Third-order differential ladder operators and supersymmetric quantum mechanics
International Nuclear Information System (INIS)
Mateo, J; Negro, J
2008-01-01
Hierarchies of one-dimensional Hamiltonians in quantum mechanics admitting third-order differential ladder operators are studied. Each Hamiltonian has associated three-step Darboux (pseudo)-cycles and Painleve IV equations as a closure condition. The whole hierarchy is generated applying some operations on the cycles. These operations are investigated in the frame of supersymmetric quantum mechanics and mainly involve algebraic manipulations. A consistent geometric representation for the hierarchy and cycles is built that also helps in understanding the operations. Three kinds of hierarchies are distinguished and a realization based on the harmonic oscillator Hamiltonian is supplied, giving an interpretation for the spectral properties of the Hamiltonians of each hierarchy
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Araz R. Aliev
2013-10-01
Full Text Available We study a third-order operator-differential equation on the semi-axis with a discontinuous coefficient and boundary conditions which include an abstract linear operator. Sufficient conditions for the well-posed and unique solvability are found by means of properties of the operator coefficients in a Sobolev-type space.
Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension
International Nuclear Information System (INIS)
Qu Gai-Zhu; Zhang Shun-Li; Li Yao-Long
2014-01-01
In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators. (general)
Green's matrix for a second-order self-adjoint matrix differential operator
International Nuclear Information System (INIS)
Sisman, Tahsin Cagri; Tekin, Bayram
2010-01-01
A systematic construction of the Green's matrix for a second-order self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first-order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.
Relative boundedness and compactness theory for second-order differential operators
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Don B. Hinton
1997-01-01
Full Text Available The problem considered is to give necessary and sufficient conditions for perturbations of a second-order ordinary differential operator to be either relatively bounded or relatively compact. Such conditions are found for three classes of operators. The conditions are expressed in terms of integral averages of the coefficients of the perturbing operator.
Approximating second-order vector differential operators on distorted meshes in two space dimensions
International Nuclear Information System (INIS)
Hermeline, F.
2008-01-01
A new finite volume method is presented for approximating second-order vector differential operators in two space dimensions. This method allows distorted triangle or quadrilateral meshes to be used without the numerical results being too much altered. The matrices that need to be inverted are symmetric positive definite therefore, the most powerful linear solvers can be applied. The method has been tested on a few second-order vector partial differential equations coming from elasticity and fluids mechanics areas. These numerical experiments show that it is second-order accurate and locking-free. (authors)
Maximum principles for boundary-degenerate second-order linear elliptic differential operators
Feehan, Paul M. N.
2012-01-01
We prove weak and strong maximum principles, including a Hopf lemma, for smooth subsolutions to equations defined by linear, second-order, partial differential operators whose principal symbols vanish along a portion of the domain boundary. The boundary regularity property of the smooth subsolutions along this boundary vanishing locus ensures that these maximum principles hold irrespective of the sign of the Fichera function. Boundary conditions need only be prescribed on the complement in th...
International Nuclear Information System (INIS)
Steinberg, S.; Wolf, K.B.
1979-01-01
The authors study the construction and action of certain Lie algebras of second- and higher-order differential operators on spaces of solutions of well-known parabolic, hyperbolic and elliptic linear differential equations. The latter include the N-dimensional quadratic quantum Hamiltonian Schroedinger equations, the one-dimensional heat and wave equations and the two-dimensional Helmholtz equation. In one approach, the usual similarity first-order differential operator algebra of the equation is embedded in the larger one, which appears as a quantum-mechanical dynamic algebra. In a second approach, the new algebra is built as the time evolution of a finite-transformation algebra on the initial conditions. In a third approach, the algebra to inhomogeneous similarity algebra is deformed to a noncompact classical one. In every case, we can integrate the algebra to a Lie group of integral transforms acting effectively on the solution space of the differential equation. (author)
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Aribindi Satyanarayan Rao
2002-01-01
Full Text Available In a Banach space, if u is a Stepanov almost periodic solution of a certain nth-order infinitesimal generator and time-dependent operator differential equation with a Stepanov almost periodic forcing function, then u,u′,…,u (n−2 are all strongly almost periodic and u (n−1 is weakly almost periodic.
Kiryakova, Virginia S.
2012-11-01
The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order
Trooshin, Igor; Yamamoto, Masahiro
2003-04-01
We consider an eigenvalue problem for a nonsymmetric first order differential operator Au( x ; ) = ( {matrix { 0 & 1 ŗ1 & 0 ŗ} } ; ){{du} / {dx}}( x ; ) + Q( x ; )u( x ; ), 0 < x < 1 , where Q is a 2 × 2 matrix whose components are of C1 class on [0, 1]. Assuming that Q(x) is known in the half interval of (0, 1), we prove the uniqueness in an inverse eigenvalue problem of determining Q(x) from the spectra.
International Nuclear Information System (INIS)
Afuwape, A.U.; Omari, P.
1987-11-01
This paper deals with the solvability of the nonlinear operator equations in normed spaces Lx=EGx+f, where L is a linear map with possible nontrivial kernel. Applications are given to the existence of periodic solutions for the third order scalar differential equation x'''+ax''+bx'+cx+g(t,x)=p(t), under various conditions on the interaction of g(t,x)/x with spectral configurations of a, b and c. (author). 48 refs
International Nuclear Information System (INIS)
Dang Xuanju; Tan Yonghong
2005-01-01
A new neural networks dynamic hysteresis model for piezoceramic actuator is proposed by combining the Preisach model with diagonal recurrent neural networks. The Preisach model is based on elementary rate-independent operators and is not suitable for modeling piezoceramic actuator across a wide frequency band because of the rate-dependent hysteresis characteristic of the piezoceramic actuator. The structure of the developed model is based on the structure of the Preisach model, in which the rate-independent relay hysteresis operators (cells) are replaced by the rate-dependent hysteresis operators of first-order differential equation. The diagonal recurrent neural networks being modified by an adjustable factor can be used to model the hysteresis behavior of the pizeoceramic actuator because its structure is similar to the structure of the modified Preisach model. Therefore, the proposed model not only possesses that of the Preisach model, but also can be used for describing its dynamic hysteresis behavior. Through the experimental results of both the approximation and the prediction, the effectiveness of the neural networks dynamic hysteresis model for the piezoceramic actuator is demonstrated
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Jianping Liu
2016-01-01
Full Text Available An operational matrix technique is proposed to solve variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials in this paper. The differential operational matrix and integral operational matrix are derived based on the second kind of Chebyshev polynomials. Using two types of operational matrixes, the original equation is transformed into the arithmetic product of several dependent matrixes, which can be viewed as an algebraic system after adopting the collocation points. Further, numerical solution of original equation is obtained by solving the algebraic system. Finally, several examples show that the numerical algorithm is computationally efficient.
Operator ordering and causality
Plimak, L. I.; Stenholm, S. T.
2011-01-01
It is shown that causality violations [M. de Haan, Physica 132A, 375, 397 (1985)], emerging when the conventional definition of the time-normal operator ordering [P.L.Kelley and W.H.Kleiner, Phys.Rev. 136, A316 (1964)] is taken outside the rotating wave approximation, disappear when the amended definition [L.P. and S.S., Annals of Physics, 323, 1989 (2008)] of this ordering is used.
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M.H.T. Alshbool
2017-01-01
Full Text Available An algorithm for approximating solutions to fractional differential equations (FDEs in a modified new Bernstein polynomial basis is introduced. Writing x→xα(0<α<1 in the operational matrices of Bernstein polynomials, the fractional Bernstein polynomials are obtained and then transformed into matrix form. Furthermore, using Caputo fractional derivative, the matrix form of the fractional derivative is constructed for the fractional Bernstein matrices. We convert each term of the problem to the matrix form by means of fractional Bernstein matrices. A basic matrix equation which corresponds to a system of fractional equations is utilized, and a new system of nonlinear algebraic equations is obtained. The method is given with some priori error estimate. By using the residual correction procedure, the absolute error can be estimated. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.
Invariant differential operators
Dobrev, Vladimir K
2016-01-01
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory.
Invariant differential operators
Dobrev, Vladimir K
With applications in quantum field theory, elementary particle physics and general relativity, this two-volume work studies invariance of differential operators under Lie algebras, quantum groups, superalgebras including infinite-dimensional cases, Schrödinger algebras, applications to holography. This first volume covers the general aspects of Lie algebras and group theory.
Algebra of pseudo-differential C*-operators
International Nuclear Information System (INIS)
Mohammad, N.
1987-11-01
In this paper the algebra of pseudo-differential operators is studied in the framework of C * -algebras. It is proved that every pseudo-differential operator of order m admits an adjoint operator, in this case, which is again a pseudo-differential operator. Consequently, the space of all pseudo-differential operators on a compact manifold is an involutive algebra. 10 refs
Finding Higher Order Differentials of MISTY1
Tsunoo, Yukiyasu; Saito, Teruo; Kawabata, Takeshi; Nakagawa, Hirokatsu
MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it is recommended for Japanese e-Government ciphers by the CRYPTREC project. In this paper, we report on 12th order differentials in 3-round MISTY1 with FL functions and 44th order differentials in 4-round MISTY1 with FL functions both previously unknown. We also report that both data complexity and computational complexity of higher order differential attacks on 6-round MISTY1 with FL functions and 7-round MISTY1 with FL functions using the 46th order differential can be reduced to as much as 1/22 of the previous values by using multiple 44th order differentials simultaneously.
On solutions of variable-order fractional differential equations
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Ali Akgül
2017-01-01
solutions to fractional differential equations are compelling to get in real applications, due to the nonlocality and complexity of the fractional differential operators, especially for variable-order fractional differential equations. Therefore, it is significant to enhanced numerical methods for fractional differential equations. In this work, we consider variable-order fractional differential equations by reproducing kernel method. There has been much attention in the use of reproducing kernels for the solutions to many problems in the recent years. We give two examples to demonstrate how efficiently our theory can be implemented in practice.
The Cauchy problem for higher order abstract differential equations
Xiao, Ti-Jun
1998-01-01
This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis.
Partial differential operators of elliptic type
Shimakura, Norio
1992-01-01
This book, which originally appeared in Japanese, was written for use in an undergraduate course or first year graduate course in partial differential equations and is likely to be of interest to researchers as well. This book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses the Laplacian in Euclidean spaces, elementary solutions, smoothness of solutions, Vishik-Sobolev problems, the Schauder theory, and degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum principles. Because elliptic operators arise in many areas, readers will appreciate this book for the way it brings together a variety of techniques that have arisen in different branches of mathematics.
Hyponormal differential operators with discrete spectrum
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Zameddin I. Ismailov
2010-01-01
Full Text Available In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.
Schwarzian conditions for linear differential operators with selected differential Galois groups
International Nuclear Information System (INIS)
Abdelaziz, Y; Maillard, J-M
2017-01-01
We show that non-linear Schwarzian differential equations emerging from covariance symmetry conditions imposed on linear differential operators with hypergeometric function solutions can be generalized to arbitrary order linear differential operators with polynomial coefficients having selected differential Galois groups. For order three and order four linear differential operators we show that this pullback invariance up to conjugation eventually reduces to symmetric powers of an underlying order-two operator. We give, precisely, the conditions to have modular correspondences solutions for such Schwarzian differential equations, which was an open question in a previous paper. We analyze in detail a pullbacked hypergeometric example generalizing modular forms, that ushers a pullback invariance up to operator homomorphisms. We finally consider the more general problem of the equivalence of two different order-four linear differential Calabi–Yau operators up to pullbacks and conjugation, and clarify the cases where they have the same Yukawa couplings. (paper)
Schwarzian conditions for linear differential operators with selected differential Galois groups
Abdelaziz, Y.; Maillard, J.-M.
2017-11-01
We show that non-linear Schwarzian differential equations emerging from covariance symmetry conditions imposed on linear differential operators with hypergeometric function solutions can be generalized to arbitrary order linear differential operators with polynomial coefficients having selected differential Galois groups. For order three and order four linear differential operators we show that this pullback invariance up to conjugation eventually reduces to symmetric powers of an underlying order-two operator. We give, precisely, the conditions to have modular correspondences solutions for such Schwarzian differential equations, which was an open question in a previous paper. We analyze in detail a pullbacked hypergeometric example generalizing modular forms, that ushers a pullback invariance up to operator homomorphisms. We finally consider the more general problem of the equivalence of two different order-four linear differential Calabi-Yau operators up to pullbacks and conjugation, and clarify the cases where they have the same Yukawa couplings.
Third order differential equations with delay
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Petr Liška
2015-05-01
Full Text Available In this paper, we study the oscillation and asymptotic properties of solutions of certain nonlinear third order differential equations with delay. In particular, we extend results of I. Mojsej (Nonlinear Analysis 68, 2008 and we improve conditions on the property B of N. Parhi and S. Padhi (Indian J. Pure Appl. Math., 33, 2002.
On Fractional Order Hybrid Differential Equations
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Mohamed A. E. Herzallah
2014-01-01
Full Text Available We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.
First-order partial differential equations
Rhee, Hyun-Ku; Amundson, Neal R
2001-01-01
This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo
The Bessel polynomials and their differential operators
International Nuclear Information System (INIS)
Onyango Otieno, V.P.
1987-10-01
Differential operators associated with the ordinary and the generalized Bessel polynomials are defined. In each case the commutator bracket is constructed and shows that the differential operators associated with the Bessel polynomials and their generalized form are not commutative. Some applications of these operators to linear differential equations are also discussed. (author). 4 refs
Theory of pseudo-differential operators over C*-Algebras
International Nuclear Information System (INIS)
Mohammad, N.
1987-06-01
In this article the behaviour of adjoints and composition of pseudo-differential operators in the framework of a C*-algebra is studied. It results that the class of pseudo-differential operators of order zero is a C*-algebra. 8 refs
Ultrasound speckle reduction based on fractional order differentiation.
Shao, Dangguo; Zhou, Ting; Liu, Fan; Yi, Sanli; Xiang, Yan; Ma, Lei; Xiong, Xin; He, Jianfeng
2017-07-01
Ultrasound images show a granular pattern of noise known as speckle that diminishes their quality and results in difficulties in diagnosis. To preserve edges and features, this paper proposes a fractional differentiation-based image operator to reduce speckle in ultrasound. An image de-noising model based on fractional partial differential equations with balance relation between k (gradient modulus threshold that controls the conduction) and v (the order of fractional differentiation) was constructed by the effective combination of fractional calculus theory and a partial differential equation, and the numerical algorithm of it was achieved using a fractional differential mask operator. The proposed algorithm has better speckle reduction and structure preservation than the three existing methods [P-M model, the speckle reducing anisotropic diffusion (SRAD) technique, and the detail preserving anisotropic diffusion (DPAD) technique]. And it is significantly faster than bilateral filtering (BF) in producing virtually the same experimental results. Ultrasound phantom testing and in vivo imaging show that the proposed method can improve the quality of an ultrasound image in terms of tissue SNR, CNR, and FOM values.
On the level order for Dirac operators
International Nuclear Information System (INIS)
Grosse, H.
1987-01-01
We start from the Dirac operator for the Coulomb potential and prove within first order perturbation theory that degenerate levels split in a definite way depending on the sign of the Laplacian of the perturbing potential. 9 refs. (Author)
Differential operators and W-algebra
International Nuclear Information System (INIS)
Vaysburd, I.; Radul, A.
1992-01-01
The connection between W-algebras and the algebra of differential operators is conjectured. The bosonized representation of the differential operator algebra with c=-2n and all the subalgebras are examined. The degenerate representations and null-state classifications for c=-2 are presented. (orig.)
Oscillation criteria for third order delay nonlinear differential equations
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E. M. Elabbasy
2012-01-01
via comparison with some first differential equations whose oscillatory characters are known. Our results generalize and improve some known results for oscillation of third order nonlinear differential equations. Some examples are given to illustrate the main results.
On weakly D-differentiable operators
DEFF Research Database (Denmark)
Christensen, Erik
2016-01-01
Let DD be a self-adjoint operator on a Hilbert space HH and aa a bounded operator on HH. We say that aa is weakly DD-differentiable, if for any pair of vectors ξ,ηξ,η from HH the function 〈eitDae−itDξ,η〉〈eitDae−itDξ,η〉 is differentiable. We give an elementary example of a bounded operator aa......, such that aa is weakly DD-differentiable, but the function eitDae−itDeitDae−itD is not uniformly differentiable. We show that weak DD-differentiability may be characterized by several other properties, some of which are related to the commutator (Da−aD)...
Wu, L.; Liu, S.; Yang, Yingjie
2016-01-01
Traditional integer order buffer operator is extended to fractional order buffer operator, the corresponding relationship between the weakening buffer operator and the strengthening buffer operator is revealed. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also realize tiny adjustment of buffer effect. The effectiveness of GM(1,1) with the fractional order buffer operator is validated by six cases.
Nonlinear partial differential equations of second order
Dong, Guangchang
1991-01-01
This book addresses a class of equations central to many areas of mathematics and its applications. Although there is no routine way of solving nonlinear partial differential equations, effective approaches that apply to a wide variety of problems are available. This book addresses a general approach that consists of the following: Choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution. The author emphasizes the derivation of various estimates, including a priori estimates. By focusing on a particular approach that has proven useful in solving a broad range of equations, this book makes a useful contribution to the literature.
Elliptic partial differential equations of second order
Gilbarg, David
2001-01-01
From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985 "Primarily addressed to graduate students this elegant book is accessible and useful to a broad spectrum of applied mathematicians". Revue Roumaine de Mathématiques Pures et Appliquées,1985.
Modeling Ability Differentiation in the Second-Order Factor Model
Molenaar, Dylan; Dolan, Conor V.; van der Maas, Han L. J.
2011-01-01
In this article we present factor models to test for ability differentiation. Ability differentiation predicts that the size of IQ subtest correlations decreases as a function of the general intelligence factor. In the Schmid-Leiman decomposition of the second-order factor model, we model differentiation by introducing heteroscedastic residuals,…
Pseudospectral collocation methods for fourth order differential equations
Malek, Alaeddin; Phillips, Timothy N.
1994-01-01
Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.
Field Method for Integrating the First Order Differential Equation
Institute of Scientific and Technical Information of China (English)
JIA Li-qun; ZHENG Shi-wang; ZHANG Yao-yu
2007-01-01
An important modern method in analytical mechanics for finding the integral, which is called the field-method, is used to research the solution of a differential equation of the first order. First, by introducing an intermediate variable, a more complicated differential equation of the first order can be expressed by two simple differential equations of the first order, then the field-method in analytical mechanics is introduced for solving the two differential equations of the first order. The conclusion shows that the field-method in analytical mechanics can be fully used to find the solutions of a differential equation of the first order, thus a new method for finding the solutions of the first order is provided.
Fractional order differentiation by integration with Jacobi polynomials
Liu, Dayan
2012-12-01
The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.
Fractional order differentiation by integration with Jacobi polynomials
Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid; Laleg-Kirati, Taous-Meriem
2012-01-01
The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.
Semi-bounded partial differential operators
Cialdea, Alberto
2014-01-01
This book examines the conditions for the semi-boundedness of partial differential operators, which are interpreted in different ways. For example, today we know a great deal about L2-semibounded differential and pseudodifferential operators, although their complete characterization in analytic terms still poses difficulties, even for fairly simple operators. In contrast, until recently almost nothing was known about analytic characterizations of semi-boundedness for differential operators in other Hilbert function spaces and in Banach function spaces. This book works to address that gap. As such, various types of semi-boundedness are considered and a number of relevant conditions which are either necessary and sufficient or best possible in a certain sense are presented. The majority of the results reported on are the authors’ own contributions.
Tchebichef polynomials of the second kind and singular differential operators
International Nuclear Information System (INIS)
Onyango-Otieno, V.P.
1985-10-01
Our purpose in this paper is to study the so called right- and left-definite problems for the Tchebichef differential equation using the classical approach given in the book ''Eigenfunction expansions associated with second-order differential equations-I'' by Titchmarsh. We link the Titchmarsh method with operator theoretic results in the Hilbert function spaces Lsub(w) 2 (-1,1) and Hsub(p,q) 2 (-1,1)
High Order Differential Frequency Hopping: Design and Analysis
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Yong Li
2015-01-01
Full Text Available This paper considers spectrally efficient differential frequency hopping (DFH system design. Relying on time-frequency diversity over large spectrum and high speed frequency hopping, DFH systems are robust against hostile jamming interference. However, the spectral efficiency of conventional DFH systems is very low due to only using the frequency of each channel. To improve the system capacity, in this paper, we propose an innovative high order differential frequency hopping (HODFH scheme. Unlike in traditional DFH where the message is carried by the frequency relationship between the adjacent hops using one order differential coding, in HODFH, the message is carried by the frequency and phase relationship using two-order or higher order differential coding. As a result, system efficiency is increased significantly since the additional information transmission is achieved by the higher order differential coding at no extra cost on either bandwidth or power. Quantitative performance analysis on the proposed scheme demonstrates that transmission through the frequency and phase relationship using two-order or higher order differential coding essentially introduces another dimension to the signal space, and the corresponding coding gain can increase the system efficiency.
Numerov iteration method for second order integral-differential equation
International Nuclear Information System (INIS)
Zeng Fanan; Zhang Jiaju; Zhao Xuan
1987-01-01
In this paper, Numerov iterative method for second order integral-differential equation and system of equations are constructed. Numerical examples show that this method is better than direct method (Gauss elimination method) in CPU time and memoy requireing. Therefore, this method is an efficient method for solving integral-differential equation in nuclear physics
Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications
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Lakshman Mahto
2013-01-01
Full Text Available We use Sadovskii's fixed point method to investigate the existence and uniqueness of solutions of Caputo impulsive fractional differential equations of order with one example of impulsive logistic model and few other examples as well. We also discuss Caputo impulsive fractional differential equations with finite delay. The results proven are new and compliment the existing one.
Asymptotic behavior of second-order impulsive differential equations
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Haifeng Liu
2011-02-01
Full Text Available In this article, we study the asymptotic behavior of all solutions of 2-th order nonlinear delay differential equation with impulses. Our main tools are impulsive differential inequalities and the Riccati transformation. We illustrate the results by an example.
Pseudo-differential operators and generalized functions
Toft, Joachim
2015-01-01
This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators. It is dedicated to Professor Michael Oberguggenberger (Innsbruck University, Austria) in honour of his 60th birthday. The topics covered were suggested by the ISAAC Group in Generalized Functions (GF) and the ISAAC Group in Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC congress in Krakow, Poland in August 2013. Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis. Featuring both essays and research articles, the book will be of great interest to graduate students and researchers working in analysis, PDE and mathematical physics, while also offering a valuable complement to the volumes on this topic previously published in the OT series.
ACCURATE ESTIMATES OF CHARACTERISTIC EXPONENTS FOR SECOND ORDER DIFFERENTIAL EQUATION
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our result.
Vector fields and differential operators: noncommutative case
International Nuclear Information System (INIS)
Borowiec, A.
1997-01-01
A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed previously. In this paper an outline is given of the construction of a noncommutative analogy of the algebra of differential operators as well as its (algebraic) Fock space realization. Co-universal vector fields and covariant derivatives will also be discussed
Relativistic differential-difference momentum operators and noncommutative differential calculus
International Nuclear Information System (INIS)
Mir-Kasimov, R.M.
2011-01-01
Full text: (author)The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics in the relativistic configuration space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated from the total Hamiltonian. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generation function for the matrix elements of the unitary irreps of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the non-commutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS
Hojman's theorem of the third-order ordinary differential equation
International Nuclear Information System (INIS)
Hong-Sheng, Lü; Hong-Bin, Zhang; Shu-Long, Gu
2009-01-01
This paper extends Hojman's conservation law to the third-order differential equation. A new conserved quantity is constructed based on the Lie group of transformation generators of the equations of motion. The generators contain variations of the time and generalized coordinates. Two independent non-trivial conserved quantities of the third-order ordinary differential equation are obtained. A simple example is presented to illustrate the applications of the results. (general)
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.
Higher-order automatic differentiation of mathematical functions
Charpentier, Isabelle; Dal Cappello, Claude
2015-04-01
Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.
Robust fractional order differentiators using generalized modulating functions method
Liu, Dayan; Laleg-Kirati, Taous-Meriem
2015-01-01
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
Robust fractional order differentiators using generalized modulating functions method
Liu, Dayan
2015-02-01
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
Zhukovsky, K
2014-01-01
We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.
High-order space charge effects using automatic differentiation
International Nuclear Information System (INIS)
Reusch, Michael F.; Bruhwiler, David L.
1997-01-01
The Northrop Grumman Topkark code has been upgraded to Fortran 90, making use of operator overloading, so the same code can be used to either track an array of particles or construct a Taylor map representation of the accelerator lattice. We review beam optics and beam dynamics simulations conducted with TOPKARK in the past and we present a new method for modeling space charge forces to high-order with automatic differentiation. This method generates an accurate, high-order, 6-D Taylor map of the phase space variable trajectories for a bunched, high-current beam. The spatial distribution is modeled as the product of a Taylor Series times a Gaussian. The variables in the argument of the Gaussian are normalized to the respective second moments of the distribution. This form allows for accurate representation of a wide range of realistic distributions, including any asymmetries, and allows for rapid calculation of the space charge fields with free space boundary conditions. An example problem is presented to illustrate our approach
High-order space charge effects using automatic differentiation
International Nuclear Information System (INIS)
Reusch, M.F.; Bruhwiler, D.L.; Computer Accelerator Physics Conference Williamsburg, Virginia 1996)
1997-01-01
The Northrop Grumman Topkark code has been upgraded to Fortran 90, making use of operator overloading, so the same code can be used to either track an array of particles or construct a Taylor map representation of the accelerator lattice. We review beam optics and beam dynamics simulations conducted with TOPKARK in the past and we present a new method for modeling space charge forces to high-order with automatic differentiation. This method generates an accurate, high-order, 6-D Taylor map of the phase space variable trajectories for a bunched, high-current beam. The spatial distribution is modeled as the product of a Taylor Series times a Gaussian. The variables in the argument of the Gaussian are normalized to the respective second moments of the distribution. This form allows for accurate representation of a wide range of realistic distributions, including any asymmetries, and allows for rapid calculation of the space charge fields with free space boundary conditions. An example problem is presented to illustrate our approach. copyright 1997 American Institute of Physics
Exact solutions to operator differential equations
International Nuclear Information System (INIS)
Bender, C.M.
1992-01-01
In this talk we consider the Heisenberg equations of motion q = -i(q, H), p = -i(p, H), for the quantum-mechanical Hamiltonian H(p, q) having one degree of freedom. It is a commonly held belief that such operator differential equations are intractable. However, a technique is presented here that allows one to obtain exact, closed-form solutions for huge classes of Hamiltonians. This technique, which is a generalization of the classical action-angle variable methods, allows us to solve, albeit formally and implicitly, the operator differential equations of two anharmonic oscillators whose Hamiltonians are H = p 2 /2 + q 4 /4 and H = p 4 /4 + q 4 /4
Gainetdinova, A A; Gazizov, R K
2017-01-01
We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.
Directory of Open Access Journals (Sweden)
Qiang Yu
Full Text Available Texture enhancement is one of the most important techniques in digital image processing and plays an essential role in medical imaging since textures discriminate information. Most image texture enhancement techniques use classical integral order differential mask operators or fractional differential mask operators using fixed fractional order. These masks can produce excessive enhancement of low spatial frequency content, insufficient enhancement of large spatial frequency content, and retention of high spatial frequency noise. To improve upon existing approaches of texture enhancement, we derive an improved Variable Order Fractional Centered Difference (VOFCD scheme which dynamically adjusts the fractional differential order instead of fixing it. The new VOFCD technique is based on the second order Riesz fractional differential operator using a Lagrange 3-point interpolation formula, for both grey scale and colour image enhancement. We then use this method to enhance photographs and a set of medical images related to patients with stroke and Parkinson's disease. The experiments show that our improved fractional differential mask has a higher signal to noise ratio value than the other fractional differential mask operators. Based on the corresponding quantitative analysis we conclude that the new method offers a superior texture enhancement over existing methods.
Liu, Da-Yan; Tian, Yang; Boutat, Driss; Laleg-Kirati, Taous-Meriem
2015-01-01
This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.
Liu, Da-Yan
2015-04-30
This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.
Multilinear operators for higher-order decompositions.
Energy Technology Data Exchange (ETDEWEB)
Kolda, Tamara Gibson
2006-04-01
We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The first operator, which we call the Tucker operator, is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor and can be employed to concisely express the Tucker decomposition. The second operator, which we call the Kruskal operator, is shorthand for the sum of the outer-products of the columns of N matrices and allows a divorce from a matricized representation and a very concise expression of the PARAFAC decomposition. We explore the properties of the Tucker and Kruskal operators independently of the related decompositions. Additionally, we provide a review of the matrix and tensor operations that are frequently used in the context of tensor decompositions.
First- and Second-Order Full-Differential in Edge Analysis of Images
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Dong-Mei Pu
2014-01-01
mathematics. We propose and reformulate them with a uniform definition framework. Based on our observation and analysis with the difference, we propose an algorithm to detect the edge from image. Experiments on Corel5K and PASCAL VOC 2007 are done to show the difference between the first order and the second order. After comparison with Canny operator and the proposed first-order differential, the main result is that the second-order differential has the better performance in analysis of changes of the context of images with good selection of control parameter.
Avellar, J.; Claudino, A. L. G. C.; Duarte, L. G. S.; da Mota, L. A. C. P.
