.

  19. Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

    Science.gov (United States)

    Zhou, L.-Q.; Meleshko, S. V.

    2017-07-01

    The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

  20. Low doses of X-rays induce prolonged and ATM-independent persistence of γH2AX foci in human gingival mesenchymal stem cells.

    Science.gov (United States)

    Osipov, Andreyan N; Pustovalova, Margarita; Grekhova, Anna; Eremin, Petr; Vorobyova, Natalia; Pulin, Andrey; Zhavoronkov, Alex; Roumiantsev, Sergey; Klokov, Dmitry Y; Eremin, Ilya

    2015-09-29

    Diagnostic imaging delivering low doses of radiation often accompany human mesenchymal stem cells (MSCs)-based therapies. However, effects of low dose radiation on MSCs are poorly characterized. Here we examine patterns of phosphorylated histone H2AX (γH2AX) and phospho-S1981 ATM (pATM) foci formation in human gingiva-derived MSCs exposed to X-rays in time-course and dose-response experiments. Both γH2AX and pATM foci accumulated linearly with dose early after irradiation (5-60 min), with a maximum induction observed at 30-60 min (37 ± 3 and 32 ± 3 foci/cell/Gy for γH2AX and pATM, respectively). The number of γH2AX foci produced by intermediate doses (160 and 250 mGy) significantly decreased (40-60%) between 60 and 240 min post-irradiation, indicating rejoining of DNA double-strand breaks. In contrast, γH2AX foci produced by low doses (20-80 mGy) did not change after 60 min. The number of pATM foci between 60 and 240 min decreased down to control values in a dose-independent manner. Similar kinetics was observed for pATM foci co-localized with γH2AX foci. Collectively, our results suggest differential DNA double-strand break signaling and processing in response to low vs. intermediate doses of X-rays in human MSCs. Furthermore, mechanisms governing the prolonged persistence of γH2AX foci in these cells appear to be ATM-independent.

  1. Some Additional Remarks on the Cumulant Expansion for Linear Stochastic Differential Equations

    NARCIS (Netherlands)

    Roerdink, J.B.T.M.

    1984-01-01

    We summarize our previous results on cumulant expansions for linear stochastic differential equations with correlated multipliclative and additive noise. The application of the general formulas to equations with statistically independent multiplicative and additive noise is reconsidered in detail,

  2. Some additional remarks on the cumulant expansion for linear stochastic differential equations

    NARCIS (Netherlands)

    Roerdink, J.B.T.M.

    1984-01-01

    We summarize our previous results on cumular expasions for linear stochastic differential equations with correlated multipliclative and additive noise. The application of the general formulas to equations with statistically independent multiplicative and additive noise is reconsidered in detail,

  3. Hyers-Ulam stability for second-order linear differential equations with boundary conditions

    Directory of Open Access Journals (Sweden)

    Pasc Gavruta

    2011-06-01

    Full Text Available We prove the Hyers-Ulam stability of linear differential equations of second-order with boundary conditions or with initial conditions. That is, if y is an approximate solution of the differential equation $y''+ eta (x y = 0$ with $y(a = y(b =0$, then there exists an exact solution of the differential equation, near y.

  4. Asymptotic integration of a linear fourth order differential equation of Poincaré type

    Directory of Open Access Journals (Sweden)

    Anibal Coronel

    2015-11-01

    Full Text Available This article deals with the asymptotic behavior of nonoscillatory solutions of fourth order linear differential equation where the coefficients are perturbations of constants. We define a change of variable and deduce that the new variable satisfies a third order nonlinear differential equation. We assume three hypotheses. The first hypothesis is related to the constant coefficients and set up that the characteristic polynomial associated with the fourth order linear equation has simple and real roots. The other two hypotheses are related to the behavior of the perturbation functions and establish asymptotic integral smallness conditions of the perturbations. Under these general hypotheses, we obtain four main results. The first two results are related to the application of a fixed point argument to prove that the nonlinear third order equation has a unique solution. The next result concerns with the asymptotic behavior of the solutions of the nonlinear third order equation. The fourth main theorem is introduced to establish the existence of a fundamental system of solutions and to precise the formulas for the asymptotic behavior of the linear fourth order differential equation. In addition, we present an example to show that the results introduced in this paper can be applied in situations where the assumptions of some classical theorems are not satisfied.

  5. On oscillation of second-order linear ordinary differential equations

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, A.; Šremr, Jiří

    2011-01-01

    Roč. 54, - (2011), s. 69-81 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z10190503 Keywords : linear second-order ordinary differential equation * Kamenev theorem * oscillation Subject RIV: BA - General Mathematics http://www.rmi.ge/jeomj/memoirs/vol54/abs54-4.htm

  6. An inhomogeneous wave equation and non-linear Diophantine approximation

    DEFF Research Database (Denmark)

    Beresnevich, V.; Dodson, M. M.; Kristensen, S.

    2008-01-01

    A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...

  7. Identifying the principal coefficient of parabolic equations with non-divergent form

    International Nuclear Information System (INIS)

    Jiang, L S; Bian, B J

    2005-01-01

    We deal with an inverse problem of determining a coefficient a(x, t) of principal part for second order parabolic equations with non-divergent form when the solution is known. Such a problem has important applications in a large fields of applied science. We propose a well-posed approximate algorithm to identify the coefficient. The existence, uniqueness and stability of such solutions a(x, t) are proved. A necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced. Our numerical simulations show that the coefficient is recovered very well

  8. Identifying the principal coefficient of parabolic equations with non-divergent form

    Science.gov (United States)

    Jiang, L. S.; Bian, B. J.

    2005-01-01

    We deal with an inverse problem of determining a coefficient a(x, t) of principal part for second order parabolic equations with non-divergent form when the solution is known. Such a problem has important applications in a large fields of applied science. We propose a well-posed approximate algorithm to identify the coefficient. The existence, uniqueness and stability of such solutions a(x, t) are proved. A necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced. Our numerical simulations show that the coefficient is recovered very well.

  9. Improved harmonic balance approach to periodic solutions of non-linear jerk equations

    International Nuclear Information System (INIS)

    Wu, B.S.; Lim, C.W.; Sun, W.P.

    2006-01-01

    An analytical approximate approach for determining periodic solutions of non-linear jerk equations involving third-order time-derivative is presented. This approach incorporates salient features of both Newton's method and the method of harmonic balance. By appropriately imposing the method of harmonic balance to the linearized equation, the approach requires only one or two iterations to predict very accurate analytical approximate solutions for a large range of initial velocity amplitude. One typical example is used to verify and illustrate the usefulness and effectiveness of the proposed approach

  10. Visualising the Roots of Quadratic Equations with Complex Coefficients

    Science.gov (United States)

    Bardell, Nicholas S.

    2014-01-01

    This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

  11. Supporting second grade lower secondary school students’ understanding of linear equation system in two variables using ethnomathematics

    Science.gov (United States)

    Nursyahidah, F.; Saputro, B. A.; Rubowo, M. R.

    2018-03-01

    The aim of this research is to know the students’ understanding of linear equation system in two variables using Ethnomathematics and to acquire learning trajectory of linear equation system in two variables for the second grade of lower secondary school students. This research used methodology of design research that consists of three phases, there are preliminary design, teaching experiment, and retrospective analysis. Subject of this study is 28 second grade students of Sekolah Menengah Pertama (SMP) 37 Semarang. The result of this research shows that the students’ understanding in linear equation system in two variables can be stimulated by using Ethnomathematics in selling buying tradition in Peterongan traditional market in Central Java as a context. All of strategies and model that was applied by students and also their result discussion shows how construction and contribution of students can help them to understand concept of linear equation system in two variables. All the activities that were done by students produce learning trajectory to gain the goal of learning. Each steps of learning trajectory of students have an important role in understanding the concept from informal to the formal level. Learning trajectory using Ethnomathematics that is produced consist of watching video of selling buying activity in Peterongan traditional market to construct linear equation in two variables, determine the solution of linear equation in two variables, construct model of linear equation system in two variables from contextual problem, and solving a contextual problem related to linear equation system in two variables.

  12. Nonoscillation criteria for half-linear second order difference equations

    Czech Academy of Sciences Publication Activity Database

    Došlý, Ondřej; Řehák, Pavel

    2001-01-01

    Roč. 42, - (2001), s. 453-464 ISSN 0898-1221 R&D Projects: GA ČR GA201/98/0677; GA ČR GA201/99/0295 Keywords : half-linear difference equation%nonoscillation criteria%variational principle Subject RIV: BA - General Mathematics Impact factor: 0.383, year: 2001

  13. Lie symmetries and differential galois groups of linear equations

    NARCIS (Netherlands)

    Oudshoorn, W.R.; Put, M. van der

    2002-01-01

    For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In

  14. Solving Fully Fuzzy Linear System of Equations in General Form

    Directory of Open Access Journals (Sweden)

    A. Yousefzadeh

    2012-06-01

    Full Text Available In this work, we propose an approach for computing the positive solution of a fully fuzzy linear system where the coefficient matrix is a fuzzy $nimes n$ matrix. To do this, we use arithmetic operations on fuzzy numbers that introduced by Kaffman in and convert the fully fuzzy linear system into two $nimes n$ and $2nimes 2n$ crisp linear systems. If the solutions of these linear systems don't satisfy in positive fuzzy solution condition, we introduce the constrained least squares problem to obtain optimal fuzzy vector solution by applying the ranking function in given fully fuzzy linear system. Using our proposed method, the fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.

  15. Linear fractional diffusion-wave equation for scientists and engineers

    CERN Document Server

    Povstenko, Yuriy

    2015-01-01

    This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and ...

  16. Genotoxicity testing: Comparison of the γH2AX focus assay with the alkaline and neutral comet assays.

    Science.gov (United States)

    Nikolova, Teodora; Marini, Federico; Kaina, Bernd

    2017-10-01

    Genotoxicity testing relies on the quantitative measurement of adverse effects, such as chromosome aberrations, micronuclei, and mutations, resulting from primary DNA damage. Ideally, assays will detect DNA damage and cellular responses with high sensitivity, reliability, and throughput. Several novel genotoxicity assays may fulfill these requirements, including the comet assay and the more recently developed γH2AX assay. Although they are thought to be specific for genotoxicants, a systematic comparison of the assays has not yet been undertaken. In the present study, we compare the γH2AX focus assay with the alkaline and neutral versions of the comet assay, as to their sensitivities and limitations for detection of genetic damage. We investigated the dose-response relationships of γH2AX foci and comet tail intensities at various times following treatment with four prototypical genotoxicants, methyl methanesulfonate (MMS), N-methyl-N'-nitro-N-nitrosoguanidine (MNNG), mitomycin C, and hydrogen peroxide (H 2 O 2 ) and we tested whether there is a correlation between the endpoints, i.e., alkali-labile sites and DNA strand breaks on the one hand and the cell's response to DNA double-strand breaks and blocked replication forks on the other. Induction of γH2AX foci gave a linear dose response and all agents tested were positive in the assay. The increase in comet tail intensity was also a function of dose; however, mitomycin C was almost completely ineffective in the comet assay, and the doses needed to achieve a significant effect were somewhat higher for some treatments in the comet assay than in the γH2AX foci assay, which was confirmed by threshold analysis. There was high correlation between tail intensity and γH2AX foci for MMS and H 2 O 2 , less for MNNG, and none for mitomycin C. From this we infer that the γH2AX foci assay is more reliable, sensitive, and robust than the comet assay for detecting genotoxicant-induced DNA damage. Copyright © 2017 Elsevier

  17. Local linearization methods for the numerical integration of ordinary differential equations: An overview

    International Nuclear Information System (INIS)

    Jimenez, J.C.

    2009-06-01

    Local Linearization (LL) methods conform a class of one-step explicit integrators for ODEs derived from the following primary and common strategy: the vector field of the differential equation is locally (piecewise) approximated through a first-order Taylor expansion at each time step, thus obtaining successive linear equations that are explicitly integrated. Hereafter, the LL approach may include some additional strategies to improve that basic affine approximation. Theoretical and practical results have shown that the LL integrators have a number of convenient properties. These include arbitrary order of convergence, A-stability, linearization preserving, regularity under quite general conditions, preservation of the dynamics of the exact solution around hyperbolic equilibrium points and periodic orbits, integration of stiff and high-dimensional equations, low computational cost, and others. In this paper, a review of the LL methods and their properties is presented. (author)

  18. On the Linearized Darboux Equation Arising in Isometric Embedding of the Alexandrov Positive Annulus

    Institute of Scientific and Technical Information of China (English)

    Chunhe LI

    2013-01-01

    In the present paper,the solvability condition of the linearized Gauss-Codazzi system and the solutions to the homogenous system are given.In the meantime,the Solvability of a relevant linearized Darboux equation is given.The equations are arising in a geometric problem which is concerned with the realization of the Alexandrov's positive annulus in R3.

  19. Non-linear partial differential equations an algebraic view of generalized solutions

    CERN Document Server

    Rosinger, Elemer E

    1990-01-01

    A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen

  20. Anti-symmetrically fused model and non-linear integral equations in the three-state Uimin-Sutherland model

    International Nuclear Information System (INIS)

    Fujii, Akira; Kluemper, Andreas

    1999-01-01

    We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation

  1. Asymptotic formulae for solutions of half-linear differential equations

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel

    2017-01-01

    Roč. 292, January (2017), s. 165-177 ISSN 0096-3003 Institutional support: RVO:67985840 Keywords : half-linear differential equation * nonoscillatory solution * regular variation Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.738, year: 2016 http://www.sciencedirect.com/science/article/pii/S0096300316304581

  2. AxTract: Toward microstructure informed tractography.

    Science.gov (United States)

    Girard, Gabriel; Daducci, Alessandro; Petit, Laurent; Thiran, Jean-Philippe; Whittingstall, Kevin; Deriche, Rachid; Wassermann, Demian; Descoteaux, Maxime

    2017-11-01

    Diffusion-weighted (DW) magnetic resonance imaging (MRI) tractography has become the tool of choice to probe the human brain's white matter in vivo. However, tractography algorithms produce a large number of erroneous streamlines (false positives), largely due to complex ambiguous tissue configurations. Moreover, the relationship between the resulting streamlines and the underlying white matter microstructure characteristics remains poorly understood. In this work, we introduce a new approach to simultaneously reconstruct white matter fascicles and characterize the apparent distribution of axon diameters within fascicles. To achieve this, our method, AxTract, takes full advantage of the recent development DW-MRI microstructure acquisition, modeling, and reconstruction techniques. This enables AxTract to separate parallel fascicles with different microstructure characteristics, hence reducing ambiguities in areas of complex tissue configuration. We report a decrease in the incidence of erroneous streamlines compared to the conventional deterministic tractography algorithms on simulated data. We also report an average increase in streamline density over 15 known fascicles of the 34 healthy subjects. Our results suggest that microstructure information improves tractography in crossing areas of the white matter. Moreover, AxTract provides additional microstructure information along the fascicle that can be studied alongside other streamline-based indices. Overall, AxTract provides the means to distinguish and follow white matter fascicles using their microstructure characteristics, bringing new insights into the white matter organization. This is a step forward in microstructure informed tractography, paving the way to a new generation of algorithms able to deal with intricate configurations of white matter fibers and providing quantitative brain connectivity analysis. Hum Brain Mapp 38:5485-5500, 2017. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  3. Calculations of stationary solutions for the non linear viscous resistive MHD equations in slab geometry

    International Nuclear Information System (INIS)

    Edery, D.

    1983-11-01

    The reduced system of the non linear resistive MHD equations is used in the 2-D one helicity approximation in the numerical computations of stationary tearing modes. The critical magnetic Raynolds number S (S=tausub(r)/tausub(H) where tausub(R) and tausub(H) are respectively the characteristic resistive and hydro magnetic times) and the corresponding linear solution are computed as a starting approximation for the full non linear equations. These equations are then treated numerically by an iterative procedure which is shown to be rapidly convergent. A numerical application is given in the last part of this paper

  4. γ-H2AX as a biomarker of DNA damage induced by ionizing radiation in human peripheral blood lymphocytes and artificial skin

    Science.gov (United States)

    Redon, Christophe E.; Dickey, Jennifer S.; Bonner, William M.; Sedelnikova, Olga A.

    2009-04-01

    Ionizing radiation (IR) exposure is inevitable in our modern society and can lead to a variety of deleterious effects including cancer and birth defects. A reliable, reproducible and sensitive assessment of exposure to IR and the individual response to that exposure would provide much needed information for the optimal treatment of each donor examined. We have developed a diagnostic test for IR exposure based on detection of the phosphorylated form of variant histone H2AX (γ-H2AX), which occurs specifically at sites of DNA double-strand breaks (DSBs). The cell responds to a nascent DSB through the phosphorylation of thousands of H2AX molecules flanking the damaged site. This highly amplified response can be visualized as a γ-H2AX focus in the chromatin that can be detected in situ with the appropriate antibody. Here we assess the usability of γ-H2AX focus formation as a possible biodosimeter for human exposure to IR using peripheral blood lymphocytes irradiated ex vivo and three-dimensional artificial models of human skin biopsies. In both systems, the tissues were exposed to 0.2-5 Gy, doses of IR that might be realistically encountered in various scenarios such as cancer radiotherapies or accidental exposure to radiation. Since the γ-H2AX response is maximal 30 min after exposure and declines over a period of hours as the cells repair the damage, we examined the time limitations of the useful detectability of γ-H2AX foci. We report that a linear response proportional to the initial radiation dose was obtained 48 and 24 h after exposure in blood samples and skin cells respectively. Thus, detection of γ-H2AX formation to monitor DNA damage in minimally invasive blood and skin tests could be useful tools to determine radiation dose exposure and analyze its effects on humans.

  5. Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

    International Nuclear Information System (INIS)

    Misguich, J.H.

    2004-04-01

    As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation

  6. Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

    Energy Technology Data Exchange (ETDEWEB)

    Misguich, J.H

    2004-04-01

    As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation.

  7. AX Tank Farm waste retrieval alternatives cost estimates

    International Nuclear Information System (INIS)

    Krieg, S.A.

    1998-01-01

    This report presents the estimated costs associated with retrieval of the wastes from the four tanks in AX Tank Farm. The engineering cost estimates developed for this report are based on previous cost data prepared for Project W-320 and the HTI 241-C-106 Heel Retrieval System. The costs presented in this report address only the retrieval of the wastes from the four AX Farm tanks. This includes costs for equipment procurement, fabrication, installation, and operation to retrieve the wastes. The costs to modify the existing plant equipment and systems to support the retrieval equipment are also included. The estimates do not include operational costs associated with pumping the waste out of the waste receiver tank (241-AY-102) between AX Farm retrieval campaigns or transportation, processing, and disposal of the retrieved waste

  8. Diffusion phenomenon for linear dissipative wave equations in an exterior domain

    Science.gov (United States)

    Ikehata, Ryo

    Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

  9. Exponential estimates for solutions of half-linear differential equations

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel

    2015-01-01

    Roč. 147, č. 1 (2015), s. 158-171 ISSN 0236-5294 Institutional support: RVO:67985840 Keywords : half-linear differential equation * decreasing solution * increasing solution * asymptotic behavior Subject RIV: BA - General Mathematics Impact factor: 0.469, year: 2015 http://link.springer.com/article/10.1007%2Fs10474-015-0522-9

  10. On the equivalence between particular types of Navier-Stokes and non-linear Schroedinger equations

    International Nuclear Information System (INIS)

    Dietrich, K.; Vautherin, D.

    1985-01-01

    We derive a Schroedinger equation equivalent to the Navier-Stokes equation in the special case of constant kinematic viscosities. This equation contains a non-linear term similar to that proposed by Kostin for a quantum description of friction [fr

  11. A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay

    Directory of Open Access Journals (Sweden)

    Gisle M. Mophou

    2010-01-01

    Full Text Available We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay: Dαx(t+Ax(t=f(t,xt, t∈[0,T], x(t=ϕ(t, t∈]−∞,0], with T>0 and 0<α<1. We prove the existence (and uniqueness of solutions, assuming that −A is a linear closed operator which generates an analytic semigroup (T(tt≥0 on a Banach space 𝕏 by means of the Banach's fixed point theorem. This generalizes some recent results.

  12. Shifted Legendre method with residual error estimation for delay linear Fredholm integro-differential equations

    Directory of Open Access Journals (Sweden)

    Şuayip Yüzbaşı

    2017-03-01

    Full Text Available In this paper, we suggest a matrix method for obtaining the approximate solutions of the delay linear Fredholm integro-differential equations with constant coefficients using the shifted Legendre polynomials. The problem is considered with mixed conditions. Using the required matrix operations, the delay linear Fredholm integro-differential equation is transformed into a matrix equation. Additionally, error analysis for the method is presented using the residual function. Illustrative examples are given to demonstrate the efficiency of the method. The results obtained in this study are compared with the known results.

  13. Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

    OpenAIRE

    Diethelm, Kai; Siegmund, Stefan; Tuan, H. T.

    2017-01-01

    In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of line...

  14. Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

    Science.gov (United States)

    Pipkins, Daniel Scott

    Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially. linear model are compared to those

  15. Using Microsoft Dynamics AX 2012 updated for version R2

    CERN Document Server

    Luszczak, Andreas

    2013-01-01

    Precise descriptions and instructions enable users, students and consultants to easily understand Microsoft Dynamics AX 2012. Microsoft offers Dynamics AX as its premium ERP solution to support large and mid-sized organizations with a complete business management solution which is easy to use. Going through a simple but comprehensive case study - the sample company 'Anso Technologies Inc.' - this book provides the required knowledge to handle all basic business processes in Dynamics AX. Exercises are there to train the processes and functionality, also making this book a good choice for self-s

  16. Using Microsoft Dynamics AX 2012 updated for version R3

    CERN Document Server

    Luszczak, Andreas

    2015-01-01

    Precise descriptions and instructions enable users, students and consultants to understand MS Dynamics AX 2012 rapidly. Microsoft offers Dynamics AX as its premium ERP solution, supporting large and mid-sized organizations with a complete business management solution which is easy to use. Going through a simple but comprehensive case study - the sample company 'Anso Technologies Inc.' - this book provides the required knowledge to handle all basic business processes in Dynamics AX. Exercises are there to train the processes and functionality, also making this book a good choice for self-study.

  17. Students' errors in solving linear equation word problems: Case ...

    African Journals Online (AJOL)

    kofi.mereku

    Development in most areas of life is based on effective knowledge of science and ... Problem solving, as used in mathematics education literature, refers ... word problems, on the other hand, are those linear equation tasks or ... taught LEWPs in the junior high school, many of them reach the senior high school without a.

  18. Effect of dose rate on residual γ-H2AX levels and frequency of micronuclei in X-irradiated mouse lymphocytes.

    Science.gov (United States)

    Turner, H C; Shuryak, I; Taveras, M; Bertucci, A; Perrier, J R; Chen, C; Elliston, C D; Johnson, G W; Smilenov, L B; Amundson, S A; Brenner, D J

    2015-03-01

    The biological risks associated with low-dose-rate (LDR) radiation exposures are not yet well defined. To assess the risk related to DNA damage, we compared the yields of two established biodosimetry end points, γ-H2AX and micronuclei (MNi), in peripheral mouse blood lymphocytes after prolonged in vivo exposure to LDR X rays (0.31 cGy/min) vs. acute high-dose-rate (HDR) exposure (1.03 Gy/min). C57BL/6 mice were total-body irradiated with 320 kVP X rays with doses of 0, 1.1, 2.2 and 4.45 Gy. Residual levels of total γ-H2AX fluorescence in lymphocytes isolated 24 h after the start of irradiation were assessed using indirect immunofluorescence methods. The terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL) assay was used to determine apoptotic cell frequency in lymphocytes sampled at 24 h. Curve fitting analysis suggested that the dose response for γ-H2AX yields after acute exposures could be described by a linear dependence. In contrast, a linear-quadratic dose-response shape was more appropriate for LDR exposure (perhaps reflecting differences in repair time after different LDR doses). Dose-rate sparing effects (P effect across the dose range 24 h or 7 days post exposure. In conclusion, the γ-H2AX biomarker showed higher sensitivity to measure dose-rate effects after low-dose LDR X rays compared to MNi formation; however, confounding factors such as variable repair times post exposure, increased cell killing and cell cycle block likely contributed to the yields of MNi with accumulating doses of ionizing radiation.

  19. On nonnegative solutions of second order linear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, Alexander; Vodstrčil, Petr

    2004-01-01

    Roč. 32, č. 1 (2004), s. 59-88 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z1019905 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics

  20. Corporeidade e sexualidade em dançarinos de rua: axé e hip hop Bodyness and sexuality of street dancers: axé and hip hop

    Directory of Open Access Journals (Sweden)

    Fernando Luiz Cardoso

    2011-12-01

    Full Text Available Analisaram-se aspectos da corporeidade e sexualidade em dançarinos de hip hop e axé (35 homens e 49 mulheres comparativamente a indivíduos não-dançarinos expectadores da plateia (21 homens e 19 mulheres, via questionário anônimo. Os dançarinos de axé foram os mais satisfeitos com suas vidas sexuais, com as preliminares sexuais e os que mais gostavam de se masturbarem em relação aos de hip hop e plateia. Dançarinos do axé apresentaram uma sexualidade mais vinculada ao conhecimento corporal e conexões afetivas. Em ambos estilos, os dançarinos homens davam maior ênfase à genitália e a libido em relação aos aspectos da afetividade.We analyzed selected aspects of the bodyness and sexuality of hip hop and axé dancers (35 men and 49 women in comparison with non-dancer controls (21 men and 19 women through anonymous questionnaire. The axé dancers were the most satisfied with their sexual lives, with sexual preliminaries and who liked more to masturbate when compared with the hip hop dancers and controls. Axé dancers of both sexes presented a strong link between their sexuality and their corporal knowledge and affective connections. Men dancers were more focused in their genitals and gave stronger sexual emphasis to libido rather than affectivity.

  1. A Hamiltonian functional for the linearized Einstein vacuum field equations

    International Nuclear Information System (INIS)

    Rosas-RodrIguez, R

    2005-01-01

    By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained

  2. New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

    Science.gov (United States)

    Hosseini, K.; Ayati, Z.; Ansari, R.

    2018-04-01

    One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

  3. An introduction to linear ordinary differential equations using the impulsive response method and factorization

    CERN Document Server

    Camporesi, Roberto

    2016-01-01

    This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana’s result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.

  4. Some applications of linear difference equations in finance with wolfram|alpha and maple

    Directory of Open Access Journals (Sweden)

    Dana Rıhová

    2014-12-01

    Full Text Available The principle objective of this paper is to show how linear difference equations can be applied to solve some issues of financial mathematics. We focus on the area of compound interest and annuities. In both cases we determine appropriate recursive rules, which constitute the first order linear difference equations with constant coefficients, and derive formulas required for calculating examples. Finally, we present possibilities of application of two selected computer algebra systems Wolfram|Alpha and Maple in this mathematical area.

  5. Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

    Science.gov (United States)

    Gnoffo, Peter A.

    2015-01-01

    Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

  6. AX Tank Farm tank removal study

    International Nuclear Information System (INIS)

    SKELLY, W.A.

    1998-01-01

    This report considers the feasibility of exposing, demolishing, and removing underground storage tanks from the 241-AX Tank Farm at the Hanford Site. For the study, it was assumed that the tanks would each contain 360 ft 3 of residual waste (corresponding to the one percent residual Inventory target cited in the Tri-Party Agreement) at the time of demolition. The 241-AX Tank Farm is being employed as a ''strawman'' in engineering studies evaluating clean and landfill closure options for Hanford single-shell tank farms. The report is one of several reports being prepared for use by the Hanford Tanks Initiative Project to explore potential closure options and to develop retrieval performance evaluation criteria for tank farms

  7. A linear multiple balance method for discrete ordinates neutron transport equations

    International Nuclear Information System (INIS)

    Park, Chang Je; Cho, Nam Zin

    2000-01-01

    A linear multiple balance method (LMB) is developed to provide more accurate and positive solutions for the discrete ordinates neutron transport equations. In this multiple balance approach, one mesh cell is divided into two subcells with quadratic approximation of angular flux distribution. Four multiple balance equations are used to relate center angular flux with average angular flux by Simpson's rule. From the analysis of spatial truncation error, the accuracy of the linear multiple balance scheme is ο(Δ 4 ) whereas that of diamond differencing is ο(Δ 2 ). To accelerate the linear multiple balance method, we also describe a simplified additive angular dependent rebalance factor scheme which combines a modified boundary projection acceleration scheme and the angular dependent rebalance factor acceleration schme. It is demonstrated, via fourier analysis of a simple model problem as well as numerical calculations, that the additive angular dependent rebalance factor acceleration scheme is unconditionally stable with spectral radius < 0.2069c (c being the scattering ration). The numerical results tested so far on slab-geometry discrete ordinates transport problems show that the solution method of linear multiple balance is effective and sufficiently efficient

  8. Nonlinear and linear wave equations for propagation in media with frequency power law losses

    Science.gov (United States)

    Szabo, Thomas L.

    2003-10-01

    The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.

  9. Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria

    Directory of Open Access Journals (Sweden)

    Mervan Pašić

    2016-10-01

    Full Text Available We study non-monotone positive solutions of the second-order linear differential equations: $(p(tx'' + q(t x = e(t$, with positive $p(t$ and $q(t$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions $\\theta (t$ of the corresponding integrable linear equation: $(p(t\\theta''=e(t$. The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions.

  10. Quasi-linear equation for magnetoplasma oscillations in the weakly relativistic approximation

    International Nuclear Information System (INIS)

    Rizzato, F.B.

    1985-01-01

    Some limitations which are present in the dynamical equations for collisionless plasmas are discussed. Some elementary corrections to the linear theories are obtained in a heuristic form, which directly lead to the so-called quasi-linear theories in its non-relativistic and relativistic forms. The effect of the relativistic variation of the gyrofrequency on the diffusion coefficient is examined in a typically perturbative approximation. (author)

  11. Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces

    Directory of Open Access Journals (Sweden)

    Yongjin Li

    2013-08-01

    Full Text Available We prove the Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces. That is, if y is an approximate solution of the differential equation $y''+ alpha y'(t +eta y = 0$ or $y''+ alpha y'(t +eta y = f(t$, then there exists an exact solution of the differential equation near to y.

  12. A three operator split-step method covering a larger set of non-linear partial differential equations

    Science.gov (United States)

    Zia, Haider

    2017-06-01

    This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

  13. Solution of second order linear fuzzy difference equation by Lagrange's multiplier method

    Directory of Open Access Journals (Sweden)

    Sankar Prasad Mondal

    2016-06-01

    Full Text Available In this paper we execute the solution procedure for second order linear fuzzy difference equation by Lagrange's multiplier method. In crisp sense the difference equation are easy to solve, but when we take in fuzzy sense it forms a system of difference equation which is not so easy to solve. By the help of Lagrange's multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.

  14. Solution of linear transport equation using Chebyshev polynomials and Laplace transform

    International Nuclear Information System (INIS)

    Cardona, A.V.; Vilhena, M.T.M.B. de

    1994-01-01

    The Chebyshev polynomials and the Laplace transform are combined to solve, analytically, the linear transport equation in planar geometry, considering isotropic scattering and the one-group model. Numerical simulation is presented. (author)

  15. On a class of strongly degenerate and singular linear elliptic equation

    International Nuclear Information System (INIS)

    Duong Minh Duc, D.M.; Le Dung.

    1992-11-01

    We consider a class of strongly degenerate linear elliptic equation. The boundedness and the Holder regularity of the weak solutions in the weighted Sobolev-Hardy spaces will be studied. (author). 9 refs

  16. A study on linear and nonlinear Schrodinger equations by the variational iteration method

    International Nuclear Information System (INIS)

    Wazwaz, Abdul-Majid

    2008-01-01

    In this work, we introduce a framework to obtain exact solutions to linear and nonlinear Schrodinger equations. The He's variational iteration method (VIM) is used for analytic treatment of these equations. Numerical examples are tested to show the pertinent features of this method

  17. Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients

    Directory of Open Access Journals (Sweden)

    Encinas A.M.

    2018-02-01

    Full Text Available In this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.

  18. Estimativa da área foliar de Sida cordifolia e Sida rhombifolia usando dimensões lineares do limbo foliar Estimate of Sida cordifolia and Sida rhombifolia leaf area using leaf blade linear dimensions

    Directory of Open Access Journals (Sweden)

    S. Bianco

    2008-01-01

    Full Text Available A estimativa da área foliar pode auxiliar na compreensão de relações de interferência entre plantas daninhas e cultivadas. Com o objetivo de obter uma equação que, por meio de parâmetros lineares dimensionais das folhas, permita a estimativa da área foliar de Sida cordifolia e Sida rhombifolia, estudaram-se as correlações entre área foliar real (Af e parâmetros dimensionais do limbo foliar, como o comprimento (C ao longo da nervura principal e a largura máxima (L perpendicular à nervura principal. Foram analisados 200 limbos foliares de cada espécie, coletados em diferentes agroecossistemas na Universidade Estadual Paulista, campus de Jaboticabal. Os modelos estatísticos utilizados foram linear: Y = a + bx; linear simples: Y = bx; geométrico: Y = ax b; e exponencial: Y = ab x. Todos os modelos analisados podem ser empregados para estimação da área foliar de S. cordifolia e S. rhombifolia. Sugere-se optar pela equação linear simples, envolvendo o produto C*L, considerando-se o coeficiente linear igual a zero, em função da praticidade desta. Desse modo, a estimativa da área foliar de S. cordifolia pode ser obtida pela fórmula Af = 0,7878*(C*L, com coeficiente de determinação de 0,9307, enquanto para S. rhombifolia a estimativa da área foliar pode ser obtida pela fórmula Af = 0,6423*(C*L, com coeficiente de determinação de 0,9711.Leaf area estimate may contribute to understand the relationship of interference between weeds and crops. The objective of this research was to obtain a mathematical equation to estimate Sida cordifolia and Sida rhombifolia leaf area based on linear measures of leaf blade. Correlation studies were conducted between real leaf area (Af and dimensional leaf blade parameters such as leaf length (C and maximum leaf width (L. Around 200 leaf blades of each species were analyzed, collected from several agro-ecosystems at São Paulo State University, in Jaboticabal, SP, Brazil. The statistical

  19. Histone H2AX participates the DNA damage-induced ATM activation through interaction with NBS1.

    Science.gov (United States)

    Kobayashi, Junya; Tauchi, Hiroshi; Chen, Benjamin; Burma, Sandeep; Bruma, Sandeep; Tashiro, Satoshi; Matsuura, Shinya; Tanimoto, Keiji; Chen, David J; Komatsu, Kenshi

    2009-03-20

    Phosphorylated histone H2AX (gamma-H2AX) functions in the recruitment of DNA damage response proteins to DNA double-strand breaks (DSBs) and facilitates DSB repair. ATM also co-localizes with gamma-H2AX at DSB sites following its auto-phosphorylation. However, it is unclear whether gamma-H2AX has a role in activation of ATM-dependent cell cycle checkpoints. Here, we show that ATM as well as NBS1 is recruited to damaged-chromatin in a gamma-H2AX-dependent manner. Foci formation of phosphorylated ATM and ATM-dependent phosphorylation is repressed in H2AX-knockdown cells. Furthermore, anti-gamma-H2AX antibody co-immunoprecipitates an ATM-like protein kinase activity in vitro and recombinant H2AX increases in vitro kinase activity of ATM from un-irradiated cells. Moreover, H2AX-deficient cells exhibited a defect in ATM-dependent cell cycle checkpoints. Taken together, gamma-H2AX has important role for effective DSB-dependent activation of ATM-related damage responses via NBS1.

  20. Histone H2AX participates the DNA damage-induced ATM activation through interaction with NBS1

    International Nuclear Information System (INIS)

    Kobayashi, Junya; Tauchi, Hiroshi; Chen, Benjamin; Bruma, Sandeep; Tashiro, Satoshi; Matsuura, Shinya; Tanimoto, Keiji; Chen, David J.; Komatsu, Kenshi

    2009-01-01

    Phosphorylated histone H2AX (γ-H2AX) functions in the recruitment of DNA damage response proteins to DNA double-strand breaks (DSBs) and facilitates DSB repair. ATM also co-localizes with γ-H2AX at DSB sites following its auto-phosphorylation. However, it is unclear whether γ-H2AX has a role in activation of ATM-dependent cell cycle checkpoints. Here, we show that ATM as well as NBS1 is recruited to damaged-chromatin in a γ-H2AX-dependent manner. Foci formation of phosphorylated ATM and ATM-dependent phosphorylation is repressed in H2AX-knockdown cells. Furthermore, anti-γ-H2AX antibody co-immunoprecipitates an ATM-like protein kinase activity in vitro and recombinant H2AX increases in vitro kinase activity of ATM from un-irradiated cells. Moreover, H2AX-deficient cells exhibited a defect in ATM-dependent cell cycle checkpoints. Taken together, γ-H2AX has important role for effective DSB-dependent activation of ATM-related damage responses via NBS1.

  1. Histone H2AX is a critical factor for cellular protection against DNA alkylating agents.

    Science.gov (United States)

    Meador, J A; Zhao, M; Su, Y; Narayan, G; Geard, C R; Balajee, A S

    2008-09-25

    Histone H2A variant H2AX is a dose-dependent suppressor of oncogenic chromosome translocations. H2AX participates in DNA double-strand break repair, but its role in other DNA repair pathways is not known. In this study, role of H2AX in cellular response to alkylation DNA damage was investigated. Cellular sensitivity to two monofunctional alkylating agents (methyl methane sulfonate and N-methyl-N'-nitro-N-nitrosoguanidine (MNNG)) was dependent on H2AX dosage, and H2AX null cells were more sensitive than heterozygous cells. In contrast to wild-type cells, H2AX-deficient cells displayed extensive apoptotic death due to a lack of cell-cycle arrest at G(2)/M phase. Lack of G(2)/M checkpoint in H2AX null cells correlated well with increased mitotic irregularities involving anaphase bridges and gross chromosomal instability. Observation of elevated poly(ADP) ribose polymerase 1 (PARP-1) cleavage suggests that MNNG-induced apoptosis occurs by PARP-1-dependent manner in H2AX-deficient cells. Consistent with this, increased activities of PARP and poly(ADP) ribose (PAR) polymer synthesis were detected in both H2AX heterozygous and null cells. Further, we demonstrate that the increased PAR synthesis and apoptotic death induced by MNNG in H2AX-deficient cells are due to impaired activation of mitogen-activated protein kinase pathway. Collectively, our novel study demonstrates that H2AX, similar to PARP-1, confers cellular protection against alkylation-induced DNA damage. Therefore, targeting either PARP-1 or histone H2AX may provide an effective way of maximizing the chemotherapeutic value of alkylating agents for cancer treatment.

  2. On the classical theory of ordinary linear differential equations of the second order and the Schroedinger equation for power law potentials

    International Nuclear Information System (INIS)

    Lima, M.L.; Mignaco, J.A.

    1983-01-01

    The power law potentials in the Schroedinger equation solved recently are shown to come from the classical treatment of the singularities of a linear, second order differential equation. This allows to enlarge the class of solvable power law potentials. (Author) [pt

  3. Radial solutions to semilinear elliptic equations via linearized operators

    Directory of Open Access Journals (Sweden)

    Phuong Le

    2017-04-01

    Full Text Available Let $u$ be a classical solution of semilinear elliptic equations in a ball or an annulus in $\\mathbb{R}^N$ with zero Dirichlet boundary condition where the nonlinearity has a convex first derivative. In this note, we prove that if the $N$-th eigenvalue of the linearized operator at $u$ is positive, then $u$ must be radially symmetric.

  4. Stochastic Parameter Development for PORFLOW Simulations of the Hanford AX Tank Farm

    International Nuclear Information System (INIS)

    Ho, C.K.; Baca, R.G.; Conrad, S.H.; Smith, G.A.; Shyr, L.; Wheeler, T.A.

    1999-01-01

    Parameters have been identified that can be modeled stochastically using PORFLOW and Latin Hypercube Sampling (LHS). These parameters include hydrologic and transport properties in the vadose and saturated zones, as well as source-term parameters and infiltration rates. A number of resources were used to define the parameter distributions, primarily those provided in the Retrieval Performance Evaluation Report (Jacobs, 1998). A linear rank regression was performed on the vadose-zone hydrologic parameters given in Khaleel and Freeman (1995) to determine if correlations existed between pairs of parameters. No strong correlations were found among the vadose-zone hydrologic parameters, and it was recommended that these parameters be sampled independently until future data or analyses reveal a strong correlation or functional relationship between parameters. Other distributions for source-term parameters, infiltration rates, and saturated-zone parameters that are required to stochastically analyze the performance of the AX Tank Farm using LHS/PORFLOW were adapted from distributions and values reported in Jacobs (1998) and other literature sources. Discussions pertaining to the geologic conceptualization, vadose-zone modeling, and saturated-zone modeling of the AX Tank Farm are also presented

  5. Non-linear mixed-effects pharmacokinetic/pharmacodynamic modelling in NLME using differential equations

    DEFF Research Database (Denmark)

    Tornøe, Christoffer Wenzel; Agersø, Henrik; Madsen, Henrik

    2004-01-01

    The standard software for non-linear mixed-effect analysis of pharmacokinetic/phar-macodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as tong as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential...... equation (ODE) solver package odesolve and the non-Linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlme...

  6. A linear functional differential equation with distributions in the input

    Directory of Open Access Journals (Sweden)

    Vadim Z. Tsalyuk

    2003-10-01

    Full Text Available This paper studies the functional differential equation $$ dot x(t = int_a^t {d_s R(t,s, x(s} + F'(t, quad t in [a,b], $$ where $F'$ is a generalized derivative, and $R(t,cdot$ and $F$ are functions of bounded variation. A solution is defined by the difference $x - F$ being absolutely continuous and satisfying the inclusion $$ frac{d}{dt} (x(t - F(t in int_a^t {d_s R(t,s,x(s}. $$ Here, the integral in the right is the multivalued Stieltjes integral presented in cite{VTs1} (in this article we review and extend the results in cite{VTs1}. We show that the solution set for the initial-value problem is nonempty, compact, and convex. A solution $x$ is said to have memory if there exists the function $x$ such that $x(a = x(a$, $x(b = x(b$, $ x(t in [x(t-0,x(t+0]$ for $t in (a,b$, and $frac{d}{dt} (x(t - F(t = int_a^t {d_s R(t,s,{x}(s}$, where Lebesgue-Stieltjes integral is used. We show that such solutions form a nonempty, compact, and convex set. It is shown that solutions with memory obey the Cauchy-type formula $$ x(t in C(t,ax(a + int_a^t C(t,s, dF(s. $$

  7. The H-N method for solving linear transport equation: theory and application

    International Nuclear Information System (INIS)

    Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.

    2002-01-01

    The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions

  8. Microsoft Dynamics AX 2012 R2 services

    CERN Document Server

    Deforche, Klaas

    2014-01-01

    This book is a tutorial guide that covers each topic in depth with examples. The step-by-step approach will help you better understand each task as you will have to perform them frequently when utilizing the services.If you are a Dynamics AX developer, new or experienced who wants to implement services with Microsoft Dynamics AX 2012, then this book is for you. A basic understanding of MorphX and X++ is assumed, but the step-by-step instructions are easy to follow even for beginners. Some examples use C# and .NET, so experience with Visual Studio is a plus but not a must.

  9. Soluble histone H2AX is induced by DNA replication stress and sensitizes cells to undergo apoptosis

    Directory of Open Access Journals (Sweden)

    Duensing Stefan

    2008-07-01

    Full Text Available Abstract Background Chromatin-associated histone H2AX is a key regulator of the cellular responses to DNA damage. However, non-nucleosomal functions of histone H2AX are poorly characterized. We have recently shown that soluble H2AX can trigger apoptosis but the mechanisms leading to non-chromatin-associated H2AX are unclear. Here, we tested whether stalling of DNA replication, a common event in cancer cells and the underlying mechanism of various chemotherapeutic agents, can trigger increased soluble H2AX. Results Transient overexpression of H2AX was found to lead to a detectable fraction of soluble H2AX and was associated with increased apoptosis. This effect was enhanced by the induction of DNA replication stress using the DNA polymerase α inhibitor aphidicolin. Cells manipulated to stably express H2AX did not contain soluble H2AX, however, short-term treatment with aphidicolin (1 h resulted in detectable amounts of H2AX in the soluble nuclear fraction and enhanced apoptosis. Similarly, soluble endogenous H2AX was detected under these conditions. We found that excessive soluble H2AX causes chromatin aggregation and inhibition of ongoing gene transcription as evidenced by the redistribution and/or loss of active RNA polymerase II as well as the transcriptional co-activators CBP and p300. Conclusion Taken together, these results show that DNA replication stress rapidly leads to increased soluble H2AX and that non-chromatin-associated H2AX can sensitize cells to undergo apoptosis. Our findings encourage further studies to explore H2AX and the cellular pathways that control its expression as anti-cancer drug targets.

  10. Piecewise linear emulator of the nonlinear Schroedinger equation and the resulting analytic solutions for Bose-Einstein condensates

    International Nuclear Information System (INIS)

    Theodorakis, Stavros

    2003-01-01

    We emulate the cubic term Ψ 3 in the nonlinear Schroedinger equation by a piecewise linear term, thus reducing the problem to a set of uncoupled linear inhomogeneous differential equations. The resulting analytic expressions constitute an excellent approximation to the exact solutions, as is explicitly shown in the case of the kink, the vortex, and a δ function trap. Such a piecewise linear emulation can be used for any differential equation where the only nonlinearity is a Ψ 3 one. In particular, it can be used for the nonlinear Schroedinger equation in the presence of harmonic traps, giving analytic Bose-Einstein condensate solutions that reproduce very accurately the numerically calculated ones in one, two, and three dimensions

  11. An implicit iterative scheme for solving large systems of linear equations

    International Nuclear Information System (INIS)

    Barry, J.M.; Pollard, J.P.

    1986-12-01

    An implicit iterative scheme for the solution of large systems of linear equations arising from neutron diffusion studies is presented. The method is applied to three-dimensional reactor studies and its performance is compared with alternative iterative approaches

  12. The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

    International Nuclear Information System (INIS)

    Lima, M.L.; Mignaco, J.A.

    1985-01-01

    It is shown that the rational power law potentials in the two-body radial Schoedinger equation admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The admissible potentials come into families evolved from equations having a fixed number of elementary singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

  13. Contact symmetries of general linear second-order ordinary differential equations: letter to the editor

    NARCIS (Netherlands)

    Martini, Ruud; Kersten, P.H.M.

    1983-01-01

    Using 1-1 mappings, the complete symmetry groups of contact transformations of general linear second-order ordinary differential equations are determined from two independent solutions of those equations, and applied to the harmonic oscillator with and without damping.

  14. On the calculation of linear stability with the aid of asymptotic solutions of Orr-Sommerfeld equation, 1

    International Nuclear Information System (INIS)

    Fujimura, Kaoru

    1980-11-01

    The numerical treatment of Orr-Sommerfeld equation which is the fundamental equation of linear hydrodynamic stability theory is described. Present calculation procedure is applied to the two-dimensional quasi-parallel flow for which linearized disturbance equation (Orr-Sommerfeld equation) contains one simple turning point and αR >> 1. The numerical procedure for this problem and one numerical example for Jeffery-Hamel flow (J-H III 1 ) are presented. These treatment can be extended to the other velocity profiles by slight midifications. (author)

  15. About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

    International Nuclear Information System (INIS)

    Dubrovsky, V. G.; Topovsky, A. V.

    2013-01-01

    New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u (n) , n= 1, …, N are constructed via Zakharov and Manakov ∂-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u (n) and calculated by ∂-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schrödinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u (n) . It is shown that the sums u=u (k 1 ) +...+u (k m ) , 1 ⩽k 1 2 m ⩽N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schrödinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

  16. Non self-similar collapses described by the non-linear Schroedinger equation

    International Nuclear Information System (INIS)

    Berge, L.; Pesme, D.

    1992-01-01

    We develop a rapid method in order to find the contraction rates of the radially symmetric collapsing solutions of the nonlinear Schroedinger equation defined for space dimensions exceeding a threshold value. We explicitly determine the asymptotic behaviour of these latter solutions by solving the non stationary linear problem relative to the nonlinear Schroedinger equation. We show that the self-similar states associated with the collapsing solutions are characterized by a spatial extent which is bounded from the top by a cut-off radius

  17. Computer programs for the solution of systems of linear algebraic equations

    Science.gov (United States)

    Sequi, W. T.

    1973-01-01

    FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.

  18. Geon-type solutions of the non-linear Heisenberg-Klein-Gordon equation

    International Nuclear Information System (INIS)

    Mielke, E.W.; Scherzer, R.

    1980-10-01

    As a model for a ''unitary'' field theory of extended particles we consider the non-linear Klein-Gordon equation - associated with a ''squared'' Heisenberg-Pauli-Weyl non-linear spinor equation - coupled to strong gravity. Using a stationary spherical ansatz for the complex scalar field as well as for the background metric generated via Einstein's field equation, we are able to study the effects of the scalar self-interaction as well as of the classical tensor forces. By numerical integration we obtain a continuous spectrum of localized, gravitational solitons resembling the geons previously constructed for the Einstein-Maxwell system by Wheeler. A self-generated curvature potential originating from the curved background partially confines the Schroedinger type wave functions within the ''scalar geon''. For zero angular momentum states and normalized scalar charge the spectrum for the total gravitational energy of these solitons exhibits a branching with respect to the number of nodes appearing in the radial part of the scalar field. Preliminary studies for higher values of the corresponding ''principal quantum number'' reveal that a kind of fine splitting of the energy levels occurs, which may indicate a rich, particle-like structure of these ''quantized geons''. (author)

  19. A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

    Science.gov (United States)

    Camporesi, Roberto

    2016-01-01

    We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors.

  20. Solving Linear Equations by Classical Jacobi-SR Based Hybrid Evolutionary Algorithm with Uniform Adaptation Technique

    OpenAIRE

    Jamali, R. M. Jalal Uddin; Hashem, M. M. A.; Hasan, M. Mahfuz; Rahman, Md. Bazlar

    2013-01-01

    Solving a set of simultaneous linear equations is probably the most important topic in numerical methods. For solving linear equations, iterative methods are preferred over the direct methods especially when the coefficient matrix is sparse. The rate of convergence of iteration method is increased by using Successive Relaxation (SR) technique. But SR technique is very much sensitive to relaxation factor, {\\omega}. Recently, hybridization of classical Gauss-Seidel based successive relaxation t...

  1. Optimal Homotopy Asymptotic Method for Solving the Linear Fredholm Integral Equations of the First Kind

    Directory of Open Access Journals (Sweden)

    Mohammad Almousa

    2013-01-01

    Full Text Available The aim of this study is to present the use of a semi analytical method called the optimal homotopy asymptotic method (OHAM for solving the linear Fredholm integral equations of the first kind. Three examples are discussed to show the ability of the method to solve the linear Fredholm integral equations of the first kind. The results indicated that the method is very effective and simple.

  2. Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

    Science.gov (United States)

    Pathak, H. K.; Grewal, A. S.

    2002-01-01

    This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

  3. The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

    International Nuclear Information System (INIS)

    Lima, M.L.; Mignaco, J.A.