2015-10-01
For the Darbouxian methods we are studying here, in order to solve first order rational ordinary differential equations (1ODEs), the most costly (computationally) step is the finding of the needed Darboux polynomials. This can be so grave that it can render the whole approach unpractical. Hereby we introduce a simple heuristics to speed up this process for a class of 1ODEs.
Higher Order Differential Attack on 6-Round MISTY1
Tsunoo, Yukiyasu; Saito, Teruo; Nakashima, Hiroki; Shigeri, Maki
MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it has been recommended for Japanese e-Government ciphers by the CRYPTREC project. This paper reports a previously unknown higher order differential characteristic of 4-round MISTY1 with the FL functions. It also shows that a higher order differential attack that utilizes this newly discovered characteristic is successful against 6-round MISTY1 with the FL functions. This attack can recover a partial subkey with a data complexity of 253.7 and a computational complexity of 264.4, which is better than any previous cryptanalysis of MISTY1.
A New Factorisation of a General Second Order Differential Equation
Clegg, Janet
2006-01-01
A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…
Conventional hamiltonian for first-order differential systems
International Nuclear Information System (INIS)
Farias, J.R.
1984-01-01
Lagrangian systems corresponding to a given set of 2n first-order ordinary differential equations are singular ones. In despite this, it is shown that these systems can be put into a Hamiltonian form in the usual manner. (Author) [pt
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
Hopf bifurcation formula for first order differential-delay equations
Rand, Richard; Verdugo, Anael
2007-09-01
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The derivation is accomplished using Lindstedt's perturbation method.
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
Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions
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Hernán R. Henríquez
2014-01-01
Full Text Available In this work we establish some existence results for abstract second order Cauchy problems modeled by a retarded differential inclusion involving nonlocal and impulsive conditions. Our results are obtained by using fixed point theory for the measure of noncompactness.
On New p-Valent Meromorphic Function Involving Certain Differential and Integral Operators
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Aabed Mohammed
2014-01-01
Full Text Available We define new subclasses of meromorphic p-valent functions by using certain differential operator. Combining the differential operator and certain integral operator, we introduce a general p-valent meromorphic function. Then we prove the sufficient conditions for the function in order to be in the new subclasses.
Pointwise estimates of pseudo-differential operators
DEFF Research Database (Denmark)
Johnsen, Jon
As a new technique it is shown how general pseudo-differential operators can be estimated at arbitrary points in Euclidean space when acting on functions u with compact spectra.The estimate is a factorisation inequality, in which one factor is the Peetre–Fefferman–Stein maximal function of u......, whilst the other is a symbol factor carrying the whole information on the symbol. The symbol factor is estimated in terms of the spectral radius of u, so that the framework is well suited for Littlewood–Paley analysis. It is also shown how it gives easy access to results on polynomial bounds...... and estimates in Lp , including a new result for type 1,1-operators that they are always bounded on Lp -functions with compact spectra....
Pointwise estimates of pseudo-differential operators
DEFF Research Database (Denmark)
Johnsen, Jon
2011-01-01
As a new technique it is shown how general pseudo-differential operators can be estimated at arbitrary points in Euclidean space when acting on functions u with compact spectra. The estimate is a factorisation inequality, in which one factor is the Peetre–Fefferman–Stein maximal function of u......, whilst the other is a symbol factor carrying the whole information on the symbol. The symbol factor is estimated in terms of the spectral radius of u, so that the framework is well suited for Littlewood–Paley analysis. It is also shown how it gives easy access to results on polynomial bounds...... and estimates in Lp, including a new result for type 1, 1-operators that they are always bounded on Lp-functions with compact spectra....
Oscillation of solutions of some higher order linear differential equations
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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.
Higher order differential calculus on SLq(N)
International Nuclear Information System (INIS)
Heckenberger, I.; Schueler, A.
1997-01-01
Let Γ be a bicovariant first order differential calculus on a Hopf algebra A. There are three possibilities to construct a differential N 0 -graded Hopf algebra Γcirconflex which contains Γ as its first order part. In all cases Γcirconflex is a quotient Γcirconflex = Γ x /J of the tensor algebra by some suitable ideal. We distinguish three possible choices u J, s J, and w J, where the first one generates the universal differential calculus (over Γ) and the last one is Woronowicz' external algebra. Let q be a transcendental complex number and let Γ be one of the N 2 -dimensional bicovariant first order differential calculi on the quantum group SL q (N). Then for N ≥ 3 the three ideals coincide. For Woronowicz' external algebra we calculate the dimensions of the spaces of left-invariant and bi-invariant k-forms. In this case each bi-invariant form is closed. In case of 4D ± calculi on SL q (2) the universal calculus is strictly larger than the other two calculi. In particular, the bi-invariant 1-form is not closed. (author)
From differential to difference equations for first order ODEs
Freed, Alan D.; Walker, Kevin P.
1991-01-01
When constructing an algorithm for the numerical integration of a differential equation, one should first convert the known ordinary differential equation (ODE) into an ordinary difference equation. Given this difference equation, one can develop an appropriate numerical algorithm. This technical note describes the derivation of two such ordinary difference equations applicable to a first order ODE. The implicit ordinary difference equation has the same asymptotic expansion as the ODE itself, whereas the explicit ordinary difference equation has an asymptotic that is similar in structure but different in value when compared with that of the ODE.
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)
Symmetries of th-Order Approximate Stochastic Ordinary Differential Equations
Fredericks, E.; Mahomed, F. M.
2012-01-01
Symmetries of $n$ th-order approximate stochastic ordinary differential equations (SODEs) are studied. The determining equations of these SODEs are derived in an Itô calculus context. These determining equations are not stochastic in nature. SODEs are normally used to model nature (e.g., earthquakes) or for testing the safety and reliability of models in construction engineering when looking at the impact of random perturbations.
A Solution to the Fundamental Linear Fractional Order Differential Equation
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.
Numerical solution of distributed order fractional differential equations
Katsikadelis, John T.
2014-02-01
In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.
Differential operators associated with Hermite polynomials
International Nuclear Information System (INIS)
Onyango Otieno, V.P.
1989-09-01
This paper considers the boundary value problems for the Hermite differential equation -(e -x2 y'(x))'+e -x2 y(x)=λe -x2 y(x), (x is an element of (-∞, ∞)) in both the so-called right-definite and left-definite cases based partly on a classical approach due to E.C. Titchmarsh. We then link the Titchmarsh approach with operator theoretic results in the spaces L w 2 (-∞, ∞) and H p,q 2 (-∞, ∞). The results in the left-definite case provide an indirect proof of the completeness of the Hermite polynomials in L w 2 (-∞, ∞). (author). 17 refs
TRENTELMAN, HL
1984-01-01
This note generalizes the geometric theory around minimal and reduced order observers to the situation in which differentiation of certain components of the observed output is allowed. A geometric theory involving the notion of PID-observer is introduced, using the concept of almost complementary
M. Denche; A. L. Marhoune
2003-01-01
In this paper, we study a mixed problem with integral boundary conditions for a high order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on energy inequality, and on the density of the range of the operator generated by the considered problem.
High order aberrations calculation of a hexapole corrector using a differential algebra method
Energy Technology Data Exchange (ETDEWEB)
Kang, Yongfeng, E-mail: yfkang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China); Liu, Xing [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China); Zhao, Jingyi, E-mail: jingyi.zhao@foxmail.com [School of Science, Chang’an University, Xi’an 710064 (China); Tang, Tiantong [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an 710049 (China)
2017-02-21
A differential algebraic (DA) method is proved as an unusual and effective tool in numerical analysis. It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis. In this paper, the differential algebra (DA) method has been employed to compute the high order aberrations up to the fifth order of a practical hexapole corrector including round lenses and hexapole lenses. The program has been developed and tested as well. The electro-magnetic fields of arbitrary point are obtained by local analytic expressions, then field potentials are transformed into new forms which can be operated in the DA calculation. In this paper, the geometric and chromatic aberrations up to fifth order of a practical hexapole corrector system are calculated by the developed program.
Directory of Open Access Journals (Sweden)
Domoshnitsky Alexander
2009-01-01
Full Text Available We obtain the maximum principles for the first-order neutral functional differential equation where , and are linear continuous operators, and are positive operators, is the space of continuous functions, and is the space of essentially bounded functions defined on . New tests on positivity of the Cauchy function and its derivative are proposed. Results on existence and uniqueness of solutions for various boundary value problems are obtained on the basis of the maximum principles.
Numerical solutions of multi-order fractional differential equations by Boubaker polynomials
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Bolandtalat A.
2016-01-01
Full Text Available In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.
International Nuclear Information System (INIS)
Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T.; Santos, Marcio G.
2015-01-01
This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)
Energy Technology Data Exchange (ETDEWEB)
Zabadal, Jorge; Borges, Volnei; Van der Laan, Flavio T., E-mail: jorge.zabadal@ufrgs.br, E-mail: borges@ufrgs.br, E-mail: ftvdl@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica. Grupo de Pesquisas Radiologicas; Ribeiro, Vinicius G., E-mail: vinicius_ribeiro@uniritter.edu.br [Centro Universitario Ritter dos Reis (UNIRITTER), Porto Alegre, RS (Brazil); Santos, Marcio G., E-mail: phd.marcio@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Tramandai, RS (Brazil). Departamento Interdisciplinar do Campus Litoral Norte
2015-07-01
This work presents a new analytical method for solving the Boltzmann equation. In this formulation, a linear differential operator is applied over the Boltzmann model, in order to produce a partial differential equation in which the scattering term is absent. This auxiliary equation is solved via reduction of order. The exact solution obtained is employed to define a precursor for the buildup factor. (author)
Einstein-Weyl spaces and third-order differential equations
Tod, K. P.
2000-08-01
The three-dimensional null-surface formalism of Tanimoto [M. Tanimoto, "On the null surface formalism," Report No. gr-qc/9703003 (1997)] and Forni et al. [Forni et al., "Null surfaces formation in 3D," J. Math Phys. (submitted)] are extended to describe Einstein-Weyl spaces, following Cartan [E. Cartan, "Les espaces généralisées et l'integration de certaines classes d'equations différentielles," C. R. Acad. Sci. 206, 1425-1429 (1938); "La geometria de las ecuaciones diferenciales de tercer order," Rev. Mat. Hispano-Am. 4, 1-31 (1941)]. In the resulting formalism, Einstein-Weyl spaces are obtained from a particular class of third-order differential equations. Some examples of the construction which include some new Einstein-Weyl spaces are given.
Seeley-Gilkey coefficients for the fourth-order operators on a Riemannian manifold
International Nuclear Information System (INIS)
Gusynin, V.P.
1989-01-01
A new covariant method for computing the coefficients in the heat kernel expansion is suggested. It allows one to calculate Seeley-Gilkey coefficients for both minimal and nonminimal differential operators acting on a vector bundle over a Riemannian manifold. The coefficients for the fourth-order minimal operators in arbitrary dimension of the space are calculated. In contrast to the second-order operators the coefficients for the fourth-order (and higher) operators turn out to be essentially dependent on the space dimension. The algorithmic character of the method suggested allows one to calculate coefficients by computer using the analytical calculation system. 19 refs.; 1 fig
Maximum principles for boundary-degenerate linear parabolic differential operators
Feehan, Paul M. N.
2013-01-01
We develop weak and strong maximum principles for boundary-degenerate, linear, parabolic, second-order partial differential operators, $Lu := -u_t-\\tr(aD^2u)-\\langle b, Du\\rangle + cu$, with \\emph{partial} Dirichlet boundary conditions. The coefficient, $a(t,x)$, is assumed to vanish along a non-empty open subset, $\\mydirac_0!\\sQ$, called the \\emph{degenerate boundary portion}, of the parabolic boundary, $\\mydirac!\\sQ$, of the domain $\\sQ\\subset\\RR^{d+1}$, while $a(t,x)$ may be non-zero at po...
Conformal symmetry breaking operators for differential forms on spheres
Kobayashi, Toshiyuki; Pevzner, Michael
2016-01-01
This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin–Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valued factorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is a general method to construct intertwining operators between C∞-induced representations or to find singular vecto...
The role of operator ordering in quantum field theory
International Nuclear Information System (INIS)
Suzuki, Tsuneo; Hirshfeld, A.C.; Leschke, H.
1980-01-01
We study the role of operator ordering in quantum field theory. Operator ordering techniques discussed in our previous papers in the quantum mechanical context are extended to field theory. In this case formally infinite terms appear which must be given a meaning in the framework of some definite regularization scheme. Different orderings for the non-commuting operators in the interaction Hamiltonian lead in general to different expressions for the Dyson-Wick expansion of the S-matrix, implying different Feynman rules. Different orderings correspond to different assignments for the initially undetermined values of the contractions occurring in closed-loop diagrams. Combining a special class of ordering schemes (u-ordering, a generalization of Weyl-ordering) with dimensional regularization leads to important simplifications, and in this case manipulations in which ordering complications are neglected may be justified. We use our methods to discuss gauge invariance in scalar electrodynamics, and the equivalent theorem for a reducible field theoretical model. (author)
Directory of Open Access Journals (Sweden)
Hossein Jafari
2016-04-01
Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.
The conformally invariant Laplace-Beltrami operator and factor ordering
International Nuclear Information System (INIS)
Ryan, Michael P.; Turbiner, Alexander V.
2004-01-01
In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the Laplace-Beltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple factor orderings and show that the only other solution for a conformally flat metric is the conformally invariant Laplace-Beltrami operator. For non-conformally-flat metrics this type of factor ordering fails, by just one term, to give the conformally invariant Laplace-Beltrami operator
Differential evolution enhanced with multiobjective sorting-based mutation operators.
Wang, Jiahai; Liao, Jianjun; Zhou, Ying; Cai, Yiqiao
2014-12-01
Differential evolution (DE) is a simple and powerful population-based evolutionary algorithm. The salient feature of DE lies in its mutation mechanism. Generally, the parents in the mutation operator of DE are randomly selected from the population. Hence, all vectors are equally likely to be selected as parents without selective pressure at all. Additionally, the diversity information is always ignored. In order to fully exploit the fitness and diversity information of the population, this paper presents a DE framework with multiobjective sorting-based mutation operator. In the proposed mutation operator, individuals in the current population are firstly sorted according to their fitness and diversity contribution by nondominated sorting. Then parents in the mutation operators are proportionally selected according to their rankings based on fitness and diversity, thus, the promising individuals with better fitness and diversity have more opportunity to be selected as parents. Since fitness and diversity information is simultaneously considered for parent selection, a good balance between exploration and exploitation can be achieved. The proposed operator is applied to original DE algorithms, as well as several advanced DE variants. Experimental results on 48 benchmark functions and 12 real-world application problems show that the proposed operator is an effective approach to enhance the performance of most DE algorithms studied.
QPFT operator algebras and commutative exterior differential calculus
International Nuclear Information System (INIS)
Yur'ev, D.V.
1993-01-01
The reduction of the structure theory of the operator algebras of quantum projective (sl(2, C)-invariant) field theory (QPFT operator algebras) to a commutative exterior differential calculus by means of the operation of renormalization of a pointwise product of operator fields is described. In the first section, the author introduces the concept of the operator algebra of quantum field theory and describes the operation of the renormalization of a pointwise product of operator fields. The second section is devoted to a brief exposition of the fundamentals of the structure theory of QPT operator algebras. The third section is devoted to commutative exterior differential calculus. In the fourth section, the author establishes the connection between the renormalized pointwise product of operator fields in QPFT operator algebras and the commutative exterior differential calculus. 5 refs
Pseudo-differential operators on manifolds with singularities
Schulze, B-W
1991-01-01
The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics. The applications and concrete models from engineering and physics are often classical but the modern structure calculus was only possible since the achievements of pseudo-differential operators. This led to deep connections with index theory, topology and mathematical physics. The present book is devoted to elliptic partial differential equations in the framework of pseudo-differential operators. The first chapter contains the Mellin pseudo-differential calculus on R+ and the functional analysis of weighted Sobolev spaces with discrete and continuous asymptotics. Chapter 2 is devoted to the analogous theory on manifolds with conical singularities, Chapter 3 to manifolds with edges. Employed are pseudo-differential operators along edges with cone-operator-valued symbols.
On the mild solutions of higher-order differential equations in Banach spaces
Directory of Open Access Journals (Sweden)
Nguyen Thanh Lan
2003-01-01
Full Text Available For the higher-order abstract differential equation u(n(t=Au(t+f(t, t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E with respect to the above-mentioned equation in terms of solvability of the operator equation AX−Xn=C. As applications, periodicity and almost periodicity of mild solutions are also proved.
Estimates of solutions of certain classes of second-order differential equations in a Hilbert space
International Nuclear Information System (INIS)
Artamonov, N V
2003-01-01
Linear second-order differential equations of the form u''(t)+(B+iD)u'(t)+(T+iS)u(t)=0 in a Hilbert space are studied. Under certain conditions on the (generally speaking, unbounded) operators T, S, B and D the correct solubility of the equation in the 'energy' space is proved and best possible (in the general case) estimates of the solutions on the half-axis are obtained
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V. N. Chetverikov
2014-01-01
Full Text Available Invertible linear differential operators with one independent variable are investigated. The problem of description of such operators is important, because it is connected with transformations and the classification of control systems, in particular, with the flatness problem.Each invertible linear differential operator represents a square matrix of scalar differential operators. Its product with an operator-column is an operator-column whose order does not exceed the sum of orders of initial operators. The operators-columns, the product with which leads to order fall, i.e. the order of the product is less than sum of orders of factors, are interesting for the description of invertible operators. In this paper the classification of invertible operators is based on dimensions dk,p of intersections of modules Gp and Fk for various k and p, where Gp is the module of all operators-columns of order not above p, and Fk is the module of compositions of the invertible operator with all operators-columns of order not above k. The invertible operators that have identical sets of numbers dk,p form one class.In the paper the general properties of tables of numbers dk,p for invertible operators are investigated. A correspondence between invertible operators and elementary-geometrical models which in the paper are named by d-schemes of squares is constructed. The invertible operator is ambiguously defined by its d-scheme of squares. The mathematical structure that must be set for its unique definition and an algorithm for the construction of the invertible operator are offered.In the proof of the main result, methods of the theory of chain complexes and their spectral sequences are used. In the paper all necessary concepts of this theory are formulated and the corresponding facts are proved.Results of the paper can be used for solving problems in which invertible linear differential operators are arisen. Namely, it is necessary to formulate the conditions on
Weyl Ordering Operator Formula Derived by IWOP Technique and Its Application for Fresnel Operator
International Nuclear Information System (INIS)
Fan Hongyi; Hu Liyun
2009-01-01
Based on the technique of integration within an ordered product of operators, the Weyl ordering operator formula is derived and the Fresnel operators' Weyl ordering is also obtained, which together with the Weyl transformation can immediately lead to Fresnel transformation kernel in classical optics. (general)
Pseudo-differential operators groups, geometry and applications
Zhu, Hongmei
2017-01-01
This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.
On spectral resolutions of differential vector-operators
International Nuclear Information System (INIS)
Ashurov, R.R.; Sokolov, M.S.
2004-04-01
We show that spectral resolutions of differential vector-operators may be represented as a specific direct sum integral operator with a kernel written in terms of generalized vector-operator eigenfunctions. Then we prove that a generalized eigenfunction measurable with respect to the spectral parameter may be decomposed using a set of analytical defining systems of coordinate operators. (author)
Weak differentiability of scalar hysteresis operators
Czech Academy of Sciences Publication Activity Database
Brokate, M.; Krejčí, Pavel
2015-01-01
Roč. 35, č. 6 (2015), s. 2405-2421 ISSN 1078-0947 R&D Projects: GA ČR GAP201/10/2315 Institutional support: RVO:67985840 Keywords : hysteresis * differentiability * variational inequality Subject RIV: BA - General Mathematics Impact factor: 1.127, year: 2015 http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10677
Operator ordering and supersymmetry (an old problem becomes new)
International Nuclear Information System (INIS)
De Alfaro, V.; Fubini, S.; Roncadelli, M.; Furlan, G.
1987-11-01
Supersymmetric quantum mechanics in curved space is investigated. The role of supersymmetry and of invariance under general coordinate transformation in solving the operator ordering ambiguity is discussed. 8 refs
On functional determinants of matrix differential operators with multiple zero modes
Falco, G.M.; Fedorenko, Andrey A; Gruzberg, Ilya A
2017-01-01
We generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by McKane and Tarlie to differential operators with multiple zero eigenvalues. We derive general formulas for such functional determinants of $r\\times r$ matrix second order differential
Developing Students' Mathematical Skills Involving Order of Operations
Ali Rahman, Ernna Sukinnah; Shahrill, Masitah; Abbas, Nor Arifahwati; Tan, Abby
2017-01-01
This small-scale action research study examines the students' ability in using their mathematical skills when performing order of operations in numerical expressions. In this study, the "hierarchy-of-operators triangle" by Ameis (2011) was introduced as an alternative BODMAS approach to help students in gaining a better understanding…
Calatroni, Luca
2013-08-01
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.
Calatroni, Luca; Dü ring, Bertram; Schö nlieb, Carola-Bibiane
2013-01-01
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.
Diagonal ordering operation technique applied to Morse oscillator
Energy Technology Data Exchange (ETDEWEB)
Popov, Dušan, E-mail: dusan_popov@yahoo.co.uk [Politehnica University Timisoara, Department of Physical Foundations of Engineering, Bd. V. Parvan No. 2, 300223 Timisoara (Romania); Dong, Shi-Hai [CIDETEC, Instituto Politecnico Nacional, Unidad Profesional Adolfo Lopez Mateos, Mexico D.F. 07700 (Mexico); Popov, Miodrag [Politehnica University Timisoara, Department of Steel Structures and Building Mechanics, Traian Lalescu Street, No. 2/A, 300223 Timisoara (Romania)
2015-11-15
We generalize the technique called as the integration within a normally ordered product (IWOP) of operators referring to the creation and annihilation operators of the harmonic oscillator coherent states to a new operatorial approach, i.e. the diagonal ordering operation technique (DOOT) about the calculations connected with the normally ordered product of generalized creation and annihilation operators that generate the generalized hypergeometric coherent states. We apply this technique to the coherent states of the Morse oscillator including the mixed (thermal) state case and get the well-known results achieved by other methods in the corresponding coherent state representation. Also, in the last section we construct the coherent states for the continuous dynamics of the Morse oscillator by using two new methods: the discrete–continuous limit, respectively by solving a finite difference equation. Finally, we construct the coherent states corresponding to the whole Morse spectrum (discrete plus continuous) and demonstrate their properties according the Klauder’s prescriptions.
Functional Determinants for Radially Separable Partial Differential Operators
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G. V. Dunne
2007-01-01
Full Text Available Functional determinants of differential operators play a prominent role in many fields of theoretical and mathematical physics, ranging from condensed matter physics, to atomic, molecular and particle physics. They are, however, difficult to compute reliably in non-trivial cases. In one dimensional problems (i.e. functional determinants of ordinary differential operators, a classic result of Gel’fand and Yaglom greatly simplifies the computation of functional determinants. Here I report some recent progress in extending this approach to higher dimensions (i.e., functional determinants of partial differential operators, with applications in quantum field theory.
Feynman's operational calculus and beyond noncommutativity and time-ordering
Johnson, George W; Nielsen, Lance
2015-01-01
This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections wi...
Seeley-Gilkey coefficients for fourth-order operators on Riemannian manifold
International Nuclear Information System (INIS)
Gusynin, V.P.
1990-01-01
The covariant pseudodifferential-operator method of Widom is developed for computing the coefficients in the heat kernel expansion. It allows one to calculate Seeley-Gilkey coefficients for both minimal and nonminimal differential operators acting on a vector bundle over a riemannian manifold. The coefficients for the fourth-order minimal operators in arbitrary dimensions of space are calculated. In contrast to the second-order operators the coefficients for the fourth-order (and higher) operators turn out to be essentially dependent on the space dimension. The algorithmic character of the method allows one to calculate the coefficients by computer using an analytical calculation system. The method also permits a simple generalization to manifolds with torsion and supermanifolds. (orig.)
Undergraduate Students' Mental Operations in Systems of Differential Equations
Whitehead, Karen; Rasmussen, Chris
2003-01-01
This paper reports on research conducted to understand undergraduate students' ways of reasoning about systems of differential equations (SDEs). As part of a semester long classroom teaching experiment in a first course in differential equations, we conducted task-based interviews with six students after their study of first order differential…
Comparison of the methods for discrete approximation of the fractional-order operator
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Zborovjan Martin
2003-12-01
Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.
Operator ordering in quantum mechanics and quantum gravity
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1984-05-01
A non-perturbative approach to the quantization of the canonical algebra of pure gravity is presented. The problem of factor ordering of operators in the constraints H-caretsub(μ)psi=0 is resolved invoking hermiticity under the invariant inner product in hyperspace - the space of all three-dimensional metrics gsub(ij)(x) - and covariance under coordinate transformations. The resulting operators H-caretsub(μ) receive corrections of order h and h 2 only, and the algebra closes up to a conformal anomaly term. It is argued that, by a convenient choice of gauge, the anomalous term can be removed. (author)
On the reduction of the degree of linear differential operators
International Nuclear Information System (INIS)
Bobieński, Marcin; Gavrilov, Lubomir
2011-01-01
Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k a be the algebraic closure of k. For a solution y 0 , Ly 0 = 0, we determine the linear differential operator of minimal degree L-tilde and coefficients in k a , such that L-tilde y 0 =0. This result is then applied to some Picard–Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka–Volterra type
On realization of nonlinear systems described by higher-order differential equations
van der Schaft, Arjan
1987-01-01
We consider systems of smooth nonlinear differential and algebraic equations in which some of the variables are distinguished as “external variables.” The realization problem is to replace the higher-order implicit differential equations by first-order explicit differential equations and the
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)
On the formalism of local variational differential operators
Igonin, S.; Verbovetsky, A.V.; Vitolo, R.
2002-01-01
The calculus of local variational differential operators introduced by B. L. Voronov, I. V. Tyutin, and Sh. S. Shakhverdiev is studied in the context of jet super space geometry. In a coordinate-free way, we relate these operators to variational multivectors, for which we introduce and compute the
Matrix form of Legendre polynomials for solving linear integro-differential equations of high order
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.
On the regularity of mild solutions to complete higher order differential equations on Banach spaces
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Nezam Iraniparast
2015-09-01
Full Text Available For the complete higher order differential equation u(n(t=Σk=0n-1Aku(k(t+f(t, t∈ R (* on a Banach space E, we give a new definition of mild solutions of (*. We then characterize the regular admissibility of a translation invariant subspace al M of BUC(R, E with respect to (* in terms of solvability of the operator equation Σj=0n-1AjXal Dj-Xal Dn = C. As application, almost periodicity of mild solutions of (* is proved.
OSCILLATION BEHAVIOR OF SOLUTIONS FOR EVEN ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
T.Candan
2006-01-01
Even order neutral functional differential equations are considered. Sufficient conditions for the oscillation behavior of solutions for this differential equation are presented. The new results are presented and some examples are also given.
Natural differential operations on manifolds: an algebraic approach
International Nuclear Information System (INIS)
Katsylo, P I; Timashev, D A
2008-01-01
Natural algebraic differential operations on geometric quantities on smooth manifolds are considered. A method for the investigation and classification of such operations is described, the method of IT-reduction. With it the investigation of natural operations reduces to the analysis of rational maps between k-jet spaces, which are equivariant with respect to certain algebraic groups. On the basis of the method of IT-reduction a finite generation theorem is proved: for tensor bundles V,W→M all the natural differential operations D:Γ(V)→Γ(W) of degree at most d can be algebraically constructed from some finite set of such operations. Conceptual proofs of known results on the classification of natural linear operations on arbitrary and symplectic manifolds are presented. A non-existence theorem is proved for natural deformation quantizations on Poisson manifolds and symplectic manifolds. Bibliography: 21 titles.
High level waste facilities - Continuing operation or orderly shutdown
International Nuclear Information System (INIS)
Decker, L.A.
1998-04-01
Two options for Environmental Impact Statement No action alternatives describe operation of the radioactive liquid waste facilities at the Idaho Chemical Processing Plant at the Idaho National Engineering and Environmental Laboratory. The first alternative describes continued operation of all facilities as planned and budgeted through 2020. Institutional control for 100 years would follow shutdown of operational facilities. Alternatively, the facilities would be shut down in an orderly fashion without completing planned activities. The facilities and associated operations are described. Remaining sodium bearing liquid waste will be converted to solid calcine in the New Waste Calcining Facility (NWCF) or will be left in the waste tanks. The calcine solids will be stored in the existing Calcine Solids Storage Facilities (CSSF). Regulatory and cost impacts are discussed
Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem
2017-01-01
This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.
Belkhatir, Zehor
2017-05-31
This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.
Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation
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S. Balaji
2014-01-01
Full Text Available A Legendre wavelet operational matrix method (LWM is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.
Directory of Open Access Journals (Sweden)
Erkinjon Karimov
2017-10-01
Full Text Available In this work we discuss higher order multi-term partial differential equation (PDE with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
Erkinjon Karimov; Sardor Pirnafasov
2017-01-01
In this work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
Operator overloading as an enabling technology for automatic differentiation
International Nuclear Information System (INIS)
Corliss, G.F.; Griewank, A.
1993-01-01
We present an example of the science that is enabled by object-oriented programming techniques. Scientific computation often needs derivatives for solving nonlinear systems such as those arising in many PDE algorithms, optimization, parameter identification, stiff ordinary differential equations, or sensitivity analysis. Automatic differentiation computes derivatives accurately and efficiently by applying the chain rule to each arithmetic operation or elementary function. Operator overloading enables the techniques of either the forward or the reverse mode of automatic differentiation to be applied to real-world scientific problems. We illustrate automatic differentiation with an example drawn from a model of unsaturated flow in a porous medium. The problem arises from planning for the long-term storage of radioactive waste
International conference Fourier Analysis and Pseudo-Differential Operators
Turunen, Ville; Fourier Analysis : Pseudo-differential Operators, Time-Frequency Analysis and Partial Differential Equations
2014-01-01
This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. This collection of 20 refereed articles is based on selected talks given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland, and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”
On nonlinear differential equation with exact solutions having various pole orders
International Nuclear Information System (INIS)
Kudryashov, N.A.
2015-01-01
We consider a nonlinear ordinary differential equation having solutions with various movable pole order on the complex plane. We show that the pole order of exact solution is determined by values of parameters of the equation. Exact solutions in the form of the solitary waves for the second order nonlinear differential equation are found taking into account the method of the logistic function. Exact solutions of differential equations are discussed and analyzed
Asymptotic behavior of solutions of linear multi-order fractional differential equation systems
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...
The differential geometry of higher order jets and tangent bundles
International Nuclear Information System (INIS)
De Leon, M.; Rodrigues, P.R.
1985-01-01
This chapter is devoted to the study of basic geometrical notions required for the development of the main object of the text. Some facts about Jet theory are reviewed. A particular case of Jet manifolds is considered: the tangent bundle of higher order. It is shown that this jet bundle possesses in a canonical way a certain kind of geometric structure, the so called almost tangent structure of higher order, and which is a generalization of the almost tangent geometry of the tangent bundle. Another important fact examined is the extension of the notion of 'spray' to higher order tangent bundles. (Auth.)
Non-asymptotic fractional order differentiators via an algebraic parametric method
Liu, Dayan
2012-08-01
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.
Non-asymptotic fractional order differentiators via an algebraic parametric method
Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid
2012-01-01
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.
International Nuclear Information System (INIS)
Fan Hongyi; Yu Shenxi
1994-01-01
We show that the differential form of the fundamental completeness relation in quantum mechanics and the technique of differentiation within an ordered product (DWOP) of operators provide a new approach for calculating normal product expansions of some nonlinear operators and study some nonlinear transformations. Their usefulness in perturbative calculations is pointed out. (orig.)
Relational motivation for conformal operator ordering in quantum cosmology
International Nuclear Information System (INIS)
Anderson, Edward
2010-01-01
Operator ordering in quantum cosmology is a major as-yet unsettled ambiguity with not only formal but also physical consequences. We determine the Lagrangian origin of the conformal invariance that underlies the conformal operator-ordering choice in quantum cosmology. This arises particularly naturally and simply from relationalist product-type actions (such as the Jacobi action for mechanics or Baierlein-Sharp-Wheeler-type actions for general relativity), for which all that is required is for the kinetic and potential factors to rescale in compensation to each other. These actions themselves mathematically sharply implement philosophical principles relevant to whole-universe modelling, so that the motivation for conformal operator ordering in quantum cosmology is thereby substantially strengthened. Relationalist product-type actions also give emergent times which amount to recovering Newtonian, proper and cosmic time in various contexts. The conformal scaling of these actions directly tells us how emergent time scales; if one follows suit with the Newtonian time or the lapse in the more commonly used difference-type Euler-Lagrange or Arnowitt-Deser-Misner-type actions, one sees how these too obey a more complicated conformal invariance. Moreover, our discovery of the conformal scaling of the emergent time permits relating how this simplifies equations of motion with how affine parametrization simplifies geodesics.
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.
Multilinear intertwining differential operators from new generalized Verma modules
International Nuclear Information System (INIS)
Dobrev, V.K.
1998-01-01
The present contribution contains two interrelated developments. First are proposed new generalized Verma modules. They are called k-Verma modules (k is a natural number) and coincide with the usual Verma modules for k=1. As a vector space, a k-Verma module is isomorphic to the symmetric tensor product of k copies of the universal enveloping algebra U(G -1 ) of the lowering generators of any simple Lie algebra G. The second development is the proposal of a procedure for constructing multilinear intertwining differential operators for semisimple Lie groups G. This procedure uses the k-Verma modules and, for k=1, coincides with our procedure for constructing linear intertwining differential operators. For all k, a central role is played by the singular vectors of the k-Verma modules. Explicit formulas for series of such singular vectors are given. With the aid of these, many new examples of multilinear intertwining differential operators are given explicitly. In particular, all bilinear intertwining differential operators are given explicitly for G=SL(2R). With the aid of the latter, (n/2)-differentials for all even natural n are constructed as an application, the ordinary Schwarzian corresponding to the case of n=4. As another application, a new hierarchy of nonlinear equations is proposed, the lowest member being the KdV equation
Maternal age, birth order, and race: differential effects on birthweight
Swamy, Geeta K; Edwards, Sharon; Gelfand, Alan; James, Sherman A; Miranda, Marie Lynn
2014-01-01
Background Studies examining the influence of maternal age and birth order on birthweight have not effectively disentangled the relative contributions of each factor to birthweight, especially as they may differ by race. Methods A population-based, cross-sectional study of North Carolina births from 1999 to 2003 was performed. Analysis was restricted to 510 288 singleton births from 28 to 42 weeks’ gestation with no congenital anomalies. Multivariable linear regression was used to model maternal age and birth order on birthweight, adjusting for infant sex, education, marital status, tobacco use and race. Results Mean birthweight was lower for non-Hispanic black individuals (NHB, 3166 g) compared with non-Hispanic white individuals (NHW, 3409 g) and Hispanic individuals (3348 g). Controlling for covariates, birthweight increased with maternal age until the early 30s. Race-specific modelling showed that the upper extremes of maternal age had a significant depressive effect on birthweight for NHW and NHB (35+ years, p<0.001), but only age less than 25 years was a significant contributor to lower birthweights for Hispanic individuals, p<0.0001. Among all racial subgroups, birth order had a greater influence on birthweight than maternal age, with the largest incremental increase from first to second births. Among NHB, birth order accounted for a smaller increment in birthweight than for NHW and Hispanic women. Conclusion Birth order exerts a greater influence on birthweight than maternal age, with signficantly different effects across racial subgroups. PMID:21081308
Denche, M.; Marhoune, A. L.
2001-01-01
We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the considered problem.
First order impulsive differential inclusions with periodic conditions
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John Graef
2008-10-01
where $\\varphi: J\\times \\mathbb{R}^n\\to{\\cal P}(\\mathbb{R}^n$ is a multi-valued map. The study of the above problems use an approach based on the topological degree combined with a Poincar\\'e operator.
Focal decompositions for linear differential equations of the second order
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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.
Hyers-Ulam stability for second-order linear differential equations with boundary conditions
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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.
SIVA/DIVA- INITIAL VALUE ORDINARY DIFFERENTIAL EQUATION SOLUTION VIA A VARIABLE ORDER ADAMS METHOD
Krogh, F. T.
1994-01-01
The SIVA/DIVA package is a collection of subroutines for the solution of ordinary differential equations. There are versions for single precision and double precision arithmetic. These solutions are applicable to stiff or nonstiff differential equations of first or second order. SIVA/DIVA requires fewer evaluations of derivatives than other variable order Adams predictor-corrector methods. There is an option for the direct integration of second order equations which can make integration of trajectory problems significantly more efficient. Other capabilities of SIVA/DIVA include: monitoring a user supplied function which can be separate from the derivative; dynamically controlling the step size; displaying or not displaying output at initial, final, and step size change points; saving the estimated local error; and reverse communication where subroutines return to the user for output or computation of derivatives instead of automatically performing calculations. The user must supply SIVA/DIVA with: 1) the number of equations; 2) initial values for the dependent and independent variables, integration stepsize, error tolerance, etc.; and 3) the driver program and operational parameters necessary for subroutine execution. SIVA/DIVA contains an extensive diagnostic message library should errors occur during execution. SIVA/DIVA is written in FORTRAN 77 for batch execution and is machine independent. It has a central memory requirement of approximately 120K of 8 bit bytes. This program was developed in 1983 and last updated in 1987.
on differential operators on w 1,2 space and fredholm operators
African Journals Online (AJOL)
A selfadjoint differential operator defined over a closed and bounded interval on Sobolev space which is a dense linear subspace of a Hilbert space over the same interval is considered and shown to be a Fredholm operator with index zero. KEY WORDS: Sobolev space, Hilbert space, dense subspace, Fredholm operator
Repeated morphine treatment influences operant and spatial learning differentially
Institute of Scientific and Technical Information of China (English)
Mei-Na WANG; Zhi-Fang DONG; Jun CAO; Lin XU
2006-01-01
Objective To investigate whether repeated morphine exposure or prolonged withdrawal could influence operant and spatial learning differentially. Methods Animals were chronically treated with morphine or subjected to morphine withdrawal. Then, they were subjected to two kinds of learning: operant conditioning and spatial learning.Results The acquisition of both simple appetitive and cued operant learning was impaired after repeated morphine treatment. Withdrawal for 5 weeks alleviated the impairments. Single morphine exposure disrupted the retrieval of operant memory but had no effect on rats after 5-week withdrawal. Contrarily, neither chronic morphine exposure nor 5-week withdrawal influenced spatial learning task of the Morris water maze. Nevertheless, the retrieval of spatial memory was impaired by repeated morphine exposure but not by 5-week withdrawal. Conclusion These observations suggest that repeated morphine exposure can influence different types of learning at different aspects, implicating that the formation of opiate addiction may usurp memory mechanisms differentially.
Wavelet Methods for Solving Fractional Order Differential Equations
A. K. Gupta; S. Saha Ray
2014-01-01
Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linea...
Symmetric positive differential equations and first order hyperbolic systems
International Nuclear Information System (INIS)
Tangmanee, S.
1981-12-01
We prove that under some conditions the first order hyperbolic system and its associated mixed initial boundary conditions considered, for example, in Kreiss (Math. Comp. 22, 703-704 (1968)) and Kreiss and Gustafsson (Math. Comp. 26, 649-686 (1972)), can be transformed into a symmetric positive system of P.D.E.'s with admissible boundary conditions of Friedrich's type (Comm. Pure Appl. Math 11, 333-418 (1958)). (author)
Analysis of the essential spectrum of singular matrix differential operators
Czech Academy of Sciences Publication Activity Database
Ibrogimov, O. O.; Siegl, Petr; Tretter, C.
2016-01-01
Roč. 260, č. 4 (2016), s. 3881-3926 ISSN 0022-0396 Institutional support: RVO:61389005 Key words : essential spectrum * system of singular differential equations * operator matrix * Schur complement * magnetohydrodynamics * Stellar equilibrium model Subject RIV: BE - Theoretical Physics Impact factor: 1.988, year: 2016
ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.
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Kunio Ichinobe
2015-01-01
Full Text Available We study the \\(k\\-summability of divergent formal solutions for the Cauchy problem of certain linear partial differential operators with coefficients which are polynomial in \\(t\\. We employ the method of successive approximation in order to construct the formal solutions and to obtain the properties of analytic continuation of the solutions of convolution equations and their exponential growth estimates.
Directory of Open Access Journals (Sweden)
Diem Dang Huan
2015-12-01
Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.
From sequences to polynomials and back, via operator orderings
Energy Technology Data Exchange (ETDEWEB)
Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118 (United States); De Angelis, Valerio, E-mail: vdeangel@xula.edu [Department of Mathematics, Xavier University of Louisiana, New Orleans, Louisiana 70125 (United States); Vignat, Christophe, E-mail: vignat@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA and L.S.S. Supelec, Universite d' Orsay (France)
2013-12-15
Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.
Fractional Order Differentiation by Integration and Error Analysis in Noisy Environment
Liu, Dayan
2015-03-31
The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess. We propose to extend this method from the integer order to the fractional order to estimate the fractional order derivatives of noisy signals. Firstly, two fractional order differentiators are deduced from the Jacobi orthogonal polynomial filter, using the Riemann-Liouville and the Caputo fractional order derivative definitions respectively. Exact and simple formulae for these differentiators are given by integral expressions. Hence, they can be used for both continuous-time and discrete-time models in on-line or off-line applications. Secondly, some error bounds are provided for the corresponding estimation errors. These bounds allow to study the design parameters\\' influence. The noise error contribution due to a large class of stochastic processes is studied in discrete case. The latter shows that the differentiator based on the Caputo fractional order derivative can cope with a class of noises, whose mean value and variance functions are polynomial time-varying. Thanks to the design parameters analysis, the proposed fractional order differentiators are significantly improved by admitting a time-delay. Thirdly, in order to reduce the calculation time for on-line applications, a recursive algorithm is proposed. Finally, the proposed differentiator based on the Riemann-Liouville fractional order derivative is used to estimate the state of a fractional order system and numerical simulations illustrate the accuracy and the robustness with respect to corrupting noises.
Algebra of pseudo-differential operators over C*-algebra
International Nuclear Information System (INIS)
Mohammad, N.
1982-08-01
Algebras of pseudo-differential operators over C*-algebras are studied for the special case when in Hormander class Ssub(rho,delta)sup(m)(Ω) Ω = Rsup(n); rho = 1, delta = 0, m any real number, and the C*-algebra is infinite dimensional non-commutative. The space B, i.e. the set of A-valued C*-functions in Rsup(n) (or Rsup(n) x Rsup(n)) whose derivatives are all bounded, plays an important role. A denotes C*-algebra. First the operator class Ssub(phi,0)sup(m) is defined, and through it, the class Lsub(1,0)sup(m) of pseudo-differential operators. Then the basic asymptotic expansion theorems concerning adjoint and product of operators of class Ssub(1,0)sup(m) are stated. Finally, proofs are given of L 2 -continuity theorem and the main theorem, which states that algebra of all pseudo-differential operators over C*-algebras is itself C*-algebra
A differential operator for integrating one-loop scattering equations
Energy Technology Data Exchange (ETDEWEB)
Wang, Tianheng [Department of Physics, Nanjing University,Nanjing, Jiangsu Province (China); Chen, Gang [Department of Physics, Zhejiang Normal University,Jinhua, Zhejiang Province (China); Department of Physics and Astronomy, Uppsala University,Uppsala (Sweden); Department of Physics, Nanjing University,Nanjing, Jiangsu Province (China); Cheung, Yeuk-Kwan E. [Department of Physics, Nanjing University,Nanjing, Jiangsu Province (China); Xu, Feng [Weavi Corporation Limited, Nanjing,Jiangsu Province (China)
2017-01-09
We propose a differential operator for computing the residues associated with a class of meromorphic n-forms that frequently appear in the Cachazo-He-Yuan form of the scattering amplitudes. This differential operator is conjectured to be uniquely determined by the local duality theorem and the intersection number of the divisors in the n-form. We use the operator to evaluate the one-loop integrand of Yang-Mills theory from their generalized CHY formulae. The method can reduce the complexity of the calculation. In addition, the expression for the 1-loop four-point Yang-Mills integrand obtained in our approach has a clear correspondence with the Q-cut results.
Higher order Riesz transforms associated with Bessel operators
Betancor, Jorge J.; Fariña, Juan C.; Martinez, Teresa; Rodríguez-Mesa, Lourdes
2008-10-01
In this paper we investigate Riesz transforms R μ ( k) of order k≥1 related to the Bessel operator Δμ f( x)=- f”( x)-((2μ+1)/ x) f’( x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We obtain that for every k≥1, R μ ( k) is a principal value operator of strong type ( p, p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ( x)= x 2μ+1 dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R μ ( k) maps L p (ω) into itself and L 1(ω) into L 1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class mathcal{A}p^μ of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman.
Completion of the Kernel of the Differentiation Operator
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Anatoly N. Morozov
2017-01-01
Full Text Available When investigating piecewise polynomial approximations in spaces \\(L_p, \\; 0~<~p~<~1,\\ the author considered the spreading of k-th derivative (of the operator from Sobolev spaces \\(W_1 ^ k\\ on spaces that are, in a sense, their successors with a low index less than one. In this article, we continue the study of the properties acquired by the differentiation operator \\(\\Lambda\\ with spreading beyond the space \\(W_1^1\\ $$\\Lambda~:~W_1^1~\\mapsto~L_1,\\; \\Lambda f = f^{\\;'} $$.The study is conducted by introducing the family of spaces \\(Y_p^1, \\; 0
differentiation operator: $$ \\bigcup_{n=1}^{m} \\Lambda (f_n = \\Lambda (\\bigcup_{n=1}^{m} f_n.$$Here, for a function \\(f_n\\ defined on \\([x_{n-1}; x_n], \\; a~=~x_0 < x_1 < \\cdots
Kulishov, Mykola; Azaña, José
2007-05-14
A simple and general approach for designing practical all-optical (all-fiber) arbitrary-order time differentiators is introduced here for the first time. Specifically, we demonstrate that the Nth time derivative of an input optical waveform can be obtained by reflection of this waveform in a single uniform fiber Bragg grating (FBG) incorporating N &pi-phase shifts properly located along its grating profile. The general design procedure of an arbitrary-order optical time differentiator based on a multiple-phase-shifted FBG is described and numerically demonstrated for up to fourth-order time differentiation. Our simulations show that the proposed approach can provide optical operation bandwidths in the tens-of-GHz regime using readily feasible FBG structures.
High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices
Dunham, Benjamin Z.
This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions--most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series--without changing data-type or modifying code line by line; this allows differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed "stencils," each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the "forward mode" is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of N--i.e., O(1)--the N x N Hessian can be found in O(N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive--e.g., a N x N x N rank-three tensor can be found in O(N2). Alternatively, a Hessian-vector product can be found in O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step differentiation (CD) technique is also shown to be capable of
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Abbas Badakaya Ja'afaru
2012-01-01
Full Text Available We study pursuit and evasion differential game problems described by infinite number of first-order differential equations with function coefficients in Hilbert space l2. Problems involving integral, geometric, and mix constraints to the control functions of the players are considered. In each case, we give sufficient conditions for completion of pursuit and for which evasion is possible. Consequently, strategy of the pursuer and control function of the evader are constructed in an explicit form for every problem considered.
Applications of ordered weighted averaging (OWA operators in environmental problems
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Carlos Llopis-Albert
2017-04-01
Full Text Available This paper presents an application of a prioritized weighted aggregation operator based on ordered weighted averaging (OWA to deal with stakeholders' constructive participation in water resources projects. They have different degree of acceptance or preference regarding the measures and policies to be carried out, which lead to different environmental and socio-economic outcomes, and hence, to different levels of stakeholders’ satisfaction. The methodology establishes a prioritization relationship upon the stakeholders, which preferences are aggregated by means of weights depending on the satisfaction of the higher priority policy maker. The methodology establishes a prioritization relationship upon the stakeholders, which preferences are aggregated by means of weights depending on the satisfaction of the higher priority policy maker. The methodology has been successfully applied to a Public Participation Project (PPP in watershed management, thus obtaining efficient environmental measures in conflict resolution problems under actors’ preference uncertainties.
Second-order differential-delay equation to describe a hybrid bistable device
Vallee, R.; Dubois, P.; Cote, M.; Delisle, C.
1987-08-01
The problem of a dynamical system with delayed feedback, a hybrid bistable device, characterized by n response times and described by an nth-order differential-delay equation (DDE) is discussed. Starting from a linear-stability analysis of the DDE, the effects of the second-order differential terms on the position of the first bifurcation and on the frequency of the resulting self-oscillation are shown. The effects of the third-order differential terms on the first bifurcation are also considered. Experimental results are shown to support the linear analysis.
Analysis of an Nth-order nonlinear differential-delay equation
Vallée, Réal; Marriott, Christopher
1989-01-01
The problem of a nonlinear dynamical system with delay and an overall response time which is distributed among N individual components is analyzed. Such a system can generally be modeled by an Nth-order nonlinear differential delay equation. A linear-stability analysis as well as a numerical simulation of that equation are performed and a comparison is made with the experimental results. Finally, a parallel is established between the first-order differential equation with delay and the Nth-order differential equation without delay.
The Oscillation of a Class of the Fractional-Order Delay Differential Equations
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Qianli Lu
2014-01-01
Full Text Available Several oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations by analysis method, and the sufficient or necessary and sufficient conditions for the oscillation of delay partial differential equation with three different boundary conditions. For this, α-exponential function which is a kind of functions that play the same role of the classical exponential functions of fractional-order derivatives is used.
International Nuclear Information System (INIS)
Cheng Min; Tang Tiantong; Lu Yilong; Yao Zhenhua
2003-01-01
The principle of differential algebra is applied to analyse and calculate arbitrary order curvilinear-axis combined geometric-chromatic aberrations of electron optical systems. Expressions of differential algebraic form of high order combined aberrations are obtained and arbitrary order combined aberrations can be calculated numerically. As an example, a typical wide electron beam focusing system with curved optical axes named magnetic immersion lens has been studied. All the second-order and third-order combined geometric-chromatic aberrations of the lens have been calculated, and the patterns of the corresponding geometric aberrations and combined aberrations have been given as well
Rusyaman, E.; Parmikanti, K.; Chaerani, D.; Asefan; Irianingsih, I.
2018-03-01
One of the application of fractional ordinary differential equation is related to the viscoelasticity, i.e., a correlation between the viscosity of fluids and the elasticity of solids. If the solution function develops into function with two or more variables, then its differential equation must be changed into fractional partial differential equation. As the preliminary study for two variables viscoelasticity problem, this paper discusses about convergence analysis of function sequence which is the solution of the homogenous fractional partial differential equation. The method used to solve the problem is Homotopy Analysis Method. The results show that if given two real number sequences (αn) and (βn) which converge to α and β respectively, then the solution function sequences of fractional partial differential equation with order (αn, βn) will also converge to the solution function of fractional partial differential equation with order (α, β).
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Ahmad Bashir
2010-01-01
Full Text Available We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.
Some properties of solutions of a functional-differential equation of second order with delay.
Ilea, Veronica Ana; Otrocol, Diana
2014-01-01
Existence, uniqueness, data dependence (monotony, continuity, and differentiability with respect to parameter), and Ulam-Hyers stability results for the solutions of a system of functional-differential equations with delays are proved. The techniques used are Perov's fixed point theorem and weakly Picard operator theory.
Some Properties of Solutions of a Functional-Differential Equation of Second Order with Delay
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Veronica Ana Ilea
2014-01-01
Full Text Available Existence, uniqueness, data dependence (monotony, continuity, and differentiability with respect to parameter, and Ulam-Hyers stability results for the solutions of a system of functional-differential equations with delays are proved. The techniques used are Perov’s fixed point theorem and weakly Picard operator theory.
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Veyis Turut
2013-01-01
Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.
Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces
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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.
Approximate solution of integro-differential equation of fractional (arbitrary order
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Asma A. Elbeleze
2016-01-01
Full Text Available In the present paper, we study the integro-differential equations which are combination of differential and Fredholm–Volterra equations that have the fractional order with constant coefficients by the homotopy perturbation and the variational iteration. The fractional derivatives are described in Caputo sense. Some illustrative examples are presented.
Variations in the Solution of Linear First-Order Differential Equations. Classroom Notes
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…
POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE
Institute of Scientific and Technical Information of China (English)
无
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.
A NEW OSCILLATION CRITERION FOR FIRST ORDER NEUTRAL DELAY DIFFERENTIAL EQUATION
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, a new sufficient condition for the oscillation of all solutions of first order neutral delay differential equations is obtained. Secondly, the result can also be extended to a general neutral differential equation, and many known results in the literatures are improved.
Application of the Lie Symmetry Analysis for second-order fractional differential equations
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Mousa Ilie
2017-12-01
Full Text Available Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to illustrate the proposed approach.
Asymptotic behavior and stability of second order neutral delay differential equations
Chen, G.L.; van Gaans, O.W.; Verduyn Lunel, Sjoerd
2014-01-01
We study the asymptotic behavior of a class of second order neutral delay differential equations by both a spectral projection method and an ordinary differential equation method approach. We discuss the relation of these two methods and illustrate some features using examples. Furthermore, a fixed
Directory of Open Access Journals (Sweden)
C. Parthasarathy
2013-03-01
Full Text Available In this paper, we study the controllability results of first order impulsive stochastic differential and neutral differential systems with state-dependent delay by using semigroup theory. The controllability results are derived by the means of Leray-SchauderAlternative fixed point theorem. An example is provided to illustrate the theory.
Antiperiodic Boundary Value Problems for Second-Order Impulsive Ordinary Differential Equations
Directory of Open Access Journals (Sweden)
2009-02-01
Full Text Available We consider a second-order ordinary differential equation with antiperiodic boundary conditions and impulses. By using Schaefer's fixed-point theorem, some existence results are obtained.
High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations
Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.
2012-01-01
© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration
EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper is concerned with nonlinear second order neutral stochastic differential equations with delay in a Hilbert space. Sufficient conditions for the existence of solution to the system are obtained by Picard iterations.
ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.
RECTC/RECTCF, 2. Order Elliptical Partial Differential Equation, Arbitrary Boundary Conditions
International Nuclear Information System (INIS)
Hackbusch, W.
1983-01-01
1 - Description of problem or function: A general linear elliptical second order partial differential equation on a rectangle with arbitrary boundary conditions is solved. 2 - Method of solution: Multi-grid iteration
International Nuclear Information System (INIS)
Dimitrova, M. B.; Donev, V. I.
2008-01-01
This paper is dealing with the oscillatory properties of first order neutral delay impulsive differential equations and corresponding to them inequalities with constant coefficients. The established sufficient conditions ensure the oscillation of every solution of this type of equations.
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.
Numerical solution for multi-term fractional (arbitrary) orders differential equations
El-Sayed, A. M. A.; El-Mesiry, A. E. M.; El-Saka, H. A. A.
2004-01-01
Our main concern here is to give a numerical scheme to solve a nonlinear multi-term fractional (arbitrary) orders differential equation. Some results concerning the existence and uniqueness have been also obtained.
Third-order ordinary differential equations Y”' = f(x, y, y'', y′”) with ...
African Journals Online (AJOL)
dimensional symmetry algebra. Mathematics Subject Classication (2010): 34A05, 34A25, 53A55, 76M60. Key words: Linearization, third order ODEs, point transformation, contact transformation, Lie symmetries, relative differential invariants.
Stability and square integrability of solutions of nonlinear fourth order differential equations
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Moussadek Remili
2016-05-01
Full Text Available The aim of the present paper is to establish a new result, which guarantees the asymptotic stability of zero solution and square integrability of solutions and their derivatives to nonlinear differential equations of fourth order.
Operational Momentum During Ordering Operations for Size and Number in 4-Month-Old Infants
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Viola Macchi Cassia
2017-12-01
Full Text Available An Operational Momentum (OM effect is shown by 9-month-old infants during non-symbolic arithmetic, whereby they overestimate the outcomes to addition problems, and underestimate the outcomes to subtraction problems. Recent evidence has shown that this effect extends to ordering operations for size-based sequences in 12-month-olds. Here we provide evidence that OM occurs for ordering operations involving numerical sequences containing multiple quantity cues, but not size-based sequences, already at 4 months of age. Infants were tested in an ordinal task in which they detected and represented increasing or decreasing variations in physical and/or numerical size, and then responded to ordinal sequences that exhibited greater or lesser sizes/numerosities, thus following or violating the OM generated during habituation. Results showed that OM was absent during size ordering (Experiment 1, but was present when infants ordered arrays of discrete elements varying on numerical and non-numerical dimensions, if both number and continuous magnitudes were available cues to discriminate between with-OM and against-OM sequences during test trials (Experiments 2 vs. 3. The presence of momentum for ordering number only when provided with multiple cues of magnitude changes suggests that OM is a complex phenomenon that blends multiple representations of magnitude early in infancy.
Spectral analysis of difference and differential operators in weighted spaces
International Nuclear Information System (INIS)
Bichegkuev, M S
2013-01-01
This paper is concerned with describing the spectrum of the difference operator K:l α p (Z,X)→l α p (Z......athscrKx)(n)=Bx(n−1), n∈Z, x∈l α p (Z,X), with a constant operator coefficient B, which is a bounded linear operator in a Banach space X. It is assumed that K acts in the weighted space l α p (Z,X), 1≤p≤∞, of two-sided sequences of vectors from X. The main results are obtained in terms of the spectrum σ(B) of the operator coefficient B and properties of the weight function. Applications to the study of the spectrum of a differential operator with an unbounded operator coefficient (the generator of a strongly continuous semigroup of operators) in weighted function spaces are given. Bibliography: 23 titles
Planar real polynomial differential systems of degree n > 3 having a weak focus of high order
International Nuclear Information System (INIS)
Llibre, J.; Rabanal, R.
2008-06-01
We construct planar polynomial differential systems of even (respectively odd) degree n > 3, of the form linear plus a nonlinear homogeneous part of degree n having a weak focus of order n 2 -1 (respectively (n 2 -1)/2 ) at the origin. As far as we know this provides the highest order known until now for a weak focus of a polynomial differential system of arbitrary degree n. (author)
Lagrange-Noether method for solving second-order differential equations
Institute of Scientific and Technical Information of China (English)
Wu Hui-Bin; Wu Run-Heng
2009-01-01
The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.
Chadha, Alka; Bora, Swaroop Nandan
2017-11-01
This paper studies the existence, uniqueness, and exponential stability in mean square for the mild solution of neutral second order stochastic partial differential equations with infinite delay and Poisson jumps. By utilizing the Banach fixed point theorem, first the existence and uniqueness of the mild solution of neutral second order stochastic differential equations is established. Then, the mean square exponential stability for the mild solution of the stochastic system with Poisson jumps is obtained with the help of an established integral inequality.