    1985-01-01

    It is shown that the rational power law potentials in the two-body radial Schrodinger equations admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The resulting potentials come into families evolved from equations having a fixed number of elementary regular singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

  4. Insights into the School Mathematics Tradition from Solving Linear Equations

    Science.gov (United States)

    Buchbinder, Orly; Chazan, Daniel; Fleming, Elizabeth

    2015-01-01

    In this article, we explore how the solving of linear equations is represented in English­-language algebra text books from the early nineteenth century when schooling was becoming institutionalized, and then survey contemporary teachers. In the text books, we identify the increasing presence of a prescribed order of steps (a canonical method) for…

  5. Oscillatory solutions of the Cauchy problem for linear differential equations

    Directory of Open Access Journals (Sweden)

    Gro Hovhannisyan

    2015-06-01

    Full Text Available We consider the Cauchy problem for second and third order linear differential equations with constant complex coefficients. We describe necessary and sufficient conditions on the data for the existence of oscillatory solutions. It is known that in the case of real coefficients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the complex case: hence in practice it is possible to control oscillatory behavior by varying the initial conditions. Our Proofs are based on asymptotic analysis of the zeros of solutions, represented as linear combinations of exponential functions.

  6. Visualisation of γH2AX Foci Caused by Heavy Ion Particle Traversal; Distinction between Core Track versus Non-Track Damage

    Science.gov (United States)

    Nakajima, Nakako Izumi; Brunton, Holly; Watanabe, Ritsuko; Shrikhande, Amruta; Hirayama, Ryoichi; Matsufuji, Naruhiro; Fujimori, Akira; Murakami, Takeshi; Okayasu, Ryuichi; Jeggo, Penny; Shibata, Atsushi

    2013-01-01

    Heavy particle irradiation produces complex DNA double strand breaks (DSBs) which can arise from primary ionisation events within the particle trajectory. Additionally, secondary electrons, termed delta-electrons, which have a range of distributions can create low linear energy transfer (LET) damage within but also distant from the track. DNA damage by delta-electrons distant from the track has not previously been carefully characterised. Using imaging with deconvolution, we show that at 8 hours after exposure to Fe (∼200 keV/µm) ions, γH2AX foci forming at DSBs within the particle track are large and encompass multiple smaller and closely localised foci, which we designate as clustered γH2AX foci. These foci are repaired with slow kinetics by DNA non-homologous end-joining (NHEJ) in G1 phase with the magnitude of complexity diminishing with time. These clustered foci (containing 10 or more individual foci) represent a signature of DSBs caused by high LET heavy particle radiation. We also identified simple γH2AX foci distant from the track, which resemble those arising after X-ray exposure, which we attribute to low LET delta-electron induced DSBs. They are rapidly repaired by NHEJ. Clustered γH2AX foci induced by heavy particle radiation cause prolonged checkpoint arrest compared to simple γH2AX foci following X-irradiation. However, mitotic entry was observed when ∼10 clustered foci remain. Thus, cells can progress into mitosis with multiple clusters of DSBs following the traversal of a heavy particle. PMID:23967070

  7. Role of statistical linearization in the solution of nonlinear stochastic equations

    International Nuclear Information System (INIS)

    Budgor, A.B.

    1977-01-01

    The solution of a generalized Langevin equation is referred to as a stochastic process. If the external forcing function is Gaussian white noise, the forward Kolmogarov equation yields the transition probability density function. Nonlinear problems must be handled by approximation procedures e.g., perturbation theories, eigenfunction expansions, and nonlinear optimization procedures. After some comments on the first two of these, attention is directed to the third, and the method of statistical linearization is used to demonstrate a relation to the former two. Nonlinear stochastic systems exhibiting sustained or forced oscillations and the centered nonlinear Schroedinger equation in the presence of Gaussian white noise excitation are considered as examples. 5 figures, 2 tables

  8. Analytical approach to linear fractional partial differential equations arising in fluid mechanics

    International Nuclear Information System (INIS)

    Momani, Shaher; Odibat, Zaid

    2006-01-01

    In this Letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equations arising in fluid mechanics. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these methods, the solution takes the form of a convergent series with easily computable components. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the two methods

  9. Local Ray-Based Traveltime Computation Using the Linearized Eikonal Equation

    KAUST Repository

    Almubarak, Mohammed S.

    2013-05-01

    The computation of traveltimes plays a critical role in the conventional implementations of Kirchhoff migration. Finite-difference-based methods are considered one of the most effective approaches for traveltime calculations and are therefore widely used. However, these eikonal solvers are mainly used to obtain early-arrival traveltime. Ray tracing can be used to pick later traveltime branches, besides the early arrivals, which may lead to an improvement in velocity estimation or in seismic imaging. In this thesis, I improved the accuracy of the solution of the linearized eikonal equation by constructing a linear system of equations (LSE) based on finite-difference approximation, which is of second-order accuracy. The ill-conditioned LSE is initially regularized and subsequently solved to calculate the traveltime update. Numerical tests proved that this method is as accurate as the second-order eikonal solver. Later arrivals are picked using ray tracing. These traveltimes are binned to the nearest node on a regular grid and empty nodes are estimated by interpolating the known values. The resulting traveltime field is used as an input to the linearized eikonal algorithm, which improves the accuracy of the interpolated nodes and yields a local ray-based traveltime. This is a preliminary study and further investigation is required to test the efficiency and the convergence of the solutions.

  10. Quantitative evaluation of radiation dose by γ-H2AX on a microfluidic chip in a miniature fluorescence cytometer

    International Nuclear Information System (INIS)

    Wang, Junsheng; Song, Wendong; Song, Yongxin; Xu, Dan; Zhang, Min; Pan, Xinxiang; Sun, Yeqing; Li, Dongqing

    2014-01-01

    Evaluation of radiation dose is very important for the detection of radiation damage. γ-H2AX is a popular biological dosimeter to evaluate the radiation effect. Typically, bulky and expensive commercial flow cytometers are used to detect γ-H2AX. This paper presents a miniaturized and high sensitive cytometer using a microfluidic chip for evaluating the radiation dose by detecting the mean immunofluorescence intensity of γ-H2AX. A compact optical focusing system and a shift-phase differential amplifier are designed to improve the detection sensitivity. Sample lymphocyte cells are stained by FITC fluorescent dye after being irradiated by UVC. Comparison experiments between the developed miniature cytometer and a commercial flow cytometer were conducted under different radiation doses. The developed microfluidic cytometer also demonstrates a good linear correlation between the measured fluorescence intensity and the irradiation dose with a detection limit similar to that of the commercial flow cytometer. The developed cytometer can evaluate quantitatively the radiation dose by the mean fluorescence intensity of γ-H2AX with a significantly smaller amount of blood samples than a commercial flow cytometer. - Highlights: • A new microfluidic cytometer for evaluating irradiation dose was developed. • The utility of this biosensor is verified by comparison experiments using FCM. • The developed cytometer is small size, high sensitivity, low cost, and simple. • The cytometer can dramatically reduce sample consumption and analysis time

  11. The profiles of gamma-H2AX along with ATM/DNA-PKcs activation in the lymphocytes and granulocytes of rat and human blood exposed to gamma rays.

    Science.gov (United States)

    Wang, Jing; Yin, Lina; Zhang, Junxiang; Zhang, Yaping; Zhang, Xuxia; Ding, Defang; Gao, Yun; Li, Qiang; Chen, Honghong

    2016-08-01

    Establishing a rat model suitable for γ-H2AX biodosimeter studies has important implications for dose assessment of internal radionuclide contamination in humans. In this study, γ-H2AX, p-ATM and p-DNA-PKcs foci were enumerated using immunocytofluorescence method, and their protein levels were measured by Western blot in rat blood lymphocytes and granulocytes exposed to γ-rays compared with human blood lymphocytes and granulocytes. It was found that DNA double-strand break repair kinetics and linear dose responses in rat lymphocytes were similar to those observed in the human counterparts. Moreover, radiation induced clear p-ATM and p-DNA-PKcs foci formation and an increase in ratio of co-localization of p-ATM or p-DNA-PKcs with γ-H2AX foci in rat lymphocytes similar to those of human lymphocytes. The level of γ-H2AX protein in irradiated rat and human lymphocytes was significantly reduced by inhibitors of ATM and DNA-PKcs. Surprisingly, unlike human granulocytes, rat granulocytes with DNA-PKcs deficiency displayed a rapid accumulation, but delayed disappearance of γ-H2AX foci with essentially no change from 10 h to 48 h post-irradiation. Furthermore, inhibition of ATM activity in rat granulocytes also decreased radiation-induced γ-H2AX foci formation. In comparison, human granulocytes showed no response to irradiation regarding γ-H2AX, p-ATM or p-DNA-PKcs foci. Importantly, incidence of γ-H2AX foci in lymphocytes after total-body radiation of rats was consistent with that of in vitro irradiation of rat lymphocytes. These findings show that rats are a useful in vivo model for validation of γ-H2AX biodosimetry for dose assessment in humans. ATM and DNA-PKcs participate together in DSB repair in rat lymphocytes similar to that of human lymphocytes. Further, rat granulocytes, which have the characteristic of delayed disappearance of γ-H2AX foci in response to radiation, may be a useful experimental system for biodosimetry studies.

  12. The profiles of gamma-H2AX along with ATM/DNA-PKcs activation in the lymphocytes and granulocytes of rat and human blood exposed to gamma rays

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Jing; Yin, Lina; Zhang, Junxiang; Zhang, Yaping; Zhang, Xuxia; Ding, Defang; Gao, Yun; Li, Qiang; Chen, Honghong [Fudan University, Department of Radiation Biology, Institute of Radiation Medicine, Shanghai (China)

    2016-08-15

    Establishing a rat model suitable for γ-H2AX biodosimeter studies has important implications for dose assessment of internal radionuclide contamination in humans. In this study, γ-H2AX, p-ATM and p-DNA-PKcs foci were enumerated using immunocytofluorescence method, and their protein levels were measured by Western blot in rat blood lymphocytes and granulocytes exposed to γ-rays compared with human blood lymphocytes and granulocytes. It was found that DNA double-strand break repair kinetics and linear dose responses in rat lymphocytes were similar to those observed in the human counterparts. Moreover, radiation induced clear p-ATM and p-DNA-PKcs foci formation and an increase in ratio of co-localization of p-ATM or p-DNA-PKcs with γ-H2AX foci in rat lymphocytes similar to those of human lymphocytes. The level of γ-H2AX protein in irradiated rat and human lymphocytes was significantly reduced by inhibitors of ATM and DNA-PKcs. Surprisingly, unlike human granulocytes, rat granulocytes with DNA-PKcs deficiency displayed a rapid accumulation, but delayed disappearance of γ-H2AX foci with essentially no change from 10 h to 48 h post-irradiation. Furthermore, inhibition of ATM activity in rat granulocytes also decreased radiation-induced γ-H2AX foci formation. In comparison, human granulocytes showed no response to irradiation regarding γ-H2AX, p-ATM or p-DNA-PKcs foci. Importantly, incidence of γ-H2AX foci in lymphocytes after total-body radiation of rats was consistent with that of in vitro irradiation of rat lymphocytes. These findings show that rats are a useful in vivo model for validation of γ-H2AX biodosimetry for dose assessment in humans. ATM and DNA-PKcs participate together in DSB repair in rat lymphocytes similar to that of human lymphocytes. Further, rat granulocytes, which have the characteristic of delayed disappearance of γ-H2AX foci in response to radiation, may be a useful experimental system for biodosimetry studies. (orig.)

  13. The profiles of gamma-H2AX along with ATM/DNA-PKcs activation in the lymphocytes and granulocytes of rat and human blood exposed to gamma rays

    International Nuclear Information System (INIS)

    Wang, Jing; Yin, Lina; Zhang, Junxiang; Zhang, Yaping; Zhang, Xuxia; Ding, Defang; Gao, Yun; Li, Qiang; Chen, Honghong

    2016-01-01

    Establishing a rat model suitable for γ-H2AX biodosimeter studies has important implications for dose assessment of internal radionuclide contamination in humans. In this study, γ-H2AX, p-ATM and p-DNA-PKcs foci were enumerated using immunocytofluorescence method, and their protein levels were measured by Western blot in rat blood lymphocytes and granulocytes exposed to γ-rays compared with human blood lymphocytes and granulocytes. It was found that DNA double-strand break repair kinetics and linear dose responses in rat lymphocytes were similar to those observed in the human counterparts. Moreover, radiation induced clear p-ATM and p-DNA-PKcs foci formation and an increase in ratio of co-localization of p-ATM or p-DNA-PKcs with γ-H2AX foci in rat lymphocytes similar to those of human lymphocytes. The level of γ-H2AX protein in irradiated rat and human lymphocytes was significantly reduced by inhibitors of ATM and DNA-PKcs. Surprisingly, unlike human granulocytes, rat granulocytes with DNA-PKcs deficiency displayed a rapid accumulation, but delayed disappearance of γ-H2AX foci with essentially no change from 10 h to 48 h post-irradiation. Furthermore, inhibition of ATM activity in rat granulocytes also decreased radiation-induced γ-H2AX foci formation. In comparison, human granulocytes showed no response to irradiation regarding γ-H2AX, p-ATM or p-DNA-PKcs foci. Importantly, incidence of γ-H2AX foci in lymphocytes after total-body radiation of rats was consistent with that of in vitro irradiation of rat lymphocytes. These findings show that rats are a useful in vivo model for validation of γ-H2AX biodosimetry for dose assessment in humans. ATM and DNA-PKcs participate together in DSB repair in rat lymphocytes similar to that of human lymphocytes. Further, rat granulocytes, which have the characteristic of delayed disappearance of γ-H2AX foci in response to radiation, may be a useful experimental system for biodosimetry studies. (orig.)

  14. Phosphorylation of Histone H2AX in the Mouse Brain from Development to Senescence

    Directory of Open Access Journals (Sweden)

    Serena Barral

    2014-01-01

    Full Text Available Phosphorylation of the histone H2AX (γH2AX form is an early response to DNA damage and a marker of aging and disease in several cells and tissues outside the nervous system. Little is known about in vivo phosphorylation of H2AX in neurons, although it was suggested that γH2AX is an early marker of neuronal endangerment thus opening the possibility to target it as a neuroprotective strategy. After experimental labeling of DNA-synthesizing cells with 5-bromo-2-deoxyuridine (BrdU, we studied the brain occurrence of γH2AX in developing, postnatal, adult and senescent (2 years mice by light and electron microscopic immunocytochemistry and Western blotting. Focal and/or diffuse γH2AX immunostaining appears in interkinetic nuclei, mitotic chromosomes, and apoptotic nuclei. Immunoreactivity is mainly associated with neurogenetic areas, i.e., the subventricular zone (SVZ of telencephalon, the cerebellar cortex, and, albeit to a much lesser extent, the subgranular zone of the hippocampal dentate gyrus. In addition, γH2AX is highly expressed in the adult and senescent cerebral cortex, particularly the piriform cortex. Double labeling experiments demonstrate that γH2AX in neurogenetic brain areas is temporally and functionally related to proliferation and apoptosis of neuronal precursors, i.e., the type C transit amplifying cells (SVZ and the granule cell precursors (cerebellum. Conversely, γH2AX-immunoreactive cortical neurons incorporating the S phase-label BrdU do not express the proliferation marker phosphorylated histone H3, indicating that these postmitotic cells undergo a significant DNA damage response. Our study paves the way for a better comprehension of the role of H2AX phosphorylation in the normal brain, and offers additional data to design novel strategies for the protection of neuronal precursors and mature neurons in central nervous system (CNS degenerative diseases.

  15. Linear stochastic differential equations with anticipating initial conditions

    DEFF Research Database (Denmark)

    Khalifa, Narjess; Kuo, Hui-Hsiung; Ouerdiane, Habib

    In this paper we use the new stochastic integral introduced by Ayed and Kuo (2008) and the results obtained by Kuo et al. (2012b) to find a solution to a drift-free linear stochastic differential equation with anticipating initial condition. Our solution is based on well-known results from...... classical Itô theory and anticipative Itô formula results from Kue et al. (2012b). We also show that the solution obtained by our method is consistent with the solution obtained by the methods of Malliavin calculus, e.g. Buckdahn and Nualart (1994)....

  16. A general method for enclosing solutions of interval linear equations

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří

    2012-01-01

    Roč. 6, č. 4 (2012), s. 709-717 ISSN 1862-4472 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * enclosure * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 1.654, year: 2012

  17. An efficient parallel algorithm for the solution of a tridiagonal linear system of equations

    Science.gov (United States)

    Stone, H. S.

    1971-01-01

    Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.

  18. Some oscillation criteria for the second-order linear delay differential equation

    Czech Academy of Sciences Publication Activity Database

    Opluštil, Z.; Šremr, Jiří

    2011-01-01

    Roč. 136, č. 2 (2011), s. 195-204 ISSN 0862-7959 Institutional research plan: CEZ:AV0Z10190503 Keywords : second-order linear differential equation with a delay * oscillatory solution Subject RIV: BA - General Mathematics http://www.dml.cz/handle/10338.dmlcz/141582

  19. Refined Fuchs inequalities for systems of linear differential equations

    International Nuclear Information System (INIS)

    Gontsov, R R

    2004-01-01

    We refine the Fuchs inequalities obtained by Corel for systems of linear meromorphic differential equations given on the Riemann sphere. Fuchs inequalities enable one to estimate the sum of exponents of the system over all its singular points. We refine these well-known inequalities by considering the Jordan structure of the leading coefficient of the Laurent series for the matrix of the right-hand side of the system in the neighbourhood of a singular point

  20. A non linear half space problem for radiative transfer equations. Application to the Rosseland approximation

    International Nuclear Information System (INIS)

    Sentis, R.

    1984-07-01

    The radiative transfer equations may be approximated by a non linear diffusion equation (called Rosseland equation) when the mean free paths of the photons are small with respect to the size of the medium. Some technical assomptions are made, namely about the initial conditions, to avoid any problem of initial layer terms

  1. Axé music: mitos, verdades e world music Axé music: myths, truths and world music

    Directory of Open Access Journals (Sweden)

    Armando Alexandre Castro

    2010-12-01

    Full Text Available O artigo discute a Axé music, oferecendo elementos na tentativa de desconstrução de três mitos nela evidenciados: monocultura, baixa qualidade técnica e sua decadência. A metodologia utilizada privilegia a análise de conteúdo, tendo como meios de verificação e coleta de dados entrevistas semi-estruturadas com músicos, técnicos, produtores e empresários musicais de Salvador, além de pesquisa documental relacionada ao campo musical baiano atual.The article discusses Axé music providing elements in an attempt to deconstruc three myths related to it: monoculture, low technical quality and its decadence. The method used focuses on content analysis, departing from verification of data collected through semi- structured interviews with musicians, technical staff, producers and music business executives from Salvador (Brazil, along with documental research related to the musical scene of Bahia today.

  2. Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampère equations VIASM 2016

    CERN Document Server

    Tran, Hung

    2017-01-01

    Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry. Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the n...

  3. Solution of linear ordinary differential equations by means of the method of variation of arbitrary constants

    DEFF Research Database (Denmark)

    Mejlbro, Leif

    1997-01-01

    An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians.......An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians....

  4. Linear and nonlinear analogues of the Schroedinger equation in the contextual approach in quantum mechanics

    International Nuclear Information System (INIS)

    Khrennikov, A.Yu.

    2005-01-01

    One derived the general evolutionary differential equation within the Hilbert space describing dynamics of the wave function. The derived contextual model is more comprehensive in contrast to a quantum one. The contextual equation may be a nonlinear one. Paper presents the conditions ensuring linearity of the evolution and derivation of the Schroedinger equation [ru

  5. Gamma-H2AX as a biomarker of DNA damage induced by ionizing radiation in targeted and bystander human artificial skin models and peripheral blood lymphocytes

    Science.gov (United States)

    Redon, Christophe; Dickey, Jennifer; Bonner, William; Sedelnikova, Olga

    Ionizing radiation (IR) exposure is inevitable. In addition to exposure from cosmic rays, the sun and radioactive substances, modern society has created new sources of radiation exposure such as space and high altitude journeys, X-ray diagnostics, radiological treatments and the increasing threat of radiobiological terrorism. For these reasons, a reliable, reproducible and sensitive assessment of dose and time exposure to IR is essential. We developed a minimally invasive diagnostic test for IR exposure based on detection of a phosphorylated variant of histone H2AX (gamma-H2AX), which occurs specifically at sites of DNA double-strand breaks (DSBs). The phosphorylation of thousands of H2AX molecules forms a gamma-H2AX focus in the chromatin flanking the DSB site that can be detected in situ. We analyzed gamma- H2AX focus formation in both directly irradiated cells as well as in un-irradiated "bystanders" in close contact with irradiated cells. In order to insure minimal invasiveness, we examined commercially available artificial skin models as a surrogate for human skin biopsies as well as peripheral blood lymphocytes. In human skin models, cells in a thin plane were microbeamirradiated and gamma-H2AX formation was measured both in irradiated and in distal bystander cells over time. In irradiated cells DSB formation reached a maximum at 15-30 minutes post- IR and then declined within several hours; all cells were affected. In marked contrast, the incidence of DSBs in bystander cells reached a maximum by 12-48 hours post-irradiation, gradually decreasing over the 7 day time course. At the maxima, 40-60% of bystander cells were affected. Similarly, we analyzed blood samples exposed to IR ex vivo at doses ranging from 0.02 to 3 Gy. The amount of DNA damage was linear in respect to radiation dose and independent of the age or sex of the blood donor. The method is highly reproducible and highly sensitive. In directly irradiated cells, the number of gamma-H2AX foci peaked

  6. Multi-point boundary value problems for linear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Domoshnitsky, A.; Hakl, Robert; Půža, Bedřich

    2017-01-01

    Roč. 24, č. 2 (2017), s. 193-206 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : boundary value problems * linear functional-differential equations * functional-differential inequalities Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0076/gmj-2016-0076. xml

  7. Multi-point boundary value problems for linear functional-differential equations

    Czech Academy of Sciences Publication Activity Database

    Domoshnitsky, A.; Hakl, Robert; Půža, Bedřich

    2017-01-01

    Roč. 24, č. 2 (2017), s. 193-206 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : boundary value problems * linear functional- differential equations * functional- differential inequalities Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0076/gmj-2016-0076.xml

  8. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

    Science.gov (United States)

    Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

    2017-04-01

    This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

  9. AX Tank farm closure settlement estimates and soil testing; TOPICAL

    International Nuclear Information System (INIS)

    BECKER, D.L.

    1999-01-01

    This study provides a conservative three-dimensional settlement study of the AX Tank Farm closure with fill materials and a surface barrier. The finite element settlement model constructed included the interaction of four tanks and the surface barrier with the site soil and bedrock. Also addressed are current soil testing techniques suitable for the site soil with recommendations applicable to the AX Tank Farm and the planned cone penetration testing

  10. First order linear ordinary differential equations in associative algebras

    Directory of Open Access Journals (Sweden)

    Gordon Erlebacher

    2004-01-01

    Full Text Available In this paper, we study the linear differential equation $$ frac{dx}{dt}=sum_{i=1}^n a_i(t x b_i(t + f(t $$ in an associative but non-commutative algebra $mathcal{A}$, where the $b_i(t$ form a set of commuting $mathcal{A}$-valued functions expressed in a time-independent spectral basis consisting of mutually annihilating idempotents and nilpotents. Explicit new closed solutions are derived, and examples are presented to illustrate the theory.

  11. Rancang Bangun Modul PAD (Packet Assembler Dissassembler Menggunakan AX.25 pada Sistem Komunikasi ITS-SAT

    Directory of Open Access Journals (Sweden)

    Pasang Arung Padang

    2013-09-01

    Full Text Available ITS-Sat merupakan jenis satelit piko yang saat ini sedang dikembangkan di Institut Teknologi Sepuluh Nopember. ITS-Sat membutuhkan suatu protokol komunikasi yang mengatur tata cara komunikasi satelit. Protokol AX.25 merupakan protokol komunikasi yang digunakan dalam sistem komunikasi ITS-Sat. Protokol ini berada pada layer data link dalam model OSI Layer. Protokol ini dapat membangun dan memutuskan link serta melakukan pengiriman data. Protokol AX.25 menggabungkan data-data field menjadi suatu frame. Makalah ini mengimplementasikan protokol AX.25 ke dalam modul PAD (Packet Assembler Dissassembler. Protokol AX.25 diimplementasikan ke dalam mikrokontroler yang merupakan otak dari modul PAD dengan menggunakan bahasa pemograman. Modul PAD berfungsi untuk mengkapsulasi data tiap field menjadi sebuah frame AX.25 sebelum dikirim dan kemudian frame AX.25 yang diterima dienkapsulasi kembali menjadi data field. Modul PAD yang dibuat dapat mengirim dan menerima data teks sebanyak 500 karakter. Hasil pengujian menunjukan bahwa modul PAD yang dibuat mampu melakukan komunikasi antar modul PAD dengan baik.