International Nuclear Information System (INIS)
Zhang Li-Min; Sun Ke-Hui; Liu Wen-Hao; He Shao-Bo
2017-01-01
In this paper, Adomian decomposition method (ADM) with high accuracy and fast convergence is introduced to solve the fractional-order piecewise-linear (PWL) hyperchaotic system. Based on the obtained hyperchaotic sequences, a novel color image encryption algorithm is proposed by employing a hybrid model of bidirectional circular permutation and DNA masking. In this scheme, the pixel positions of image are scrambled by circular permutation, and the pixel values are substituted by DNA sequence operations. In the DNA sequence operations, addition and substraction operations are performed according to traditional addition and subtraction in the binary, and two rounds of addition rules are used to encrypt the pixel values. The simulation results and security analysis show that the hyperchaotic map is suitable for image encryption, and the proposed encryption algorithm has good encryption effect and strong key sensitivity. It can resist brute-force attack, statistical attack, differential attack, known-plaintext, and chosen-plaintext attacks. (paper)
International Nuclear Information System (INIS)
Nguyen Thanh Van
2006-12-01
This paper deals with the initial value problem of the type φw / φt = L (t, x, w, φw / φx i ) (1) w(0, x) = φ(x) (2) where t is the time, L is a linear first order operator in a Clifford Analysis and φ is a generalized monogenic function. We give sufficient conditions on the coefficients of operator L under which L is associated to differential equations with anti-monogenic right-hand sides. For such operator L the initial problem (1),(2) is solvable for an arbitrary generalized monogenic initial function φ and the solution is also generalized monogenic for each t. (author)
Directory of Open Access Journals (Sweden)
M. Mallika Arjunan
2014-01-01
Full Text Available In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii's fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provided to illustrate the main results.
Spectral methods for a nonlinear initial value problem involving pseudo differential operators
International Nuclear Information System (INIS)
Pasciak, J.E.
1982-01-01
Spectral methods (Fourier methods) for approximating the solution of a nonlinear initial value problem involving pseudo differential operators are defined and analyzed. A semidiscrete approximation to the nonlinear equation based on an L 2 projection is described. The semidiscrete L 2 approximation is shown to be a priori stable and convergent under sufficient decay and smoothness assumptions on the initial data. It is shown that the semidiscrete method converges with infinite order, that is, higher order decay and smoothness assumptions imply higher order error bounds. Spectral schemes based on spacial collocation are also discussed
A differential equation for Lerch's transcendent and associated symmetric operators in Hilbert space
International Nuclear Information System (INIS)
Kaplitskii, V M
2014-01-01
The function Ψ(x,y,s)=e iy Φ(−e iy ,s,x), where Φ(z,s,v) is Lerch's transcendent, satisfies the following two-dimensional formally self-adjoint second-order hyperbolic differential equation, where s=1/2+iλ. The corresponding differential expression determines a densely defined symmetric operator (the minimal operator) on the Hilbert space L 2 (Π), where Π=(0,1)×(0,2π). We obtain a description of the domains of definition of some symmetric extensions of the minimal operator. We show that formal solutions of the eigenvalue problem for these symmetric extensions are represented by functional series whose structure resembles that of the Fourier series of Ψ(x,y,s). We discuss sufficient conditions for these formal solutions to be eigenfunctions of the resulting symmetric differential operators. We also demonstrate a close relationship between the spectral properties of these symmetric differential operators and the distribution of the zeros of some special analytic functions analogous to the Riemann zeta function. Bibliography: 15 titles
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Resat Yilmazer
2016-02-01
Full Text Available In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs. Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.
Understanding operational risk capital approximations: First and second orders
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Gareth W. Peters
2013-07-01
Full Text Available We set the context for capital approximation within the framework of the Basel II / III regulatory capital accords. This is particularly topical as the Basel III accord is shortly due to take effect. In this regard, we provide a summary of the role of capital adequacy in the new accord, highlighting along the way the significant loss events that have been attributed to the Operational Risk class that was introduced in the Basel II and III accords. Then we provide a semi-tutorial discussion on the modelling aspects of capital estimation under a Loss Distributional Approach (LDA. Our emphasis is to focuss on the important loss processes with regard to those that contribute most to capital, the so called “high consequence, low frequency" loss processes. This leads us to provide a tutorial overview of heavy tailed loss process modelling in OpRisk under Basel III, with discussion on the implications of such tail assumptions for the severity model in an LDA structure. This provides practitioners with a clear understanding of the features that they may wish to consider when developing OpRisk severity models in practice. From this discussion on heavy tailed severity models, we then develop an understanding of the impact such models have on the right tail asymptotics of the compound loss process and we provide detailed presentation of what are known as first and second order tail approximations for the resulting heavy tailed loss process. From this we develop a tutorial on three key families of risk measures and their equivalent second order asymptotic approximations: Value-at-Risk (Basel III industry standard; Expected Shortfall (ES and the Spectral Risk Measure. These then form the capital approximations. We then provide a few example case studies to illustrate the accuracy of these asymptotic captial approximations, the rate of the convergence of the assymptotic result as a function of the LDA frequency and severity model parameters, the sensitivity
Differential-difference equations associated with the fractional Lax operators
Energy Technology Data Exchange (ETDEWEB)
Adler, V E [LD Landau Institute for Theoretical Physics, 1A Ak. Semenov, Chernogolovka 142432 (Russian Federation); Postnikov, V V, E-mail: adler@itp.ac.ru, E-mail: postnikofvv@mail.ru [Sochi Branch of Peoples' Friendship University of Russia, 32 Kuibyshev str., 354000 Sochi (Russian Federation)
2011-10-14
We study integrable hierarchies associated with spectral problems of the form P{psi} = {lambda}Q{psi}, where P and Q are difference operators. The corresponding nonlinear differential-difference equations can be viewed as inhomogeneous generalizations of the Bogoyavlensky-type lattices. While the latter turn into the Korteweg-de Vries equation under the continuous limit, the lattices under consideration provide discrete analogs of the Sawada-Kotera and Kaup-Kupershmidt equations. The r-matrix formulation and several of the simplest explicit solutions are presented. (paper)
Periodic solutions of certain third order nonlinear differential systems with delay
International Nuclear Information System (INIS)
Tejumola, H.O.; Afuwape, A.U.
1990-12-01
This paper investigates the existence of 2π-periodic solutions of systems of third-order nonlinear differential equations, with delay, under varied assumptions. The results obtained extend earlier works of Tejumola and generalize to third order systems those of Conti, Iannacci and Nkashama as well as DePascale and Iannacci and Iannacci and Nkashama. 16 refs
A note on monotone solutions for a nonconvex second-order functional differential inclusion
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Aurelian Cernea
2011-12-01
Full Text Available The existence of monotone solutions for a second-order functional differential inclusion with Carath\\'{e}odory perturbation is obtained in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the Fr\\'{e}chet subdifferential of a $\\phi $-convex function of order two.
The Convergence Problems of Eigenfunction Expansions of Elliptic Differential Operators
Ahmedov, Anvarjon
2018-03-01
In the present research we investigate the problems concerning the almost everywhere convergence of multiple Fourier series summed over the elliptic levels in the classes of Liouville. The sufficient conditions for the almost everywhere convergence problems, which are most difficult problems in Harmonic analysis, are obtained. The methods of approximation by multiple Fourier series summed over elliptic curves are applied to obtain suitable estimations for the maximal operator of the spectral decompositions. Obtaining of such estimations involves very complicated calculations which depends on the functional structure of the classes of functions. The main idea on the proving the almost everywhere convergence of the eigenfunction expansions in the interpolation spaces is estimation of the maximal operator of the partial sums in the boundary classes and application of the interpolation Theorem of the family of linear operators. In the present work the maximal operator of the elliptic partial sums are estimated in the interpolation classes of Liouville and the almost everywhere convergence of the multiple Fourier series by elliptic summation methods are established. The considering multiple Fourier series as an eigenfunction expansions of the differential operators helps to translate the functional properties (for example smoothness) of the Liouville classes into Fourier coefficients of the functions which being expanded into such expansions. The sufficient conditions for convergence of the multiple Fourier series of functions from Liouville classes are obtained in terms of the smoothness and dimensions. Such results are highly effective in solving the boundary problems with periodic boundary conditions occurring in the spectral theory of differential operators. The investigations of multiple Fourier series in modern methods of harmonic analysis incorporates the wide use of methods from functional analysis, mathematical physics, modern operator theory and spectral
Institute of Scientific and Technical Information of China (English)
CHENG Min; TANG Tiantong; YAO Zhenhua; ZHU Jingping
2001-01-01
Differential algebraic method is apowerful technique in computer numerical analysisbased on nonstandard analysis and formal series the-ory. It can compute arbitrary high order derivativeswith excellent accuracy. The principle of differentialalgebraic method is applied to calculate high orderaberrations of combined electromagnetic focusing sys-tems. As an example, third-order geometric aberra-tion coefficients of an actual combined electromagneticfocusing system were calculated. The arbitrary highorder aberrations are conveniently calculated by dif-ferential algebraic method and the fifth-order aberra-tion diagrams are given.
Jumarie, Guy
2013-04-01
By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.
Unusual poles of the {zeta}-functions for some regular singular differential operators
Energy Technology Data Exchange (ETDEWEB)
Falomir, H [IFLP, Departamento de Fisica-Facultad de Ciencias Exactas, UNLP, CC 67 (1900) La Plata (Argentina); Muschietti, M A [Departamento de Matematica-Facultad de Ciencias Exactas, UNLP, CC 172 (1900) La Plata (Argentina); Pisani, P A G [IFLP, Departamento de Fisica-Facultad de Ciencias Exactas, UNLP, CC 67 (1900) La Plata (Argentina); Seeley, R [University of Massachusetts at Boston, Boston, MA 02125 (United States)
2003-10-03
We consider the resolvent of a system of first-order differential operators with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents powers of {lambda} which depend on the singularity, and can take even irrational values. The consequences for the pole structure of the corresponding {zeta}- and {eta}-functions are also discussed.
International Nuclear Information System (INIS)
Bayramoglu, Mehmet; Tasci, Fatih; Zeynalov, Djafar
2004-01-01
We study the discrete part of spectrum of a singular non-self-adjoint second-order differential equation on a semiaxis with an operator coefficient. Its boundedness is proved. The result is applied to the Schroedinger boundary value problem -Δu+q(x)u=λ 2 u, u vertical bar ∂D =0, with a complex potential q(x) in an angular domain
Construction of a Smooth Lyapunov Function for the Robust and Exact Second-Order Differentiator
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Tonametl Sanchez
2016-01-01
Full Text Available Differentiators play an important role in (continuous feedback control systems. In particular, the robust and exact second-order differentiator has shown some very interesting properties and it has been used successfully in sliding mode control, in spite of the lack of a Lyapunov based procedure to design its gains. As contribution of this paper, we provide a constructive method to determine a differentiable Lyapunov function for such a differentiator. Moreover, the Lyapunov function is used to provide a procedure to design the differentiator’s parameters. Also, some sets of such parameters are provided. The determination of the positive definiteness of the Lyapunov function and negative definiteness of its derivative is converted to the problem of solving a system of inequalities linear in the parameters of the Lyapunov function candidate and also linear in the gains of the differentiator, but bilinear in both.
Zúñiga-Aguilar, C. J.; Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Alvarado-Martínez, V. M.; Romero-Ugalde, H. M.
2018-02-01
In this paper, we approximate the solution of fractional differential equations with delay using a new approach based on artificial neural networks. We consider fractional differential equations of variable order with the Mittag-Leffler kernel in the Liouville-Caputo sense. With this new neural network approach, an approximate solution of the fractional delay differential equation is obtained. Synaptic weights are optimized using the Levenberg-Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional delay differential equations, linear systems with delay, nonlinear systems with delay and a system of differential equations, for instance, the Newton-Leipnik oscillator. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network, different performance indices were calculated.
On integration of the first order differential equations in a finite terms
International Nuclear Information System (INIS)
Malykh, M D
2017-01-01
There are several approaches to the description of the concept called briefly as integration of the first order differential equations in a finite terms or symbolical integration. In the report three of them are considered: 1.) finding of a rational integral (Beaune or Poincaré problem), 2.) integration by quadratures and 3.) integration when the general solution of given differential equation is an algebraical function of a constant (Painlevé problem). Their realizations in Sage are presented. (paper)
Thandapani, Ethiraju; Kannan, Manju; Pinelas, Sandra
2016-01-01
In this paper, we present some sufficient conditions for the oscillation of all solutions of a second order forced impulsive delay differential equation with damping term. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. The results obtained in this paper extend and generalize some of the the known results for forced impulsive differential equations. An example is provided to illustrate the main result.
Growth of meromorphic solutions of higher-order linear differential equations
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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.
Numerical solution of second-order stochastic differential equations with Gaussian random parameters
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Rahman Farnoosh
2014-07-01
Full Text Available In this paper, we present the numerical solution of ordinary differential equations (or SDEs, from each orderespecially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysisfor second-order equations in specially case of scalar linear second-order equations (damped harmonicoscillators with additive or multiplicative noises. Making stochastic differential equations system from thisequation, it could be approximated or solved numerically by different numerical methods. In the case oflinear stochastic differential equations system by Computing fundamental matrix of this system, it could becalculated based on the exact solution of this system. Finally, this stochastic equation is solved by numericallymethod like E.M. and Milstein. Also its Asymptotic stability and statistical concepts like expectationand variance of solutions are discussed.
Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations
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Rutwig Campoamor-Stursberg
2016-03-01
Full Text Available A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems.
Integrating Mission Type Orders into Operational Level Intelligence Collection
2011-05-27
Techniques, and Procedures U.S. United States UAS Unmanned Aircraft System UAV Unmanned Aerial Vehicle UNICORN Unified Collection Operation Reporting...MTOs. If these suggestions result in doctrinal changes, that will help grow the amount of existing literature pertaining to this topic. Existing...SIUs), Air Force ISR liaison officers (ISRLOs), and operational collection managers began maturing processes and growing techniques for employing MTOs.2
High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations
Abdulle, Assyr
2012-01-01
© 2012 Society for Industrial and Applied Mathematics. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.
ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations
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.
Iterative oscillation results for second-order differential equations with advanced argument
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Irena Jadlovska
2017-07-01
Full Text Available This article concerns the oscillation of solutions to a linear second-order differential equation with advanced argument. Sufficient oscillation conditions involving limit inferior are given which essentially improve known results. We base our technique on the iterative construction of solution estimates and some of the recent ideas developed for first-order advanced differential equations. We demonstrate the advantage of our results on Euler-type advanced equation. Using MATLAB software, a comparison of the effectiveness of newly obtained criteria as well as the necessary iteration length in particular cases are discussed.
Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
Abdulle, Assyr
2013-01-01
We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer from the step size reduction faced by standard explicit methods. The family is based on the standard second order orthogonal Runge-Kutta-Chebyshev (ROCK2) methods for deterministic problems. The convergence, meansquare, and asymptotic stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations are presented and confirm the theoretical results. © 2013 Society for Industrial and Applied Mathematics.
The Pauli equation with differential operators for the spin
International Nuclear Information System (INIS)
Kern, E.
1978-01-01
The spin operator s = (h/2) sigma in the Pauli equation fulfills the commutation relation of the angular momentum and leads to half-integer eigenvalues of the eigenfunctions for s. If one tries to express s by canonically conjugated operators PHI and π = ( /i)delta/deltaPHI the formal angular momentum term s = PHIxπ fails because it leads only to whole-integer eigenvalues. However, the modification of this term in the form s = 1/2(π+PHI(PHI π)+PHIxπ) leads to the required result. The eigenfunction system belonging to this differential operator s(PHI, π) consists of (2s + 1) spin eigenfunctions xim(PHI) which are given explicitly. They form a basis for the wave functions of a particle of spin s. Applying this formalism to particles with s = 1/2, agreement is reached with Pauli's spin theory. The function s(PHI, π) follows from the theory of rotating rigid bodies. The continuous spin-variable PHI = ( x, y, z) can be interpreted classically as a 'turning vector' which defines the orientation in space of a rigid body. PHI is the positioning coordinate of the rigid body or the spin coordinate of the particle in analogy to the cartesian coordinate x. The spin s is a vector fixed to the body. (orig.) [de
Block Hybrid Collocation Method with Application to Fourth Order Differential Equations
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Lee Ken Yap
2015-01-01
Full Text Available The block hybrid collocation method with three off-step points is proposed for the direct solution of fourth order ordinary differential equations. The interpolation and collocation techniques are applied on basic polynomial to generate the main and additional methods. These methods are implemented in block form to obtain the approximation at seven points simultaneously. Numerical experiments are conducted to illustrate the efficiency of the method. The method is also applied to solve the fourth order problem from ship dynamics.
Initial-value problems for first-order differential recurrence equations with auto-convolution
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Mircea Cirnu
2011-01-01
Full Text Available A differential recurrence equation consists of a sequence of differential equations, from which must be determined by recurrence a sequence of unknown functions. In this article, we solve two initial-value problems for some new types of nonlinear (quadratic first order homogeneous differential recurrence equations, namely with discrete auto-convolution and with combinatorial auto-convolution of the unknown functions. In both problems, all initial values form a geometric progression, but in the second problem the first initial value is exempted and has a prescribed form. Some preliminary results showing the importance of the initial conditions are obtained by reducing the differential recurrence equations to algebraic type. Final results about solving the considered initial value problems, are shown by mathematical induction. However, they can also be shown by changing the unknown functions, or by the generating function method. So in a remark, we give a proof of the first theorem by the generating function method.
The ordering operator technique applied to open systems
International Nuclear Information System (INIS)
Pedrosa, I.A.; Baseia, B.
1982-01-01
A normal ordering technique and the coherent representation are used to discribe the time evolution of an open system of a single oscillator, linearly coupled with an infinite number of reservoir oscillators and it is shown how to include the dissipation and get the exponential decay. (Author) [pt
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.
Czech Academy of Sciences Publication Activity Database
Mukhigulashvili, Sulkhan
-, č. 35 (2015), s. 23-50 ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili.pdf
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
N-th order impulsive integro-differential equations in Banach spaces
Directory of Open Access Journals (Sweden)
Manfeng Hu
2004-03-01
Full Text Available We investigate the maximal and minimal solutions of initial value problem for N-th order nonlinear impulsive integro-differential equation in Banach space by establishing a comparison result and using the upper and lower solutions methods.
Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
2013-01-01
We introduce a new family of explicit integrators for stiff Itô stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of one-step stabilized methods with extended stability domains and do not suffer
EXISTENCE OF PERIODIC SOLUTION TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of periodic solutions to the equations are obtained. In addition,we give an example to illustrate the main results.
m-POINT BOUNDARY VALUE PROBLEM FOR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION AT RESONANCE
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In his paper,we obtain a general theorem concerning the existence of solutions to an m-point boundary value problem for the second-order differential equation with impulses.Moreover,the result can also be applied to study the usual m-point boundary value problem at resonance without impulses.
FORCED OSCILLATIONS OF SECOND ORDER SUPER-LINEAR DIFFERENTIAL EQUATION WITH IMPULSES
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
At first,by means of Kartsatos technique,we reduce the impulsive differential equation to a second order nonlinear impulsive homogeneous equation.We find some suitable impulse functions such that all the solutions to the equation are oscillatory.Several criteria on the oscillations of solutions are given.At last,we give an example to demonstrate our results.
Oscillation of certain higher-order neutral partial functional differential equations.
Li, Wei Nian; Sheng, Weihong
2016-01-01
In this paper, we study the oscillation of certain higher-order neutral partial functional differential equations with the Robin boundary conditions. Some oscillation criteria are established. Two examples are given to illustrate the main results in the end of this paper.
Korkmaz, Erdal
2017-01-01
In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.
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
Oscillation Criteria of First Order Neutral Delay Differential Equations with Variable Coefficients
Directory of Open Access Journals (Sweden)
Fatima N. Ahmed
2013-01-01
Full Text Available Some new oscillation criteria are given for first order neutral delay differential equations with variable coefficients. Our results generalize and extend some of the well-known results in the literature. Some examples are considered to illustrate the main results.
Directory of Open Access Journals (Sweden)
Erdal Korkmaz
2017-06-01
Full Text Available Abstract In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov’s second method. The results obtained essentially improve, include and complement the results in the literature.
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
Triple positive solutions of nth order impulsive integro-differential equations
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Zeyong Qiu
2011-07-01
Full Text Available In this paper, we prove the existence of at least three positive solutions of boundary value problems for nth order nonlinear impulsive integro-differential equations of mixed type on infinite interval with infinite number of impulsive times. Our results are obtained by applying a new fixed point theorem introduced by Avery and Peterson.
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.
Czech Academy of Sciences Publication Activity Database
Lomtatidze, Alexander; Vodstrčil, Petr
2005-01-01
Roč. 84, č. 2 (2005), s. 197-209 ISSN 0003-6811 Institutional research plan: CEZ:AV0Z10190503 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics http://www.tandfonline.com/doi/full/10.1080/00036810410001724427
Khataybeh, S. N.; Hashim, I.
2018-04-01
In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.
Solving Second-Order Ordinary Differential Equations without Using Complex Numbers
Kougias, Ioannis E.
2009-01-01
Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…
Periodic solutions of singular second order differential equations : upper and lower functions
Czech Academy of Sciences Publication Activity Database
Hakl, Robert; Torres, P.J.; Zamora, M.
2011-01-01
Roč. 74, č. 18 (2011), s. 7078-7093 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : second-order differential equation * singularity at the phase variable * Rayleigh-Plesset equation Subject RIV: BA - General Mathematics Impact factor: 1.536, year: 2011 http://www.sciencedirect.com/science/article/pii/S0362546X11005049
Czech Academy of Sciences Publication Activity Database
Mukhigulashvili, Sulkhan; Půža, B.
2015-01-01
Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1
Boundary-value problems for first and second order functional differential inclusions
Directory of Open Access Journals (Sweden)
Shihuang Hong
2003-03-01
Full Text Available This paper presents sufficient conditions for the existence of solutions to boundary-value problems of first and second order multi-valued differential equations in Banach spaces. Our results obtained using fixed point theorems, and lead to new existence principles.
46 CFR 113.35-13 - Mechanical engine order telegraph systems; operation.
2010-10-01
... 46 Shipping 4 2010-10-01 2010-10-01 false Mechanical engine order telegraph systems; operation...) ELECTRICAL ENGINEERING COMMUNICATION AND ALARM SYSTEMS AND EQUIPMENT Engine Order Telegraph Systems § 113.35-13 Mechanical engine order telegraph systems; operation. If more than one transmitter operates a...
Deterministic factor analysis: methods of integro-differentiation of non-integral order
Directory of Open Access Journals (Sweden)
Valentina V. Tarasova
2016-12-01
Full Text Available Objective to summarize the methods of deterministic factor economic analysis namely the differential calculus and the integral method. nbsp Methods mathematical methods for integrodifferentiation of nonintegral order the theory of derivatives and integrals of fractional nonintegral order. Results the basic concepts are formulated and the new methods are developed that take into account the memory and nonlocality effects in the quantitative description of the influence of individual factors on the change in the effective economic indicator. Two methods are proposed for integrodifferentiation of nonintegral order for the deterministic factor analysis of economic processes with memory and nonlocality. It is shown that the method of integrodifferentiation of nonintegral order can give more accurate results compared with standard methods method of differentiation using the first order derivatives and the integral method using the integration of the first order for a wide class of functions describing effective economic indicators. Scientific novelty the new methods of deterministic factor analysis are proposed the method of differential calculus of nonintegral order and the integral method of nonintegral order. Practical significance the basic concepts and formulas of the article can be used in scientific and analytical activity for factor analysis of economic processes. The proposed method for integrodifferentiation of nonintegral order extends the capabilities of the determined factorial economic analysis. The new quantitative method of deterministic factor analysis may become the beginning of quantitative studies of economic agents behavior with memory hereditarity and spatial nonlocality. The proposed methods of deterministic factor analysis can be used in the study of economic processes which follow the exponential law in which the indicators endogenous variables are power functions of the factors exogenous variables including the processes
Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.
2012-10-01
We present a set of software routines in Maple 14 for solving first order ordinary differential equations (FOODEs). The package implements the Prelle-Singer method in its original form together with its extension to include integrating factors in terms of elementary functions. The package also presents a theoretical extension to deal with all FOODEs presenting Liouvillian solutions. Applications to ODEs taken from standard references show that it solves ODEs which remain unsolved using Maple's standard ODE solution routines. New version program summary Program title: PSsolver Catalogue identifier: ADPR_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADPR_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2302 No. of bytes in distributed program, including test data, etc.: 31962 Distribution format: tar.gz Programming language: Maple 14 (also tested using Maple 15 and 16). Computer: Intel Pentium Processor P6000, 1.86 GHz. Operating system: Windows 7. RAM: 4 GB DDR3 Memory Classification: 4.3. Catalogue identifier of previous version: ADPR_v1_0 Journal reference of previous version: Comput. Phys. Comm. 144 (2002) 46 Does the new version supersede the previous version?: Yes Nature of problem: Symbolic solution of first order differential equations via the Prelle-Singer method. Solution method: The method of solution is based on the standard Prelle-Singer method, with extensions for the cases when the FOODE contains elementary functions. Additionally, an extension of our own which solves FOODEs with Liouvillian solutions is included. Reasons for new version: The program was not running anymore due to changes in the latest versions of Maple. Additionally, we corrected/changed some bugs/details that were hampering the smoother functioning of the routines. Summary
International Nuclear Information System (INIS)
Zhu, Wu; Fang, Jian-an; Tang, Yang; Zhang, Wenbing; Xu, Yulong
2012-01-01
In this Letter, a differential evolution variant, called switching DE (SDE), has been employed to estimate the orders and parameters in incommensurate fractional-order chaotic systems. The proposed algorithm includes a switching population utilization strategy, where the population size is adjusted dynamically based on the solution-searching status. Thus, this adaptive control method realizes the identification of fractional-order Lorenz, Lü and Chen systems in both deterministic and stochastic environments, respectively. Numerical simulations are provided, where comparisons are made with five other State-of-the-Art evolutionary algorithms (EAs) to verify the effectiveness of the proposed method. -- Highlights: ► Switching population utilization strategy is applied for differential evolution. ► The parameters are estimated in both deterministic and stochastic environments. ► Comparisons with five other EAs verify the effectiveness of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Zhu, Wu, E-mail: dtzhuwu@gmail.com [College of Information Science and Technology, Donghua University, Shanghai 201620 (China); Fang, Jian-an [College of Information Science and Technology, Donghua University, Shanghai 201620 (China); Tang, Yang, E-mail: yang.tang@pik-potsdam.de [Institute of Physics, Humboldt University, Berlin 12489 (Germany); Potsdam Institute for Climate Impact Research, Potsdam 14415 (Germany); Research Institute for Intelligent Control and System, Harbin Institute of Technology, Harbin 150006 (China); Zhang, Wenbing [Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hong Kong (China); Xu, Yulong [College of Information Science and Technology, Donghua University, Shanghai 201620 (China)
2012-10-01
In this Letter, a differential evolution variant, called switching DE (SDE), has been employed to estimate the orders and parameters in incommensurate fractional-order chaotic systems. The proposed algorithm includes a switching population utilization strategy, where the population size is adjusted dynamically based on the solution-searching status. Thus, this adaptive control method realizes the identification of fractional-order Lorenz, Lü and Chen systems in both deterministic and stochastic environments, respectively. Numerical simulations are provided, where comparisons are made with five other State-of-the-Art evolutionary algorithms (EAs) to verify the effectiveness of the proposed method. -- Highlights: ► Switching population utilization strategy is applied for differential evolution. ► The parameters are estimated in both deterministic and stochastic environments. ► Comparisons with five other EAs verify the effectiveness of the proposed method.
International Nuclear Information System (INIS)
Pradeep, R Gladwin; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M
2011-01-01
In this paper, we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries, we obtain reduction transformations and reduced equations to specific examples. We find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second-order nonlinear ODEs. (paper)
Security Analysis of 7-Round MISTY1 against Higher Order Differential Attacks
Tsunoo, Yukiyasu; Saito, Teruo; Shigeri, Maki; Kawabata, Takeshi
MISTY1 is a 64-bit block cipher that has provable security against differential and linear cryptanalysis. MISTY1 is one of the algorithms selected in the European NESSIE project, and it has been recommended for Japanese e-Government ciphers by the CRYPTREC project. This paper shows that higher order differential attacks can be successful against 7-round versions of MISTY1 with FL functions. The attack on 7-round MISTY1 can recover a partial subkey with a data complexity of 254.1 and a computational complexity of 2120.8, which signifies the first successful attack on 7-round MISTY1 with no limitation such as a weak key. This paper also evaluates the complexity of this higher order differential attack on MISTY1 in which the key schedule is replaced by a pseudorandom function. It is shown that resistance to the higher order differential attack is not substantially improved even in 7-round MISTY1 in which the key schedule is replaced by a pseudorandom function.