  12. Myshkis type oscillation criteria for second-order linear delay differential equations

    Czech Academy of Sciences Publication Activity Database

    Opluštil, Z.; Šremr, Jiří

    2015-01-01

    Roč. 178, č. 1 (2015), s. 143-161 ISSN 0026-9255 Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillation criteria Subject RIV: BA - General Mathematics Impact factor: 0.664, year: 2015 http://link.springer.com/article/10.1007%2Fs00605-014-0719-y

  13. Comparison of nonlinearities in oscillation theory of half-linear differential equations

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel

    2008-01-01

    Roč. 121, č. 2 (2008), s. 93-105 ISSN 0236-5294 R&D Projects: GA AV ČR KJB100190701 Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear differential equation * comparison theorem * Riccati technique Subject RIV: BA - General Mathematics Impact factor: 0.317, year: 2008

  14. Linear hyperbolic functional-differential equations with essentially bounded right-hand side

    Czech Academy of Sciences Publication Activity Database

    Domoshnitsky, A.; Lomtatidze, Alexander; Maghakyan, A.; Šremr, Jiří

    2011-01-01

    Roč. 2011, - (2011), s. 242965 ISSN 1085-3375 Institutional research plan: CEZ:AV0Z10190503 Keywords : linear functional-differential equation of hyperbolic type * Darboux problem * unique solvability Subject RIV: BA - General Mathematics Impact factor: 1.318, year: 2011 http://www.hindawi.com/journals/ aaa /2011/242965/

  15. Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations

    Directory of Open Access Journals (Sweden)

    Matt Challacombe

    2014-03-01

    Full Text Available A new approach to solving the Time-Dependent Self-Consistent-Field equations is developed based on the double quotient formulation of Tsiper 2001 (J. Phys. B. Dual channel, quasi-independent non-linear optimization of these quotients is found to yield convergence rates approaching those of the best case (single channel Tamm-Dancoff approximation. This formulation is variational with respect to matrix truncation, admitting linear scaling solution of the matrix-eigenvalue problem, which is demonstrated for bulk excitons in the polyphenylene vinylene oligomer and the (4,3 carbon nanotube segment.

  16. A novel algebraic procedure for solving non-linear evolution equations of higher order

    International Nuclear Information System (INIS)

    Huber, Alfred

    2007-01-01

    We report here a systematic approach that can easily be used for solving non-linear partial differential equations (nPDE), especially of higher order. We restrict the analysis to the so called evolution equations describing any wave propagation. The proposed new algebraic approach leads us to traveling wave solutions and moreover, new class of solution can be obtained. The crucial step of our method is the basic assumption that the solutions satisfy an ordinary differential equation (ODE) of first order that can be easily integrated. The validity and reliability of the method is tested by its application to some non-linear evolution equations. The important aspect of this paper however is the fact that we are able to calculate distinctive class of solutions which cannot be found in the current literature. In other words, using this new algebraic method the solution manifold is augmented to new class of solution functions. Simultaneously we would like to stress the necessity of such sophisticated methods since a general theory of nPDE does not exist. Otherwise, for practical use the algebraic construction of new class of solutions is of fundamental interest

  17. OSCILLATION OF A SECOND-ORDER HALF-LINEAR NEUTRAL DAMPED DIFFERENTIAL EQUATION WITH TIME-DELAY

    Institute of Scientific and Technical Information of China (English)

    2012-01-01

    In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain function,some new sufficient conditions for the oscillation are given for all solutions to the equation.

  18. Mathematics Literacy of Secondary Students in Solving Simultanenous Linear Equations

    Science.gov (United States)

    Sitompul, R. S. I.; Budayasa, I. K.; Masriyah

    2018-01-01

    This study examines the profile of secondary students’ mathematical literacy in solving simultanenous linear equations problems in terms of cognitive style of visualizer and verbalizer. This research is a descriptive research with qualitative approach. The subjects in this research consist of one student with cognitive style of visualizer and one student with cognitive style of verbalizer. The main instrument in this research is the researcher herself and supporting instruments are cognitive style tests, mathematics skills tests, problem-solving tests and interview guidelines. Research was begun by determining the cognitive style test and mathematics skill test. The subjects chosen were given problem-solving test about simultaneous linear equations and continued with interview. To ensure the validity of the data, the researcher conducted data triangulation; the steps of data reduction, data presentation, data interpretation, and conclusion drawing. The results show that there is a similarity of visualizer and verbalizer-cognitive style in identifying and understanding the mathematical structure in the process of formulating. There are differences in how to represent problems in the process of implementing, there are differences in designing strategies and in the process of interpreting, and there are differences in explaining the logical reasons.

  19. Hadronic equation of state in the statistical bootstrap model and linear graph theory

    International Nuclear Information System (INIS)

    Fre, P.; Page, R.

    1976-01-01

    Taking a statistical mechanical point og view, the statistical bootstrap model is discussed and, from a critical analysis of the bootstrap volume comcept, it is reached a physical ipothesis, which leads immediately to the hadronic equation of state provided by the bootstrap integral equation. In this context also the connection between the statistical bootstrap and the linear graph theory approach to interacting gases is analyzed

  20. On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity

    International Nuclear Information System (INIS)

    Aristov, Anatoly I

    2011-01-01

    We investigate the asymptotic behaviour as t→∞ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.

  1. A generalized variational algebra and conserved densities for linear evolution equations

    International Nuclear Information System (INIS)

    Abellanas, L.; Galindo, A.

    1978-01-01

    The symbolic algebra of Gel'fand and Dikii is generalized to the case of n variables. Using this algebraic approach a rigorous characterization of the polynomial kernel of the variational derivative is given. This is applied to classify all the conservation laws for linear polynomial evolution equations of arbitrary order. (Auth.)

  2. Peculiarities in power type comparison results for half-linear dynamic equations

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel

    2012-01-01

    Roč. 42, č. 6 (2012), s. 1995-2013 ISSN 0035-7596 R&D Projects: GA AV ČR KJB100190701 Institutional support: RVO:67985840 Keywords : half-linear dynamic equation * time scale * comparison theorem Subject RIV: BA - General Mathematics Impact factor: 0.389, year: 2012 http://projecteuclid.org/euclid.rmjm/1361800616

  3. Microscopic evaluation of nuclear foci (gamma H2AX) in cells irradiated with protons and lithium ions

    International Nuclear Information System (INIS)

    Bracalente, C.; Molinari, Beatriz L.; Duran, Hebe; Ibanez, I.; Palmieri, M.; Kreiner, Andres J.; Burlon, Alejandro; Valda, Alejandro; Davidson, J.; Davidson, M.; Vazquez, Monica; Ozafran, Mabel J.

    2007-01-01

    Full text: The special properties of both physical and biological radiation particles with high-LET (Linear Transfer of Energy) have led to its increased use in cancer therapy. In this work, the effect of high and low LET radiation on cell lines with different radiosensitivity (Irs-20 and CHO-10B2) quantifying the number and size of nuclear foci obtained from histone H2AX (γH2AX) phosphorylation which plays an important role in DNA damage reparation is compared. Foci detection was performed by immunocytochemical methods and fluorescence microscopy. The cells cultures were irradiated with plateau-phase protons (14 MeV, LET: 3 keV/μ), on Bragg peak (3 MeV. LET: 14 KeV/μ) and with Lithium ions (7 MeV, LET: 250 KeV//μ) on the Tandar accelerator. A clonogenic analysis of the two cell lines was made. Irradiation with protons (low LET) showed a significant difference (p [es

  4. About simple nonlinear and linear superpositions of special exact solutions of Veselov-Novikov equation

    Energy Technology Data Exchange (ETDEWEB)

    Dubrovsky, V. G.; Topovsky, A. V. [Novosibirsk State Technical University, Karl Marx prosp. 20, Novosibirsk 630092 (Russian Federation)

    2013-03-15

    New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums of special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.

  5. Chaotic dynamics and diffusion in a piecewise linear equation

    International Nuclear Information System (INIS)

    Shahrear, Pabel; Glass, Leon; Edwards, Rod

    2015-01-01

    Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems

  6. Chaotic dynamics and diffusion in a piecewise linear equation

    Science.gov (United States)

    Shahrear, Pabel; Glass, Leon; Edwards, Rod

    2015-03-01

    Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.

  7. Dyson-Schwinger equations for the non-linear σ-model

    International Nuclear Information System (INIS)

    Drouffe, J.M.; Flyvbjerg, H.

    1989-08-01

    Dyson-Schwinger equations for the O(N)-symmetric non-linear σ-model are derived. They are polynomials in N, hence 1/N-expanded ab initio. A finite, closed set of equations is obtained by keeping only the leading term and the first correction term in this 1/N-series. These equations are solved numerically in two dimensions on square lattices measuring 50x50, 100x100, 200x200, and 400x400. They are also solved analytically at strong coupling and at weak coupling in a finite volume. In these two limits the solution is asymptotically identical to the exact strong- and weak-coupling series through the first three terms. Between these two limits, results for the magnetic susceptibility and the mass gap are identical to the Monte Carlo results available for N=3 and N=4 within a uniform systematic error of O(1/N 3 ), i.e. the results seem good to O(1/N 2 ), though obtained from equations that are exact only to O(1/N). This is understood by seeing the results as summed infinite subseries of the 1/N-series for the exact susceptibility and mass gap. We conclude that the kind of 1/N-expansion presented here converges as well as one might ever hope for, even for N as small as 3. (orig.)

  8. An Interface Tracking Algorithm for the Porous Medium Equation.

    Science.gov (United States)

    1983-03-01

    equation (1.11). N [v n n 2(2) = n . AV k + wk---IY" 2] +l~ x A t K Ax E E 2+ VeTA i;- 2k1 n- o (nr+l) <k-<.(n+l) N [Av] [ n+l <Ax Z m(v ) I~+lIAxAt...RD-R127 685 AN INTERFACE TRACKING ALGORITHM FOR THE POROUS MEDIUM / EQURTION(U) WISCONSIN UNIV-MRDISON MATHEMATICS RESEARCH CENTER E DIBENEDETTO ET...RL. MAR 83 NRC-TSR-249 UNCLASSIFIED DAG29-88-C-8041 F/G 12/1i N E -EEonshhhhI EhhhMhhhhhhhhE mhhhhhhhhhhhhE mhhhhhhhhhhhhI IMhhhhhhhMhhhE

  9. An Improved Recurrent Neural Network for Complex-Valued Systems of Linear Equation and Its Application to Robotic Motion Tracking.

    Science.gov (United States)

    Ding, Lei; Xiao, Lin; Liao, Bolin; Lu, Rongbo; Peng, Hua

    2017-01-01

    To obtain the online solution of complex-valued systems of linear equation in complex domain with higher precision and higher convergence rate, a new neural network based on Zhang neural network (ZNN) is investigated in this paper. First, this new neural network for complex-valued systems of linear equation in complex domain is proposed and theoretically proved to be convergent within finite time. Then, the illustrative results show that the new neural network model has the higher precision and the higher convergence rate, as compared with the gradient neural network (GNN) model and the ZNN model. Finally, the application for controlling the robot using the proposed method for the complex-valued systems of linear equation is realized, and the simulation results verify the effectiveness and superiorness of the new neural network for the complex-valued systems of linear equation.

  10. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, T S; Adams, M L [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B; Zika, M R [Lawrence Livermore National Lab., Livermore, CA (United States)

    2005-07-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

  11. Solutions of half-linear differential equations in the classes Gamma and Pi

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel; Taddei, V.

    2016-01-01

    Roč. 29, 7-8 (2016), s. 683-714 ISSN 0893-4983 Institutional support: RVO:67985840 Keywords : half-linear differential equation * positive solution * asymptotic formula Subject RIV: BA - General Mathematics Impact factor: 0.565, year: 2016 http://projecteuclid.org/euclid.die/1462298681

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

    Science.gov (United States)

    Camporesi, Roberto

    2011-01-01

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

  13. Ultrasound-induced DNA damage and signal transductions indicated by gammaH2AX

    Science.gov (United States)

    Furusawa, Yukihiro; Fujiwara, Yoshisada; Zhao, Qing-Li; Hassan, Mariame Ali; Ogawa, Ryohei; Tabuchi, Yoshiaki; Takasaki, Ichiro; Takahashi, Akihisa; Ohnishi, Takeo; Kondo, Takashi

    2011-09-01

    Ultrasound (US) has been shown to induce cancer cell death via different forms including apoptosis. Here, we report the potential of low-intensity pulsed US (LIPUS) to induce genomic DNA damage and subsequent DNA damage response. Using the ionizing radiation-induced DNA double-strand breaks (DSBs) as the positive control, we were able to observe the induction of DSBs (as neutral comet tails) and the subsequent formation of gammaH2AX-positive foci (by immunofluorescence detection) in human leukemia cells following exposure to LIPUS. The LIPUS-induced DNA damage arose most likely from the mechanical, but not sonochemical, effect of cavitation, based on our observation that the suppression of inertial cavitation abrogated the gammH2AX foci formation, whereas scavenging of free radical formation (e.g., hydroxyl radical) had no protective effect on it. Treatment with the specific kinase inhibitor of ATM or DNA-PKcs, which can phosphorylate H2AX Ser139, revealed that US-induced gammaH2AX was inhibited more effectively by the DNA-PK inhibitor than ATM kinase inhibitor. Notably, these inhibitor effects were opposite to those with radiation-induced gammH2AX. In conclusion, we report, for the first time that US can induce DNA damage and the DNA damage response as indicated by gammaH2AX was triggered by the cavitational mechanical effects. Thus, it is expected that the data shown here may provide a better understanding of the cellular responses to US.

  14. Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

    International Nuclear Information System (INIS)

    Granita; Bahar, A.

    2015-01-01

    This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found

  15. Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

    Energy Technology Data Exchange (ETDEWEB)

    Granita, E-mail: granitafc@gmail.com [Dept. Mathematical Education, State Islamic University of Sultan Syarif Kasim Riau, 28293 Indonesia and Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor (Malaysia); Bahar, A. [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor Malaysia and UTM Center for Industrial and Applied Mathematics (UTM-CIAM) (Malaysia)

    2015-03-09

    This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

  16. γ-H2AX foci are increased in lymphocytes in vivo in young children 1 h after very low-dose X-irradiation: a pilot study

    International Nuclear Information System (INIS)

    Halm, Brunhild M.; Franke, Adrian A.; Lai, Jennifer F.; Turner, Helen C.; Brenner, David J.; Zohrabian, Vatche M.; DiMauro, Robert

    2014-01-01

    Computed tomography (CT) is an imaging modality involving ionizing radiation. The presence of γ-H2AX foci after low to moderate ionizing radiation exposure has been demonstrated; however it is unknown whether very low ionizing radiation exposure doses from CT exams can induce γ-H2AX formation in vivo in young children. To test whether very low ionizing radiation doses from CT exams can induce lymphocytic γ-H2AX foci (phosphorylated histones used as a marker of DNA damage) formation in vivo in young children. Parents of participating children signed a consent form. Blood samples from three children (ages 3-21 months) undergoing CT exams involving very low blood ionizing radiation exposure doses (blood doses of 0.22-1.22 mGy) were collected immediately before and 1 h post CT exams. Isolated lymphocytes were quantified for γ-H2AX foci by a technician blinded to the radiation status and dose of the patients. Paired t-tests and regression analyses were performed with significance levels set at P < 0.05. We observed a dose-dependent increase in γ-H2AX foci post-CT exams (P = 0.046) among the three children. Ionizing radiation exposure doses led to a linear increase of foci per cell in post-CT samples (102% between lowest and highest dose). We found a significant induction of γ-H2AX foci in lymphocytes from post-CT samples of three very young children. When possible, CT exams should be limited or avoided by possibly applying non-ionizing radiation exposure techniques such as US or MRI. (orig.)

  17. γ-H2AX foci are increased in lymphocytes in vivo in young children 1 h after very low-dose X-irradiation: a pilot study

    Energy Technology Data Exchange (ETDEWEB)

    Halm, Brunhild M.; Franke, Adrian A.; Lai, Jennifer F. [University of Hawaii Cancer Center, Honolulu, HI (United States); Turner, Helen C.; Brenner, David J.; Zohrabian, Vatche M. [Columbia University Medical Center, Center for Radiological Research, New York, NY (United States); DiMauro, Robert [Kapi' olani Medical Center for Women and Children, Honolulu, HI (United States)

    2014-10-15

    Computed tomography (CT) is an imaging modality involving ionizing radiation. The presence of γ-H2AX foci after low to moderate ionizing radiation exposure has been demonstrated; however it is unknown whether very low ionizing radiation exposure doses from CT exams can induce γ-H2AX formation in vivo in young children. To test whether very low ionizing radiation doses from CT exams can induce lymphocytic γ-H2AX foci (phosphorylated histones used as a marker of DNA damage) formation in vivo in young children. Parents of participating children signed a consent form. Blood samples from three children (ages 3-21 months) undergoing CT exams involving very low blood ionizing radiation exposure doses (blood doses of 0.22-1.22 mGy) were collected immediately before and 1 h post CT exams. Isolated lymphocytes were quantified for γ-H2AX foci by a technician blinded to the radiation status and dose of the patients. Paired t-tests and regression analyses were performed with significance levels set at P < 0.05. We observed a dose-dependent increase in γ-H2AX foci post-CT exams (P = 0.046) among the three children. Ionizing radiation exposure doses led to a linear increase of foci per cell in post-CT samples (102% between lowest and highest dose). We found a significant induction of γ-H2AX foci in lymphocytes from post-CT samples of three very young children. When possible, CT exams should be limited or avoided by possibly applying non-ionizing radiation exposure techniques such as US or MRI. (orig.)

  18. Disformal invariance of continuous media with linear equation of state

    Energy Technology Data Exchange (ETDEWEB)

    Celoria, Marco [Gran Sasso Science Institute (INFN), Viale Francesco Crispi 7, L' Aquila, I-67100 Italy (Italy); Matarrese, Sabino [Dipartimento di Fisica e Astronomia ' G. Galilei' , Università degli Studi di Padova, via Marzolo 8, Padova, I-35131 Italy (Italy); Pilo, Luigi, E-mail: marco.celoria@gssi.infn.it, E-mail: sabino.matarrese@pd.infn.it, E-mail: luigi.pilo@aquila.infn.it [Dipartimento di Fisica, Università di L' Aquila, L' Aquila, I-67010 Italy (Italy)

    2017-02-01

    We show that the effective theory describing single component continuous media with a linear and constant equation of state of the form p = w ρ is invariant under a 1-parameter family of continuous disformal transformations. In the special case of w =1/3 (ultrarelativistic gas), such a family reduces to conformal transformations. As examples, perfect fluids, irrotational dust (mimetic matter) and homogeneous and isotropic solids are discussed.

  19. Path integral solution of linear second order partial differential equations I: the general construction

    International Nuclear Information System (INIS)

    LaChapelle, J.

    2004-01-01

    A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette

  20. Improved pedagogy for linear differential equations by reconsidering how we measure the size of solutions

    Science.gov (United States)

    Tisdell, Christopher C.

    2017-11-01

    For over 50 years, the learning of teaching of a priori bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to a priori bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving second-order, linear problems with constant co-efficients, we believe it is not pedagogically optimal. Moreover, the Euclidean method becomes pedagogically unwieldy in the proofs involving higher-order cases. The purpose of this work is to propose a simpler pedagogical approach to establish a priori bounds on solutions by considering a different way of measuring the size of a solution to linear problems, which we refer to as the Uber size. The Uber form enables a simplification of pedagogy from the literature and the ideas are accessible to learners who have an understanding of the Fundamental Theorem of Calculus and the exponential function, both usually seen in a first course in calculus. We believe that this work will be of mathematical and pedagogical interest to those who are learning and teaching in the area of differential equations or in any of the numerous disciplines where linear differential equations are used.

  1. On oscillations of solutions to second-order linear delay differential equations

    Czech Academy of Sciences Publication Activity Database

    Opluštil, Z.; Šremr, Jiří

    2013-01-01

    Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001.xml?format=INT

  2. On oscillations of solutions to second-order linear delay differential equations

    Czech Academy of Sciences Publication Activity Database

    Opluštil, Z.; Šremr, Jiří

    2013-01-01

    Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001. xml ?format=INT

  3. Linear representation of algebras with non-associative operations which are satisfy in the balanced functional equations

    International Nuclear Information System (INIS)

    Ehsani, Amir

    2015-01-01

    Algebras with a pair of non-associative binary operations (f, g) which are satisfy in the balanced quadratic functional equations with four object variables considered. First, we obtain a linear representation for the operations, of this kind of binary algebras (A,f,g), over an abelian group (A, +) and then we generalize the linear representation of operations, to an algebra (A,F) with non-associative binary operations which are satisfy in the balanced quadratic functional equations with four object variables. (paper)

  4. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)

    2005-07-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

  5. KAM for the non-linear Schroedinger equation a short presentation

    CERN Document Server

    Eliasson, H L

    2006-01-01

    We consider the $d$-dimensional nonlinear Schr\\"o\\-dinger equation under periodic boundary conditions:-i\\dot u=\\Delta u+V(x)*u+\\ep \\frac{\\p F}{\\p \\bar u}(x,u,\\bar u) ;\\quad u=u(t,x),\\;x\\in\\T^dwhere $V(x)=\\sum \\hat V(a)e^{i\\sc{a,x}}$ is an analytic function with $\\hat V$ real and $F$ is a real analytic function in $\\Re u$, $\\Im u$ and $x$. (This equation is a popular model for the `real' NLS equation, where instead of the convolution term $V*u$ we have the potential term $Vu$.) For $\\ep=0$ the equation is linear and has time--quasi-periodic solutions $u$,u(t,x)=\\sum_{s\\in \\AA}\\hat u_0(a)e^{i(|a|^2+\\hat V(a))t}e^{i\\sc{a,x}}, \\quad 0<|\\hat u_0(a)|\\le1,where $\\AA$ is any finite subset of $\\Z^d$. We shall treat $\\omega_a=|a|^2+\\hat V(a)$, $a\\in\\AA$, as free parameters in some domain $U\\subset\\R^{\\AA}$. This is a Hamiltonian system in infinite degrees of freedom, degenerate but with external parameters, and we shall describe a KAM-theory which, in particular, will have the following consequence: \\smallskip {\\it ...

  6. Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming

    KAUST Repository

    Claudel, Christian G.; Chamoin, Timothee; Bayen, Alexandre M.

    2014-01-01

    This brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton-Jacobi (HJ) equations. Using a semi-analytic formula, we show that the constraints resulting from a HJ equation are convex, and can be written as a set of linear inequalities. We use this fact to pose various (and seemingly unrelated) estimation problems related to traffic flow-engineering as a set of linear programs. In particular, we solve data assimilation and data reconciliation problems for estimating the state of a system when the model and measurement constraints are incompatible. We also solve traffic estimation problems, such as travel time estimation or density estimation. For all these problems, a numerical implementation is performed using experimental data from the Mobile Century experiment. In the context of reproducible research, the code and data used to compute the results presented in this brief have been posted online and are accessible to regenerate the results. © 2013 IEEE.

  7. Approximate Forward Difference Equations for the Lower Order Non-Stationary Statistics of Geometrically Non-Linear Systems subject to Random Excitation

    DEFF Research Database (Denmark)

    Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.

    Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....

  8. Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

    Science.gov (United States)

    Scott, M

    2012-08-01

    The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

  9. Airy function approach and Numerov method to study the anharmonic oscillator potentials V(x = Ax2α + Bx2

    Directory of Open Access Journals (Sweden)

    N. Al Sdran

    2016-06-01

    Full Text Available The numerical solutions of the time independent Schrödinger equation of different one-dimensional potentials forms are sometime achieved by the asymptotic iteration method. Its importance appears, for example, on its efficiency to describe vibrational system in quantum mechanics. In this paper, the Airy function approach and the Numerov method have been used and presented to study the oscillator anharmonic potential V(x = Ax2α + Bx2, (A>0, B<0, with (α = 2 for quadratic, (α =3 for sextic and (α =4 for octic anharmonic oscillators. The Airy function approach is based on the replacement of the real potential V(x by a piecewise-linear potential v(x, while, the Numerov method is based on the discretization of the wave function on the x-axis. The first energies levels have been calculated and the wave functions for the sextic system have been evaluated. These specific values are unlimited by the magnitude of A, B and α. It’s found that the obtained results are in good agreement with the previous results obtained by the asymptotic iteration method for α =3.

  10. Iterative approximation of the solution of a monotone operator equation in certain Banach spaces

    International Nuclear Information System (INIS)

    Chidume, C.E.

    1988-01-01

    Let X=L p (or l p ), p ≥ 2. The solution of the equation Ax=f, f is an element of X is approximated in X by an iteration process in each of the following two cases: (i) A is a bounded linear mapping of X into itself which is also bounded below; and, (ii) A is a nonlinear Lipschitz mapping of X into itself and satisfies ≥ m |x-y| 2 , for some constant m > 0 and for all x, y in X, where j is the single-valued normalized duality mapping of X into X* (the dual space of X). A related result deals with the iterative approximation of the fixed point of a Lipschitz strictly pseudocontractive mapping in X. (author). 12 refs

  11. An Explicit Enclosure of the Solution Set of Overdetermined Interval Linear Equations

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří

    2017-01-01

    Roč. 24, February (2017), s. 1-10 ISSN 1573-1340 Institutional support: RVO:67985807 Keywords : interval linear equations * interval hull * unit midpoint * enclosure Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics http://interval.louisiana.edu/ reliable -computing-journal/volume-24/ reliable -computing-24-pp-001-010.pdf

  12. Scilab software as an alternative low-cost computing in solving the linear equations problem

    Science.gov (United States)

    Agus, Fahrul; Haviluddin

    2017-02-01

    Numerical computation packages are widely used both in teaching and research. These packages consist of license (proprietary) and open source software (non-proprietary). One of the reasons to use the package is a complexity of mathematics function (i.e., linear problems). Also, number of variables in a linear or non-linear function has been increased. The aim of this paper was to reflect on key aspects related to the method, didactics and creative praxis in the teaching of linear equations in higher education. If implemented, it could be contribute to a better learning in mathematics area (i.e., solving simultaneous linear equations) that essential for future engineers. The focus of this study was to introduce an additional numerical computation package of Scilab as an alternative low-cost computing programming. In this paper, Scilab software was proposed some activities that related to the mathematical models. In this experiment, four numerical methods such as Gaussian Elimination, Gauss-Jordan, Inverse Matrix, and Lower-Upper Decomposition (LU) have been implemented. The results of this study showed that a routine or procedure in numerical methods have been created and explored by using Scilab procedures. Then, the routine of numerical method that could be as a teaching material course has exploited.

  13. Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions

    International Nuclear Information System (INIS)

    Kalmykov, Mikhail Yu.; Kniehl, Bernd A.

    2012-05-01

    We argue that the Mellin-Barnes representations of Feynman diagrams can be used for obtaining linear systems of homogeneous differential equations for the original Feynman diagrams with arbitrary powers of propagators without recourse to the integration-by-parts technique. These systems of differential equation can be used (i) for the differential reductions to sets of basic functions and (ii) for counting the numbers of master-integrals.

  14. q-analogue of summability of formal solutions of some linear q-difference-differential equations

    Directory of Open Access Journals (Sweden)

    Hidetoshi Tahara

    2015-01-01

    Full Text Available Let \\(q\\gt 1\\. The paper considers a linear \\(q\\-difference-differential equation: it is a \\(q\\-difference equation in the time variable \\(t\\, and a partial differential equation in the space variable \\(z\\. Under suitable conditions and by using \\(q\\-Borel and \\(q\\-Laplace transforms (introduced by J.-P. Ramis and C. Zhang, the authors show that if it has a formal power series solution \\(\\hat{X}(t,z\\ one can construct an actual holomorphic solution which admits \\(\\hat{X}(t,z\\ as a \\(q\\-Gevrey asymptotic expansion of order \\(1\\.

  15. Ionizing radiation-induced DNA double-strand break and repair assessed by γ-H2AX foci analysis in neurons in mice

    International Nuclear Information System (INIS)

    Dong Xiaorong; Wu Gang; Ruebe Claudia; Ruebe Christian

    2009-01-01

    Objective: To investigate if the γ-H2AX foci is a precise index for the DSB formation and repair in mature neurons of brain in vivo after clinically relevant doses irradiation. Methods: For the DSB formation experiment, the mature neurons in the neocortex of brain tissue of C57BL/6 mice were analyzed at 10 rain after whole-body irradiation with 0.1, 0.5 and 1.0 Gy. For the DSB repair kinetics experiment, the mature neurons in the neocortex of brain tissue of repair-proficient (C57BL/6 mice) and repair-deficient mouse strains (BALB/c, A-T and SCID mice) were analyzed at 0.5, 2.5, 5, 24 and 48 h after whole-body irradiation with 2 Gy. The mature neurons in the neocortex of brain tissue of sham-irradiated mice of each strain served as controls. γ-H2AX immunohistochemistry and γ-H2AX and NeuN double immunofluorescence analysis was used to measure DSBs formation and repair in the mature neurons in the neocortex of brain tissue of the different mouse strains. Results: For the DSB formation experiment, γ-H2AX foci levels with a clear linear close correlation and very low backgrounds in the nuclei in the neocortex of brain tissue were observed. Scoring the loss of γ-H2AX foci allowed us to verify the different, genetically determined DSB repair deficiencies, including the minor impairment of BALB/c mice. Repair-proficient C57BL/6 mice exhibited the fastest decrease in foci number with time, and displayed low levels of residual damage at 24 h and 48 h post-irradiation. In contrast, SCID mice showed highly increased γ-H2AX foci levels at all repair times (0.5 h to 48 h) while A-T mice exhibited a lesser defect which was most significant at later repair times (≥ 5 h). Radiosensitive BALB/c mice exhibited slightly elevated foci numbers compared with C57BL/6 mice at 5 h and 24 h but not at 48 h post-irradiation. Conclusion: Quantifying the γ-H2AX foci in normal tissue represents a sensitivie tool for the detection of induction and repair of radiation-induced DSBs at

  16. Residual γH2AX foci as an indication of lethal DNA lesions

    Directory of Open Access Journals (Sweden)

    Banuelos C Adriana

    2010-01-01

    Full Text Available Abstract Background Evidence suggests that tumor cells exposed to some DNA damaging agents are more likely to die if they retain microscopically visible γH2AX foci that are known to mark sites of double-strand breaks. This appears to be true even after exposure to the alkylating agent MNNG that does not cause direct double-strand breaks but does produce γH2AX foci when damaged DNA undergoes replication. Methods To examine this predictive ability further, SiHa human cervical carcinoma cells were exposed to 8 DNA damaging drugs (camptothecin, cisplatin, doxorubicin, etoposide, hydrogen peroxide, MNNG, temozolomide, and tirapazamine and the fraction of cells that retained γH2AX foci 24 hours after a 30 or 60 min treatment was compared with the fraction of cells that lost clonogenicity. To determine if cells with residual repair foci are the cells that die, SiHa cervical cancer cells were stably transfected with a RAD51-GFP construct and live cell analysis was used to follow the fate of irradiated cells with RAD51-GFP foci. Results For all drugs regardless of their mechanism of interaction with DNA, close to a 1:1 correlation was observed between clonogenic surviving fraction and the fraction of cells that retained γH2AX foci 24 hours after treatment. Initial studies established that the fraction of cells that retained RAD51 foci after irradiation was similar to the fraction of cells that retained γH2AX foci and subsequently lost clonogenicity. Tracking individual irradiated live cells confirmed that SiHa cells with RAD51-GFP foci 24 hours after irradiation were more likely to die. Conclusion Retention of DNA damage-induced γH2AX foci appears to be indicative of lethal DNA damage so that it may be possible to predict tumor cell killing by a wide variety of DNA damaging agents simply by scoring the fraction of cells that retain γH2AX foci.

  17. Residual γH2AX foci as an indication of lethal DNA lesions

    International Nuclear Information System (INIS)

    Banáth, Judit P; Klokov, Dmitry; MacPhail, Susan H; Banuelos, C Adriana; Olive, Peggy L

    2010-01-01

    Evidence suggests that tumor cells exposed to some DNA damaging agents are more likely to die if they retain microscopically visible γH2AX foci that are known to mark sites of double-strand breaks. This appears to be true even after exposure to the alkylating agent MNNG that does not cause direct double-strand breaks but does produce γH2AX foci when damaged DNA undergoes replication. To examine this predictive ability further, SiHa human cervical carcinoma cells were exposed to 8 DNA damaging drugs (camptothecin, cisplatin, doxorubicin, etoposide, hydrogen peroxide, MNNG, temozolomide, and tirapazamine) and the fraction of cells that retained γH2AX foci 24 hours after a 30 or 60 min treatment was compared with the fraction of cells that lost clonogenicity. To determine if cells with residual repair foci are the cells that die, SiHa cervical cancer cells were stably transfected with a RAD51-GFP construct and live cell analysis was used to follow the fate of irradiated cells with RAD51-GFP foci. For all drugs regardless of their mechanism of interaction with DNA, close to a 1:1 correlation was observed between clonogenic surviving fraction and the fraction of cells that retained γH2AX foci 24 hours after treatment. Initial studies established that the fraction of cells that retained RAD51 foci after irradiation was similar to the fraction of cells that retained γH2AX foci and subsequently lost clonogenicity. Tracking individual irradiated live cells confirmed that SiHa cells with RAD51-GFP foci 24 hours after irradiation were more likely to die. Retention of DNA damage-induced γH2AX foci appears to be indicative of lethal DNA damage so that it may be possible to predict tumor cell killing by a wide variety of DNA damaging agents simply by scoring the fraction of cells that retain γH2AX foci

  18. Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations

    Directory of Open Access Journals (Sweden)

    Luo Li-Qin

    2016-01-01

    Full Text Available In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.

  19. Quadratic-linear pattern in cancer fractional radiotherapy. Equations for a computering program

    International Nuclear Information System (INIS)

    Burgos, D.; Bullejos, J.; Garcia Puche, J.L.; Pedraza, V.

    1990-01-01

    Knowledge of equivalence between different tratment schemes with the same iso-effect is the essential thing in clinical cancer radiotherapy. For this purpose it is very useful the group of ideas derived from quadratic-linear pattern (Q-L) proposed in order to analyze cell survival curve to radiation. Iso-effect definition caused by several irradiation rules is done by extrapolated tolerance dose (ETD). Because equations for ETD are complex, a computering program have been carried out. In this paper, iso-effect equations for well defined therapeutic situations and flow diagram proposed for resolution, have been studied. (Author)

  20. Approximate solution to neutron transport equation with linear anisotropic scattering

    International Nuclear Information System (INIS)

    Coppa, G.; Ravetto, P.; Sumini, M.

    1983-01-01

    A method to obtain an approximate solution to the transport equation, when both sources and collisions show a linearly anisotropic behavior, is outlined and the possible implications for numerical calculations in applied neutronics as well as shielding evaluations are investigated. The form of the differential system of equations taken by the method is quite handy and looks simpler and more manageable than any other today available technique. To go deeper into the efficiency of the method, some typical calculations concerning critical dimension of multiplying systems are then performed and the results are compared with the ones coming from the classical Ssub(N) approximations. The outcome of such calculations leads us to think of interesting developments of the method which could be quite useful in alternative to other today widespread approximate procedures, for any geometry, but especially for curved ones. (author)

  1. Generalized multivariate Fokker-Planck equations derived from kinetic transport theory and linear nonequilibrium thermodynamics

    International Nuclear Information System (INIS)

    Frank, T.D.

    2002-01-01

    We study many particle systems in the context of mean field forces, concentration-dependent diffusion coefficients, generalized equilibrium distributions, and quantum statistics. Using kinetic transport theory and linear nonequilibrium thermodynamics we derive for these systems a generalized multivariate Fokker-Planck equation. It is shown that this Fokker-Planck equation describes relaxation processes, has stationary maximum entropy distributions, can have multiple stationary solutions and stationary solutions that differ from Boltzmann distributions

  2. Exact solutions of linearized Schwinger endash Dyson equation of fermion self-energy

    International Nuclear Information System (INIS)

    Zhou, B.

    1997-01-01

    The Schwinger endash Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the independent solutions, which, respectively, submit to irregular and regular ultraviolet boundary condition are derived and expounded. copyright 1997 American Institute of Physics

  3. Oscillation of solutions of some higher order linear differential equations

    Directory of Open Access Journals (Sweden)

    Hong-Yan Xu

    2009-11-01

    Full Text Available In this paper, we deal with the order of growth and the hyper order of solutions of higher order linear differential equations $$f^{(k}+B_{k-1}f^{(k-1}+\\cdots+B_1f'+B_0f=F$$ where $B_j(z (j=0,1,\\ldots,k-1$ and $F$ are entire functions or polynomials. Some results are obtained which improve and extend previous results given by Z.-X. Chen, J. Wang, T.-B. Cao and C.-H. Li.

  4. Hardy inequality on time scales and its application to half-linear dynamic equations

    Directory of Open Access Journals (Sweden)

    Řehák Pavel

    2005-01-01

    Full Text Available A time-scale version of the Hardy inequality is presented, which unifies and extends well-known Hardy inequalities in the continuous and in the discrete setting. An application in the oscillation theory of half-linear dynamic equations is given.

  5. Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

    Science.gov (United States)

    Hasegawa, Chihiro; Duffull, Stephen B

    2018-02-01

    Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

  6. TBA equations for the mass gap in the O(2r) non-linear σ-models

    International Nuclear Information System (INIS)

    Balog, Janos; Hegedues, Arpad

    2005-01-01

    We propose TBA integral equations for 1-particle states in the O(n) non-linear σ-model for even n. The equations are conjectured on the basis of the analytic properties of the large volume asymptotics of the problem, which is explicitly constructed starting from Luscher's asymptotic formula. For small volumes the mass gap values computed numerically from the TBA equations agree very well with results of three-loop perturbation theory calculations, providing support for the validity of the proposed TBA system

  7. Equations for the non linear evolution of the resistive tearing modes in toroidal plasmas

    International Nuclear Information System (INIS)

    Edery, D.; Pellat, R.; Soule, J.L.

    1979-09-01

    Following the tokamak ordering, we simplify the resistive MHD equations in toroidal geometry. We obtain a closed system of non linear equations for two scalar potentials of the magnetic and velocity fields and for plasma density and temperature. If we expand these equations in the inverse of aspect ratio they are exact to the two first orders. Our formalism should correctly describe the mode coupling by curvature effects /1/ and the toroidal displacement of magnetic surfaces /2/. It provides a natural extension of the well known cylindrical model /3/ and is now being solved on computer

  8. Tank 241-AX-104 tank characterization plan

    International Nuclear Information System (INIS)

    Sathyanarayana, P.

    1994-01-01

    This document is a plan which serves as the contractual agreement between the Characterization Program, Sampling Operations, WHC 222-S Laboratory, and PNL 325 Analytical Chemistry Laboratory. The scope of this plan is to provide guidance for the sampling and analysis of auger samples from tank 241-AX-104

  9. Tank 241-AX-102 tank characterization plan

    International Nuclear Information System (INIS)

    Carpenter, B.C.

    1994-01-01

    This document is a plan which serves as the contractual agreement between the Characterization Program, Sampling Operations, WHC 222-S Laboratory, and PNL 325 Analytical Chemistry Laboratory. The scope of this plan is to provide guidance for the sampling and analysis of auger samples from tank 241-AX-102

  10. High throughput measurement of γH2AX DSB repair kinetics in a healthy human population.

    Directory of Open Access Journals (Sweden)

    Preety M Sharma

    Full Text Available The Columbia University RABiT (Rapid Automated Biodosimetry Tool quantifies DNA damage using fingerstick volumes of blood. One RABiT protocol quantifies the total γ-H2AX fluorescence per nucleus, a measure of DNA double strand breaks (DSB by an immunofluorescent assay at a single time point. Using the recently extended RABiT system, that assays the γ-H2AX repair kinetics at multiple time points, the present small scale study followed its kinetics post irradiation at 0.5 h, 2 h, 4 h, 7 h and 24 h in lymphocytes from 94 healthy adults. The lymphocytes were irradiated ex vivo with 4 Gy γ rays using an external Cs-137 source. The effect of age, gender, race, ethnicity, alcohol use on the endogenous and post irradiation total γ-H2AX protein yields at various time points were statistically analyzed. The endogenous γ-H2AX levels were influenced by age, race and alcohol use within Hispanics. In response to radiation, induction of γ-H2AX yields at 0.5 h and peak formation at 2 h were independent of age, gender, ethnicity except for race and alcohol use that delayed the peak to 4 h time point. Despite the shift in the peak observed, the γ-H2AX yields reached close to baseline at 24 h for all groups. Age and race affected the rate of progression of the DSB repair soon after the yields reached maximum. Finally we show a positive correlation between endogenous γ-H2AX levels with radiation induced γ-H2AX yields (RIY (r=0.257, P=0.02 and a negative correlation with residuals (r=-0.521, P=<0.0001. A positive correlation was also observed between RIY and DNA repair rate (r=0.634, P<0.0001. Our findings suggest age, race, ethnicity and alcohol use influence DSB γ-H2AX repair kinetics as measured by RABiT immunofluorescent assay.

  11. Anisotropic compacts stars on paraboloidal spacetime with linear equation of state

    Energy Technology Data Exchange (ETDEWEB)

    Thomas, V.O. [The Maharaja Sayajirao University of Baroda, Department of Mathematics, Faculty of Science, Vadodara, Gujarat (India); Pandya, D.M. [Pandit Deendayal Petroleum University, Department of Mathematics and Computer Science, Gandhinagar, Gujarat (India)

    2017-06-15

    New exact solutions of Einstein's field equations (EFEs) by assuming a linear equation of state, p{sub r} = α(ρ-ρ{sub R}), where p{sub r} is the radial pressure and ρ{sub R} is the surface density, are obtained on the background of a paraboloidal spacetime. By assuming estimated mass and radius of strange star candidate 4U 1820-30, various physical and energy conditions are used for estimating the range of parameter α. The suitability of the model for describing pulsars like PSR J1903+327, Vela X-1, Her X-1 and SAX J1808.4-3658 has been explored and respective ranges of α, for which all physical and energy conditions are satisfied throughout the distribution, are obtained. (orig.)

  12. Remark on zeros of solutions of second-order linear ordinary differential equations

    Czech Academy of Sciences Publication Activity Database

    Dosoudilová, M.; Lomtatidze, Alexander

    2016-01-01

    Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zeros of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052. xml

  13. Remark on zeros of solutions of second-order linear ordinary differential equations

    Czech Academy of Sciences Publication Activity Database

    Dosoudilová, M.; Lomtatidze, Alexander

    2016-01-01

    Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zero s of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052.xml

  14. A General Construction of Linear Differential Equations with Solutions of Prescribed Properties

    Czech Academy of Sciences Publication Activity Database

    Neuman, František

    2004-01-01

    Roč. 17, č. 1 (2004), s. 71-76 ISSN 0893-9659 R&D Projects: GA AV ČR IAA1019902; GA ČR GA201/99/0295 Institutional research plan: CEZ:AV0Z1019905 Keywords : construction of linear differential equations * prescribed qualitative properties of solutions Subject RIV: BA - General Mathematics Impact factor: 0.414, year: 2004

  15. An Empirical Comparison of Five Linear Equating Methods for the NEAT Design

    Science.gov (United States)

    Suh, Youngsuk; Mroch, Andrew A.; Kane, Michael T.; Ripkey, Douglas R.

    2009-01-01

    In this study, a data base containing the responses of 40,000 candidates to 90 multiple-choice questions was used to mimic data sets for 50-item tests under the "nonequivalent groups with anchor test" (NEAT) design. Using these smaller data sets, we evaluated the performance of five linear equating methods for the NEAT design with five levels of…

  16. Linear Equating for the NEAT Design: A Rejoinder and Some Further Comments

    Science.gov (United States)

    Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

    2010-01-01

    This article presents the authors' rejoinder to commentaries on linear equating and the NEAT design. The authors appreciate the insightful work of the commentary writers. Each has made a number of interesting points, many of which the authors had not considered at all. Before responding to some of those points, the authors reiterate what they see…

  17. On the prolongation structure and Backlund transformation for new non-linear Klein-Gordon equations

    International Nuclear Information System (INIS)

    Roy Chowdhury, A.; Mukherjee, J.

    1986-07-01

    We have considered the complete integrability of two nonlinear equations which are some kind of extensions of usual Sine-Gordon and Sinh-Gordon equations. The first one is of non-autonomous version of Sinh-Gordon system and the second is closely related to the usual Sine-Gordon theory. The first problem indicates how (x,t) dependent non-linear equations can be treated in the prolongation theory and how a Backlund map can be constructed. The second one is a variation of the usual Sine-Gordon equation and suggests that there may be other equations (similar to Sine-Gordon) which are completely integrable. In both cases we have been able to construct the Lax pair. We then construct an auto-Backlund map by following the idea of Konno and Wadati, for the generation of multisolution states. (author)

  18. A frequency domain linearized Navier-Stokes equations approach to acoustic propagation in flow ducts with sharp edges.

    Science.gov (United States)

    Kierkegaard, Axel; Boij, Susann; Efraimsson, Gunilla

    2010-02-01

    Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier-Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier-Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.

  19. State-space representation of the reactor dynamics equations

    International Nuclear Information System (INIS)

    Bernard, J.A.

    1995-01-01

    This paper describes a novel formulation of the reactor space-independent kinetics equations. The intent is to present these equations in a form that is both compatible with modern control theory and mathematically rigorous. It is desired to write the kinetics equations in the standard state variable representation, x = Ax, where x is the state vector and A is the system matrix and, at the same time, avoid mathematical compromises such as the linearization of an equation about a particular operating point. The advantage to this proposed formulation is that it may allow the lateral transfer of existing control concepts, some that have been developed for other fields, to the operation of nuclear reactors. For example, sliding mode control has been developed to allow robots to function in a robust manner in the presence of changes in the system model. This is necessary because a robot is expected to be capable of picking up an object of unknown mass and moving that object along a specified trajectory. The variability of the object's mass introduces an uncertainty into the system model that is used to deduce the appropriate control action. Thus, the robot controller must be made robust against such variations. Sliding mode control is one means of accomplishing this. A reactor controller might benefit from the same concept if its objective were to cause the reactor power to move along a demanded trajectory despite the presence of some uncertainty in the net amount of reactivity that is present

  20. On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations; Sur la stabilite, les solutions periodiques et la resolution de certaines categories d'equations et systemes d'equations differentielles couplees non lineaires apparaissant dans les oscillations betatroniques

    Energy Technology Data Exchange (ETDEWEB)

    Valat, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1960-12-15

    Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [French] Pour les equations du genre de Hill-Meissner a coefficients creneles, on a calcule des diagrammes universels de stabilite et ceux-ci ont ete verifies experimentalement. L'etude de ces equations dans le plan de phase a permis ensuite d'etendre le calcul des solutions periodiques au cas des equations differentielles non lineaires a coefficients periodiques creneles. Cette theorie a ete verifiee experimentalement. Pour Jes systemes couples non lineaires a coefficients constants, on a d'abord cherche les solutions menant a des mouvements algebriques. Les fonctions elliptiques et fuchsiennes uniformisent de tels mouvements. L'etude de mouvements non algebriques est plus delicate, a part l'etude des mouvements de Lissajous non lineaires. Une analyse fonctionnelle montre qu'il est toutefois possible dans certains cas de decoupler le systeme et de trouver des solutions generales. Pour les

  1. NBS1 localizes to gamma-H2AX foci through interaction with the FHA/BRCT domain

    International Nuclear Information System (INIS)

    Kobayashi, J.; Chen, D.J.; Sakamoto, S.; Matsuura, S.; Tanimoto, K.; Komatsu, K.

    2003-01-01

    Full text: DNA double-strand breaks (DSBs) represent the most potentially serious damage to a genome, and hence, many repair proteins are recruited to nuclear damage sites by as yet poorly characterized sensor mechanisms. Histone H2AX, one of histone H2A family, is phosphorylated within a few minutes in response to ionizing radiation (IR) and the phosphorylated H2AX (gamma-H2AX) forms foci at the region of DSBs. Moreover, Histone H2AX is essential for the IR-induced focus formation of DNA repair proteins such as BRCA1, NBS1 and 53BP1. Hence, we investigated that the function of histone H2AX for the recruitment of NBS1/hMRE11/ hRAD50 complex to DSBs sites. We clarify that NBS1 physically interacts with histone H2AX independent of DNA. We also show that the NBS1-binding can occur in the absence of interaction with hMRE11 or BRCA1. Furthermore, this NBS1 physical interaction was reduced when anti-gamma-H2AX antibody was introduced into normal cells. We also demonstrate that the FHA/BRCT domain of NBS1 is essential for this physical interaction by the immunoprecipitation studies and a pull-down assay with recombinant FHA/BRCT domain. These findings suggest that the FHA/BRCT domain have a crucial role for both binding to histone and for re-localization of hMRE11/hRAD50 nuclease complex to the vicinity of DNA damage

  2. Excited-state lifetime measurements: Linearization of the Foerster equation by the phase-plane method

    International Nuclear Information System (INIS)

    Love, J.C.; Demas, J.N.

    1983-01-01

    The Foerster equation describes excited-state decay curves involving resonance intermolecular energy transfer. A linearized solution based on the phase-plane method has been developed. The new method is quick, insensitive to the fitting region, accurate, and precise

  3. Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with local conditions⋆

    Directory of Open Access Journals (Sweden)

    Rubio Gerardo

    2011-03-01

    Full Text Available We consider the Cauchy problem in ℝd for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. The linear equations involved can not be solved with the traditional results. Therefore, we construct a classical solution to the linear Cauchy problem under the same hypotheses on the coefficients for the semilinear equation. Our approach is using stochastic differential equations and parabolic differential equations in bounded domains. Finally, we apply the results to a stochastic optimal consumption problem. Nous considérons le problème de Cauchy dans ℝd pour une classe d’équations aux dérivées partielles paraboliques semi linéaires qui se pose dans certains problèmes de contrôle stochastique. Nous supposons que les coefficients ne sont pas bornés et sont localement Lipschitziennes, pas nécessairement différentiables, avec des données continues et ellipticité local uniforme. Nous construisons une solution classique par approximation avec les équations paraboliques linéaires. Les équations linéaires impliquées ne peuvent être résolues avec les résultats traditionnels. Par conséquent, nous construisons une solution classique au problème de Cauchy linéaire sous les mêmes hypothèses sur les coefficients pour l’équation semi-linéaire. Notre approche utilise les équations différentielles stochastiques et les équations différentielles paraboliques dans les domaines bornés. Enfin, nous appliquons les résultats à un problème stochastique de consommation optimale.

  4. Airy function approach and Numerov method to study the anharmonic oscillator potentials V(x) = Ax{sup 2α} + Bx{sup 2}

    Energy Technology Data Exchange (ETDEWEB)

    Al Sdran, N. [King Khalid University, Faculty of Science, Physics Department P.O. Box 9004 Abha (Saudi Arabia); Najran University, Faculty of Sciences and Arts, Najran (Saudi Arabia); Maiz, F., E-mail: fethimaiz@gmail.com [King Khalid University, Faculty of Science, Physics Department P.O. Box 9004 Abha (Saudi Arabia); Thermal Process Laboratory Research and Technologies Centre of Energy, BP 95, 2050 Hammam-lif (Tunisia)

    2016-06-15

    The numerical solutions of the time independent Schrödinger equation of different one-dimensional potentials forms are sometime achieved by the asymptotic iteration method. Its importance appears, for example, on its efficiency to describe vibrational system in quantum mechanics. In this paper, the Airy function approach and the Numerov method have been used and presented to study the oscillator anharmonic potential V(x) = Ax{sup 2α} + Bx{sup 2}, (A>0, B<0), with (α = 2) for quadratic, (α =3) for sextic and (α =4) for octic anharmonic oscillators. The Airy function approach is based on the replacement of the real potential V(x) by a piecewise-linear potential v(x), while, the Numerov method is based on the discretization of the wave function on the x-axis. The first energies levels have been calculated and the wave functions for the sextic system have been evaluated. These specific values are unlimited by the magnitude of A, B and α. It’s found that the obtained results are in good agreement with the previous results obtained by the asymptotic iteration method for α =3.