All-optical temporal fractional order differentiator using an in-fiber ellipsoidal air-microcavity
Zhang, Lihong; Sun, Shuqian; Li, Ming; Zhu, Ninghua
2017-12-01
An all-optical temporal fractional order differentiator with ultrabroad bandwidth (~1.6 THz) and extremely simple fabrication is proposed and experimentally demonstrated based on an in-fiber ellipsoidal air-microcavity. The ellipsoidal air-microcavity is fabricated by splicing a single mode fiber (SMF) and a photonic crystal fiber (PCF) together using a simple arc-discharging technology. By changing the arc-discharging times, the propagation loss can be adjusted and then the differentiation order is tuned. A nearly Gaussian-like optical pulse with 3 dB bandwidth of 8 nm is launched into the differentiator and a 0.65 order differentiation of the input pulse is achieved with a processing error of 2.55%. Project supported by the the National Natural Science Foundation of China (Nos. 61522509, 61377002, 61535012), the National High-Tech Research & Development Program of China (No. SS2015AA011002), and the Beijing Natural Science Foundation (No. 4152052). Ming Li was supported in part by the Thousand Young Talent Program.
LSODE, 1. Order Stiff or Non-Stiff Ordinary Differential Equations System Initial Value Problems
International Nuclear Information System (INIS)
Hindmarsh, A.C.; Petzold, L.R.
2005-01-01
1 - Description of program or function: LSODE (Livermore Solver for Ordinary Differential Equations) solves stiff and non-stiff systems of the form dy/dt = f. In the stiff case, it treats the Jacobian matrix df/dy as either a dense (full) or a banded matrix, and as either user-supplied or internally approximated by difference quotients. It uses Adams methods (predictor-corrector) in the non-stiff case, and Backward Differentiation Formula (BDF) methods (the Gear methods) in the stiff case. The linear systems that arise are solved by direct methods (LU factor/solve). The LSODE source is commented extensively to facilitate modification. Both a single-precision version and a double-precision version are available. 2 - Methods: It is assumed that the ODEs are given explicitly, so that the system can be written in the form dy/dt = f(t,y), where y is the vector of dependent variables, and t is the independent variable. LSODE contains two variable-order, variable- step (with interpolatory step-changing) integration methods. The first is the implicit Adams or non-stiff method, of orders one through twelve. The second is the backward differentiation or stiff method (or BDF method, or Gear's method), of orders one through five. 3 - Restrictions on the complexity of the problem: The differential equations must be given in explicit form, i.e., dy/dt = f(y,t). Problems with intermittent high-speed transients may cause inefficient or unstable performance
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.
Priya, B. Ganesh; Muthukumar, P.
2018-02-01
This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.
Lie group classification of first-order delay ordinary differential equations
Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel
2018-05-01
A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.
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
Lattice Boltzmann model for high-order nonlinear partial differential equations
Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang
2018-01-01
In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.
Lattice Boltzmann model for high-order nonlinear partial differential equations.
Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang
2018-01-01
In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.
Implementation of fractional order integrator/differentiator on field programmable gate array
K.P.S. Rana; V. Kumar; N. Mittra; N. Pramanik
2016-01-01
Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus. For the past two decades, applications of fractional order calculus, in system modeling, control and signal processing, have grown rapidly. This paper presents a systematic procedure for hardware implementation of the basic operators of fractio...
Optimality Conditions in Differentiable Vector Optimization via Second-Order Tangent Sets
International Nuclear Information System (INIS)
Jimenez, Bienvenido; Novo, Vicente
2004-01-01
We provide second-order necessary and sufficient conditions for a point to be an efficient element of a set with respect to a cone in a normed space, so that there is only a small gap between necessary and sufficient conditions. To this aim, we use the common second-order tangent set and the asymptotic second-order cone utilized by Penot. As an application we establish second-order necessary conditions for a point to be a solution of a vector optimization problem with an arbitrary feasible set and a twice Frechet differentiable objective function between two normed spaces. We also establish second-order sufficient conditions when the initial space is finite-dimensional so that there is no gap with necessary conditions. Lagrange multiplier rules are also given
Oscillation criteria for third order nonlinear delay differential equations with damping
Directory of Open Access Journals (Sweden)
Said R. Grace
2015-01-01
Full Text Available This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \\[\\label{*} \\left( r_{2}(t\\left( r_{1}(ty^{\\prime}(t\\right^{\\prime}\\right^{\\prime}+p(ty^{\\prime}(t+q(tf(y(g(t=0.\\tag{\\(\\ast\\}\\] In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007, 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010, 756-762], the authors established some sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates or converges to zero, provided that the second order equation \\[\\left( r_{2}(tz^{\\prime }(t\\right^{\\prime}+\\left(p(t/r_{1}(t\\right z(t=0\\tag{\\(\\ast\\ast\\}\\] is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates if equation (\\(\\ast\\ast\\ is nonoscillatory. We also establish results for the oscillation of equation (\\(\\ast\\ when equation (\\(\\ast\\ast\\ is oscillatory.
An ethnographic study of differentiated practice in an operating room.
Graff, C; Roberts, K; Thornton, K
1999-01-01
An ethnographic study was conducted to investigate implementation of the clinical nurse III or team leader (TL) role as part of a newly executed nursing differentiated practice model. The six TLs studied were employed in the operating room (OR). Through participant observation, interviews, and document analysis, the TL role--as well as perceptions of the role by the TLs and OR staff--were studied. Problems related to performance of the role and its evolutionary process were delineated. Data analysis involved identifying categories and subcategories of data and developing a coding system to identify themes. Salient themes were related to the culture of the OR. Because of the OR's highly technical environment, the TLs defined their roles in relation to the organizational and technical needs of their surgical service. Refinement of surgeon "preference cards" and "instrument count sheets" was considered the initial priority for the TLs. Various controllable and uncontrollable factors were identified that affected implementation of the new TL role. Findings suggest that introduction of the role requires insight into setting and an emphasis on staging and orientation of employees to the new role.
Periodic solutions of first-order functional differential equations in population dynamics
Padhi, Seshadev; Srinivasu, P D N
2014-01-01
This book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied to study the existence of two or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowflies model, and some models with Allee effects. Many interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the global appeal of solutions to the models considered in the earlier chapters. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students and researchers in the field of differential equations with applications to biology, ecology, a...
Domains of pseudo-differential operators: a case for the Triebel-Lizorkin spaces
Directory of Open Access Journals (Sweden)
Jon Johnsen
2005-01-01
Full Text Available The main result is that every pseudo-differential operator of type 1, 1 and order d is continuous from the Triebel-Lizorkin space Fp,1d to Lp, 1≤p≺∞, and that this is optimal within the Besov and Triebel-Lizorkin scales. The proof also leads to the known continuity for s≻d, while for all real s the sufficiency of Hörmander's condition on the twisted diagonal is carried over to the Besov and Triebel-Lizorkin framework. To obtain this, type 1, 1-operators are extended to distributions with compact spectrum, and Fourier transformed operators of this type are on such distributions proved to satisfy a support rule, generalising the rule for convolutions. Thereby the use of reduced symbols, as introduced by Coifman and Meyer, is replaced by direct application of the paradifferential methods. A few flaws in the literature have been detected and corrected.
Kepner, Gordon R
2010-04-13
The numerous natural phenomena that exhibit saturation behavior, e.g., ligand binding and enzyme kinetics, have been approached, to date, via empirical and particular analyses. This paper presents a mechanism-free, and assumption-free, second-order differential equation, designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation, based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. For the general saturation curve, described in terms of its independent (x) and dependent (y) variables, a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free, which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena, the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases, including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants, in terms of the variables pertinent to the phenomenon under study. The second-order differential equation revealed the basic underlying relations that describe these saturation phenomena, and the basic mathematical properties of the standard experimental data plot. It was shown how to integrate this differential equation, and define the common basic properties of these phenomena. The results regarding the importance of the slope and the new perspectives on the empirical
Fractional Order Stochastic Differential Equation with Application in European Option Pricing
Directory of Open Access Journals (Sweden)
Qing Li
2014-01-01
Full Text Available Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study.
International Nuclear Information System (INIS)
Li Xicheng; Xu Mingyu; Wang Shaowei
2008-01-01
In this paper, we give similarity solutions of partial differential equations of fractional order with a moving boundary condition. The solutions are given in terms of a generalized Wright function. The time-fractional Caputo derivative and two types of space-fractional derivatives are considered. The scale-invariant variable and the form of the solution of the moving boundary are obtained by the Lie group analysis. A comparison between the solutions corresponding to two types of fractional derivative is also given
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
Energy Technology Data Exchange (ETDEWEB)
El-Sayed, A.M.A. [Faculty of Science University of Alexandria (Egypt)]. E-mail: amasyed@hotmail.com; Gaber, M. [Faculty of Education Al-Arish, Suez Canal University (Egypt)]. E-mail: mghf408@hotmail.com
2006-11-20
The Adomian decomposition method has been successively used to find the explicit and numerical solutions of the time fractional partial differential equations. A different examples of special interest with fractional time and space derivatives of order {alpha}, 0<{alpha}=<1 are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of {alpha} are shown graphically for some examples.
2018-03-14
UNIVERSITY OF TECHNOLOGY Final Report 03/14/2018 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research (AFOSR...optimal control problems involving fractional-order differential equations Wang, Song Curtin University of Technology Kent Street, Bentley WA6102...Article history : Received 3 October 2016 Accepted 26 March 2017 Available online 29 April 2017 Keywords: Hamilton–Jacobi–Bellman equation Financial
Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems
Directory of Open Access Journals (Sweden)
Hai Zhang
2014-01-01
Full Text Available We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.
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
The solutions of second-order linear differential systems with constant delays
Diblík, Josef; Svoboda, Zdeněk
2017-07-01
The representations of solutions to initial problems for non-homogenous n-dimensional second-order differential equations with delays x″(t )-2 A x'(t -τ )+(A2+B2)x (t -2 τ )=f (t ) by means of special matrix delayed functions are derived. Square matrices A and B are commuting and τ > 0. Derived representations use what is called a delayed exponential of a matrix and results generalize some of known results previously derived for homogenous systems.
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
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
Directory of Open Access Journals (Sweden)
Fairouz Zouyed
2015-01-01
Full Text Available This paper discusses the inverse problem of determining an unknown source in a second order differential equation from measured final data. This problem is ill-posed; that is, the solution (if it exists does not depend continuously on the data. In order to solve the considered problem, an iterative method is proposed. Using this method a regularized solution is constructed and an a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method.
Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel
2018-05-01
A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.
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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.
Energy Technology Data Exchange (ETDEWEB)
Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)
2013-09-02
We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.
BRST-operator for quantum Lie algebra and differential calculus on quantum groups
International Nuclear Information System (INIS)
Isaev, A.P.; Ogievetskij, O.V.
2001-01-01
For A Hopf algebra one determined structure of differential complex in two dual external Hopf algebras: A external expansion and in A* dual algebra external expansion. The Heisenberg double of these two Hopf algebras governs the differential algebra for the Cartan differential calculus on A algebra. The forst differential complex is the analog of the de Rame complex. The second complex coincide with the standard complex. Differential is realized as (anti)commutator with Q BRST-operator. Paper contains recursion relation that determines unequivocally Q operator. For U q (gl(N)) Lie quantum algebra one constructed BRST- and anti-BRST-operators and formulated the theorem of the Hodge expansion [ru
Design of fractional order differentiator using type-III and type-IV discrete cosine transform
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Manjeet Kumar
2017-02-01
Full Text Available In this paper, an interpolation method based on discrete cosine transform (DCT is employed for digital finite impulse response-fractional order differentiator (FIR-FOD design. Here, a fractional order digital differentiator is modeled as finite impulse response (FIR system to get an optimized frequency response that approximates the ideal response of a fractional order differentiator. Next, DCT-III and DCT-IV are utilized to determine the filter coefficients of FIR filter that compute the Fractional derivative of a given signal. To improve the frequency response of the proposed FIR-FOD, the filter coefficients are further modified using windows. Several design examples are presented to demonstrate the superiority of the proposed method. The simulation results have also been compared with the existing FIR-FOD design methods such as DFT interpolation, radial basis function (RBF interpolation, DCT-II interpolation and DST interpolation methods. The result reveals that the proposed FIR-FOD design technique using DCT-III and DCT-IV outperforms DFT interpolation, RBF interpolation, DCT-II interpolation and DST interpolation methods in terms of magnitude error.
Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations
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Maamar Andasmas
2016-04-01
Full Text Available The main purpose of this article is to investigate the growth of meromorphic solutions to homogeneous and non-homogeneous second order linear differential equations f00+Af0+Bf = F, where A(z, B (z and F (z are meromorphic functions with finite order having only finitely many poles. We show that, if there exist a positive constants σ > 0, α > 0 such that |A(z| ≥ eα|z|σ as |z| → +∞, z ∈ H, where dens{|z| : z ∈ H} > 0 and ρ = max{ρ(B, ρ(F} < σ, then every transcendental meromorphic solution f has an infinite order. Further, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros.
Directory of Open Access Journals (Sweden)
Waleed M. Abd-Elhameed
2016-09-01
Full Text Available Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fibonacci expansion were carefully investigated. Some numerical examples with comparisons are presented to ensure the efficiency, applicability and high accuracy of the proposed algorithms. Two accurate semi-analytic polynomial solutions for linear and nonlinear fractional differential equations are the result.
Limit cycles via higher order perturbations for some piecewise differential systems
Buzzi, Claudio A.; Lima, Maurício Firmino Silva; Torregrosa, Joan
2018-05-01
A classical perturbation problem is the polynomial perturbation of the harmonic oscillator, (x‧ ,y‧) =(- y + εf(x , y , ε) , x + εg(x , y , ε)) . In this paper we study the limit cycles that bifurcate from the period annulus via piecewise polynomial perturbations in two zones separated by a straight line. We prove that, for polynomial perturbations of degree n , no more than Nn - 1 limit cycles appear up to a study of order N. We also show that this upper bound is reached for orders one and two. Moreover, we study this problem in some classes of piecewise Liénard differential systems providing better upper bounds for higher order perturbation in ε, showing also when they are reached. The Poincaré-Pontryagin-Melnikov theory is the main technique used to prove all the results.
High-order fractional partial differential equation transform for molecular surface construction.
Hu, Langhua; Chen, Duan; Wei, Guo-Wei
2013-01-01
Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model
Directory of Open Access Journals (Sweden)
Athanasios D. Karageorgos
2009-01-01
Full Text Available In many applications, and generally speaking in many dynamical differential systems, the problem of transferring the initial state of the system to a desired state in (almost zero-time time is desirable but difficult to achieve. Theoretically, this can be achieved by using a linear combination of Dirac -function and its derivatives. Obviously, such an input is physically unrealizable. However, we can think of it approximately as a combination of small pulses of very high magnitude and infinitely small duration. In this paper, the approximation process of the distributional behaviour of higher-order linear descriptor (regular differential systems is presented. Thus, new analytical formulae based on linear algebra methods and generalized inverses theory are provided. Our approach is quite general and some significant conditions are derived. Finally, a numerical example is presented and discussed.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.
On the algebra of deformed differential operators, and induced integrable Toda field theory
International Nuclear Information System (INIS)
Hssaini, M.; Kessabi, M.; Maroufi, B.; Sedra, M.B.
2000-07-01
We build in this paper the algebra of q-deformed pseudo-differential operators shown to be an essential step towards setting a q-deformed integrability program. In fact, using the results of this q-deformed algebra, we derive the q-analogues of the generalised KdV hierarchy. We focus in particular the first leading orders of this q-deformed hierarchy namely the q-KdV and q-Boussinesq integrable systems. We also present the q-generalisation of the conformal transformations of the currents u n , n ≥ 2 and discuss the primary condition of the fields w n , n ≥ 2 by using the Volterra gauge group transformations for the q-covariant Lax operators. An induced su(n)-Toda(su(2)-Liouville) field theory construction is discussed and other important features are presented. (author)
Operator ordering in quantum optics theory and the development of Dirac's symbolic method
International Nuclear Information System (INIS)
Fan Hongyi
2003-01-01
We present a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering (or symmetric ordering)) by fashioning Dirac's symbolic method and representation theory. We propose the technique of integration within an ordered product (IWOP) of operators to realize our goal. The IWOP makes Dirac's representation theory and the symbolic method more transparent and consequently more easily understood. The beauty of Dirac's symbolic method is further revealed. Various applications of the IWOP technique, such as in developing the entangled state representation theory, nonlinear coherent state theory, Wigner function theory, etc, are presented. (review article)
Estimation of periodic solutions number of first-order differential equations
Ivanov, Gennady; Alferov, Gennady; Gorovenko, Polina; Sharlay, Artem
2018-05-01
The paper deals with first-order differential equations under the assumption that the right-hand side is a periodic function of time and continuous in the set of arguments. Pliss V.A. obtained the first results for a particular class of equations and showed that a number of theorems can not be continued. In this paper, it was possible to reduce the restrictions on the degree of smoothness of the right-hand side of the equation and obtain upper and lower bounds on the number of possible periodic solutions.
Sturm-Picone type theorems for second-order nonlinear differential equations
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Aydin Tiryaki
2014-06-01
Full Text Available The aim of this article is to give Sturm-Picone type theorems for the pair of second-order nonlinear differential equations $$\\displaylines{ (p_1(t|x'|^{\\alpha-1}x''+q_1(tf_1(x=0 \\cr (p_2(t|y'|^{\\alpha-1}y''+q_2(tf_2(y=0,\\quad t_1
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.
On Delay-Independent Criteria for Oscillation of Higher-Order Functional Differential Equations
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Yuangong Sun
2011-01-01
Full Text Available We investigate the oscillation of the following higher-order functional differential equation: x(n(t+q(t|x(t-τ|λ-1x(t-τ=e(t, where q(t and e(t are continuous functions on [t0,∞, 1>λ>0 and τ≠0 are constants. Unlike most of delay-dependent oscillation results in the literature, two delay-independent oscillation criteria for the equation are established in both the case τ>0 and the case τ<0 under the assumption that the potentials q(t and e(t change signs on [t0,∞.
International Nuclear Information System (INIS)
Luks, A.; Perinova, V.
1993-01-01
A suitable ordering of phase exponential operators has been compared with the antinormal ordering of the annihilation and creation operators of a single mode optical field. The extended Wigner function for number and phase in the enlarged Hilbert space has been used for the derivation of the Wigner function for number and phase in the original Hilbert space. (orig.)
Oscillation of two-dimensional linear second-order differential systems
International Nuclear Information System (INIS)
Kwong, M.K.; Kaper, H.G.
1985-01-01
This article is concerned with the oscillatory behavior at infinity of the solution y: [a, ∞) → R 2 of a system of two second-order differential equations, y''(t) + Q(t) y(t) = 0, t epsilon[a, ∞); Q is a continuous matrix-valued function on [a, ∞) whose values are real symmetric matrices of order 2. It is shown that the solution is oscillatory at infinity if the largest eigenvalue of the matrix integral/sub a//sup t/ Q(s) ds tends to infinity as t → ∞. This proves a conjecture of D. Hinton and R.T. Lewis for the two-dimensional case. Furthermore, it is shown that considerably weaker forms of the condition still suffice for oscillatory behavior at infinity. 7 references
International Nuclear Information System (INIS)
Paris, R.B.; Wood, A.D.
1984-11-01
The asymptotic expansions of solutions of a class of linear ordinary differential equations of arbitrary order n, containing a factor zsup(m) multiplying the lower order derivatives, are investigated for large values of z in the complex plane. Four classes of solutions are considered which exhibit the following behaviour as /z/ → infinity in certain sectors: (i) solutions whose behaviour is either exponentially large or algebraic (involving p ( < n) algebraic expansions), (ii) solutions which are exponentially small (iii) solutions with a single algebraic expansion and (iv) solutions which are even and odd functions of z whenever n+m is even. The asymptotic expansions of these solutions in a full neigbourhood of the point at infinity are obtained by means of the theory of the solutions in the case m=O developed in a previous paper
International Nuclear Information System (INIS)
He Qiu-Yan; Yuan Xiao; Yu Bo
2017-01-01
The performance analysis of the generalized Carlson iterating process, which can realize the rational approximation of fractional operator with arbitrary order, is presented in this paper. The reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained. K-index, P-index, O-index, and complexity index are introduced to contribute to performance analysis. Considering nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order, these rational approximation impedance functions calculated by the iterating function meet computational rationality, positive reality, and operational validity. Then they are capable of having the operational performance of fractional operators and being physical realization. The approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited. (paper)
29 CFR 570.62 - Occupations involved in the operation of bakery machines (Order 11).
2010-07-01
... 29 Labor 3 2010-07-01 2010-07-01 false Occupations involved in the operation of bakery machines... Health or Well-Being § 570.62 Occupations involved in the operation of bakery machines (Order 11). Link... following occupations involved in the operation of power-driven bakery machines are particularly hazardous...
International Nuclear Information System (INIS)
Leaf, G.K.; Minkoff, M.
1982-01-01
1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code
Directory of Open Access Journals (Sweden)
Ana M. Cortizo
2016-01-01
Full Text Available Bone and cartilage regeneration can be improved by designing a functionalized biomaterial that includes bioactive drugs in a biocompatible and biodegradable scaffold. Based on our previous studies, we designed a vanadium-loaded collagen scaffold for osteochondral tissue engineering. Collagen-vanadium loaded scaffolds were characterized by SEM, FTIR, and permeability studies. Rat bone marrow progenitor cells were plated on collagen or vanadium-loaded membranes to evaluate differences in cell attachment, growth and osteogenic or chondrocytic differentiation. The potential cytotoxicity of the scaffolds was assessed by the MTT assay and by evaluation of morphological changes in cultured RAW 264.7 macrophages. Our results show that loading of VOAsc did not alter the grooved ordered structure of the collagen membrane although it increased membrane permeability, suggesting a more open structure. The VOAsc was released to the media, suggesting diffusion-controlled drug release. Vanadium-loaded membranes proved to be a better substratum than C0 for all evaluated aspects of BMPC biocompatibility (adhesion, growth, and osteoblastic and chondrocytic differentiation. In addition, there was no detectable effect of collagen or vanadium-loaded scaffolds on macrophage viability or cytotoxicity. Based on these findings, we have developed a new ordered collagen scaffold loaded with VOAsc that shows potential for osteochondral tissue engineering.
Differential Higgs boson pair production at next-to-next-to-leading order in QCD
International Nuclear Information System (INIS)
Florian, Daniel de; Mazzitelli, Javier; Grazzini, Massimiliano; Hanga, Catalin; Lindert, Jonas M.; Kallweit, Stefan; Maierhoefer, Philipp; Rathlev, Dirk
2016-06-01
We report on the first fully differential calculation for double Higgs boson production through gluon fusion in hadron collisions up to next-to-next-to-leading order (NNLO) in QCD perturbation theory. The calculation is performed in the heavy-top limit of the Standard Model, and in the phenomenological results we focus on pp collisions at √(s)=14 TeV. We present differential distributions through NNLO for various observables including the transverse-momentum and rapidity distributions of the two Higgs bosons. NNLO corrections are at the level of 10%-25% with respect to the next-to-leading order (NLO) prediction with a residual scale uncertainty of 5%-15% and an overall mild phase-space dependence. Only at NNLO the perturbative expansion starts to converge yielding overlapping scale uncertainty bands between NNLO and NLO in most of the phase-space. The calculation includes NLO predictions for pp→HH+jet+X. Corrections to the corresponding distributions exceed 50% with a residual scale dependence of 20%-30%.
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Jaroslav Jaroš
2015-01-01
Full Text Available We consider \\(n\\-dimensional cyclic systems of second order differential equations \\[(p_i(t|x_{i}'|^{\\alpha_i -1}x_{i}'' = q_{i}(t|x_{i+1}|^{\\beta_i-1}x_{i+1},\\] \\[\\quad i = 1,\\ldots,n, \\quad (x_{n+1} = x_1 \\tag{\\(\\ast\\}\\] under the assumption that the positive constants \\(\\alpha_i\\ and \\(\\beta_i\\ satisfy \\(\\alpha_1{\\ldots}\\alpha_n \\gt \\beta_1{\\ldots}\\beta_n\\ and \\(p_i(t\\ and \\(q_i(t\\ are regularly varying functions, and analyze positive strongly increasing solutions of system (\\(\\ast\\ in the framework of regular variation. We show that the situation for the existence of regularly varying solutions of positive indices for (\\(\\ast\\ can be characterized completely, and moreover that the asymptotic behavior of such solutions is governed by the unique formula describing their order of growth precisely. We give examples demonstrating that the main results for (\\(\\ast\\ can be applied to some classes of partial differential equations with radial symmetry to acquire accurate information about the existence and the asymptotic behavior of their radial positive strongly increasing solutions.
A modification of \\mathsf {WKB} method for fractional differential operators of Schrödinger's type
Sayevand, K.; Pichaghchi, K.
2017-09-01
In this paper, we were concerned with the description of the singularly perturbed differential equations within the scope of fractional calculus. However, we shall note that one of the main methods used to solve these problems is the so-called WKB method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the WKB to the scope of fractional derivative, we proposed a relatively new derivative called the local fractional derivative. By use of properties of local fractional derivative, we extend the WKB method in the scope of the fractional differential equation. By means of this extension, the WKB analysis based on the Borel resummation, for fractional differential operators of WKB type are investigated. The convergence and the Mittag-Leffler stability of the proposed approach is proven. The obtained results are in excellent agreement with the existing ones in open literature and it is shown that the present approach is very effective and accurate. Furthermore, we are mainly interested to construct the solution of fractional Schrödinger equation in the Mittag-Leffler form and how it leads naturally to this semi-classical approximation namely modified WKB.
Higher-order stochastic differential equations and the positive Wigner function
Drummond, P. D.
2017-12-01
General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.
Some properties for integro-differential operator defined by a fractional formal.
Abdulnaby, Zainab E; Ibrahim, Rabha W; Kılıçman, Adem
2016-01-01
Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.
Frechet differentiation of nonlinear operators between fuzzy normed spaces
International Nuclear Information System (INIS)
Yilmaz, Yilmaz
2009-01-01
By the rapid advances in linear theory of fuzzy normed spaces and fuzzy bounded linear operators it is natural idea to set and improve its nonlinear peer. We aimed in this work to realize this idea by introducing fuzzy Frechet derivative based on the fuzzy norm definition in Bag and Samanta [Bag T, Samanta SK. Finite dimensional fuzzy normed linear spaces. J Fuzzy Math 2003;11(3):687-705]. The definition is divided into two part as strong and weak fuzzy Frechet derivative so that it is compatible with strong and weak fuzzy continuity of operators. Also we restate fuzzy compact operator definition of Lael and Nouroizi [Lael F, Nouroizi K. Fuzzy compact linear operators. Chaos, Solitons and Fractals 2007;34(5):1584-89] as strongly and weakly fuzzy compact by taking into account the compatibility. We prove also that weak Frechet derivative of a nonlinear weakly fuzzy compact operator is also weakly fuzzy compact.
Differential operators associated with Gegenbauer polynomials - 3. The regular case
International Nuclear Information System (INIS)
Onyango-Otieno, V.P.
1989-07-01
We study the regular case of the Gegenbauer differential equation - ((1-x 2 ) v+1/2 y 1 (x)) 1 +v 2 (1-x 2 ) v-1/2 y(x) = λ(1-x 2 ) v-1/2 y(x), (x is an element of (-1,1),-1/2 w 2 (-1,1) and H p,q 2 (-1,1). (author). 13 refs
Belkhatir, Zehor
2015-11-05
This paper deals with the joint estimation of the unknown input and the fractional differentiation orders of a linear fractional order system. A two-stage algorithm combining the modulating functions with a first-order Newton method is applied to solve this estimation problem. First, the modulating functions approach is used to estimate the unknown input for a given fractional differentiation orders. Then, the method is combined with a first-order Newton technique to identify the fractional orders jointly with the input. To show the efficiency of the proposed method, numerical examples illustrating the estimation of the neural activity, considered as input of a fractional model of the neurovascular coupling, along with the fractional differentiation orders are presented in both noise-free and noisy cases.
Directory of Open Access Journals (Sweden)
Sufia Zulfa Ahmad
2016-01-01
Full Text Available We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.
International Nuclear Information System (INIS)
Tran Duc Van
1994-01-01
The notion of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations is presented, some uniqueness theorems and a stability result are established by the method based on the theory of differential inclusions. In particular, the answer to an open problem of S.N. Kruzhkov is given. (author). 10 refs, 1 fig
Effective quadrature formula in solving linear integro-differential equations of order two
Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.
2017-08-01
In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.
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.
Partial differential equations of first order and their applications to physics
López, Gustavo
2012-01-01
This book tries to point out the mathematical importance of the Partial Differential Equations of First Order (PDEFO) in Physics and Applied Sciences. The intention is to provide mathematicians with a wide view of the applications of this branch in physics, and to give physicists and applied scientists a powerful tool for solving some problems appearing in Classical Mechanics, Quantum Mechanics, Optics, and General Relativity. This book is intended for senior or first year graduate students in mathematics, physics, or engineering curricula. This book is unique in the sense that it covers the applications of PDEFO in several branches of applied mathematics, and fills the theoretical gap between the formal mathematical presentation of the theory and the pure applied tool to physical problems that are contained in other books. Improvements made in this second edition include corrected typographical errors; rewritten text to improve the flow and enrich the material; added exercises in all chapters; new applicati...
Oscillation criteria for second order Emden-Fowler functional differential equations of neutral type
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Yingzhu Wu
2016-12-01
Full Text Available Abstract In this article, some new oscillation criterion for the second order Emden-Fowler functional differential equation of neutral type ( r ( t | z ′ ( t | α − 1 z ′ ( t ′ + q ( t | x ( σ ( t | β − 1 x ( σ ( t = 0 , $$\\bigl(r(t\\bigl\\vert z^{\\prime}(t\\bigr\\vert ^{\\alpha-1}z^{\\prime}(t \\bigr^{\\prime}+q(t\\bigl\\vert x\\bigl(\\sigma(t\\bigr\\bigr\\vert ^{\\beta-1}x \\bigl(\\sigma(t \\bigr=0, $$ where z ( t = x ( t + p ( t x ( τ ( t $z(t=x(t+p(tx(\\tau(t$ , α > 0 $\\alpha>0$ and β > 0 $\\beta>0$ are established. Our results improve some well-known results which were published recently in the literature. Some illustrating examples are also provided to show the importance of our results.