  5. On the solution of a class of fuzzy system of linear equations

    Indian Academy of Sciences (India)

    J. Mathematics and Comput. Sci. 1: 1–5. Salkuyeh D K 2011 On the solution of the fuzzy Sylvester matrix equation. Soft Computing 15: 953–961. Senthilkumar P and Rajendran G 2011 New approach to solve symmetric fully fuzzy linear systems. S¯adhan¯a 36: 933–940. Wang K and Zheng B 2007 Block iterative methods ...

  6. Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

    Science.gov (United States)

    Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

    2016-01-01

    Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

  7. Operational matrices with respect to Hermite polynomials and their applications in solving linear dierential equations with variable coecients

    Directory of Open Access Journals (Sweden)

    A. Aminataei

    2014-05-01

    Full Text Available In this paper, a new and ecient approach is applied for numerical approximation of the linear dierential equations with variable coecients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansioncoecients for the moments of derivatives of any dierentiable function in terms of the original expansion coecients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear dierentialequations to solve a system of linear algebraic equations, thus greatly simplifying the problem. In addition, two experiments are given to demonstrate the validity and applicability of the method

  8. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Science.gov (United States)

    Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

    2017-07-01

    This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  9. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Directory of Open Access Journals (Sweden)

    Shahid Hasnain

    2017-07-01

    Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  10. The Induced Dimension Reduction method applied to convection-diffusion-reaction problems

    NARCIS (Netherlands)

    Astudillo, R.; Van Gijzen, M.B.

    2016-01-01

    Discretization of (linearized) convection-diffusion-reaction problems yields a large and sparse non symmetric linear system of equations, Ax = b. (1) In this work, we compare the computational behavior of the Induced Dimension Reduction method (IDR(s)) [10], with other short-recurrences Krylov

  11. Oscillation and nonoscillation results for solutions of half-linear equations with deviated argument

    Czech Academy of Sciences Publication Activity Database

    Drábek, P.; Kufner, Alois; Kuliev, K.

    2017-01-01

    Roč. 447, č. 1 (2017), s. 371-382 ISSN 0022-247X Institutional support: RVO:67985840 Keywords : half-linear equation * oscillatory solution * nonoscillatory solution Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.064, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022247X16306059

  12. Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

    Science.gov (United States)

    Fu, Wei; Nijhoff, Frank W

    2017-07-01

    A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

  13. Hölder Regularity of the 2D Dual Semigeostrophic Equations via Analysis of Linearized Monge-Ampère Equations

    Science.gov (United States)

    Le, Nam Q.

    2018-05-01

    We obtain the Hölder regularity of time derivative of solutions to the dual semigeostrophic equations in two dimensions when the initial potential density is bounded away from zero and infinity. Our main tool is an interior Hölder estimate in two dimensions for an inhomogeneous linearized Monge-Ampère equation with right hand side being the divergence of a bounded vector field. As a further application of our Hölder estimate, we prove the Hölder regularity of the polar factorization for time-dependent maps in two dimensions with densities bounded away from zero and infinity. Our applications improve previous work by G. Loeper who considered the cases of densities sufficiently close to a positive constant.

  14. A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation

    Directory of Open Access Journals (Sweden)

    Jinsong Hu

    2013-01-01

    Full Text Available We study the initial-boundary value problem for Rosenau-RLW equation. We propose a three-level linear finite difference scheme, which has the theoretical accuracy of Oτ2+h4. The scheme simulates two conservative properties of original problem well. The existence, uniqueness of difference solution, and a priori estimates in infinite norm are obtained. Furthermore, we analyze the convergence and stability of the scheme by energy method. At last, numerical experiments demonstrate the theoretical results.

  15. Decoherence of histories and hydrodynamic equations for a linear oscillator chain

    International Nuclear Information System (INIS)

    Halliwell, J.J.

    2003-01-01

    We investigate the decoherence of histories of local densities for linear oscillators models. It is shown that histories of local number, momentum and energy density are approximately decoherent, when coarse grained over sufficiently large volumes. Decoherence arises directly from the proximity of these variables to exactly conserved quantities (which are exactly decoherent), and not from environmentally induced decoherence. We discuss the approach to local equilibrium and the subsequent emergence of hydrodynamic equations for the local densities

  16. A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems.

    Science.gov (United States)

    Liu, Tao; Huang, Jie

    2017-04-17

    This paper presents a discrete-time recurrent neural network approach to solving systems of linear equations with two features. First, the system of linear equations may not have a unique solution. Second, the system matrix is not known precisely, but a sequence of matrices that converges to the unknown system matrix exponentially is known. The problem is motivated from solving the output regulation problem for linear systems. Thus, an application of our main result leads to an online solution to the output regulation problem for linear systems.

  17. The Arabidopsis flagellin receptor FLS2 mediates the perception of Xanthomonas Ax21 secreted peptides.

    Science.gov (United States)

    Danna, Cristian H; Millet, Yves A; Koller, Teresa; Han, Sang-Wook; Bent, Andrew F; Ronald, Pamela C; Ausubel, Frederick M

    2011-05-31

    Detection of microbes by plants relies in part on an array of pattern-recognition receptors that recognize conserved microbial signatures, so-called "microbe-associated molecular patterns." The Arabidopsis thaliana receptor-like kinase FLS2 is the pattern-recognition receptor for bacterial flagellin. Similarly to FLS2, the rice transmembrane protein XA21 is the receptor for the sulfated form of the Xanthomonas oryzae pv. oryzae secreted protein Ax21. Here we show that Ax21-derived peptides activate Arabidopsis immunity, triggering responses similar to those elicited by flagellin, including an oxidative burst, induction of defense-response genes, and enhanced resistance to bacterial pathogens. To identify Arabidopsis Xa21 functional homologs, we used a reverse genetics approach to screen T-DNA insertion mutants corresponding to all 47 of the Arabidopsis genes encoding non-RD kinases belonging to the interleukin-1 receptor-associated kinase (IRAK) family. Surprisingly, among all of these mutant lines, only fls2 mutants exhibited a significant loss of response to Ax21-derived peptides. Ax21 peptides also failed to activate defense-related responses in an fls2-24 mutant that does not bind Flg22. Moreover, a Flg22Δ2 variant of Flg22 that binds to FLS2 but does not activate FLS2-mediated signaling suppressed Ax21-derived peptide signaling, indicating mutually exclusive perception of Flg22 or Ax21 peptides by FLS2. The data indicate that FLS2 functions beyond flagellin perception to detect other microbe-associated molecular patterns.

  18. Remark on periodic boundary-value problem for second-order linear ordinary differential equations

    Czech Academy of Sciences Publication Activity Database

    Dosoudilová, M.; Lomtatidze, Alexander

    2018-01-01

    Roč. 2018, č. 13 (2018), s. 1-7 ISSN 1072-6691 Institutional support: RVO:67985840 Keywords : second-order linear equation * periodic boundary value problem * unique solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2018/13/abstr.html

  19. DNA damage and γH2AX expression in EJ cells induced by 60Co gamma-rays

    International Nuclear Information System (INIS)

    Pan Yan; Tian Mei; Liu Jianxiang; Ruan Jianlei; Su Xu

    2009-01-01

    Objective: To investigate 60 Co γ-rays induced DNA damage of human bladder cancer cell line EJ cells and the relationship between different doses of 60 Co γ-rays, γH2AX foci number and γH2AX expression level. Methods: EJ cells were exposed to different doses of 60 Co γ-rays and the oliver tail moment (TM) of EJ cells were analyzed with single cell gel electrophoresis (SCGE) . Immunofluorescent microscopy was used to analysis γH2AX foci formation in EJ cells after exposure to different doses of γ-ray irradiation and time-course after exposure to 2 Gy γ-ray irradiation. FACSAria was used to detect the changes of γH2AX protein expression in EJ cells. Results: The TMs of EJ cells were increased with the irradiation dose. The TM of 0 Gy group and 4 Gy group was 0.24 and 5.26, respectively. Immunofluorescent analysis demonstrated that γH2AX foci could be induced by γ-ray irradiation in dose-dependent and time-dependent manners. The foci number and size in nuclei of EJ cells was significantly increased after exposed to different doses of γ-ray irradiation and the foci remained detectable at 24 h after exposed to irradiation. The dose range in which foci could be clearly detected was from 0.1 to 4 Gy. FACSDiva showed that γH2AX protein expression was increased after exposure to different doses of γ-ray irradiation. γH2AX protein expression level of 0.1 Gy group and 4 Gy group was 7.4% and 29.2% , respectively. Conclusions: γH2AX foci could be the most sensitive indicator for DNA damage and repair in mammalian cells, and it might be a new biomarker for radiological emergency. (authors)

  20. A Lie-Deprit perturbation algorithm for linear differential equations with periodic coefficients

    OpenAIRE

    Casas Pérez, Fernando; Chiralt Monleon, Cristina

    2014-01-01

    A perturbative procedure based on the Lie-Deprit algorithm of classical mechanics is proposed to compute analytic approximations to the fundamental matrix of linear di erential equations with periodic coe cients. These approximations reproduce the structure assured by the Floquet theorem. Alternatively, the algorithm provides explicit approximations to the Lyapunov transformation reducing the original periodic problem to an autonomous sys- tem and also to its characteristic ...

  1. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, Teresa S. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: baileyte@tamu.edu; Adams, Marvin L. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: mladams@tamu.edu; Yang, Brian [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Zika, Michael R. [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States)], E-mail: zika@llnl.gov

    2008-04-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.

  2. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    International Nuclear Information System (INIS)

    Bailey, Teresa S.; Adams, Marvin L.; Yang, Brian; Zika, Michael R.

    2008-01-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids

  3. The structure of solutions of the matrix linear unilateral polynomial equation with two variables

    Directory of Open Access Journals (Sweden)

    N. S. Dzhaliuk

    2017-07-01

    Full Text Available We investigate the structure of solutions of the matrix linear polynomial equation $A(\\lambdaX(\\lambda+B(\\lambdaY(\\lambda=C(\\lambda,$ in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices $A (\\lambda, B(\\lambda$ \\ and \\ $C(\\lambda$ are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients $A(\\lambda$ and $B(\\lambda.$ 

  4. A linear evolution for non-linear dynamics and correlations in realistic nuclei

    International Nuclear Information System (INIS)

    Levin, E.; Lublinsky, M.

    2004-01-01

    A new approach to high energy evolution based on a linear equation for QCD generating functional is developed. This approach opens a possibility for systematic study of correlations inside targets, and, in particular, inside realistic nuclei. Our results are presented as three new equations. The first one is a linear equation for QCD generating functional (and for scattering amplitude) that sums the 'fan' diagrams. For the amplitude this equation is equivalent to the non-linear Balitsky-Kovchegov equation. The second equation is a generalization of the Balitsky-Kovchegov non-linear equation to interactions with realistic nuclei. It includes a new correlation parameter which incorporates, in a model-dependent way, correlations inside the nuclei. The third equation is a non-linear equation for QCD generating functional (and for scattering amplitude) that in addition to the 'fan' diagrams sums the Glauber-Mueller multiple rescatterings

  5. A critical oscillation constant as a variable of time scales for half-linear dynamic equations

    Czech Academy of Sciences Publication Activity Database

    Řehák, Pavel

    2010-01-01

    Roč. 60, č. 2 (2010), s. 237-256 ISSN 0139-9918 R&D Projects: GA AV ČR KJB100190701 Institutional research plan: CEZ:AV0Z10190503 Keywords : dynamic equation * time scale * half-linear equation * (non)oscillation criteria * Hille-Nehari criteria * Kneser criteria * critical constant * oscillation constant * Hardy inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0009-7

  6. The induced dimension reduction method applied to convection-diffusion-reaction problems

    NARCIS (Netherlands)

    Astudillo Rengifo, R.A.; van Gijzen, M.B.

    2016-01-01

    Discretization of (linearized) convection-diusion-reaction problems yields
    a large and sparse non symmetric linear system of equations,
    Ax
    = b: (1)
    In this work, we compare the computational behavior of the Induced Dimension
    Reduction method (IDR(s)) [10], with other

  7. On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations

    Directory of Open Access Journals (Sweden)

    Yoshitsugu Takei

    2015-01-01

    Full Text Available Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.

  8. A parallel algorithm for solving linear equations arising from one-dimensional network problems

    International Nuclear Information System (INIS)

    Mesina, G.L.

    1991-01-01

    One-dimensional (1-D) network problems, such as those arising from 1- D fluid simulations and electrical circuitry, produce systems of sparse linear equations which are nearly tridiagonal and contain a few non-zero entries outside the tridiagonal. Most direct solution techniques for such problems either do not take advantage of the special structure of the matrix or do not fully utilize parallel computer architectures. We describe a new parallel direct linear equation solution algorithm, called TRBR, which is especially designed to take advantage of this structure on MIMD shared memory machines. The new method belongs to a family of methods which split the coefficient matrix into the sum of a tridiagonal matrix T and a matrix comprised of the remaining coefficients R. Efficient tridiagonal methods are used to algebraically simplify the linear system. A smaller auxiliary subsystem is created and solved and its solution is used to calculate the solution of the original system. The newly devised BR method solves the subsystem. The serial and parallel operation counts are given for the new method and related earlier methods. TRBR is shown to have the smallest operation count in this class of direct methods. Numerical results are given. Although the algorithm is designed for one-dimensional networks, it has been applied successfully to three-dimensional problems as well. 20 refs., 2 figs., 4 tabs

  9. Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation

    Science.gov (United States)

    Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua

    2018-06-01

    Comparing with the well-known classic Cahn-Hilliard equation, the nonlocal Cahn-Hilliard equation is equipped with a nonlocal diffusion operator and can describe more practical phenomena for modeling phase transitions of microstructures in materials. On the other hand, it evidently brings more computational costs in numerical simulations, thus efficient and accurate time integration schemes are highly desired. In this paper, we propose two energy-stable linear semi-implicit methods with first and second order temporal accuracies respectively for solving the nonlocal Cahn-Hilliard equation. The temporal discretization is done by using the stabilization technique with the nonlocal diffusion term treated implicitly, while the spatial discretization is carried out by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are rigorously established for both methods in the fully discrete sense. Numerical experiments are conducted for a typical case involving Gaussian kernels. We test the temporal convergence rates of the proposed schemes and make a comparison of the nonlocal phase transition process with the corresponding local one. In addition, long-time simulations of the coarsening dynamics are also performed to predict the power law of the energy decay.

  10. Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

    Czech Academy of Sciences Publication Activity Database

    Dilna, N.; Rontó, András

    2010-01-01

    Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

  11. Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains

    Science.gov (United States)

    Ji, Songsong; Yang, Yibo; Pang, Gang; Antoine, Xavier

    2018-01-01

    The aim of this paper is to design some accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations in rectangular domains. The Laplace transform in time and discrete Fourier transform in space are applied to get Green's functions of the semi-discretized equations in unbounded domains with single-source. An algorithm is given to compute these Green's functions accurately through some recurrence relations. Furthermore, the finite-difference method is used to discretize the reduced problem with accurate boundary conditions. Numerical simulations are presented to illustrate the accuracy of our method in the case of the linear Schrödinger and heat equations. It is shown that the reflection at the corners is correctly eliminated.

  12. Processing, disulfide pattern, and biological activity of a sugar beet defensin, AX2, expressed in Pichia pastoris

    DEFF Research Database (Denmark)

    Kristensen, A K; Brunstedt, J; Nielsen, J E

    1999-01-01

    AX2 is a 46-amino-acid cysteine-rich peptide isolated from sugar beet leaves infected with the fungus Cercospora beticola (Sacc.). AX2 strongly inhibits the growth of C. beticola and other filamentous fungi, but has little or no effect against bacteria. AX2 is produced in very low amounts in suga...

  13. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

    International Nuclear Information System (INIS)

    Bonnet, M.; Meurant, G.

    1978-01-01

    Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

  14. Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

    International Nuclear Information System (INIS)

    Bonnet, M.; Meurant, G.

    1978-01-01

    The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

  15. Linear indices in nonlinear structural equation models : best fitting proper indices and other composites

    NARCIS (Netherlands)

    Dijkstra, T.K.; Henseler, J.

    2011-01-01

    The recent advent of nonlinear structural equation models with indices poses a new challenge to the measurement of scientific constructs. We discuss, exemplify and add to a family of statistical methods aimed at creating linear indices, and compare their suitability in a complex path model with

  16. A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate

    Directory of Open Access Journals (Sweden)

    Min Sun

    2014-01-01

    Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.

  17. Assessment of γ-H2AX levels in circulating tumor cells from patients receiving chemotherapy

    Energy Technology Data Exchange (ETDEWEB)

    Garcia-Villa, Alejandra; Balasubramanian, Priya; Miller, Brandon L. [William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, OH (United States); Lustberg, Maryam B.; Ramaswamy, Bhuvaneswari [Department of Internal Medicine, Breast Medical Oncology, James Cancer Hospital and Ohio State University Comprehensive Cancer Center, Columbus, OH (United States); Chalmers, Jeffrey J., E-mail: chalmers.1@osu.edu [William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, OH (United States)

    2012-10-25

    Circulating tumor cells (CTCs) are prognostic markers in a variety of solid tumor malignancies. The potential of CTCs to be used as a “liquid biopsy” to monitor a patient’s condition and predict drug response and resistance is currently under investigation. Using a negative depletion, enrichment methodology, CTCs isolated from the peripheral blood of breast cancer patients with stage IV breast cancer undergoing DNA damaging therapy with platinum-based therapy were enriched. The enriched cell suspensions were stained with an optimized labeling protocol targeting: nuclei, cytokeratins 8, 18, and 19, the surface marker CD45, and the presence of the protein γ-H2AX. As a direct or indirect result of platinum therapy, double-strand break of DNA initiates phosphorylation of the histone H2AX, at serine 139; this phosphorylated form is referred to as γ-H2AX. In addition to γ-H2AX staining in specific locations with the cell nuclei, consistent with previous reports and referred to as foci, more general staining in the cell cytoplasm was also observed in some cells suggesting the potential of cell apoptosis. Our study underscores the utility and the complexity of investigating CTCs as predictive markers of response to various therapies. Additional studies are ongoing to evaluate the diverse γ-H2AX staining patterns we report here which needs to be further correlated with patient outcomes.

  18. Visualising the Complex Roots of Quadratic Equations with Real Coefficients

    Science.gov (United States)

    Bardell, Nicholas S.

    2012-01-01

    The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

  19. Radiosensitivity in breast cancer assessed by the histone γ-H2AX and 53BP1 foci

    International Nuclear Information System (INIS)

    Djuzenova, Cholpon S; Elsner, Ines; Katzer, Astrid; Worschech, Eike; Distel, Luitpold V; Flentje, Michael; Polat, Bülent

    2013-01-01

    High expression of constitutive histone γ-H2AX, a sensitive marker of DNA damage, might be indicative of defective DNA repair pathway or genomic instability. 53BP1 (p53-binding protein 1) is a conserved checkpoint protein with properties of a DNA double-strand breaks sensor. This study explores the relationship between the clinical radiosensitivity of tumor patients and the expression/induction of γ-H2AX and 53BP1 in vitro. Using immunostaining, we assessed spontaneous and radiation-induced foci of γ-H2AX and 53 BP1 in peripheral blood mononuclear cells derived from unselected breast cancer (BC) patients (n=57) undergoing radiotherapy (RT). Cells from apparently healthy donors (n=12) served as references. Non-irradiated cells from controls and unselected BC patients exhibited similar baseline levels of DNA damage assessed by γ-H2AX and 53BP1 foci. At the same time, the γ-H2AX assay of in vitro irradiated cells revealed significant differences between the control group and the group of unselected BC patients with respect to the initial (0.5 Gy, 30 min) and residual (2 Gy, 24 h post-radiation) DNA damage. The numbers of 53BP1 foci analyzed in 35 BC patients were significantly higher than in controls only in case of residual DNA damage. A weak correlation was found between residual foci of both proteins tested. In addition, cells from cancer patients with an adverse acute skin reaction (grade 3) to RT showed significantly increased radiation-induced γ-H2AX foci and their protracted disappearance compared to the group of BC patients with normal skin reaction (grade 0–1). The mean number of γ-H2AX foci after 5 clinical fractions was significantly higher than that before RT, especially in clinically radiosensitive patients. The γ-H2AX assay may have potential for screening individual radiosensitivity of breast cancer patients.

  20. Perturbation Solutions for Random Linear Structural Systems subject to Random Excitation using Stochastic Differential Equations

    DEFF Research Database (Denmark)

    Köyluoglu, H.U.; Nielsen, Søren R.K.; Cakmak, A.S.

    1994-01-01

    perturbation method using stochastic differential equations. The joint statistical moments entering the perturbation solution are determined by considering an augmented dynamic system with state variables made up of the displacement and velocity vector and their first and second derivatives with respect......The paper deals with the first and second order statistical moments of the response of linear systems with random parameters subject to random excitation modelled as white-noise multiplied by an envelope function with random parameters. The method of analysis is basically a second order...... to the random parameters of the problem. Equations for partial derivatives are obtained from the partial differentiation of the equations of motion. The zero time-lag joint statistical moment equations for the augmented state vector are derived from the Itô differential formula. General formulation is given...

  1. Stationary solutions of linear stochastic delay differential equations: applications to biological systems.

    Science.gov (United States)

    Frank, T D; Beek, P J

    2001-08-01

    Recently, Küchler and Mensch [Stochastics Stochastics Rep. 40, 23 (1992)] derived exact stationary probability densities for linear stochastic delay differential equations. This paper presents an alternative derivation of these solutions by means of the Fokker-Planck approach introduced by Guillouzic [Phys. Rev. E 59, 3970 (1999); 61, 4906 (2000)]. Applications of this approach, which is argued to have greater generality, are discussed in the context of stochastic models for population growth and tracking movements.

  2. Stationary distributions of stochastic processes described by a linear neutral delay differential equation

    International Nuclear Information System (INIS)

    Frank, T D

    2005-01-01

    Stationary distributions of processes are derived that involve a time delay and are defined by a linear stochastic neutral delay differential equation. The distributions are Gaussian distributions. The variances of the Gaussian distributions are either monotonically increasing or decreasing functions of the time delays. The variances become infinite when fixed points of corresponding deterministic processes become unstable. (letter to the editor)

  3. On one two-point BVP for the fourth order linear ordinary differential equation

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Manjikashvili, M.

    2017-01-01

    Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077. xml

  4. On one two-point BVP for the fourth order linear ordinary differential equation

    Czech Academy of Sciences Publication Activity Database

    Mukhigulashvili, Sulkhan; Manjikashvili, M.

    2017-01-01

    Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077.xml

  5. Oscillation theory of linear differential equations

    Czech Academy of Sciences Publication Activity Database

    Došlý, Ondřej

    2000-01-01

    Roč. 36, č. 5 (2000), s. 329-343 ISSN 0044-8753 R&D Projects: GA ČR GA201/98/0677 Keywords : discrete oscillation theory %Sturm-Liouville equation%Riccati equation Subject RIV: BA - General Mathematics

  6. Resummation of the 1/N-expansion of the non-linear σ-model by Dyson-Schwinger equations

    International Nuclear Information System (INIS)

    Drouffe, J.M.; Flyvbjerg, H.

    1988-02-01

    Dyson-Schwinger equations for the O(N)-symmetric non-linear σ-model are derived and expanded in 1/N. A closed set of equations is obtained by keeping only the leading term and the first correction term in this expansion. These equations are solved numerically in 2 dimensions on square lattices of sizes 50x50 and 100x100. Results for the magnetic susceptibility and the mass gap are compared with predictions of the ordinary 1/N-expansion and with Monte Carlo results. The results obtained with the Dyson-Schwinger equations show the same scaling behavior as found in the Monte Carlo results. This is not the behavior predicted by the perturbative renormalization group. (orig.)

  7. Inhomogeneous Linear Random Differential Equations with Mutual Correlations between Multiplicative, Additive and Initial-Value Terms

    NARCIS (Netherlands)

    Roerdink, J.B.T.M.

    1981-01-01

    The cumulant expansion for linear stochastic differential equations is extended to the general case in which the coefficient matrix, the inhomogeneous part and the initial condition are all random and, moreover, statistically interdependent. The expansion now involves not only the autocorrelation

  8. Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients.

    Science.gov (United States)

    Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M

    2013-01-01

    Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.

  9. A block Krylov subspace time-exact solution method for linear ordinary differential equation systems

    NARCIS (Netherlands)

    Bochev, Mikhail A.

    2013-01-01

    We propose a time-exact Krylov-subspace-based method for solving linear ordinary differential equation systems of the form $y'=-Ay+g(t)$ and $y"=-Ay+g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an accurate piecewise polynomial approximation of

  10. Development and adjustment of programs for solving systems of linear equations

    International Nuclear Information System (INIS)

    Fujimura, Toichiro

    1978-03-01

    Programs for solving the systems of linear equations have been adjusted and developed in expanding the scientific subroutine library SSL. The principal programs adjusted are based on the congruent method, method of product form of the inverse, orthogonal method, Crout's method for sparse system, and acceleration of iterative methods. The programs developed are based on the escalator method, direct parallel residue method and block tridiagonal method for band system. Described are usage of the programs developed and their future improvement. FORTRAN lists with simple examples in tests of the programs are also given. (auth.)

  11. "Real-Time Optical Laboratory Linear Algebra Solution Of Partial Differential Equations"

    Science.gov (United States)

    Casasent, David; Jackson, James

    1986-03-01

    A Space Integrating (SI) Optical Linear Algebra Processor (OLAP) employing space and frequency-multiplexing, new partitioning and data flow, and achieving high accuracy performance with a non base-2 number system is described. Laboratory data on the performance of this system and the solution of parabolic Partial Differential Equations (PDEs) is provided. A multi-processor OLAP system is also described for the first time. It use in the solution of multiple banded matrices that frequently arise is then discussed. The utility and flexibility of this processor compared to digital systolic architectures should be apparent.

  12. Regulatory issues associated with closure of the Hanford AX Tank Farm ancillary equipment

    International Nuclear Information System (INIS)

    Becker, D.L.

    1998-01-01

    Liquid mixed, high-level radioactive waste has been stored in underground single-shell tanks at the US Department of Energy's (DOE's) Hanford Site. After retrieval of the waste from the single-shell tanks, the DOE will proceed with closure of the tank farm. The 241-AX Tank Farm includes four one-million gallon single-shell tanks in addition to sluice lines, transfer lines, ventilation headers, risers, pits, cribs, catch tanks, buildings, well and associated buried piping. This equipment is classified as ancillary equipment. This document addresses the requirements for regulatory close of the ancillary equipment in the Hanford Site 241-AX Tank Farm. The options identified for physical closure of the ancillary equipment include disposal in place, disposal in place after treatment, excavation and disposal on site in an empty single-shell tank, and excavation and disposal outside the AX Tank Farm. The document addresses the background of the Hanford Site and ancillary equipment in the AX Tank Farm, regulations for decontamination and decommissioning of radioactively contaminated equipment, requirements for the cleanup and disposal of radioactive wastes, cleanup and disposal requirements governing hazardous and mixed waste, and regulatory requirements and issues associated with each of the four physical closure options. This investigation was conducted by the Sandia National Laboratories, Albuquerque, New Mexico, during Fiscal Year 1998 for the Hanford Tanks Initiative Project

  13. Generalized Stabilities of Euler-Lagrange-Jensen (a,b-Sextic Functional Equations in Quasi-β-Normed Spaces

    Directory of Open Access Journals (Sweden)

    John Michael Rassias

    2017-07-01

    Full Text Available The aim of this paper is to investigate generalized Ulam-Hyers stabilities of the following Euler-Lagrange-Jensen-$(a,b$-sextic functional equation $$ f(ax+by+f(bx+ay+(a-b^6\\left[f\\left(\\frac{ax-by}{a-b}\\right+f\\left(\\frac{bx-ay}{b-a}\\right\\right]\\\\ = 64(ab^2\\left(a^2+b^2\\right\\left[f\\left(\\frac{x+y}{2}\\right+f\\left(\\frac{x-y}{2}\\right\\right]\\\\ +2\\left(a^2-b^2\\right\\left(a^4-b^4\\right[f(x+f(y] $$ where $a\

  14. Higher derivative discontinuous solutions to linear ordinary differential equations: a new route to complexity?

    International Nuclear Information System (INIS)

    Datta, Dhurjati Prasad; Bose, Manoj Kumar

    2004-01-01

    We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of higher derivative discontinuous solutions as well. The discontinuity can occur only for a subset of even order derivatives, viz., 2nd, 4th, 8th, 16th,.... The solutions are shown to break the discrete parity (reflection) symmetry of the underlying equation. These results are expected to gain significance in the contemporary search of a new dynamical principle for understanding complex phenomena in nature

  15. Engineering equations for characterizing non-linear laser intensity propagation in air with loss.

    Science.gov (United States)

    Karr, Thomas; Stotts, Larry B; Tellez, Jason A; Schmidt, Jason D; Mansell, Justin D

    2018-02-19

    The propagation of high peak-power laser beams in real atmospheres will be affected at long range by both linear and nonlinear effects contained therein. Arguably, J. H. Marburger is associated with the mathematical characterization of this phenomenon. This paper provides a validated set of engineering equations for characterizing the self-focusing distance from a laser beam propagating through non-turbulent air with, and without, loss as well as three source configurations: (1) no lens, (2) converging lens and (3) diverging lens. The validation was done against wave-optics simulation results. Some validated equations follow Marburger completely, but others do not, requiring modification of the original theory. Our results can provide a guide for numerical simulations and field experiments.

  16. The linearized pressure Poisson equation for global instability analysis of incompressible flows

    Science.gov (United States)

    Theofilis, Vassilis

    2017-12-01

    The linearized pressure Poisson equation (LPPE) is used in two and three spatial dimensions in the respective matrix-forming solution of the BiGlobal and TriGlobal eigenvalue problem in primitive variables on collocated grids. It provides a disturbance pressure boundary condition which is compatible with the recovery of perturbation velocity components that satisfy exactly the linearized continuity equation. The LPPE is employed to analyze instability in wall-bounded flows and in the prototype open Blasius boundary layer flow. In the closed flows, excellent agreement is shown between results of the LPPE and those of global linear instability analyses based on the time-stepping nektar++, Semtex and nek5000 codes, as well as with those obtained from the FreeFEM++ matrix-forming code. In the flat plate boundary layer, solutions extracted from the two-dimensional LPPE eigenvector at constant streamwise locations are found to be in very good agreement with profiles delivered by the NOLOT/PSE space marching code. Benchmark eigenvalue data are provided in all flows analyzed. The performance of the LPPE is seen to be superior to that of the commonly used pressure compatibility (PC) boundary condition: at any given resolution, the discrete part of the LPPE eigenspectrum contains converged and not converged, but physically correct, eigenvalues. By contrast, the PC boundary closure delivers some of the LPPE eigenvalues and, in addition, physically wrong eigenmodes. It is concluded that the LPPE should be used in place of the PC pressure boundary closure, when BiGlobal or TriGlobal eigenvalue problems are solved in primitive variables by the matrix-forming approach on collocated grids.

  17. Chemical Equation Balancing.

    Science.gov (United States)

    Blakley, G. R.

    1982-01-01

    Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

  18. On the Evaluation of Computational Results Obtained from Solving System of linear Equations With matlab The Dual affine Scalling interior Point

    International Nuclear Information System (INIS)

    Murfi, Hendri; Basaruddin, T.

    2001-01-01

    The interior point method for linear programming has gained extraordinary interest as an alternative to simplex method since Karmarkar presented a polynomial-time algorithm for linear programming based on interior point method. In implementation of the algorithm of this method, there are two important things that have impact heavily to performance of the algorithm; they are data structure and used method to solve linear equation system in the algorithm. This paper describes about solving linear equation system in variants of the algorithm called dual-affine scaling algorithm. Next, we evaluate experimentally results of some used methods, either direct method or iterative method. The experimental evaluation used Matlab

  19. Transgenic rice plants expressing synthetic cry2AX1 gene exhibits resistance to rice leaffolder (Cnaphalocrosis medinalis).

    Science.gov (United States)

    Manikandan, R; Balakrishnan, N; Sudhakar, D; Udayasuriyan, V

    2016-06-01

    Bacillus thuringiensis is a major source of insecticidal genes imparting insect resistance in transgenic plants. Level of expression of transgenes in transgenic plants is important to achieve desirable level of resistance against target insects. In order to achieve desirable level of expression, rice chloroplast transit peptide sequence was fused with synthetic cry2AX1 gene to target its protein in chloroplasts. Sixteen PCR positive lines of rice were generated by Agrobacterium mediated transformation using immature embryos. Southern blot hybridization analysis of T 0 transgenic plants confirmed the integration of cry2AX1 gene in two to five locations of rice genome and ELISA demonstrated its expression. Concentration of Cry2AX1 in transgenic rice events ranged 5.0-120 ng/g of fresh leaf tissue. Insect bioassay of T 0 transgenic rice plants against neonate larvae of rice leaffolder showed larval mortality ranging between 20 and 80 % in comparison to control plant. Stable inheritance and expression of cry2AX1 gene was demonstrated in T 1 progenies through Southern and ELISA. In T 1 progenies, the highest concentration of Cry2AX1 and mortality of rice leaffolder larvae were recorded as 150 ng/g of fresh leaf tissue and 80 %, respectively. The Cry2AX1 expression even at a very low concentration (120-150 ng/g) in transgenic rice plants was found effective against rice leaffolder larvae.

  20. An implicit meshless scheme for the solution of transient non-linear Poisson-type equations

    KAUST Repository

    Bourantas, Georgios

    2013-07-01

    A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.

  1. An implicit meshless scheme for the solution of transient non-linear Poisson-type equations

    KAUST Repository

    Bourantas, Georgios; Burganos, Vasilis N.

    2013-01-01

    A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.

  2. Modeling Individual Damped Linear Oscillator Processes with Differential Equations: Using Surrogate Data Analysis to Estimate the Smoothing Parameter

    Science.gov (United States)

    Deboeck, Pascal R.; Boker, Steven M.; Bergeman, C. S.

    2008-01-01

    Among the many methods available for modeling intraindividual time series, differential equation modeling has several advantages that make it promising for applications to psychological data. One interesting differential equation model is that of the damped linear oscillator (DLO), which can be used to model variables that have a tendency to…

  3. Interpolation problem for the solutions of linear elasticity equations based on monogenic functions

    Science.gov (United States)

    Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii

    2017-11-01

    Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.

  4. On the Use of Linearized Euler Equations in the Prediction of Jet Noise

    Science.gov (United States)

    Mankbadi, Reda R.; Hixon, R.; Shih, S.-H.; Povinelli, L. A.

    1995-01-01

    Linearized Euler equations are used to simulate supersonic jet noise generation and propagation. Special attention is given to boundary treatment. The resulting solution is stable and nearly free from boundary reflections without the need for artificial dissipation, filtering, or a sponge layer. The computed solution is in good agreement with theory and observation and is much less CPU-intensive as compared to large-eddy simulations.

  5. Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

    Science.gov (United States)

    Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

    2018-02-01

    In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

  6. Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

    Science.gov (United States)

    Hunt, L. R.; Villarreal, Ramiro

    1987-01-01

    System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

  7. Solving large-scale sparse eigenvalue problems and linear systems of equations for accelerator modeling

    International Nuclear Information System (INIS)

    Gene Golub; Kwok Ko

    2009-01-01

    The solutions of sparse eigenvalue problems and linear systems constitute one of the key computational kernels in the discretization of partial differential equations for the modeling of linear accelerators. The computational challenges faced by existing techniques for solving those sparse eigenvalue problems and linear systems call for continuing research to improve on the algorithms so that ever increasing problem size as required by the physics application can be tackled. Under the support of this award, the filter algorithm for solving large sparse eigenvalue problems was developed at Stanford to address the computational difficulties in the previous methods with the goal to enable accelerator simulations on then the world largest unclassified supercomputer at NERSC for this class of problems. Specifically, a new method, the Hemitian skew-Hemitian splitting method, was proposed and researched as an improved method for solving linear systems with non-Hermitian positive definite and semidefinite matrices.

  8. Difference equations theory, applications and advanced topics

    CERN Document Server

    Mickens, Ronald E

    2015-01-01

    THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...

  9. Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

    Science.gov (United States)

    Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

    2017-11-01

    When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

  10. Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

    International Nuclear Information System (INIS)

    Hernandez-Walls, R; Martín-Atienza, B; Salinas-Matus, M; Castillo, J

    2017-01-01

    When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations. (paper)

  11. First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

    Directory of Open Access Journals (Sweden)

    Heinz Toparkus

    2014-04-01

    Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

  12. miR-24-mediated down-regulation of H2AX suppresses DNA repair in terminally differentiated blood cells

    Science.gov (United States)

    Lal, Ashish; Pan, Yunfeng; Navarro, Francisco; Dykxhoorn, Derek M.; Moreau, Lisa; Meire, Eti; Bentwich, Zvi; Lieberman, Judy; Chowdhury, Dipanjan

    2010-01-01

    Terminally differentiated cells have reduced capacity to repair double strand breaks (DSB), but the molecular mechanism behind this down-regulation is unclear. Here we find that miR-24 is consistently up-regulated during post-mitotic differentiation of hematopoietic cell lines and regulates the histone variant H2AX, a key DSB repair protein that activates cell cycle checkpoint proteins and retains DSB repair factors at DSB foci. The H2AX 3’UTR contains conserved miR-24 binding sites regulated by miR-24. Both H2AX mRNA and protein are substantially reduced during hematopoietic cell terminal differentiation by miR-24 up-regulation both in in vitro differentiated cells and primary human blood cells. miR-24 suppression of H2AX renders cells hypersensitive to γ-irradiation and genotoxic drugs. Antagonizing miR-24 in differentiating cells protects them from DNA damage-induced cell death, while transfecting miR-24 mimics in dividing cells increases chromosomal breaks and unrepaired DNA damage and reduces viability in response to DNA damage. This DNA repair phenotype can be fully rescued by over-expressing miR-24-insensitive H2AX. Therefore, miR-24 up-regulation in post-replicative cells reduces H2AX and thereby renders them highly vulnerable to DNA damage. PMID:19377482

  13. An implementation of Kovacic's algorithm for solving ordinary differential equations in FORMAC

    International Nuclear Information System (INIS)

    Zharkov, A.Yu.

    1987-01-01

    An implementation of Kovacic's algorithm for finding Liouvillian solutions of the differential equations y'' + a(x)y' + b(x)y = 0 with rational coefficients a(x) and b(x) in the Computer Algebra System FORMAC is described. The algorithm description is presented in such a way that one can easily implement it in a suitable Computer Algebra System

  14. Linear analysis of neoclassical tearing mode based on the four-field reduced neoclassical MHD equation

    International Nuclear Information System (INIS)

    Furuya, Atsushi; Yagi, Masatoshi; Itoh, Sanae-I.

    2003-01-01

    The linear neoclassical tearing mode is investigated using the four-field reduced neoclassical MHD equations, in which the fluctuating ion parallel flow and ion neoclassical viscosity are taken into account. The dependences of the neoclassical tearing mode on collisionality, diamagnetic drift and q profile are investigated. These results are compared with the results from the conventional three-field model. It is shown that the linear neoclassical tearing mode is stabilized by the ion neoclassical viscosity in the banana regime even if Δ' > 0. (author)

  15. Asymptotically linear Schrodinger equation with zero on the boundary of the spectrum

    Directory of Open Access Journals (Sweden)

    Dongdong Qin

    2015-08-01

    Full Text Available This article concerns the Schr\\"odinger equation $$\\displaylines{ -\\Delta u+V(xu=f(x, u, \\quad \\text{for } x\\in\\mathbb{R}^N,\\cr u(x\\to 0, \\quad \\text{as } |x| \\to \\infty, }$$ where V and f are periodic in x, and 0 is a boundary point of the spectrum $\\sigma(-\\Delta+V$. Assuming that f(x,u is asymptotically linear as $|u|\\to\\infty$, existence of a ground state solution is established using some new techniques.

  16. Monge-Ampere equations and tensorial functors

    International Nuclear Information System (INIS)

    Tunitsky, Dmitry V

    2009-01-01

    We consider differential-geometric structures associated with Monge-Ampere equations on manifolds and use them to study the contact linearization of such equations. We also consider the category of Monge-Ampere equations (the morphisms are contact diffeomorphisms) and a number of subcategories. We are chiefly interested in subcategories of Monge-Ampere equations whose objects are locally contact equivalent to equations linear in the second derivatives (semilinear equations), linear in derivatives, almost linear, linear in the second derivatives and independent of the first derivatives, linear, linear and independent of the first derivatives, equations with constant coefficients or evolution equations. We construct a number of functors from the category of Monge-Ampere equations and from some of its subcategories to the category of tensorial objects (that is, multi-valued sections of tensor bundles). In particular, we construct a pseudo-Riemannian metric for every generic Monge-Ampere equation. These functors enable us to establish effectively verifiable criteria for a Monge-Ampere equation to belong to the subcategories listed above.

  17. Introduction to differential equations

    CERN Document Server

    Taylor, Michael E

    2011-01-01

    The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen

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

    Science.gov (United States)

    Camporesi, Roberto

    2016-01-01

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

  19. Absence of DNA double-strand breaks in human peripheral blood mononuclear cells after 3 Tesla magnetic resonance imaging assessed by γH2AX flow cytometry

    Energy Technology Data Exchange (ETDEWEB)

    Fasshauer, Martin; Staab, Wieland; Sohns, Jan M.; Ritter, Christian; Lotz, Joachim [Goettingen Heart Center, Department of Diagnostic and Interventional Radiology, University Medical Center Goettingen (Germany); German Centre for Cardiovascular Research (DZHK), Goettingen (Germany); Kruewel, Thomas; Stahnke, Vera C. [Goettingen Heart Center, Department of Diagnostic and Interventional Radiology, University Medical Center Goettingen (Germany); Zapf, Antonia [University Medical Center Goettingen, Department of Medical Statistics, Goettingen (Germany); Rave-Fraenk, Margret [University Medical Center Goettingen, Department of Radiotherapy and Radiooncology, Goettingen (Germany); Steinmetz, Michael [German Centre for Cardiovascular Research (DZHK), Goettingen (Germany); Goettingen Heart Center, Department of Pediatric Cardiology and Intensive Care Medicine, University Medical Center Goettingen (Germany); Unterberg-Buchwald, Christina [Goettingen Heart Center, Department of Diagnostic and Interventional Radiology, University Medical Center Goettingen (Germany); German Centre for Cardiovascular Research (DZHK), Goettingen (Germany); Goettingen Heart Center, Department of Cardiology and Pneumology, University Medical Center Goettingen (Germany); Schuster, Andreas [German Centre for Cardiovascular Research (DZHK), Goettingen (Germany); Goettingen Heart Center, Department of Cardiology and Pneumology, University Medical Center Goettingen (Germany)

    2018-03-15

    Magnetic resonance imaging (MRI) is regarded as a non-harming and non-invasive imaging modality with high tissue contrast and almost no side effects. Compared to other cross-sectional imaging modalities, MRI does not use ionising radiation. Recently, however, strong magnetic fields as applied in clinical MRI scanners have been suspected to induce DNA double-strand breaks in human lymphocytes. In this study we investigated the impact of 3-T cardiac MRI examinations on the induction of DNA double-strand breaks in peripheral mononuclear cells by γH2AX staining and flow cytometry analysis. The study cohort consisted of 73 healthy non-smoking volunteers with 36 volunteers undergoing CMRI and 37 controls without intervention. Differences between the two cohorts were analysed by a mixed linear model with repeated measures. Both cohorts showed a significant increase in the γH2AX signal from baseline to post-procedure of 6.7 % (SD 7.18 %) and 7.8 % (SD 6.61 %), respectively. However, the difference between the two groups was not significant. Based on our study, γH2AX flow cytometry shows no evidence that 3-T MRI examinations as used in cardiac scans impair DNA integrity in peripheral mononuclear cells. (orig.)

  20. NoRC Recruitment by H2A.X Deposition at rRNA Gene Promoter Limits Embryonic Stem Cell Proliferation

    Directory of Open Access Journals (Sweden)

    Boris Eleuteri

    2018-05-01

    Full Text Available Summary: Embryonic stem cells (ESCs display an abbreviated cell cycle, resulting in a short doubling time and rapid proliferation. The histone variant H2A.X is critical for proliferation of stem cells, although mechanistic insights have remained obscure. Here, we show that H2A.X defines the rate of mouse ESC proliferation independently of the DNA damage response pathway, and it associates with three major chromatin-modifying complexes. Our functional and biochemical analyses demonstrate that H2A.X-associated factors mediate the H2A.X-dependent effect on ESC proliferation and involve the nucleolar remodeling complex (NoRC. A specific H2A.X deposition at rDNA promoters determines the chromatin recruitment of the NoRC, histone modifications, the rRNA transcription, and the rate of proliferation. Collectively, our results suggest that NoRC assembly by H2A.X deposition at rRNA promoters silences transcription, and this represents an important regulatory component for ESC proliferation. : Histone variant H2A.X defines the rate of embryonic stem cell proliferation. Eleuteri et al. identify H2A.X-interacting proteins, and they show that H2A.X deposition at rDNA promoters assembles the NoRC, which represses rRNA transcription and determines the rate of self-renewal. Keywords: ribosomal biogenesis, rRNA, rDNA, stem cells, TIP5, SNF2H, SPT16, BRG1, H2A.X, G1, cell cycle, cell cycle arrest, proliferation

  1. DNA DSB measurements and modelling approaches based on gamma-H2AX foci time evolution

    Science.gov (United States)

    Esposito, Giuseppe; Campa, Alessandro; Antonelli, Francesca; Mariotti, Luca; Belli, Mauro; Giardullo, Paola; Simone, Giustina; Antonella Tabocchini, Maria; Ottolenghi, Andrea

    DNA double strand breaks (DSBs) induced by ionising radiation are considered the main dam-age related to the deleterious consequences in the cells. Unrepaired or mis-repaired DSBs can cause mutations or loss of chromosome regions which can eventually lead to cell death or neo-plastic transformation. Quantification of the number and complexity of DSBs induced by low doses of radiation remains a complex problem. About ten years ago Rogakou et al. proposed an immunofluorescent technique able to detect even a single DSB per cell. This approach is based on the serine 139 phosphorylation of many molecules (up to 2000) of histone H2AX (γg-H2AX) following the induction of a DSB in the DNA. DSB can be visualized as foci by immunofluores-cence by using phospho-specific antibodies, so that enumeration of foci can be used to measure DSB induction and processing. It is still not completely clear how γ-H2AX dephosphorylation takes place; however it has been related with DSB repair, in particular with the efficiency of DSB repair. In this work we analyse the H2AX phosphorylation-dephosphorylation kinetics after irradiation of primary human fibroblasts (AG1522 cell line) with radiation of differing quality, that is γ-rays and α-particles (125 keV/µm), with the aim of comparing the time evolution of γ-H2AX foci. Our results show that, after a dose of 0.5 Gy, both γ-rays and α-particles induce the maximum number of γ-H2AX foci within 30 minutes from irradiation, that this number depends on the radiation type and is consistent with the number of track traversal in α-irradiated nuclei, that the dephosphorylation kinetics are very different, being the α-induced foci rate of disappearence slower than that of γ-induced foci. In this work a modellistic approach to estimate the number of DSB induced by γ-rays detectable by using the γ-H2AX assay is presented. The competing processes of appearance and disappearance of visible foci will be modeled taking into account the

  2. Endogenous and radiation-induced expression of γH2AX in biopsies from patients treated for carcinoma of the uterine cervix

    International Nuclear Information System (INIS)

    Olive, Peggy L.; Banuelos, C. Adriana; Durand, Ralph E.; Kim, Joo-Young; Aquino-Parsons, Christina

    2010-01-01

    Background and purpose: The possibility of using γH2AX foci as a marker of DNA damage and as a potential predictor of tumour response to treatment was examined using biopsies from 3 sets of patients with advanced carcinoma of the cervix. The relation between endogenous γH2AX expression and hypoxia was also examined. Materials and methods: Set 1 consisted of 26 biopsies that included pre-treatment and 24 h post-radiation treatment samples. Pre-treatment biopsies from 12 patients in Set 2 were used to develop image analysis software while pre-treatment biopsies from 33 patients in Set 3 were examined for the relation between staining for the hypoxia marker pimonidazole and endogenous γH2AX expression. Formalin-fixed paraffin-embedded sections were analyzed after antigen retrieval and fluorescence antibody labeling for the hypoxia markers CAIX or pimonidazole in combination with γH2AX staining. Results: Before treatment, 24 ± 19% of cells contained γH2AX foci, with most positive cells containing fewer than 5 foci per nucleus. Twenty-four hours after exposure to the first fraction of 1.8-2.5 Gy, 38 ± 19% contained foci. CAIX positive cells were 1.4 times more likely to exhibit endogenous γH2AX foci, and pimonidazole-positive cells were 2.8 times more likely to contain γH2AX foci. For 18 patients for whom both pre-treatment and 24 h post-irradiation biopsies were available, local control was unrelated to the fraction of cells that retained γH2AX foci. However, 24 h after irradiation, tumours that had received 2.5 Gy showed a significantly higher fraction of cells with residual γH2AX foci than tumours given 1.8 Gy. Conclusions: Endogenous γH2AX foci are enriched in hypoxic tumour regions. Small differences in delivered dose can produce quantifiable differences in residual DNA damage that can overshadow inter-tumour differences in response.

  3. Conductive sapwood area prediction from stem and canopy areas - allometric equations of Kalahari trees, Botswana

    NARCIS (Netherlands)

    Lubczynski, M.W.; Chavarro-Rincon, D.C.; Rossiter, David

    2017-01-01

    Conductive sapwood (xylem) area (Ax) of all trees in a given forested area is the main factor contributing to spatial tree transpiration. One hundred ninety-five trees of 9 species in the Kalahari region of Botswana were felled, stained, cut into discs, and measured to develop allometric equations

  4. Optimal Control Strategies in a Two Dimensional Differential Game Using Linear Equation under a Perturbed System

    Directory of Open Access Journals (Sweden)

    Musa Danjuma SHEHU

    2008-06-01

    Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.

  5. COSTANZA-AX, 1-D Neutronics and Thermodynamics of Liquid Cooled Reactor in Axial Geometry. COSTANZA-CYL, 1-D Neutronics and Thermodynamics of Liquid Cooled Reactor in Cylindrical Geometry

    International Nuclear Information System (INIS)

    Agazzi, A.; Forti, G.; Vincenti, E.