Directory of Open Access Journals (Sweden)
Zhonghai Guo
2012-01-01
Full Text Available We study the following second order mixed nonlinear impulsive differential equations with delay (r(tΦα(x′(t′+p0(tΦα(x(t+∑i=1npi(tΦβi(x(t-σ=e(t, t≥t0, t≠τk,x(τk+=akx(τk, x'(τk+=bkx'(τk, k=1,2,…, where Φ*(u=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence, and τk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.
International Nuclear Information System (INIS)
Srivastava, A.C.; Hazarika, G.C.
1990-01-01
An algorithm based on the shooting method has been developed for the solution of a two-point boundary value problem consisting of a system of third order simultaneous ordinary differential equations. The Falkner-Skan equations for electrically conducting viscous fluid with applied magnetic field has been solved by using this algorithm for various values of the wedge angle and magnetic parameters. The shooting method seems to be well convergent for a system as the results are in good agreement with those obtained by other methods. It is observed that both viscous boundary layer and magnetic boundary layer decrease while velocity as well as magnetic field increase with the increase of the wedge angle. (author). 6 tabs., 7 refs
Periodic solutions of Lienard differential equations via averaging theory of order two.
Llibre, Jaume; Novaes, Douglas D; Teixeira, Marco A
2015-01-01
For ε ≠ 0 sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x'' + f (x) x' + n2x + g (x) = ε2p1 (t) + ε3 p2(t), where n is a positive integer, f : ℝ → ℝ is a C 3 function, g : ℝ → ℝ is a C 4 function, and p i : ℝ → ℝ for i = 1, 2 are continuous 2π-periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.
Periodic solutions of Lienard differential equations via averaging theory of order two
Directory of Open Access Journals (Sweden)
JAUME LLIBRE
2015-12-01
Full Text Available Abstract For ε ≠ 0sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x ′′ + f ( x x ′ + n 2 x + g ( x = ε 2 p 1 ( t + ε 3 p 2 ( t , where n is a positive integer, f : ℝ → ℝis a C 3function, g : ℝ → ℝis a C 4function, and p i : ℝ → ℝfor i = 1 , 2are continuous 2 π–periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained.
International Nuclear Information System (INIS)
Kinoshita, Takehiro; Fujiyama, Shinya; Idogaki, Toshihiro; Tokita, Masahiko
2009-01-01
The non-equilibrium phase transition in a ferromagnetic Ising model is investigated by use of a new type of effective field theory (EFT) which correctly accounts for all the single-site kinematic relations by differential operator technique. In the presence of a time dependent oscillating external field, with decrease of the temperature the system undergoes a dynamic phase transition, which is characterized by the period averaged magnetization Q, from a dynamically disordered state Q = 0 to the dynamically ordered state Q ≠ 0. The results of the dynamic phase transition point T c determined from the behavior of the dynamic magnetization and the Liapunov exponent provided by EFT are improved than that of the standard mean field theory (MFT), especially for the one dimensional lattice where the standard MFT gives incorrect result of T c = 0 even in the case of zero external field.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.
Energy Technology Data Exchange (ETDEWEB)
Benci, V; Fortunato, D [Istituto di Matematica Applicata, Bari (Italy)
1981-04-21
Some self-adjoint operators, which are the Friedrichs realization in L/sup 2/ of a class of nonelliptic differential operators, are shown to have a positive, discrete spectrum. The results obtained are applied to study operators which occur in the dynamical description of some elementary particles.
Gil', M. I.
2005-08-01
We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.
Order release strategies to control outsourced operations in a supply chain
Boulaksil, Y.; Fransoo, J.C.
2007-01-01
In this paper, we propose and compare three different order release strategies to plan and control outsourced operations in a supply chian where the contract manfacturer is producing different variants of a certain product.
International Nuclear Information System (INIS)
Semenova, V.N.
2016-01-01
A boundary value problem for a nonlinear second order differential equation has been considered. A numerical method has been proposed to solve this problem using power series. Results of numerical experiments have been presented in the paper [ru
Ahmed M. A. El-Sayed; Ebtisam O. Bin-Taher
2011-01-01
In this article, we prove the existence of positive nondecreasing solutions for a multi-term fractional-order functional differential equations. We consider Cauchy boundary problems with: nonlocal conditions, two-point boundary conditions, integral conditions, and deviated arguments.
Molenaar, Dylan; Dolan, Conor V.; Wicherts, Jelte M.; van der Maas, Han L. J.
2010-01-01
The general differentiation hypothesis states that the strength of the correlations among a set of IQ subtests varies with a given variable. Instances of the general differentiation hypothesis that have been considered in the literature include age and ability differentiation. Traditionally, the differentiation effect is attributed to the varying…
Constructive Solution of Ellipticity Problem for the First Order Differential System
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Vladimir E. Balabaev
2017-01-01
Full Text Available We built first order elliptic systems with any possible number of unknown functions and the maximum possible number of unknowns, i.e, in general. These systems provide the basis for studying the properties of any first order elliptic systems. The study of the Cauchy-Riemann system and its generalizations led to the identification of a class of elliptic systems of first-order of a special structure. An integral representation of solutions is of great importance in the study of these systems. Only by means of a constructive method of integral representations we can solve a number of problems in the theory of elliptic systems related mainly to the boundary properties of solutions. The obtained integral representation could be applied to solve a number of problems that are hard to solve, if you rely only on the non-constructive methods. Some analogues of the theorems of Liouville, Weierstrass, Cauchy, Gauss, Morera, an analogue of Green’s formula are established, as well as an analogue of the maximum principle. The used matrix operators allow the new structural arrangement of the maximum number of linearly independent vector fields on spheres of any possible dimension. Also the built operators allow to obtain a constructive solution of the extended problem ”of the sum of squares” known in algebra.
International Nuclear Information System (INIS)
Fakhar, K.; Kara, A. H.
2012-01-01
We study the symmetries, conservation laws and reduction of third-order equations that evolve from a prior reduction of models that arise in fluid phenomena. These could be the ordinary differential equations (ODEs) that are reductions of partial differential equations (PDEs) or, alternatively, PDEs related to given ODEs. In this class, the analysis includes the well-known Blasius, Chazy, and other associated third-order ODEs. (general)
Nuclear axial current operators to fourth order in chiral effective field theory
Energy Technology Data Exchange (ETDEWEB)
Krebs, H., E-mail: hermann.krebs@rub.de [Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Epelbaum, E., E-mail: evgeny.epelbaum@rub.de [Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93016 (United States); Meißner, U.-G., E-mail: meissner@hiskp.uni-bonn.de [Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn (Germany); Institut für Kernphysik, Institute for Advanced Simulation, and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich (Germany); JARA - High Performance Computing, Forschungszentrum Jülich, D-52425 Jülich (Germany)
2017-03-15
We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators including the relevant relativistic corrections. We also verify explicitly the validity of the continuity equation.
The inverse spectral problem for pencils of differential operators
International Nuclear Information System (INIS)
Guseinov, I M; Nabiev, I M
2007-01-01
The inverse problem of spectral analysis for a quadratic pencil of Sturm-Liouville operators on a finite interval is considered. A uniqueness theorem is proved, a solution algorithm is presented, and sufficient conditions for the solubility of the inverse problem are obtained. Bibliography: 31 titles.
On differential operators generating iterative systems of linear ODEs of maximal symmetry algebra
Ndogmo, J. C.
2017-06-01
Although every iterative scalar linear ordinary differential equation is of maximal symmetry algebra, the situation is different and far more complex for systems of linear ordinary differential equations, and an iterative system of linear equations need not be of maximal symmetry algebra. We illustrate these facts by examples and derive families of vector differential operators whose iterations are all linear systems of equations of maximal symmetry algebra. Some consequences of these results are also discussed.
2010-09-17
... NUCLEAR REGULATORY COMMISSION [NRC-2010-0178; Docket No. 50-228; License No. R-98] In the Matter of Aerotest Operations, Inc. (Aerotest Radiography and Research Reactor); Order Extending the... possession, use, and operation of the Aerotest Radiography and Research Reactor (ARRR) located in San Ramon...
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Hossein Jafari
2016-04-01
Full Text Available In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.
Intrinsic-normal-ordered vertex operators from the multiloop N-tachyon amplitude
International Nuclear Information System (INIS)
Aldazabal, G.; Nunez, C.; Bonini, M.; Iengo, R.
1987-09-01
We construct vertex operators for arbitrary mass level states of the closed bosonic string. Starting from a generalization of the Koba-Nielsen amplitude which is suitable for an arbitrary genus Riemann surface, we read the vertex operators from the residues of the poles for the intermediate states. Since the original expression is metric independent and normal ordered without the need of inventing any regularization scheme, our vertex operators also possess these properties. We discuss their general features. (author). 17 refs
Managing Variety in Configure-to-Order Products - An Operational Method
DEFF Research Database (Denmark)
Myrodia, Anna; Hvam, Lars
2014-01-01
is to develop an operational method to analyze profitability of Configure-To-Order (CTO) products. The operational method consists of a four-step: analysis of product assortment, profitability analysis on configured products, market and competitor analysis and, product assortment scenarios analysis....... The proposed operational method is firstly developed based on both available literature and practitioners experience and subsequently tested on a company that produces CTO products. The results from this application are further discussed and opportunities for further research identified....
Low rank approach to computing first and higher order derivatives using automatic differentiation
International Nuclear Information System (INIS)
Reed, J. A.; Abdel-Khalik, H. S.; Utke, J.
2012-01-01
This manuscript outlines a new approach for increasing the efficiency of applying automatic differentiation (AD) to large scale computational models. By using the principles of the Efficient Subspace Method (ESM), low rank approximations of the derivatives for first and higher orders can be calculated using minimized computational resources. The output obtained from nuclear reactor calculations typically has a much smaller numerical rank compared to the number of inputs and outputs. This rank deficiency can be exploited to reduce the number of derivatives that need to be calculated using AD. The effective rank can be determined according to ESM by computing derivatives with AD at random inputs. Reduced or pseudo variables are then defined and new derivatives are calculated with respect to the pseudo variables. Two different AD packages are used: OpenAD and Rapsodia. OpenAD is used to determine the effective rank and the subspace that contains the derivatives. Rapsodia is then used to calculate derivatives with respect to the pseudo variables for the desired order. The overall approach is applied to two simple problems and to MATWS, a safety code for sodium cooled reactors. (authors)
Directory of Open Access Journals (Sweden)
Yunjiao Bai
2015-01-01
Full Text Available The traditional fourth-order nonlinear diffusion denoising model suffers the isolated speckles and the loss of fine details in the processed image. For this reason, a new fourth-order partial differential equation based on the patch similarity modulus and the difference curvature is proposed for image denoising. First, based on the intensity similarity of neighbor pixels, this paper presents a new edge indicator called patch similarity modulus, which is strongly robust to noise. Furthermore, the difference curvature which can effectively distinguish between edges and noise is incorporated into the denoising algorithm to determine the diffusion process by adaptively adjusting the size of the diffusion coefficient. The experimental results show that the proposed algorithm can not only preserve edges and texture details, but also avoid isolated speckles and staircase effect while filtering out noise. And the proposed algorithm has a better performance for the images with abundant details. Additionally, the subjective visual quality and objective evaluation index of the denoised image obtained by the proposed algorithm are higher than the ones from the related methods.
Diffusion with space memory modelled with distributed order space fractional differential equations
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M. Caputo
2003-06-01
Full Text Available Distributed order fractional differential equations (Caputo, 1995, 2001; Bagley and Torvik, 2000a,b were fi rst used in the time domain; they are here considered in the space domain and introduced in the constitutive equation of diffusion. The solution of the classic problems are obtained, with closed form formulae. In general, the Green functions act as low pass fi lters in the frequency domain. The major difference with the case when a single space fractional derivative is present in the constitutive equations of diffusion (Caputo and Plastino, 2002 is that the solutions found here are potentially more fl exible to represent more complex media (Caputo, 2001a. The difference between the space memory medium and that with the time memory is that the former is more fl exible to represent local phenomena while the latter is more fl exible to represent variations in space. Concerning the boundary value problem, the difference with the solution of the classic diffusion medium, in the case when a constant boundary pressure is assigned and in the medium the pressure is initially nil, is that one also needs to assign the fi rst order space derivative at the boundary.
Pirnapasov, Sardor; Karimov, Erkinjon
2017-01-01
In the present work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. We investigate a boundary value problem for fractional heat equation involving higher order Caputo-Fabrizio derivatives in time-variable. Using method of separation of variables and integration by parts, we reduce fractional order PDE to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
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Akira Shirai
2015-01-01
Full Text Available In this paper, we study the following nonlinear first order partial differential equation: \\[f(t,x,u,\\partial_t u,\\partial_x u=0\\quad\\text{with}\\quad u(0,x\\equiv 0.\\] The purpose of this paper is to determine the estimate of Gevrey order under the condition that the equation is singular of a totally characteristic type. The Gevrey order is indicated by the rate of divergence of a formal power series. This paper is a continuation of the previous papers [Convergence of formal solutions of singular first order nonlinear partial differential equations of totally characteristic type, Funkcial. Ekvac. 45 (2002, 187-208] and [Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type, Surikaiseki Kenkyujo Kokyuroku, Kyoto University 1431 (2005, 94-106]. Especially the last-mentioned paper is regarded as part I of this paper.
On computing Gröbner bases in rings of differential operators
Ma, Xiaodong; Sun, Yao; Wang, Dingkang
2011-05-01
Insa and Pauer presented a basic theory of Groebner basis for differential operators with coefficients in a commutative ring in 1998, and a criterion was proposed to determine if a set of differential operators is a Groebner basis. In this paper, we will give a new criterion such that Insa and Pauer's criterion could be concluded as a special case and one could compute the Groebner basis more efficiently by this new criterion.
Beshtokov, M. Kh.
2017-12-01
Boundary value problems for loaded third-order pseudo-parabolic equations with variable coefficients are considered. A priori estimates for the solutions of the problems in the differential and difference formulations are obtained. These a priori estimates imply the uniqueness and stability of the solution with respect to the initial data and the right-hand side on a layer, as well as the convergence of the solution of each difference problem to the solution of the corresponding differential problem.
An abstract approach to some spectral problems of direct sum differential operators
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Maksim S. Sokolov
2003-07-01
Full Text Available In this paper, we study the common spectral properties of abstract self-adjoint direct sum operators, considered in a direct sum Hilbert space. Applications of such operators arise in the modelling of processes of multi-particle quantum mechanics, quantum field theory and, specifically, in multi-interval boundary problems of differential equations. We show that a direct sum operator does not depend in a straightforward manner on the separate operators involved. That is, on having a set of self-adjoint operators giving a direct sum operator, we show how the spectral representation for this operator depends on the spectral representations for the individual operators (the coordinate operators involved in forming this sum operator. In particular it is shown that this problem is not immediately solved by taking a direct sum of the spectral properties of the coordinate operators. Primarily, these results are to be applied to operators generated by a multi-interval quasi-differential system studied, in the earlier works of Ashurov, Everitt, Gesztezy, Kirsch, Markus and Zettl. The abstract approach in this paper indicates the need for further development of spectral theory for direct sum differential operators.
Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators
Lerner, Nicolas
2010-01-01
This book is devoted to the study of pseudo-differential operators, with special emphasis on non-selfadjoint operators, a priori estimates and localization in the phase space. We expose the most recent developments of the theory with its applications to local solvability and semi-classical estimates for nonselfadjoint operators. The first chapter is introductory and gives a presentation of classical classes of pseudo-differential operators. The second chapter is dealing with the general notion of metrics on the phase space. We expose some elements of the so-called Wick calculus and introduce g
Islam, Shofiq; Taylor, Christopher J; Ahmed, Siddiq; Ormiston, Ian W; Hayter, Jonathan P
2015-12-01
The authors explored consistency of the observed running order in operating sequence compared with prior scheduled listing. We analysed potential variables felt to be predictive in the chances of a patient having their procedure as previously scheduled. Data were retrospectively collected for a consecutive group of patients who underwent elective maxillofacial procedures over a four week period. The consistency of scheduled and observed running order was documented. We considered four independent variables (original list position, day of week, morning or afternoon list, seniority of surgeon) and analysed their relationship to the probability of a patient undergoing their operation as per listing. Logistic regression analysis was used to determine significant associations between predictor variables with an altered list order. Data were available for 35 lists (n = 133). 49% of lists were found to run according to prior given order, the remainder subject to some alteration. Logistic regression analysis showed a statistically significant association between original scheduled position and day of week, with list position consistency. Patients listed first were twelve times more likely to have their operation as listed compared to those placed fourth (OR 12.7, 95% CI 3.7-43, p lists at the start of a week were subject to less alteration (p lists showed some alteration to the previously printed order. It appears that being first on an elective list offers the greatest guarantee that a patient will have their operation as per prior schedule. It may be reasonable for clinicians to be mindful of potential operating list alterations when preparing their patients for elective surgery. Copyright © 2014 Royal College of Surgeons of Edinburgh (Scottish charity number SC005317) and Royal College of Surgeons in Ireland. Published by Elsevier Ltd. All rights reserved.
Analyzing a stochastic time series obeying a second-order differential equation.
Lehle, B; Peinke, J
2015-06-01
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second-order differential equation can be analyzed this way by employing a particular embedding approach: To obtain a Markovian process in 2N dimensions from a non-Markovian signal in N dimensions, the system is described in a phase space that is extended by the temporal derivative of the signal. For a discrete time series, however, this derivative can only be calculated by a differencing scheme, which introduces an error. If the effects of this error are not accounted for, this leads to systematic errors in the estimation of the drift and diffusion functions of the process. In this paper we will analyze these errors and we will propose an approach that correctly accounts for them. This approach allows an accurate parameter estimation and, additionally, is able to cope with weak measurement noise, which may be superimposed to a given time series.
Wehde, M. E.
1995-01-01
The common method of digital image comparison by subtraction imposes various constraints on the image contents. Precise registration of images is required to assure proper evaluation of surface locations. The attribute being measured and the calibration and scaling of the sensor are also important to the validity and interpretability of the subtraction result. Influences of sensor gains and offsets complicate the subtraction process. The presence of any uniform systematic transformation component in one of two images to be compared distorts the subtraction results and requires analyst intervention to interpret or remove it. A new technique has been developed to overcome these constraints. Images to be compared are first transformed using the cumulative relative frequency as a transfer function. The transformed images represent the contextual relationship of each surface location with respect to all others within the image. The process of differentiating between the transformed images results in a percentile rank ordered difference. This process produces consistent terrain-change information even when the above requirements necessary for subtraction are relaxed. This technique may be valuable to an appropriately designed hierarchical terrain-monitoring methodology because it does not require human participation in the process.
High-order asynchrony-tolerant finite difference schemes for partial differential equations
Aditya, Konduri; Donzis, Diego A.
2017-12-01
Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2012-06-01
Full Text Available We study boundary value problems of nonlinear fractional differential equations and inclusions of order $q in (m-1, m]$, $m ge 2$ with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: $$ x(1=sum_{i=1}^{n-2}alpha_i int^{eta_i}_{zeta_i} x(sds, $$ which can be viewed as an extension of a multi-point nonlocal boundary condition: $$ x(1=sum_{i=1}^{n-2}alpha_i x(eta_i. $$ In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments $(zeta_i,eta_i$ of the interval $[0,1]$ and the effect of these strips is accumulated at $x=1$. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.
Energy Technology Data Exchange (ETDEWEB)
Singhatanadgid, Pairod; Jommalai, Panupan [Chulalongkorn University, Bangkok (Thailand)
2016-05-15
The extended Kantorovich method using multi-term displacement functions is applied to the buckling problem of laminated plates with various boundary conditions. The out-of-plane displacement of the buckled plate is written as a series of products of functions of parameter x and functions of parameter y. With known functions in parameter x or parameter y, a set of governing equations and a set of boundary conditions are obtained after applying the variational principle to the total potential energy of the system. The higher order differential equations are then transformed into a set of first-order differential equations and solved for the buckling load and mode. Since the governing equations are first-order differential equations, solutions can be obtained analytically with the out-of-plane displacement written in the form of an exponential function. The solutions from the proposed technique are verified with solutions from the literature and FEM solutions. The bucking loads correspond very well to other available solutions in most of the comparisons. The buckling modes also compare very well with the finite element solutions. The proposed solution technique transforms higher-order differential equations to first-order differential equations, and they are analytically solved for out-of-plane displacement in the form of an exponential function. Therefore, the proposed solution technique yields a solution which can be considered as an analytical solution.
Verification of the Monte Carlo differential operator technique for MCNP trademark
International Nuclear Information System (INIS)
McKinney, G.W.; Iverson, J.L.
1996-02-01
The differential operator perturbation technique has been incorporated into the Monte Carlo N-Particle transport code MCNP and will become a standard feature of future releases. This feature includes first and second order terms of the Taylor series expansion for response perturbations related to cross-section data (i.e., density, composition, etc.). Perturbation and sensitivity analyses can benefit from this technique in that predicted changes in one or more tally responses may be obtained for multiple perturbations in a single run. The user interface is intuitive, yet flexible enough to allow for changes in a specific microscopic cross section over a specified energy range. With this technique, a precise estimate of a small change in response is easily obtained, even when the standard deviation of the unperturbed tally is greater than the change. Furthermore, results presented in this report demonstrate that first and second order terms can offer acceptable accuracy, to within a few percent, for up to 20-30% changes in a response
International Nuclear Information System (INIS)
Li, Huihua
1992-01-01
The traditional generalization methods such as FIKE's macro-operator learning and Explanation-Based Learning (EBL) deal with totally ordered plans. They generalize only the plan operators and the conditions under which the generalized plan can be applied in its initial total order, but not the partial order among operators in which the generalized plan can be successfully executed. In this paper, we extend the notion of the EBL on the partial order of plans. A new method is presented for learning, from a totally or partially ordered plan, partially ordered macro-operators (generalized plans) each of which requires a set of the weakest conditions for its reuse. It is also valuable for generalizing partially ordered plans. The operators are generalized in the FIKE's triangle table. We introduce the domain axioms to generate the constraints for the consistency of generalized states. After completing the triangle table with the information concerning the operator destructions (interactions), we obtain the global explanation of the partial order on the operators. Then, we represent all the necessary ordering relations by a directed graph. The exploitation of this graph permits to explicate the dependence between the partial orders and the constraints among the parameters of generalized operators, and allows all the solutions to be obtained. (author) [fr
The theory of pseudo-differential operators on the noncommutative n-torus
Tao, J.
2018-02-01
The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct analogy with the theory of pseudo-differential operators on finite-dimensional real vector spaces, one may derive a similar pseudo-differential calculus on noncommutative n-tori, and with the development of this calculus came many results concerning the local differential geometry of noncommutative tori for n=2,4, as shown in the groundbreaking paper in which the Gauss-Bonnet theorem on the noncommutative two-torus is proved and later papers. Certain details of the proofs in the original derivation of the calculus were omitted, such as the evaluation of oscillatory integrals, so we make it the objective of this paper to fill in all the details. After reproving in more detail the formula for the symbol of the adjoint of a pseudo-differential operator and the formula for the symbol of a product of two pseudo-differential operators, we extend these results to finitely generated projective right modules over the noncommutative n-torus. Then we define the corresponding analog of Sobolev spaces and prove equivalents of the Sobolev and Rellich lemmas.
A new fractional operator of variable order: Application in the description of anomalous diffusion
Yang, Xiao-Jun; Machado, J. A. Tenreiro
2017-09-01
In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.
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Vujaković Jelena
2016-01-01
Full Text Available The study of complex differential equations in recent years has opened up some of questions concerning the determination of the frequency of zero solutions, the distribution of zero, oscillation of the solution, asymptotic behavior, rank growth and so on. Besides, this is solved by only some classes of differential equations. In this paper, our aim was to determine the number of zeros and their arrangement in the first quadrant, for the complex canonical differential equation of the second order. The accuracy of our results, we illustrate with two examples.
Spectral function for a nonsymmetric differential operator on the half line
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Wuqing Ning
2017-05-01
Full Text Available In this article we study the spectral function for a nonsymmetric differential operator on the half line. Two cases of the coefficient matrix are considered, and for each case we prove by Marchenko's method that, to the boundary value problem, there corresponds a spectral function related to which a Marchenko-Parseval equality and an expansion formula are established. Our results extend the classical spectral theory for self-adjoint Sturm-Liouville operators and Dirac operators.
Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order
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Ming Li
2013-01-01
Full Text Available This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type.
The design of a 4’th order Bandpass Butterworth filter with one operational amplifier.
Gaunholt, Hans
2008-01-01
A numerical design method is presented for the design of all pole band pass active-RC filters applying just one operational amplifier. The operational amplifier model used is the integrator model: ωt/s where ωt is the unity gain fre-quency. The design method is used for the design of a fourth order band pass filter with Butterworth poles applying just one operational amplifier coupled as a unity gain amplifier. The unity gain amplifiers have the advantage of providing low power consumption, y...
A closed graph theorem for order bounded operators | Harm van der ...
African Journals Online (AJOL)
... theory to prove a version of the closed graph theorem for order bounded operators on Archimedean vector lattices. This illustrates the usefulness of convergence spaces in dealing with problems in vector lattice theory, problems that may fail to be amenable to the usual Hausdorff-Kuratowski-Bourbaki concept of topology.
2010-07-13
... NUCLEAR REGULATORY COMMISSION [NRC-2010-0178; Docket No. 50-228; License No. R-98] In the Matter of Aerotest Operations, Inc. (Aerotest Radiography and Research Reactor); Order Approving Indirect... of the Aerotest Radiography and Research Reactor (ARRR) located in San Ramon, California, under the...
Diethelm, Kai
2010-01-01
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
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Navnit Jha
2014-04-01
Full Text Available An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors.
International Nuclear Information System (INIS)
Supriyono; Miyoshi, T.
1997-01-01
NECD Method and runge-Kutta method for large system of second order ordinary differential equations in comparing algorithm. The paper introduce a extrapolation method used for solving the large system of second order ordinary differential equation. We call this method the modified extrapolated central difference (MECD) method. for the accuracy and efficiency MECD method. we compare the method with 4-th order runge-Kutta method. The comparison results show that, this method has almost the same accuracy as the 4-th order runge-Kutta method, but the computation time is about half of runge-Kutta. The MECD was declare by the author and Tetsuhiko Miyoshi of the Dept. Applied Science Yamaguchi University Japan
Differential operators and spectral theory M. Sh. Birman's 70th anniversary collection
Buslaev, V; Yafaev, D
1999-01-01
This volume contains a collection of original papers in mathematical physics, spectral theory, and differential equations. The papers are dedicated to the outstanding mathematician, Professor M. Sh. Birman, on the occasion of his 70th birthday. Contributing authors are leading specialists and close professional colleagues of Birman. The main topics discussed are spectral and scattering theory of differential operators, trace formulas, and boundary value problems for PDEs. Several papers are devoted to the magnetic Schrödinger operator, which is within Birman's current scope of interests and re
Operational method of solution of linear non-integer ordinary and partial differential equations.
Zhukovsky, K V
2016-01-01
We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.
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Aleksandr Alekseev
2015-07-01
Full Text Available We establish necessary and sufficient conditions for existence of an integrating multiplier of a special form for systems of two cubic differential equations of the first order. We further study bifurcations of such systems with the change of parameters of their integrating multipliers.
On the periodic orbits of the Third-order differential equation x ' ' '- x ' ' x'- x= F(x,x',x ' ')
Llibre, Jaume
2013-01-01
Agraïments: The second author is partially supported by CAPES/MECD-DGU 222/2010 Brazil and Spain In this paper we study the periodic orbits of the third-order differential equation x''' − µx'' + x' − µx = εF(x, x', x''), where ε is a small parameter and the function F is of class C2.
OSCILLATION OF A SECOND-ORDER HALF-LINEAR NEUTRAL DAMPED DIFFERENTIAL EQUATION WITH TIME-DELAY
Institute of Scientific and Technical Information of China (English)
无
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.
Tisdell, Christopher C.
2017-01-01
Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching "well posedness" of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a…
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Youliang Fu
2016-01-01
Full Text Available This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.
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Wang Li
2008-01-01
Full Text Available We investigate the existence of almost-periodic weak solutions of second-order neutral delay-differential equations with piecewise constant argument of the form , where denotes the greatest integer function, is a real nonzero constant, and is almost periodic.
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Bashir Ahmad
2013-02-01
Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.
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Ahmed M. A. El-Sayed
2011-12-01
Full Text Available In this article, we prove the existence of positive nondecreasing solutions for a multi-term fractional-order functional differential equations. We consider Cauchy boundary problems with: nonlocal conditions, two-point boundary conditions, integral conditions, and deviated arguments.