    1984-01-01

    1 - Nature of physical problem solved: Purpose of the programmes is to study reactor dynamics, considering the variation of the spatial flux distribution. The two programmes COSTANZA-CYL and COSTANZA-AX, solve the kinetics diffusion equations in two groups and one dimension (plane geometry for COSTANZA-AX, radial geometry for COSTANZA-CYL). The neutronic calculation is coupled with the calculation of the heat transmission from the fuel to the cladding and to the coolant, and with the thermo-hydraulics of channels with forced circulation of liquid coolant. The geometry of fuel element and channel may be cylindrical or slab. Up to ten groups of delayed neutrons are allowed. Temperature feedback of fuel (Doppler) and coolant are considered independently and affect the nuclear constants. Control rod movement or diffused poison concentrations are simulated by externally imposed variations of the thermal absorption cross section in the different regions of the reactors. Inlet temperatures and mass flow in the coolant channels may be varied according to any externally given time table. 2 - Method of solution: The kinetic diffusion equations in two groups are solved by finite-difference method. 3 - Restrictions on the complexity of the problem: 10 concentric regions; 10 coolant channels; 10 groups of delayed neutrons

  6. Linear and nonlinear properties of numerical methods for the rotating shallow water equations

    Science.gov (United States)

    Eldred, Chris

    The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. It is desirable that numerical models posses similar properties, and the prototypical example of such a scheme is the 1981 Arakawa and Lamb (AL81) staggered (C-grid) total energy and potential enstrophy conserving scheme, based on the vector invariant form of the continuous equations. However, this scheme is restricted to a subset of logically square, orthogonal grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos and others) and Discrete Exterior Calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp and others). It is also possible to obtain these properties (along with arguably superior wave dispersion properties) through the use of a collocated (Z-grid) scheme based on the vorticity-divergence form of the continuous equations. Unfortunately, existing examples of these schemes in the literature for general, spherical grids either contain computational modes; or do not conserve total energy and potential enstrophy. This dissertation extends an existing scheme for planar grids to spherical grids, through the use of Nambu brackets (as pioneered by Rick Salmon). To compare these two schemes, the linear modes (balanced states, stationary modes and propagating modes; with and without dissipation) are examined on both uniform planar grids (square, hexagonal) and quasi-uniform spherical grids (geodesic, cubed-sphere). In addition to evaluating the linear modes, the results of the two schemes applied to a set of standard shallow water test cases and a recently developed forced-dissipative turbulence test case from John Thuburn (intended to evaluate the ability the suitability of schemes as the basis for a climate model) on both hexagonal

  7. Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

    Science.gov (United States)

    Shah, A A; Xing, W W; Triantafyllidis, V

    2017-04-01

    In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

  8. Improved Harmony Search Algorithm with Chaos for Absolute Value Equation

    Directory of Open Access Journals (Sweden)

    Shouheng Tuo

    2013-11-01

    Full Text Available In this paper, an improved harmony search with chaos (HSCH is presented for solving NP-hard absolute value equation (AVE Ax - |x| = b, where A is an arbitrary square matrix whose singular values exceed one. The simulation results in solving some given AVE problems demonstrate that the HSCH algorithm is valid and outperforms the classical HS algorithm (CHS and HS algorithm with differential mutation operator (HSDE.

  9. An algorithm for computing the hull of the solution set of interval linear equations

    Czech Academy of Sciences Publication Activity Database

    Rohn, Jiří

    2011-01-01

    Roč. 435, č. 2 (2011), s. 193-201 ISSN 0024-3795 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * interval hull * algorithm * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 0.974, year: 2011

  10. Genetic engineering of cotton with a novel cry2AX1 gene to impart insect resistance against Helicoverpa armigera

    Directory of Open Access Journals (Sweden)

    Karunamurthy Dhivya

    2016-09-01

    Full Text Available Embryogenic calli of cotton (Coker310 were cocultivated with the Agrobacterium tumefaciens strain LBA4404 harbouring the codon-optimised, chimeric cry2AX1 gene consisting of sequences from cry2Aa and cry2Ac genes isolated from Indian strains of Bacillus thuringiensis. Forty-eight putative transgenic plants were regenerated, and PCR analysis of these plants revealed the presence of the cry2AX1 gene in 40 plants. Southern blot hybridisation analysis of selected transgenic plants confirmed stable T-DNA integration in the genome of transformed plants. The level of Cry2AX1 protein expression in PCR positive plants ranged from 4.9 to 187.5 ng g-1 of fresh tissue. A transgenic cotton event, TP31, expressing the cry2AX1 gene showed insecticidal activity of 56.66 per cent mortality against Helicoverpa armigera in detached leaf disc bioassay. These results indicate that the chimeric cry2AX1 gene expressed in transgenic cotton has insecticidal activity against H. armigera.

  11. On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

    Science.gov (United States)

    Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

    1994-01-01

    It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

  12. Stability of Linear Equations--Algebraic Approach

    Science.gov (United States)

    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…

  13. Diffusion-accelerated solution of the 2-D x-y Sn equations with linear-bilinear nodal differencing

    International Nuclear Information System (INIS)

    Wareing, T.A.; Walters, W.F.; Morel, J.E.

    1994-01-01

    Recently a new diffusion-synthetic acceleration scheme was developed for solving the 2-D S n Equations in x-y geometry with bilinear-discontinuous finite element spatial discretization using a bilinear-discontinuous diffusion differencing scheme for the diffusion acceleration equations. This method differs from previous methods in that it is conditional efficient for problems with isotropic or nearly isotropic scattering. We have used the same bilinear-discontinuous diffusion scheme, and associated solution technique, to accelerate the x-y geometry S n equations with linear-bilinear nodal spatial differencing. We find that this leads to an unconditionally efficient solution method for problems with isotropic or nearly isotropic scattering. computational results are given which demonstrate this property

  14. Improved Pedagogy for Linear Differential Equations by Reconsidering How We Measure the Size of Solutions

    Science.gov (United States)

    Tisdell, Christopher C.

    2017-01-01

    For over 50 years, the learning of teaching of "a priori" bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to "a priori" bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving…

  15. Relativistic wave equations without the Velo-Zwanziger pathology

    International Nuclear Information System (INIS)

    Khalil, M.A.K.

    1976-06-01

    For particles described by relativistic wave equations of the form: (-iGAMMA x delta + m) psi(x) = 0 interacting with an external field B(x) it is known that the ''noncausal'' propagation characteristics are not present when (1) GAMMA 0 is diagonalizable and (2) B(x) = -eGAMMA/sub mu/A/sup mu/(x) (Amar--Dozzio). The ''noncausality''difficulties arise for the Rarita--Schwinger spin 3 / 2 equation, with nondiagonalizable GAMMA 0 , in minimal coupling (i.e., B(x) = -eGAMMA x A(x)) and the PDK spin 1 equation, with diagonalizable GAMMA 0 , in a quadrupole coupling (Velo--Zwanziger) where either (1) or (2) of the Amar--Dozzio (sufficient) conditions are violated. Some sufficient conditions are derived and explored where the Velo--Zwanziger ''noncausality'' pathology can be avoided, even though one, or the other, or both of the conditions (1) and (2) are violated. Examples with both reducible and irreducible wave equations are included

  16. Hyper-recombinogenity of the chimeric protein RecAX53 (Esherichia coli/Pseudomonas aeruginosa is caused by its increased dynamics

    Directory of Open Access Journals (Sweden)

    Daria B Chervyakova

    2008-12-01

    Full Text Available RecAX53 is the most recombinogenic protein among the chimeric RecA proteins composed ofEsherichia coli RecA (RecAEc and Pseudomonas aeruginosa RecA (RecAPa protein fragments. We found out that RecAX53 protein is more rapid in ATP hydrolysis, dissociation from single-stranded DNA (ssDNA, SSB protein displacement from ssDNA and in association with doublestranded DNA (dsDNA, as compared with RecAEc and RecAPa proteins. These results indicate that the RecAX53 hyper-recombinogenity is caused by high dynamics of this protein - by its rapid association with and dissociation from ssDNA. The ability of RecAX53 to bind actively with dsDNA accounts for the SOS-independent mechanism of hyper-recombination used by this protein.

  17. Should Pruning be a Pre-Processor of any Linear System?

    Science.gov (United States)

    Sen, Syamal K.; Ramakrishnan, Suja; Agarwal, Ravi P.; Shaykhian, Gholam Ali

    2011-01-01

    There are many real-world problems whose mathematical models turn out to be linear systems Ax = b, where A is an m x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as an equation 4x(sub 1) + 6x(sub 2) + 5x(sub 3) = 10 , where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. It is assumed that at least one information, i.e. one equation is known to be correct and which will be our first equation. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually

  18. Generation of an alpaca-derived nanobody recognizing γ-H2AX

    Science.gov (United States)

    Rajan, Malini; Mortusewicz, Oliver; Rothbauer, Ulrich; Hastert, Florian D.; Schmidthals, Katrin; Rapp, Alexander; Leonhardt, Heinrich; Cardoso, M. Cristina

    2015-01-01

    Post-translational modifications are difficult to visualize in living cells and are conveniently analyzed using antibodies. Single-chain antibody fragments derived from alpacas and called nanobodies can be expressed and bind to the target antigenic sites in living cells. As a proof of concept, we generated and characterized nanobodies against the commonly used biomarker for DNA double strand breaks γ-H2AX. In vitro and in vivo characterization showed the specificity of the γ-H2AX nanobody. Mammalian cells were transfected with fluorescent fusions called chromobodies and DNA breaks induced by laser microirradiation. We found that alternative epitope recognition and masking of the epitope in living cells compromised the chromobody function. These pitfalls should be considered in the future development and screening of intracellular antibody biomarkers. PMID:26500838

  19. Hartree Fock-type equations in relativistic quantum electrodynamics with non-linear gauge fixing

    International Nuclear Information System (INIS)

    Dietz, K.; Hess, B.A.

    1990-08-01

    Relativistic mean-field equations are obtained by minimizing the effective energy obtained from the gauge-invariant energy density by eliminating electro-magnetic degrees of freedom in certain characteristic non-linear gauges. It is shown that by an appropriate choice of gauge many-body correlations, e.g. screening, three-body 'forces' etc. can be included already at the mean-field level. The many-body perturbation theory built on the latter is then expected to show improved 'convergence'. (orig.)

  20. Analytical solutions of linear diffusion and wave equations in semi-infinite domains by using a new integral transform

    Directory of Open Access Journals (Sweden)

    Gao Lin

    2017-01-01

    Full Text Available Recently, a new integral transform similar to Sumudu transform has been proposed by Yang [1]. Some of the properties of the integral transform are expanded in the present article. Meanwhile, new applications to the linear wave and diffusion equations in semi-infinite domains are discussed in detail. The proposed method provides an alternative approach to solve the partial differential equations in mathematical physics.

  1. THE A-X INFRARED BANDS OF ALUMINUM OXIDE IN STARS: SEARCH AND NEW DETECTIONS

    Energy Technology Data Exchange (ETDEWEB)

    Banerjee, D. P. K.; Mathew, Blesson; Ashok, N. M. [Astronomy and Astrophysics Division, Physical Research Laboratory, Navrangpura, Ahmedabad, Gujarat 380009 (India); Varricatt, W. P. [Joint Astronomy Centre, 660 N. Aohoku Place, University Park, Hilo, Hawaii, HI 96720 (United States); Launila, O., E-mail: orion@prl.res.in [KTH-AlbaNova, Applied Physics, Roslagstullsbacken 21, 106 91 Stockholm (Sweden)

    2012-07-01

    We describe a search for the A-X infrared bands of AlO with a view toward better understanding the characteristics of this radical. These bands are infrequently encountered in astronomical sources but surprisingly were very prominent in the spectra of two well-known, novalike variables (V838 Mon and V4332 Sgr) thereby motivating us to explore the physical conditions necessary for their excitation. In this study, we present the detection of A-X bands in the spectra of 13 out of 17 stars, selected on the basis of their J - K colors as potential candidates for detection of these bands. The majority of the AlO detections are in asymptotic giant branch (AGB) stars, viz., nine OH/IR stars, two Mira variables, and two bright infrared sources. Our study shows that the A-X bands are fairly prevalent in sources with low temperature and O-rich environments. Interesting variation in the strength of the AlO bands in one of the sources (IRAS 18530+0817) is reported and the cause for this is examined. Possible applications of the present study are discussed in terms of the role of AlO in alumina dust formation, the scope for estimating the radioactive {sup 26}Al content in AGB stars from the A-X bands, and providing possible targets for further mm/radio studies of AlO which has recently been discovered at millimeter wavelengths.

  2. Differential Equation over Banach Algebra

    OpenAIRE

    Kleyn, Aleks

    2018-01-01

    In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.

  3. Compact tunable silicon photonic differential-equation solver for general linear time-invariant systems.

    Science.gov (United States)

    Wu, Jiayang; Cao, Pan; Hu, Xiaofeng; Jiang, Xinhong; Pan, Ting; Yang, Yuxing; Qiu, Ciyuan; Tremblay, Christine; Su, Yikai

    2014-10-20

    We propose and experimentally demonstrate an all-optical temporal differential-equation solver that can be used to solve ordinary differential equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE solver.

  4. Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

    DEFF Research Database (Denmark)

    Larsen, Jon Steffen; Santos, Ilmar

    2015-01-01

    An efficient finite element scheme for solving the non-linear Reynolds equation for compressible fluid coupled to compliant structures is presented. The method is general and fast and can be used in the analysis of airfoil bearings with simplified or complex foil structure models. To illustrate...

  5. AX-PET: A novel PET concept with G-APD readout

    CERN Document Server

    Heller, M; Casella, C; Chesi, E; De Leo, R; Dissertori, G; Fanti, V; Gillam, J E; Joram, C; Lustermann, W; Nappi, E; Oliver, J F; Pauss, F; Rafecas, M; Rudge, A; Ruotsalainen, U; Schinzel, D; Schneider, T; Seguinot, J; Solevi, P; Stapnes, S; Tuna, U; Weilhammer, P

    2012-01-01

    The AX-PET collaboration has developed a novel concept for high resolution PET imaging to overcome some of the performance limitations of classical PET cameras, in particular the compromise between spatial resolution and sensitivity introduced by the parallax error. The detector consists of an arrangement of long LYSO scintillating crystals axially oriented around the field of view together with arrays of wave length shifter strips orthogonal to the crystals. This matrix allows a precise 3D measurement of the photon interaction point. This is valid both for photoelectric absorption at 511 key and for Compton scattering down to deposited energies of about 100 keV. Crystals and WLS strips are individually read out using Geiger-mode Avalanche Photo Diodes (G-APDs). The sensitivity of such a detector can be adjusted by changing the number of layers and the resolution is defined by the crystal and strip dimensions. Two AX-PET modules were built and fully characterized in dedicated test set-ups at CERN, with point-...

  6. Explicit estimating equations for semiparametric generalized linear latent variable models

    KAUST Repository

    Ma, Yanyuan

    2010-07-05

    We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n consistency and asymptotic normality. We explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies. The advantage of our estimators over the existing likelihood approach is also shown via numerical comparison. We employ the method to analyse a real data example from economics. © 2010 Royal Statistical Society.

  7. Finite-dimensional linear algebra

    CERN Document Server

    Gockenbach, Mark S

    2010-01-01

    Some Problems Posed on Vector SpacesLinear equationsBest approximationDiagonalizationSummaryFields and Vector SpacesFields Vector spaces Subspaces Linear combinations and spanning sets Linear independence Basis and dimension Properties of bases Polynomial interpolation and the Lagrange basis Continuous piecewise polynomial functionsLinear OperatorsLinear operatorsMore properties of linear operatorsIsomorphic vector spaces Linear operator equations Existence and uniqueness of solutions The fundamental theorem; inverse operatorsGaussian elimination Newton's method Linear ordinary differential eq

  8. 3D-structured illumination microscopy reveals clustered DNA double-strand break formation in widespread γH2AX foci after high LET heavy-ion particle radiation.

    Science.gov (United States)

    Hagiwara, Yoshihiko; Niimi, Atsuko; Isono, Mayu; Yamauchi, Motohiro; Yasuhara, Takaaki; Limsirichaikul, Siripan; Oike, Takahiro; Sato, Hiro; Held, Kathryn D; Nakano, Takashi; Shibata, Atsushi

    2017-12-12

    DNA double-strand breaks (DSBs) induced by ionising radiation are considered the major cause of genotoxic mutations and cell death. While DSBs are dispersed throughout chromatin after X-rays or γ-irradiation, multiple types of DNA damage including DSBs, single-strand breaks and base damage can be generated within 1-2 helical DNA turns, defined as a complex DNA lesion, after high Linear Energy Transfer (LET) particle irradiation. In addition to the formation of complex DNA lesions, recent evidence suggests that multiple DSBs can be closely generated along the tracks of high LET particle irradiation. Herein, by using three dimensional (3D)-structured illumination microscopy, we identified the formation of 3D widespread γH2AX foci after high LET carbon-ion irradiation. The large γH2AX foci in G 2 -phase cells encompassed multiple foci of replication protein A (RPA), a marker of DSBs undergoing resection during homologous recombination. Furthermore, we demonstrated by 3D analysis that the distance between two individual RPA foci within γH2AX foci was approximately 700 nm. Together, our findings suggest that high LET heavy-ion particles induce clustered DSB formation on a scale of approximately 1 μm 3 . These closely localised DSBs are considered to be a risk for the formation of chromosomal rearrangement after heavy-ion irradiation.

  9. Asymptotic Comparison of the Solutions of Linear Time-Delay Systems with Point and Distributed Lags with Those of Their Limiting Equations

    Directory of Open Access Journals (Sweden)

    M. De la Sen

    2009-01-01

    Full Text Available This paper investigates the relations between the particular eigensolutions of a limiting functional differential equation of any order, which is the nominal (unperturbed linear autonomous differential equations, and the associate ones of the corresponding perturbed functional differential equation. Both differential equations involve point and distributed delayed dynamics including Volterra class dynamics. The proofs are based on a Perron-type theorem for functional equations so that the comparison is governed by the real part of a dominant zero of the characteristic equation of the nominal differential equation. The obtained results are also applied to investigate the global stability of the perturbed equation based on that of its corresponding limiting equation.

  10. Performance prediction of gas turbines by solving a system of non-linear equations

    Energy Technology Data Exchange (ETDEWEB)

    Kaikko, J

    1998-09-01

    This study presents a novel method for implementing the performance prediction of gas turbines from the component models. It is based on solving the non-linear set of equations that corresponds to the process equations, and the mass and energy balances for the engine. General models have been presented for determining the steady state operation of single components. Single and multiple shad arrangements have been examined with consideration also being given to heat regeneration and intercooling. Emphasis has been placed upon axial gas turbines of an industrial scale. Applying the models requires no information of the structural dimensions of the gas turbines. On comparison with the commonly applied component matching procedures, this method incorporates several advantages. The application of the models for providing results is facilitated as less attention needs to be paid to calculation sequences and routines. Solving the set of equations is based on zeroing co-ordinate functions that are directly derived from the modelling equations. Therefore, controlling the accuracy of the results is easy. This method gives more freedom for the selection of the modelling parameters since, unlike for the matching procedures, exchanging these criteria does not itself affect the algorithms. Implicit relationships between the variables are of no significance, thus increasing the freedom for the modelling equations as well. The mathematical models developed in this thesis will provide facilities to optimise the operation of any major gas turbine configuration with respect to the desired process parameters. The computational methods used in this study may also be adapted to any other modelling problems arising in industry. (orig.) 36 refs.

  11. SoAx: A generic C++ Structure of Arrays for handling particles in HPC codes

    Science.gov (United States)

    Homann, Holger; Laenen, Francois

    2018-03-01

    The numerical study of physical problems often require integrating the dynamics of a large number of particles evolving according to a given set of equations. Particles are characterized by the information they are carrying such as an identity, a position other. There are generally speaking two different possibilities for handling particles in high performance computing (HPC) codes. The concept of an Array of Structures (AoS) is in the spirit of the object-oriented programming (OOP) paradigm in that the particle information is implemented as a structure. Here, an object (realization of the structure) represents one particle and a set of many particles is stored in an array. In contrast, using the concept of a Structure of Arrays (SoA), a single structure holds several arrays each representing one property (such as the identity) of the whole set of particles. The AoS approach is often implemented in HPC codes due to its handiness and flexibility. For a class of problems, however, it is known that the performance of SoA is much better than that of AoS. We confirm this observation for our particle problem. Using a benchmark we show that on modern Intel Xeon processors the SoA implementation is typically several times faster than the AoS one. On Intel's MIC co-processors the performance gap even attains a factor of ten. The same is true for GPU computing, using both computational and multi-purpose GPUs. Combining performance and handiness, we present the library SoAx that has optimal performance (on CPUs, MICs, and GPUs) while providing the same handiness as AoS. For this, SoAx uses modern C++ design techniques such template meta programming that allows to automatically generate code for user defined heterogeneous data structures.

  12. Replication protein A and γ-H2AX foci assembly is triggered by cellular response to DNA double-strand breaks

    International Nuclear Information System (INIS)

    Balajee, Adayabalam S.; Geard, Charles R.

    2004-01-01

    Human replication protein A (RPA p34), a crucial component of diverse DNA excision repair pathways, is implicated in DNA double-strand break (DSB) repair. To evaluate its role in DSB repair, the intranuclear dynamics of RPA was investigated after DNA damage and replication blockage in human cells. Using two different agents [ionizing radiation (IR) and hydroxyurea (HU)] to generate DSBs, we found that RPA relocated into distinct nuclear foci and colocalized with a well-known DSB binding factor, γ-H2AX, at the sites of DNA damage in a time-dependent manner. Colocalization of RPA and γ-H2AX foci peaked at 2 h after IR treatment and subsequently declined with increasing postrecovery times. The time course of RPA and γ-H2AX foci association correlated well with the DSB repair activity detected by a neutral comet assay. A phosphatidylinositol-3 (PI-3) kinase inhibitor, wortmannin, completely abolished both RPA and γ-H2AX foci formation triggered by IR. Additionally, radiosensitive ataxia telangiectasia (AT) cells harboring mutations in ATM gene product were found to be deficient in RPA and γ-H2AX colocalization after IR. Transfection of AT cells with ATM cDNA fully restored the association of RPA foci with γ-H2AX illustrating the requirement of ATM gene product for this process. The exact coincidence of RPA and γ-H2AX in response to HU specifically in S-phase cells supports their role in DNA replication checkpoint control. Depletion of RPA by small interfering RNA (SiRNA) substantially elevated the frequencies of IR-induced micronuclei (MN) and apoptosis in human cells suggestive of a role for RPA in DSB repair. We propose that RPA in association with γ-H2AX contributes to both DNA damage checkpoint control and repair in response to strand breaks and stalled replication forks in human cells

  13. Linear algebra

    CERN Document Server

    Said-Houari, Belkacem

    2017-01-01

    This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...

  14. Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method

    Directory of Open Access Journals (Sweden)

    Olumuyiwa A. Agbolade

    2017-01-01

    Full Text Available The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.

  15. Reproducing kernel method with Taylor expansion for linear Volterra integro-differential equations

    Directory of Open Access Journals (Sweden)

    Azizallah Alvandi

    2017-06-01

    Full Text Available This research aims of the present a new and single algorithm for linear integro-differential equations (LIDE. To apply the reproducing Hilbert kernel method, there is made an equivalent transformation by using Taylor series for solving LIDEs. Shown in series form is the analytical solution in the reproducing kernel space and the approximate solution $ u_{N} $ is constructed by truncating the series to $ N $ terms. It is easy to prove the convergence of $ u_{N} $ to the analytical solution. The numerical solutions from the proposed method indicate that this approach can be implemented easily which shows attractive features.

  16. Comparison of different methods for the solution of sets of linear equations

    International Nuclear Information System (INIS)

    Bilfinger, T.; Schmidt, F.

    1978-06-01

    The application of the conjugate-gradient methods as novel general iterative methods for the solution of sets of linear equations with symmetrical systems matrices led to this paper, where a comparison of these methods with the conventional differently accelerated Gauss-Seidel iteration was carried out. In additon, the direct Cholesky method was also included in the comparison. The studies referred mainly to memory requirement, computing time, speed of convergence, and accuracy of different conditions of the systems matrices, by which also the sensibility of the methods with respect to the influence of truncation errors may be recognized. (orig.) 891 RW [de

  17. Solution of the Schrodinger Equation for a Diatomic Oscillator Using Linear Algebra: An Undergraduate Computational Experiment

    Science.gov (United States)

    Gasyna, Zbigniew L.

    2008-01-01

    Computational experiment is proposed in which a linear algebra method is applied to the solution of the Schrodinger equation for a diatomic oscillator. Calculations of the vibration-rotation spectrum for the HCl molecule are presented and the results show excellent agreement with experimental data. (Contains 1 table and 1 figure.)

  18. Aspects on increase and decrease within a national economy as eigenvalue problem of linear homogeneous equations

    International Nuclear Information System (INIS)

    Mueller, E.

    2007-01-01

    The paper presents an approach which treats topics of macroeconomics by methods familiar in physics and technology, especially in nuclear reactor technology and in quantum mechanics. Such methods are applied to simplified models for the money flows within a national economy, their variation in time and thereby for the annual national growth rate. As usual, money flows stand for economic activities. The money flows between the economic groups are described by a set of difference equations or by a set of approximative differential equations or eventually by a set of linear algebraic equations. Thus this paper especially deals with the time behaviour of model economies which are under the influence of imbalances and of delay processes, thereby dealing also with economic growth and recession rates. These differential equations are solved by a completely numerical Runge-Kutta algorithm. Case studies are presented for cases with 12 groups only and are to show the capability of the methods which have been worked out. (orig.)

  19. Aspects on increase and decrease within a national economy as eigenvalue problem of linear homogeneous equations

    Energy Technology Data Exchange (ETDEWEB)

    Mueller, E.

    2007-12-15

    The paper presents an approach which treats topics of macroeconomics by methods familiar in physics and technology, especially in nuclear reactor technology and in quantum mechanics. Such methods are applied to simplified models for the money flows within a national economy, their variation in time and thereby for the annual national growth rate. As usual, money flows stand for economic activities. The money flows between the economic groups are described by a set of difference equations or by a set of approximative differential equations or eventually by a set of linear algebraic equations. Thus this paper especially deals with the time behaviour of model economies which are under the influence of imbalances and of delay processes, thereby dealing also with economic growth and recession rates. These differential equations are solved by a completely numerical Runge-Kutta algorithm. Case studies are presented for cases with 12 groups only and are to show the capability of the methods which have been worked out. (orig.)

  20. The Use of Graphs in Specific Situations of the Initial Conditions of Linear Differential Equations

    Science.gov (United States)

    Buendía, Gabriela; Cordero, Francisco

    2013-01-01

    In this article, we present a discussion on the role of graphs and its significance in the relation between the number of initial conditions and the order of a linear differential equation, which is known as the initial value problem. We propose to make a functional framework for the use of graphs that intends to broaden the explanations of the…