International Nuclear Information System (INIS)
Yang Yi; Tang Xiangyang
2012-01-01
Purpose: The x-ray differential phase contrast imaging implemented with the Talbot interferometry has recently been reported to be capable of providing tomographic images corresponding to attenuation-contrast, phase-contrast, and dark-field contrast, simultaneously, from a single set of projection data. The authors believe that, along with small-angle x-ray scattering, the second-order phase derivative Φ ″ s (x) plays a role in the generation of dark-field contrast. In this paper, the authors derive the analytic formulae to characterize the contribution made by the second-order phase derivative to the dark-field contrast (namely, second-order differential phase contrast) and validate them via computer simulation study. By proposing a practical retrieval method, the authors investigate the potential of second-order differential phase contrast imaging for extensive applications. Methods: The theoretical derivation starts at assuming that the refractive index decrement of an object can be decomposed into δ=δ s +δ f , where δ f corresponds to the object's fine structures and manifests itself in the dark-field contrast via small-angle scattering. Based on the paraxial Fresnel-Kirchhoff theory, the analytic formulae to characterize the contribution made by δ s , which corresponds to the object's smooth structures, to the dark-field contrast are derived. Through computer simulation with specially designed numerical phantoms, an x-ray differential phase contrast imaging system implemented with the Talbot interferometry is utilized to evaluate and validate the derived formulae. The same imaging system is also utilized to evaluate and verify the capability of the proposed method to retrieve the second-order differential phase contrast for imaging, as well as its robustness over the dimension of detector cell and the number of steps in grating shifting. Results: Both analytic formulae and computer simulations show that, in addition to small-angle scattering, the
On the solution of nonlinear differential equations over the field of Mikusinski operators
International Nuclear Information System (INIS)
Sharkawi, I.E.; El-Sabagh, M.A.
1983-08-01
The nonlinear differential equation X'(lambda)+a(lambda)X(lambda)=sb(lambda)Xsup(n+1)(lambda) with the initial condition X(0)=I, over the field of Mikusinski operators [Mikusinski, J. Operational Calculus, Pergamon Press (1957)] is discussed, where a(lambda) and b(lambda) are continuous numerical functions, s is the operator of differentiation, and I is the unit operator. A solution is constructed of the following form: X(lambda)=F(lambda) ([tsup((1/n)-1)]/[GAMMA(1/n)(ng(lambda))sup(1/n)])exp(t/(ng(lambda))), where F(lambda)=exp(-integ 0 sup(lambda)a(lambda)d(lambda) and g(lambda)=integ 0 sup(lambda)[b(lambda)exp(n integ 0 sup(lambda)a(lambda))]dlambda are numerical functions
Analytic theory of alternate multilayer gratings operating in single-order regime.
Yang, Xiaowei; Kozhevnikov, Igor V; Huang, Qiushi; Wang, Hongchang; Hand, Matthew; Sawhney, Kawal; Wang, Zhanshan
2017-07-10
Using the coupled wave approach (CWA), we introduce the analytical theory for alternate multilayer grating (AMG) operating in the single-order regime, in which only one diffraction order is excited. Differing from previous study analogizing AMG to crystals, we conclude that symmetrical structure, or equal thickness of the two multilayer materials, is not the optimal design for AMG and may result in significant reduction in diffraction efficiency. The peculiarities of AMG compared with other multilayer gratings are analyzed. An influence of multilayer structure materials on diffraction efficiency is considered. The validity conditions of analytical theory are also discussed.
Spectral theory of differential operators M. Sh. Birman 80th anniversary collection
Suslina, T
2009-01-01
This volume is dedicated to Professor M. Sh. Birman in honor of his eightieth birthday. It contains original articles in spectral and scattering theory of differential operators, in particular, Schrodinger operators, and in homogenization theory. All articles are written by members of M. Sh. Birman's research group who are affiliated with different universities all over the world. A specific feature of the majority of the papers is a combination of traditional methods with new modern ideas.
Semi-groups of operators and some of their applications to partial differential equations
International Nuclear Information System (INIS)
Kisynski, J.
1976-01-01
Basic notions and theorems of the theory of one-parameter semi-groups of linear operators are given, illustrated by some examples concerned with linear partial differential operators. For brevity, some important and widely developed parts of the semi-group theory such as the general theory of holomorphic semi-groups or the theory of temporally inhomogeneous evolution equations are omitted. This omission includes also the very important application of semi-groups to investigating stochastic processes. (author)
Behavior analysis of container ship in maritime accident in order to redefine the operating criteria
Ancuţa, C.; Stanca, C.; Andrei, C.; Acomi, N.
2017-08-01
In order to enhance the efficiency of maritime transport, container ships operators proceeded to increase the sizes of ships. The latest generation of ships in operation has 19,000 TEU capacity and the perspective is 21,000 TEU within the next years. The increasing of the sizes of container ships involves risks of maritime accidents occurrences. Nowadays, the general rules on operational security, tend to be adjusted as a result of the evaluation for each vessel. To create the premises for making an informed decision, the captain have to be aware of ships behavior in such situations. Not less important is to assure permanent review of the procedures for operation of ship, including the specific procedures in special areas, confined waters or separation schemes. This paper aims at analysing the behavior of the vessel and the respond of the structure of a container ship in maritime accident, in order to redefine the operating criteria. The method selected by authors for carrying out the research is computer simulations. Computer program provides the responses of the container ship model in various situations. Therefore, the simulations allow acquisition of a large category of data, in the scope of improving the prevention of accidents or mitigation of effects as much as possible. Simulations and assessments of certain situations that the ship might experience will be carried out to redefine the operating criteria. The envisaged scenarios are: introducing of maneuver speed for specific areas with high risk of collision or grounding, introducing of flooding scenarios of some compartments in loading programs, conducting of complex simulations in various situations for each vessel type. The main results of this work are documented proposals for operating criteria, intended to improve the safety in case of marine accidents, collisions and groundings. Introducing of such measures requires complex cost benefit analysis, that should not neglect the extreme economic impact
Geometrical aspects of operator ordering terms in gauge invariant quantum models
International Nuclear Information System (INIS)
Houston, P.J.
1990-01-01
Finite-dimensional quantum models with both boson and fermion degrees of freedom, and which have a gauge invariance, are studied here as simple versions of gauge invariant quantum field theories. The configuration space of these finite-dimensional models has the structure of a principal fibre bundle and has defined on it a metric which is invariant under the action of the bundle or gauge group. When the gauge-dependent degrees of freedom are removed, thereby defining the quantum models on the base of the principal fibre bundle, extra operator ordering terms arise. By making use of dimensional reduction methods in removing the gauge dependence, expressions are obtained here for the operator ordering terms which show clearly their dependence on the geometry of the principal fibre bundle structure. (author)
Choosing order of operations to accelerate strip structure analysis in parameter range
Kuksenko, S. P.; Akhunov, R. R.; Gazizov, T. R.
2018-05-01
The paper considers the issue of using iteration methods in solving the sequence of linear algebraic systems obtained in quasistatic analysis of strip structures with the method of moments. Using the analysis of 4 strip structures, the authors have proved that additional acceleration (up to 2.21 times) of the iterative process can be obtained during the process of solving linear systems repeatedly by means of choosing a proper order of operations and a preconditioner. The obtained results can be used to accelerate the process of computer-aided design of various strip structures. The choice of the order of operations to accelerate the process is quite simple, universal and could be used not only for strip structure analysis but also for a wide range of computational problems.
q-deformed differential operator algebra and new braid group representation
International Nuclear Information System (INIS)
Wang Luyu; Dai Jianghui; Zhang Jun
1991-01-01
It is proved that the q-deformed differential operator algebra introduced is consistent with quantum hyperplane described by Wess and Zumino. At the same time, a new braid group representation associated with sl q (2) is obtained by adding the terms of weight conservation to the standard universal R-matrix. (author). 10 refs
Eck, van H.J.N.; Koppers, W.R.; Rooij, van G.J.; Goedheer, W.J.; Engeln, R.A.H.; Schram, D.C.; Lopes Cardozo, N.J.; Kleyn, A.W.
2009-01-01
The direct simulation Monte Carlo (DSMC) method was used to investigate the efficiency of differential pumping in linear plasma generators operating at high gas flows. Skimmers are used to separate the neutrals from the plasma beam, which is guided from the source to the target by a strong axial
On a non classical oblique derivative problem for parabolic singular integro-differential operators
International Nuclear Information System (INIS)
Nguyen Minh Chuong; Le Quang Trung
1989-10-01
In this paper an oblique derivative problem for parabolic singular integro-differential operators was studied. In this problem the direction of the derivative may be tangent to the boundary of the domain. By the large parameter method theorems of existence and uniqueness of solutions of the problem were obtained. (author). 10 refs
Invariant differential operators for non-compact Lie groups: the SO* (12) case
Dobrev, V. K.
2015-04-01
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra so* (12). We give the main multiplets of indecomposable elementary representations. Due to the recently established parabolic relations the multiplet classification results are valid also for the algebra so(6, 6) with suitably chosen maximal parabolic subalgebra.
International Nuclear Information System (INIS)
Dobrev, V.K.
1986-11-01
Let G be a real linear connected semisimple Lie group. We present a canonical construction of the differential operators intertwining elementary (≡ generalized principal series) representations of G. The results are easily extended to real linear reductive Lie groups. (author). 20 refs
Differentiable absorption of Hilbert C*-modules, connections and lifts of unbounded operators
DEFF Research Database (Denmark)
Kaad, Jens
2017-01-01
. The differentiable absorption theorem is then applied to construct densely defined connections (or correpondences) on Hilbert C∗C∗-modules. These connections can in turn be used to define selfadjoint and regular "lifts" of unbounded operators which act on an auxiliary Hilbert C∗C∗-module....
Applications of the differential operator to a class of meromorphic univalent functions
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Khalida Inayat Noor
2016-04-01
Full Text Available In this paper, we define a new subclass of meromorphic close-to-convex univalent functions defined in the punctured open unit disc by using a differential operator. Some inclusion results, convolution properties and several other properties of this class are studied.
Properties of solutions to a class of differential models incorporating Preisach hysteresis operator
Czech Academy of Sciences Publication Activity Database
Krejčí, Pavel; O'Kane, J.P.; Pokrovskii, A.; Rachinskii, D.
2012-01-01
Roč. 241, č. 22 (2012), s. 2010-2028 ISSN 0167-2789 R&D Projects: GA ČR GAP201/10/2315 Institutional support: RVO:67985840 Keywords : Preisach operator * differential equation * periodic solution Subject RIV: BA - General Mathematics Impact factor: 1.669, year: 2012 http://www.sciencedirect.com/science/article/pii/S0167278911001126
Analysis of the F. Calogero Type Projection-Algebraic Scheme for Differential Operator Equations
International Nuclear Information System (INIS)
Lustyk, Miroslaw; Bogolubov, Nikolai N. Jr.; Blackmore, Denis; Prykarpatsky, Anatoliy K.
2010-12-01
The existence, convergence, realizability and stability of solutions of differential operator equations obtained via a novel projection-algebraic scheme are analyzed in detail. This analysis is based upon classical discrete approximation techniques coupled with a recent generalization of the Leray-Schauder fixed point theorem. An example is included to illustrate the efficacy of the projection scheme and analysis strategy. (author)
Tisdell, Christopher C.
2017-07-01
Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching 'well posedness' of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a first-order system of equations. We show that this excursion is unnecessary and present a direct approach regarding second- and higher-order problems that does not require an understanding of systems.
Renormalization of dijet operators at order 1 /Q 2 in soft-collinear effective theory
Goerke, Raymond; Inglis-Whalen, Matthew
2018-05-01
We make progress towards resummation of power-suppressed logarithms in dijet event shapes such as thrust, which have the potential to improve high-precision fits for the value of the strong coupling constant. Using a newly developed formalism for Soft-Collinear Effective Theory (SCET), we identify and compute the anomalous dimensions of all the operators that contribute to event shapes at order 1 /Q 2. These anomalous dimensions are necessary to resum power-suppressed logarithms in dijet event shape distributions, although an additional matching step and running of observable-dependent soft functions will be necessary to complete the resummation. In contrast to standard SCET, the new formalism does not make reference to modes or λ-scaling. Since the formalism does not distinguish between collinear and ultrasoft degrees of freedom at the matching scale, fewer subleading operators are required when compared to recent similar work. We demonstrate how the overlap subtraction prescription extends to these subleading operators.
The Differential Effect of Sustained Operations on Psychomotor Skills of Helicopter Pilots.
McMahon, Terry W; Newman, David G
2018-06-01
Flying a helicopter is a complex psychomotor skill requiring constant control inputs from pilots. A deterioration in psychomotor performance of a helicopter pilot may be detrimental to operational safety. The aim of this study was to test the hypothesis that psychomotor performance deteriorates over time during sustained operations and that the effect is more pronounced in the feet than the hands. The subjects were helicopter pilots conducting sustained multicrew offshore flight operations in a demanding environment. The remote flight operations involved constant workload in hot environmental conditions with complex operational tasking. Over a period of 6 d 10 helicopter pilots were tested. At the completion of daily flying duties, a helicopter-specific screen-based compensatory tracking task measuring tracking accuracy (over a 5-min period) tested both hands and feet. Data were compared over time and tested for statistical significance for both deterioration and differential effect. A statistically significant deterioration of psychomotor performance was evident in the pilots over time for both hands and feet. There was also a statistically significant differential effect between the hands and the feet in terms of tracking accuracy. The hands recorded a 22.6% decrease in tracking accuracy, while the feet recorded a 39.9% decrease in tracking accuracy. The differential effect may be due to prioritization of limb movement by the motor cortex due to factors such as workload-induced cognitive fatigue. This may result in a greater reduction in performance in the feet than the hands, posing a significant risk to operational safety.McMahon TW, Newman DG. The differential effect of sustained operations on psychomotor skills of helicopter pilots. Aerosp Med Hum Perform. 2018; 89(6):496-502.
Domoshnitsky, Alexander; Maghakyan, Abraham; Berezansky, Leonid
2017-01-01
In this paper a method for studying stability of the equation [Formula: see text] not including explicitly the first derivative is proposed. We demonstrate that although the corresponding ordinary differential equation [Formula: see text] is not exponentially stable, the delay equation can be exponentially stable.
Analysis of a first-order delay differential-delay equation containing two delays
Marriott, C.; Vallée, R.; Delisle, C.
1989-09-01
An experimental and numerical analysis of the behavior of a two-delay differential equation is presented. It is shown that much of the system's behavior can be related to the stability behavior of the underlying linearized modes. A new phenomenon, mode crossing, is explored.
Fractional Order Differentiation by Integration and Error Analysis in Noisy Environment
Liu, Dayan; Gibaru, Olivier; Perruquetti, Wilfrid; Laleg-Kirati, Taous-Meriem
2015-01-01
respectively. Exact and simple formulae for these differentiators are given by integral expressions. Hence, they can be used for both continuous-time and discrete-time models in on-line or off-line applications. Secondly, some error bounds are provided
International Nuclear Information System (INIS)
McCarthy, S; Rachinskii, D
2011-01-01
We describe two Euler type numerical schemes obtained by discretisation of a stochastic differential equation which contains the Preisach memory operator. Equations of this type are of interest in areas such as macroeconomics and terrestrial hydrology where deterministic models containing the Preisach operator have been developed but do not fully encapsulate stochastic aspects of the area. A simple price dynamics model is presented as one motivating example for our studies. Some numerical evidence is given that the two numerical schemes converge to the same limit as the time step decreases. We show that the Preisach term introduces a damping effect which increases on the parts of the trajectory demonstrating a stronger upwards or downwards trend. The results are preliminary to a broader programme of research of stochastic differential equations with the Preisach hysteresis operator.
Richland Operations Office (DOE-RL) Implementation Plan for DOE Order 435.1
International Nuclear Information System (INIS)
FRITZ, D.W.
2000-01-01
The U.S. Department of Energy issued U.S. Department of Energy Order 435.1, Radioactive Waste Management, and U.S. Department of Energy Manual 435.1-1, Radioactive Waste Management Manual, on July 9, 1999, to replace U.S. Department of Energy Order 5820.2A. Compliance is required by July 9, 2000, where compliance is defined as ''implementing the requirements, or an approved implementation, or corrective action plan'' (refer to Manual, Introduction, paragraph four). This implementation plan identifies the status of each requirement for U.S. Department of Energy, Richland Operations Office Site contractors, and provides the plan, cost, and length of time required for achieving full implementation. The U.S. Department of Energy, Richland Operations Office contractors (Fluor Hanford, Incorporated, DynCorp Tri-Cities Services, Bechtel Hanford, Inc., and Pacific Northwest National Laboratory) conducted a line-by-line review of DOE Order 435.1 and associated manuals to determine which requirements were new, and which requirements already are used for compliance with the previous DOE Order 5820.2A or other requirements. The Gap Analysis for DOE Order 435.1 (HNF-5465) identified compliance gaps, along with other issues that would impact efforts for achieving compliance. The gap analysis also contained a series of assumptions made by the various projects in determining compliance status. The details and section-by-section analysis are contained in Appendix A. Some of the DOE Order 435.1 requirements invoke sections of other DOE Orders not incorporated in various U.S. Department of Energy, Richland Operations Office contracts (refer to Section 2.0, Table 2-1). Those additional DOE Orders are identified by contractor and will be left for evaluation in accordance with each contractor's requirements. No attempt was made to evaluate all of those orders at this time, although in many cases, contractors follow a similar older DOE Order, which is cited in the Appendix. In some areas
Gunnarsson, Robert; Sönnerhed, Wang Wei; Hernell, Bernt
2016-01-01
The hypothesis that mathematically superfluous brackets can be useful when teaching the rules for the order of operations is challenged. The idea of the hypothesis is that with brackets it is possible to emphasize the order priority of one operation over another. An experiment was conducted where expressions with mixed operations were studied,…
Barbot, Antoine; Landy, Michael S.; Carrasco, Marisa
2012-01-01
The visual system can use a rich variety of contours to segment visual scenes into distinct perceptually coherent regions. However, successfully segmenting an image is a computationally expensive process. Previously we have shown that exogenous attention—the more automatic, stimulus-driven component of spatial attention—helps extract contours by enhancing contrast sensitivity for second-order, texture-defined patterns at the attended location, while reducing sensitivity at unattended locations, relative to a neutral condition. Interestingly, the effects of exogenous attention depended on the second-order spatial frequency of the stimulus. At parafoveal locations, attention enhanced second-order contrast sensitivity to relatively high, but not to low second-order spatial frequencies. In the present study we investigated whether endogenous attention—the more voluntary, conceptually-driven component of spatial attention—affects second-order contrast sensitivity, and if so, whether its effects are similar to those of exogenous attention. To that end, we compared the effects of exogenous and endogenous attention on the sensitivity to second-order, orientation-defined, texture patterns of either high or low second-order spatial frequencies. The results show that, like exogenous attention, endogenous attention enhances second-order contrast sensitivity at the attended location and reduces it at unattended locations. However, whereas the effects of exogenous attention are a function of the second-order spatial frequency content, endogenous attention affected second-order contrast sensitivity independent of the second-order spatial frequency content. This finding supports the notion that both exogenous and endogenous attention can affect second-order contrast sensitivity, but that endogenous attention is more flexible, benefitting performance under different conditions. PMID:22895879
ANALYTICAL SOLUTION OF THE K-TH ORDER AUTONOMOUS ORDINARY DIFFERENTIAL EQUATION
Directory of Open Access Journals (Sweden)
Ronald Orozco López
2017-04-01
Full Text Available The main objective of this paper is to find the analytical solution of the autonomous equation y(k = f (y and prove its convergence using autonomous polynomials of order k, define here in addition of the formula of Faá di Bruno for composition of functions and Bell polynomials. Autonomous polynomials of order k are defined in terms of the boundary values of the equation. Also special values of autonomous polynomials of order 1 are given.
Barbot, Antoine; Landy, Michael S; Carrasco, Marisa
2012-08-15
The visual system can use a rich variety of contours to segment visual scenes into distinct perceptually coherent regions. However, successfully segmenting an image is a computationally expensive process. Previously we have shown that exogenous attention--the more automatic, stimulus-driven component of spatial attention--helps extract contours by enhancing contrast sensitivity for second-order, texture-defined patterns at the attended location, while reducing sensitivity at unattended locations, relative to a neutral condition. Interestingly, the effects of exogenous attention depended on the second-order spatial frequency of the stimulus. At parafoveal locations, attention enhanced second-order contrast sensitivity to relatively high, but not to low second-order spatial frequencies. In the present study we investigated whether endogenous attention-the more voluntary, conceptually-driven component of spatial attention--affects second-order contrast sensitivity, and if so, whether its effects are similar to those of exogenous attention. To that end, we compared the effects of exogenous and endogenous attention on the sensitivity to second-order, orientation-defined, texture patterns of either high or low second-order spatial frequencies. The results show that, like exogenous attention, endogenous attention enhances second-order contrast sensitivity at the attended location and reduces it at unattended locations. However, whereas the effects of exogenous attention are a function of the second-order spatial frequency content, endogenous attention affected second-order contrast sensitivity independent of the second-order spatial frequency content. This finding supports the notion that both exogenous and endogenous attention can affect second-order contrast sensitivity, but that endogenous attention is more flexible, benefitting performance under different conditions.
Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing
2015-12-01
The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.
Xing, Yanyuan; Yan, Yubin
2018-03-01
Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.
The gravitational waves from the first-order phase transition with a dimension-six operator
Energy Technology Data Exchange (ETDEWEB)
Cai, Rong-Gen; Wang, Shao-Jiang [CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, No.55 Zhong Guan Cun East Road, Beijing 100190 (China); Sasaki, Misao, E-mail: cairg@itp.ac.cn, E-mail: misao@yukawa.kyoto-u.ac.jp, E-mail: schwang@itp.ac.cn [Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2017-08-01
We investigate in details the gravitational wave (GW) from the first-order phase transition (PT) in the extended standard model of particle physics with a dimension-six operator, which is capable of exhibiting the recently discovered slow first-order PT in addition to the usually studied fast first-order PT. To simplify the discussion, it is sufficient to work with an example of a toy model with the sextic term, and we propose an unified description for both slow and fast first-order PTs. We next study the full one-loop effective potential of the model with fixed/running renormalization-group (RG) scales. Compared to the prediction of GW energy density spectrum from the fixed RG scale, we find that the presence of running RG scale could amplify the peak amplitude by amount of one order of magnitude while shift the peak frequency to the lower frequency regime, and the promising regime of detection within the sensitivity ranges of various space-based GW detectors shrinks down to a lower cut-off value of the sextic term rather than the previous expectation.
Computation of rational solutions for a first-order nonlinear differential equation
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Djilali Behloul
2011-09-01
Full Text Available In this article, we study differential equations of the form $y'=sum A_i(xy^i/sum B_i(xy^i$ which can be elliptic, hyperbolic, parabolic, Riccati, or quasi-linear. We show how rational solutions can be computed in a systematic manner. Such results are most likely to find applications in the theory of limit cycles as indicated by Gine et al [4].
Czech Academy of Sciences Publication Activity Database
Lomtatidze, Alexander
2017-01-01
Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability 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-2017-0009/gmj-2017-0009.xml
Czech Academy of Sciences Publication Activity Database
Lomtatidze, Alexander
2017-01-01
Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability 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-2017-0009/gmj-2017-0009. xml
Exact polynomial solutions of second order differential equations and their applications
International Nuclear Information System (INIS)
Zhang Yaozhong
2012-01-01
We find all polynomials Z(z) such that the differential equation where X(z), Y(z), Z(z) are polynomials of degree at most 4, 3, 2, respectively, has polynomial solutions S(z) = ∏ n i=1 (z − z i ) of degree n with distinct roots z i . We derive a set of n algebraic equations which determine these roots. We also find all polynomials Z(z) which give polynomial solutions to the differential equation when the coefficients of X(z) and Y(z) are algebraically dependent. As applications to our general results, we obtain the exact (closed-form) solutions of the Schrödinger-type differential equations describing: (1) two Coulombically repelling electrons on a sphere; (2) Schrödinger equation from the kink stability analysis of φ 6 -type field theory; (3) static perturbations for the non-extremal Reissner–Nordström solution; (4) planar Dirac electron in Coulomb and magnetic fields; and (5) O(N) invariant decatic anharmonic oscillator. (paper)
Energy Technology Data Exchange (ETDEWEB)
Lukkassen, D.
1996-12-31
When partial differential equations are set up to model physical processes in strongly heterogeneous materials, effective parameters for heat transfer, electric conductivity etc. are usually required. Averaging methods often lead to convergence problems and in homogenization theory one is therefore led to study how certain integral functionals behave asymptotically. This mathematical doctoral thesis discusses (1) means and bounds connected to homogenization of integral functionals, (2) reiterated homogenization of integral functionals, (3) bounds and homogenization of some particular partial differential operators, (4) applications and further results. 154 refs., 11 figs., 8 tabs.
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Masanao Ozawa
2017-01-01
Full Text Available In quantum logic there is well-known arbitrariness in choosing a binary operation for conditional. Currently, we have at least three candidates, called the Sasaki conditional, the contrapositive Sasaki conditional, and the relevance conditional. A fundamental problem is to show how the form of the conditional follows from an analysis of operational concepts in quantum theory. Here, we attempt such an analysis through quantum set theory (QST. In this paper, we develop quantum set theory based on quantum logics with those three conditionals, each of which defines different quantum logical truth value assignment. We show that those three models satisfy the transfer principle of the same form to determine the quantum logical truth values of theorems of the ZFC set theory. We also show that the reals in the model and the truth values of their equality are the same for those models. Interestingly, however, the order relation between quantum reals significantly depends on the underlying conditionals. We characterize the operational meanings of those order relations in terms of joint probability obtained by the successive projective measurements of arbitrary two observables. Those characterizations clearly show their individual features and will play a fundamental role in future applications to quantum physics.
International Nuclear Information System (INIS)
Sidell, J.
1976-08-01
EXTRA is a program written for the Winfrith KDF9 enabling the user to solve first order initial value differential equations. In this report general numerical integration methods are discussed with emphasis on their application to the solution of stiff sets of equations. A method of particular applicability to stiff sets of equations is described. This method is incorporated in the program EXTRA and full instructions for its use are given. A comparison with other methods of computation is included. (author)
Tunç, Cemil; Tunç, Osman
2016-01-01
In this paper, certain system of linear homogeneous differential equations of second-order is considered. By using integral inequalities, some new criteria for bounded and [Formula: see text]-solutions, upper bounds for values of improper integrals of the solutions and their derivatives are established to the considered system. The obtained results in this paper are considered as extension to the results obtained by Kroopnick (2014) [1]. An example is given to illustrate the obtained results.
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Xiao-Bao Shu
2005-01-01
Full Text Available By means of variational structure and Z2 group index theory, we obtain multiple periodic solutions to a class of second-order mixed-type differential equations x''(t−τ+f(t,x(t,x(t−τ,x(t−2τ=0 and x''(t−τ+λ(tf1(t,x(t,x(t−τ,x(t−2τ=x(t−τ.
Kudryashov, Nikolay A.; Volkov, Alexandr K.
2017-01-01
We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the Fermi-Pasta-Ulam model. We use the potential of interaction between neighbouring masses with both quadratic and cubic terms. The equation is derived using the continuous limit. Unlike the previous works, we take into account higher order terms in the Taylor series expansions. We investigate the equation using the Painlevé approach. We show that the equation does not pass the Painlevé test and can not be integrated by the inverse scattering transform. We use the logistic function method and the Laurent expansion method to find travelling wave solutions of the fifth-order equation. We use the pseudospectral method for the numerical simulation of wave processes, described by the equation.
Improved iterative oscillation tests for first-order deviating differential equations
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George E. Chatzarakis
2018-01-01
Full Text Available In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing \\(\\lim \\sup\\ and \\(\\lim \\inf\\ on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.
Limit Properties of Solutions of Singular Second-Order Differential Equations
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Weinmüller Ewa
2009-01-01
Full Text Available We discuss the properties of the differential equation , a.e. on , where , and satisfies the -Carathéodory conditions on for some . A full description of the asymptotic behavior for of functions satisfying the equation a.e. on is given. We also describe the structure of boundary conditions which are necessary and sufficient for to be at least in . As an application of the theory, new existence and/or uniqueness results for solutions of periodic boundary value problems are shown.
Growth of solutions of an $n$-th order linear differential equation with entire coefficients
Bela\\"{i}di, Benharrat; Hamouda, Saada
2002-01-01
We consider a differential equation $f^{\\left( n\\right) }+A_{n-1}\\left( z\\right) f^{\\left( n-1\\right) }+...+A_{1}\\left( z\\right) f^{^{/}}+A_{0}\\left( z\\right) f=0,$ where $A_{0}\\left( z\\right) ,...,A_{n-1}\\left( z\\right) $ are entire functions with $A_{0}\\left( z\\right) \\hbox{$/\\hskip -11pt\\equiv$}0$. Suppose that there exist a positive number $\\mu ,$\\ and a sequence $\\left( z_{j}\\right) _{j\\in N}$ with $\\stackunder{j\\rightarrow +\\infty }{\\lim }z_{j}=\\infty ,$ \\ and also ...
International Nuclear Information System (INIS)
Kaseda, Shizuka; Ikeda, Takaaki; Sakai, Tadaaki; Tomaru, Hiroko; Ishihara, Tsuneo; Kikuchi, Keiichi.
1982-01-01
For the purpose of clarifying the relationship between the percentage of perfusion and that of vital capacity or oxygen uptake on the affected lung, perfusion scintigraphy using sup(99m)Tc-MAA and differential spirometry were performed in twenty patients including sixteen patients with lung cancer. Both examinations were performed before and after the operation. The results are as follows: (1) There is a significant correlation between the percentage of perfusion and that of vital capacity or oxygen uptake of the affected lung before and after the operation. (2) The estimation of the percentage of vital capacity or oxygen uptake of the affected lung is possible by combining the spirometry and sup(99m)Tc-MAA pulmonary scintigraphy. (author)
Directory of Open Access Journals (Sweden)
Yaoyao Wang
2014-01-01
Full Text Available For the 4-DOF (degrees of freedom trajectory tracking control problem of underwater remotely operated vehicles (ROVs in the presence of model uncertainties and external disturbances, a novel output feedback fractional-order nonsingular terminal sliding mode control (FO-NTSMC technique is introduced in light of the equivalent output injection sliding mode observer (SMO and TSMC principle and fractional calculus technology. The equivalent output injection SMO is applied to reconstruct the full states in finite time. Meanwhile, the FO-NTSMC algorithm, based on a new proposed fractional-order switching manifold, is designed to stabilize the tracking error to equilibrium points in finite time. The corresponding stability analysis of the closed-loop system is presented using the fractional-order version of the Lyapunov stability theory. Comparative numerical simulation results are presented and analyzed to demonstrate the effectiveness of the proposed method. Finally, it is noteworthy that the proposed output feedback FO-NTSMC technique can be used to control a broad range of nonlinear second-order dynamical systems in finite time.
Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.; Valtierra-Rodríguez, M.
2017-12-01
In this paper, we propose a state-observer-based approach to synchronize variable-order fractional (VOF) chaotic systems. In particular, this work is focused on complete synchronization with a so-called unidirectional master-slave topology. The master is described by a dynamical system in state-space representation whereas the slave is described by a state observer. The slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization. The differential equations of the VOF chaotic system are described by the Liouville-Caputo and Atangana-Baleanu-Caputo derivatives. Numerical simulations involving the synchronization of Rössler oscillators, Chua's systems and multi-scrolls are studied. The simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval (0 , 1 ] are used as the variable order of the fractional derivatives. Furthermore, simulations show that the VOF chaotic systems can be synchronized.
Oldham, Keith B
1974-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
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Stephen M. Paneitz
2008-03-01
Full Text Available This is the original manuscript dated March 9th 1983, typeset by the Editors for the Proceedings of the Midwest Geometry Conference 2007 held in memory of Thomas Branson. Stephen Paneitz passed away on September 1st 1983 while attending a conference in Clausthal and the manuscript was never published. For more than 20 years these few pages were circulated informally. In November 2004, as a service to the mathematical community, Tom Branson added a scan of the manuscript to his website. Here we make it available more formally. It is surely one of the most cited unpublished articles. The differential operator defined in this article plays a key rôle in conformal differential geometry in dimension 4 and is now known as the Paneitz operator.
Weighted Differentiation Composition Operator from Logarithmic Bloch Spaces to Zygmund-Type Spaces
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Huiying Qu
2014-01-01
Full Text Available Let H( denote the space of all holomorphic functions on the unit disk of ℂ, u∈H( and let n be a positive integer, φ a holomorphic self-map of , and μ a weight. In this paper, we investigate the boundedness and compactness of a weighted differentiation composition operator φ,unf(z=u(zf(n(φ(z,f∈H(, from the logarithmic Bloch spaces to the Zygmund-type spaces.
Global solvability of the differential operators non-invariants on semi-simple Lie groups
International Nuclear Information System (INIS)
El Hussein, K.
1991-09-01
Let G be a connected semi-simple Lie group with finite centre and let G=KAN be the Iwasawa decomposition of G. Let P be a differential operator on G, which is right invariant by the sub-group AN and left invariant by the sub-group K. In this paper, we give a necessary and sufficient condition for the global solvability of P on G. (author). 5 refs
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Abdellatif HAMOUDA
2011-12-01
Full Text Available Economic power dispatch (EPD is one of the main tools for optimal operation and planning of modern power systems. To solve effectively the EPD problem, most of the conventional calculus methods rely on the assumption that the fuel cost characteristic of a generating unit is a continuous and convex function, resulting in inaccurate dispatch. This paper presents the design and application of efficient adaptive differential evolution (ADE algorithm for the solution of the economic power dispatch problem, where the non-convex characteristics of the generators, such us prohibited operating zones and ramp rate limits of the practical generator operation are considered. The 26 bus benchmark test system with 6 units having prohibited operating zones and ramp rate limits was used for testing and validation purposes. The results obtained demonstrate the effectiveness of the proposed method for solving the non-convex economic dispatch problem.
Fractional order differentiation by integration: An application to fractional linear systems
Liu, Dayan
2013-02-04
In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.
Oscillation and nonoscillation of solutions to even order self-adjoint differential equations
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Ondrej Dosly
2003-11-01
Full Text Available We establish oscillation and nonoscilation criteria for the linear differential equation $$ (-1^nig(t^alpha y^{(n}ig^{(n}- frac{gamma_{n,alpha}}{t^{2n-alpha}}y=q(ty,quad alpha otin {1, 3, dots , 2n-1}, $$ where $$ gamma_{n,alpha}=frac{1}{4^n}prod_{k=1}^n(2k-1-alpha^2 $$ and $q$ is a real-valued continuous function. It is proved, using these criteria, that the equation $$ (-1^nig(t^alpha y^{(n}ig^{(n} -ig(frac{gamma_{n,alpha}}{t^{2n-alpha}} + frac{gamma}{t^{2n-alpha}lg^2 t}igy = 0 $$ is nonoscillatory if and only if $$ gamma leq ilde gamma_{n,alpha}:= frac{1}{4^n}prod_{k=1}^n(2k-1-alpha^2 sum_{k=1}^nfrac{1}{(2k-1-alpha^2}. $$
Fractional order differentiation and robust control design crone, h-infinity and motion control
Sabatier, Jocelyn; Melchior, Pierre; Oustaloup, Alain
2015-01-01
This monograph collates the past decade’s work on fractional models and fractional systems in the fields of analysis, robust control and path tracking. Themes such as PID control, robust path tracking design and motion control methodologies involving fractional differentiation are amongst those explored. It juxtaposes recent theoretical results at the forefront in the field, and applications that can be used as exercises that will help the reader to assimilate the proposed methodologies. The first part of the book deals with fractional derivative and fractional model definitions, as well as recent results for stability analysis, fractional model physical interpretation, controllability, and H-infinity norm computation. It also presents a critical point of view on model pseudo-state and “real state”, tackling the problem of fractional model initialization. Readers will find coverage of PID, Fractional PID and robust control in the second part of the book, which rounds off with an extension of H-infinity ...
Differential structures in C*-algebras
Indian Academy of Sciences (India)
Second and higher order differential structure defined by a closed symmetric operator. Differential ... (1) General theory – differential seminorm approach and growth conditions ...... S is dual of a Banach space, and the weak ∗-topology on A2.
Owolabi, Kolade M.
2017-03-01
In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE) on a finite but large spatial domain x ∈ [0, L], x = x(x , y , z) and t ∈ [0, T] are considered. Also in this work, the standard reaction-diffusion system with boundary conditions is generalized by replacing the second-order spatial derivatives with Riemann-Liouville space-fractional derivatives of order α, for 0 Fourier spectral method is introduced as a better alternative to existing low order schemes for the integration of fractional in space reaction-diffusion problems in conjunction with an adaptive exponential time differencing method, and solve a range of one-, two- and three-components SFORDE numerically to obtain patterns in one- and two-dimensions with a straight forward extension to three spatial dimensions in a sub-diffusive (0 reaction-diffusion case. With application to models in biology and physics, different spatiotemporal dynamics are observed and displayed.
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Xiangbing Zhou
2012-01-01
Full Text Available We generalize a fixed point theorem in partially ordered complete metric spaces in the study of A. Amini-Harandi and H. Emami (2010. We also give an application on the existence and uniqueness of the positive solution of a multipoint boundary value problem with fractional derivatives.
Threshold implementations : as countermeasure against higher-order differential power analysis
Bilgin, Begül
2015-01-01
Embedded devices are used pervasively in a wide range of applications some of which require cryptographic algorithms in order to provide security. Today’s standardized algorithms are secure in the black-box model where an adversary has access to several inputs and/or outputs of the algorithm.
TaylUR 3, a multivariate arbitrary-order automatic differentiation package for Fortran 95
International Nuclear Information System (INIS)
Hippel, G.M. von
2009-09-01
The new version of TaylUR is based on a completely new core, which now is able to compute the numerical values of all of a complex-valued function's partial derivatives up to an arbitrary order, including mixed partial derivatives. (orig.)
Czech Academy of Sciences Publication Activity Database
Escudero, C.; Gazzola, F.; Hakl, Robert; Torres, P.J.
2015-01-01
Roč. 140, č. 4 (2015), s. 385-393 ISSN 0862-7959 Institutional support: RVO:67985840 Keywords : higher order parabolic equation * existence of solution * blow-up in finite time Subject RIV: BA - General Mathematics http://hdl.handle.net/10338.dmlcz/144457
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
Gómez-Aguilar, J. F.
2018-03-01
In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.
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
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
First and second order operator splitting methods for the phase field crystal equation
International Nuclear Information System (INIS)
Lee, Hyun Geun; Shin, Jaemin; Lee, June-Yub
2015-01-01
In this paper, we present operator splitting methods for solving the phase field crystal equation which is a model for the microstructural evolution of two-phase systems on atomic length and diffusive time scales. A core idea of the methods is to decompose the original equation into linear and nonlinear subequations, in which the linear subequation has a closed-form solution in the Fourier space. We apply a nonlinear Newton-type iterative method to solve the nonlinear subequation at the implicit time level and thus a considerably large time step can be used. By combining these subequations, we achieve the first- and second-order accuracy in time. We present numerical experiments to show the accuracy and efficiency of the proposed methods
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Chuanyi Zhang
2008-06-01
Full Text Available We investigate the existence of almost-periodic weak solutions of second-order neutral delay-differential equations with piecewise constant argument of the form (x(t+x(tÃ¢ÂˆÂ’1Ã¢Â€Â²Ã¢Â€Â²=qx(2[(t+1/2]+f(t, where [Ã¢Â‹Â…] denotes the greatest integer function, q is a real nonzero constant, and f(t is almost periodic.
International Nuclear Information System (INIS)
Ding Xiaohua; Su Huan; Liu Mingzhu
2008-01-01
The paper analyzes a discrete second-order, nonlinear delay differential equation with negative feedback. The characteristic equation of linear stability is solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The existence of local Hopf bifurcations is investigated, and the direction and stability of periodic solutions bifurcating from the Hopf bifurcation of the discrete model are determined by the Hopf bifurcation theory of discrete system. Finally, some numerical simulations are performed to illustrate the analytical results found
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Mervan Pašić
2014-01-01
Full Text Available We study oscillatory behaviour of a large class of second-order functional differential equations with three freedom real nonnegative parameters. According to a new oscillation criterion, we show that if at least one of these three parameters is large enough, then the main equation must be oscillatory. As an application, we study a class of Duffing type quasilinear equations with nonlinear time delayed feedback and their oscillations excited by the control gain parameter or amplitude of forcing term. Finally, some open questions and comments are given for the purpose of further study on this topic.
Tang, Chen; Han, Lin; Ren, Hongwei; Zhou, Dongjian; Chang, Yiming; Wang, Xiaohang; Cui, Xiaolong
2008-10-01
We derive the second-order oriented partial-differential equations (PDEs) for denoising in electronic-speckle-pattern interferometry fringe patterns from two points of view. The first is based on variational methods, and the second is based on controlling diffusion direction. Our oriented PDE models make the diffusion along only the fringe orientation. The main advantage of our filtering method, based on oriented PDE models, is that it is very easy to implement compared with the published filtering methods along the fringe orientation. We demonstrate the performance of our oriented PDE models via application to two computer-simulated and experimentally obtained speckle fringes and compare with related PDE models.
Second-order sliding mode controller with model reference adaptation for automatic train operation
Ganesan, M.; Ezhilarasi, D.; Benni, Jijo
2017-11-01
In this paper, a new approach to model reference based adaptive second-order sliding mode control together with adaptive state feedback is presented to control the longitudinal dynamic motion of a high speed train for automatic train operation with the objective of minimal jerk travel by the passengers. The nonlinear dynamic model for the longitudinal motion of the train comprises of a locomotive and coach subsystems is constructed using multiple point-mass model by considering the forces acting on the vehicle. An adaptation scheme using Lyapunov criterion is derived to tune the controller gains by considering a linear, stable reference model that ensures the stability of the system in closed loop. The effectiveness of the controller tracking performance is tested under uncertain passenger load, coupler-draft gear parameters, propulsion resistance coefficients variations and environmental disturbances due to side wind and wet rail conditions. The results demonstrate improved tracking performance of the proposed control scheme with a least jerk under maximum parameter uncertainties when compared to constant gain second-order sliding mode control.
Tartakoff, David S.
1994-01-01
We prove global analytic hypoellipticity on a product of tori for partial differential operators which are constructed as rigid (variable coefficient) quadratic polynomials in real vector fields satisfying the H\\"ormander condition and where $P$ satisfies a `maximal' estimate. We also prove an analyticity result that is local in some variables and global in others for operators whose prototype is $$ P= \\left({\\partial \\over {\\partial x_1}}\\right)^2 + \\left({\\partial \\over {\\partial x_2}}\\righ...
Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em
2017-12-01
Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.
Directory of Open Access Journals (Sweden)
Longquan Yong
2012-01-01
Full Text Available Harmony search (HS method is an emerging metaheuristic optimization algorithm. In this paper, an improved harmony search method based on differential mutation operator (IHSDE is proposed to deal with the optimization problems. Since the population diversity plays an important role in the behavior of evolution algorithm, the aim of this paper is to calculate the expected population mean and variance of IHSDE from theoretical viewpoint. Numerical results, compared with the HSDE, NGHS, show that the IHSDE method has good convergence property over a test-suite of well-known benchmark functions.
Bianucci, Marco
2018-05-01
Finding the generalized Fokker-Planck Equation (FPE) for the reduced probability density function of a subpart of a given complex system is a classical issue of statistical mechanics. Zwanzig projection perturbation approach to this issue leads to the trouble of resumming a series of commutators of differential operators that we show to correspond to solving the Lie evolution of first order differential operators along the unperturbed Liouvillian of the dynamical system of interest. In this paper, we develop in a systematic way the procedure to formally solve this problem. In particular, here we show which the basic assumptions are, concerning the dynamical system of interest, necessary for the Lie evolution to be a group on the space of first order differential operators, and we obtain the coefficients of the so-evolved operators. It is thus demonstrated that if the Liouvillian of the system of interest is not a first order differential operator, in general, the FPE structure breaks down and the master equation contains all the power of the partial derivatives, up to infinity. Therefore, this work shed some light on the trouble of the ubiquitous emergence of both thermodynamics from microscopic systems and regular regression laws at macroscopic scales. However these results are very general and can be applied also in other contexts that are non-Hamiltonian as, for example, geophysical fluid dynamics, where important events, like El Niño, can be considered as large time scale phenomena emerging from the observation of few ocean degrees of freedom of a more complex system, including the interaction with the atmosphere.
Directory of Open Access Journals (Sweden)
Emran Tohidi
2013-01-01
Full Text Available The idea of approximation by monomials together with the collocation technique over a uniform mesh for solving state-space analysis and optimal control problems (OCPs has been proposed in this paper. After imposing the Pontryagins maximum principle to the main OCPs, the problems reduce to a linear or nonlinear boundary value problem. In the linear case we propose a monomial collocation matrix approach, while in the nonlinear case, the general collocation method has been applied. We also show the efficiency of the operational matrices of differentiation with respect to the operational matrices of integration in our numerical examples. These matrices of integration are related to the Bessel, Walsh, Triangular, Laguerre, and Hermite functions.
Hoefman, Sven; van der Ha, David; Boon, Nico; Vandamme, Peter; De Vos, Paul; Heylen, Kim
2014-04-04
The currently accepted thesis on nitrogenous fertilizer additions on methane oxidation activity assumes niche partitioning among methanotrophic species, with activity responses to changes in nitrogen content being dependent on the in situ methanotrophic community structure Unfortunately, widely applied tools for microbial community assessment only have a limited phylogenetic resolution mostly restricted to genus level diversity, and not to species level as often mistakenly assumed. As a consequence, intragenus or intraspecies metabolic versatility in nitrogen metabolism was never evaluated nor considered among methanotrophic bacteria as a source of differential responses of methane oxidation to nitrogen amendments. We demonstrated that fourteen genotypically different Methylomonas strains, thus distinct below the level at which most techniques assign operational taxonomic units (OTU), show a versatile physiology in their nitrogen metabolism. Differential responses, even among strains with identical 16S rRNA or pmoA gene sequences, were observed for production of nitrite and nitrous oxide from nitrate or ammonium, nitrogen fixation and tolerance to high levels of ammonium, nitrate, and hydroxylamine. Overall, reduction of nitrate to nitrite, nitrogen fixation, higher tolerance to ammonium than nitrate and tolerance and assimilation of nitrite were general features. Differential responses among closely related methanotrophic strains to overcome inhibition and toxicity from high nitrogen loads and assimilation of various nitrogen sources yield competitive fitness advantages to individual methane-oxidizing bacteria. Our observations proved that community structure at the deepest phylogenetic resolution potentially influences in situ functioning.
Directory of Open Access Journals (Sweden)
Cheol-Hwan You
2014-01-01
Full Text Available To assess the performance of rainfall estimation using specific differential phase observed by Bislsan radar, the first polarimetric radar in Korea, three rainfall cases occurring in 2011 were selected, each caused by different conditions: the first is the Changma front and typhoon, the second is only the Changma front, and the third is only a typhoon. For quantitative use of specific differential phase (KDP, a data quality algorithm was developed for differential phase shift (ΦDP, composed of two steps; the first involves removal of scattered noise and the second is unfolding of ΦDP. This order of the algorithm is necessary so as not to remove unfolded areas, which are the real meteorological target. All noise was removed and the folded ΦDP were unfolded successfully for this study. RKDP relations for S-band radar were calculated for 84,754 samples of observed drop size distribution (DSD using different drop shape assumptions. The relation for the Bringi drop shape showed the best statistics: 0.28 for normalized error, and 6.7 mm for root mean square error for rainfall heavier than 10 mm h-1. Because the drop shape assumption affects the accuracy of rainfall estimation differently for different rainfall types, such characteristics should be taken into account to estimate rainfall more accurately using polarimetric variables.
Bilyeu, David
This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For
2013-04-02
...'') \\1\\ from certain regional transmission organizations (``RTOs'') and independent system operators... include three RTOs (Midwest Independent Transmission System Operator, Inc. (``MISO''); ISO New England..., responsibilities and services of ISOs and RTOs are substantially similar.\\29\\ As described in the Proposed Order...
Noise-induced transitions at a Hopf bifurcation in a first-order delay-differential equation
International Nuclear Information System (INIS)
Longtin, A.
1991-01-01
The influence of colored noise on the Hopf bifurcation in a first-order delay-differential equation (DDE), a model paradigm for nonlinear delayed feedback systems, is considered. First, it is shown, using a stability analysis, how the properties of the DDE depend on the ratio R of system delay to response time. When this ratio is small, the DDE behaves more like a low-dimensional system of ordinary differential equations (ODE's); when R is large, one obtains a singular perturbation limit in which the behavior of the DDE approaches that of a discrete time map. The relative magnitude of the additive and multiplicative noise-induced postponements of the Hopf bifurcation are numerically shown to depend on the ratio R. Although both types of postponements are minute in the large-R limit, they are almost equal due to an equivalence of additive and parametric noise for discrete time maps. When R is small, the multiplicative shift is larger than the additive one at large correlation times, but the shifts are equal for small correlation times. In fact, at constant noise power, the postponement is only slightly affected by the correlation time of the noise, except when the noise becomes white, in which case the postponement drastically decreases. This is a numerical study of the stochastic Hopf bifurcation, in ODE's or DDE's, that looks at the effect of noise correlation time at constant power. Further, it is found that the slope at the fixed point averaged over the stochastic-parameter motion acts, under certain conditions, as a quantitative indicator of oscillation onset in the presence of noise. The problem of how properties of the DDE carry over to ODE's and to maps is discussed, along with the proper theoretical framework in which to study nonequilibrium phase transitions in this class of functional differential equations
This document may be of assistance in applying the Title V air operating permit regulations. This document is part of the Title V Petition Database available at www2.epa.gov/title-v-operating-permits/title-v-petition-database.
2010-07-01
... woodworking machines (Order 5). 570.55 Section 570.55 Labor Regulations Relating to Labor (Continued) WAGE AND... woodworking machines (Order 5). Link to an amendment published at 75 FR 28455, May 20, 2010. (a) Finding and declaration of fact. The following occupations involved in the operation of power-driven wood-working machines...
Li, Huibin
2011-09-01
This paper presents a mesh-based approach for 3D face recognition using a novel local shape descriptor and a SIFT-like matching process. Both maximum and minimum curvatures estimated in the 3D Gaussian scale space are employed to detect salient points. To comprehensively characterize 3D facial surfaces and their variations, we calculate weighted statistical distributions of multiple order surface differential quantities, including histogram of mesh gradient (HoG), histogram of shape index (HoS) and histogram of gradient of shape index (HoGS) within a local neighborhood of each salient point. The subsequent matching step then robustly associates corresponding points of two facial surfaces, leading to much more matched points between different scans of a same person than the ones of different persons. Experimental results on the Bosphorus dataset highlight the effectiveness of the proposed method and its robustness to facial expression variations. © 2011 IEEE.
International Nuclear Information System (INIS)
Anastasiou, C
2004-01-01
The authors present a calculation of the fully differential cross section for Higgs boson production in the gluon fusion channel through next-to-next-to-leading order in perturbative QCD. They apply the method introduced in [1] to compute double real emission corrections. The calculation permits arbitrary cuts on the final state in the reaction hh → H + X. it can be easily extended to include decays of the Higgs boson into observable final states. In this Letter, they discuss the most important features of the calculation, and present some examples of physical applications that illustrate the range of observables that can be studied using the result. They compute the NNLO rapidity distribution of the Higgs boson, and also calculate the NNLO rapidity distribution with a veto on jet activity
National Research Council Canada - National Science Library
Mitchell, Jason
2002-01-01
A method is presented for the generation of exact numerical coefficients found in two families of implicit Chebyshev methods for the numerical integration of first- and second-order ordinary differential equations...
Nadi, S.; Delavar, M. R.
2011-06-01
This paper presents a generic model for using different decision strategies in multi-criteria, personalized route planning. Some researchers have considered user preferences in navigation systems. However, these prior studies typically employed a high tradeoff decision strategy, which used a weighted linear aggregation rule, and neglected other decision strategies. The proposed model integrates a pairwise comparison method and quantifier-guided ordered weighted averaging (OWA) aggregation operators to form a personalized route planning method that incorporates different decision strategies. The model can be used to calculate the impedance of each link regarding user preferences in terms of the route criteria, criteria importance and the selected decision strategy. Regarding the decision strategy, the calculated impedance lies between aggregations that use a logical "and" (which requires all the criteria to be satisfied) and a logical "or" (which requires at least one criterion to be satisfied). The calculated impedance also includes taking the average of the criteria scores. The model results in multiple alternative routes, which apply different decision strategies and provide users with the flexibility to select one of them en-route based on the real world situation. The model also defines the robust personalized route under different decision strategies. The influence of different decision strategies on the results are investigated in an illustrative example. This model is implemented in a web-based geographical information system (GIS) for Isfahan in Iran and verified in a tourist routing scenario. The results demonstrated, in real world situations, the validity of the route planning carried out in the model.
Directory of Open Access Journals (Sweden)
Abdel-Ouahab Boudraa
2005-10-01
Full Text Available In white-light interference microscopy, measurement of surface shape generally requires peak extraction of the fringe function envelope. In this paper the Teager-Kaiser energy and higher-order energy operators are proposed for efficient extraction of the fringe envelope. These energy operators are compared in terms of precision, robustness to noise, and subsampling. Flexible energy operators, depending on order and lag parameters, can be obtained. Results show that smoothing and interpolation of envelope approximation using spline model performs better than Gaussian-based approach.
Energy Technology Data Exchange (ETDEWEB)
Wang, Bin, E-mail: wangbinmaths@gmail.com [Department of Mathematics, Nanjing University, State Key Laboratory for Novel Software Technology at Nanjing University, Nanjing 210093 (China); Wu, Xinyuan, E-mail: xywu@nju.edu.cn [Department of Mathematics, Nanjing University, State Key Laboratory for Novel Software Technology at Nanjing University, Nanjing 210093 (China)
2012-03-05
This Letter proposes a new high precision energy-preserving integrator for system of oscillatory second-order differential equations q{sup ″}(t)+Mq(t)=f(q(t)) with a symmetric and positive semi-definite matrix M and f(q)=−∇U(q). The system is equivalent to a separable Hamiltonian system with Hamiltonian H(p,q)=1/2 p{sup T}p+1/2 q{sup T}Mq+U(q). The properties of the new energy-preserving integrator are analyzed. The well-known Fermi–Pasta–Ulam problem is performed numerically to show that the new integrator preserves the energy integral with higher accuracy than Average Vector Field (AVF) method and an energy-preserving collocation method. -- Highlights: ► A novel high order energy-preserving integrator AAVF-GL is proposed. ► The important properties of the new integrator AAVF-GL are shown. ► Numerical experiment is carried out compared with AVF method etc. appeared recently.
2017-06-09
joint operational planning . 15. SUBJECT TERMS Complexity Theory , Complex Systems Theory , Complex Adaptive Systems, Dynamical Systems, Joint...complexity theory to analyze military problems and increase joint staff understanding of the operational environment during joint operational planning ?” the...13). Complex Systems Theory : “the study of the behavior of [complex adaptive] systems” (Ilachinski 2004, 4). For the purpose of this thesis there is
Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators
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Allaberen Ashyralyev
2014-01-01
Full Text Available The nonlocal boundary value problem for the parabolic differential equation v'(t+A(tv(t=f(t (0≤t≤T, v(0=v(λ+φ, 0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t is investigated. The well-posedness of this problem is established in Banach spaces C0β,γ(Eα-β of all Eα-β-valued continuous functions φ(t on [0,T] satisfying a Hölder condition with a weight (t+τγ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.
Differential operators associated with Gegenbauer polynomials - 2: The limit-point case
International Nuclear Information System (INIS)
Onyango Otieno, V.P.
1987-10-01
In this paper we study the limit-point case of the Gegenbauer differential equation -((1-x 2 ) υ+1/2 y'(x)) 1 +υ 2 (1-x 2 ) υ-1/2 y(x)=λ(1-x 2 ) υ-1/2 y(x), (x ε (-1,1), λ ε C) in both the so-called right-definite and left-definite cases based partially on a classical approach due to E.C. Titchmarsh. We then link the Titchmarsh approach with operator theoretic results in the spaces L 2 w (-1,1) and H 2 p,q (-1,1). (author). 19 refs
International Nuclear Information System (INIS)
Jamalipour, Mostafa; Sayareh, Reza; Gharib, Morteza; Khoshahval, Farrokh; Karimi, Mahmood Reza
2013-01-01
Highlights: ► A new method called QPSO-DM is applied to BNPP in-core fuel management optimization. ► It is found that QPSO-DM performs better than PSO and QPSO. ► This method provides a permissible arrangement for optimum loading pattern. - Abstract: This paper presents a new method using Quantum Particle Swarm Optimization with Differential Mutation operator (QPSO-DM) for optimizing WWER-1000 core fuel management. Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) have shown good performance on in-core fuel management optimization (ICFMO). The objective of this paper is to show that QPSO-DM performs very well and is comparable to PSO and Quantum Particle Swarm Optimization (QPSO). Most of the strategies for ICFMO are based on maximizing multiplication factor (k eff ) to increase cycle length and minimizing power peaking factor (P q ) in order to improve fuel integrity. PSO, QPSO and QPSO-DM have been implemented to fulfill these requirements for the first operating cycle of WWER-1000 Bushehr Nuclear Power Plant (BNPP). The results show that QPSO-DM performs better than the others. A program has been written in MATLAB to map PSO, QPSO and QPSO-DM for loading pattern optimization. WIMS and CITATION have been used to simulate reactor core for neutronic calculations
Objective ARX Model Order Selection for Multi-Channel Human Operator Identification
Roggenkämper, N; Pool, D.M.; Drop, F.M.; van Paassen, M.M.; Mulder, M.
2016-01-01
In manual control, the human operator primarily responds to visual inputs but may elect to make use of other available feedback paths such as physical motion, adopting a multi-channel control strategy. Hu- man operator identification procedures generally require a priori selection of the model
International Nuclear Information System (INIS)
Zwingelstein, G.C.
1980-12-01
After a short description of a disturbance analysis system for nuclear plant based on real time dynamic modelling and simulation, a scheme for generating aggregated reduced models of high order systems is presented. This method allows the choice of dominant dynamic modes and its efficiency is illustrated for the case of a 29th order nuclear plant model
46 CFR 113.35-7 - Electric engine order telegraph systems; operations.
2010-10-01
... transmitter handle automatically connects that transmitter electrically to the engineroom indicator and simultaneously disconnects electrically all other transmitters. The reply pointers of all transmitters must... manually operated transfer switch which will disconnect the system in the unattended navigating bridge must...
Safety and Mission Assurance (SMA) Automated Task Order Management System (ATOMS) Operation Manual
Wallace, Shawn; Fikes, Lou A.
2016-01-01
This document describes operational aspects of the ATOMS system. The information provided is limited to the functionality provided by ATOMS and does not include information provided in the contractor's proprietary financial and task management system.
Identification and non-integer order modelling of synchronous machines operating as generator
Directory of Open Access Journals (Sweden)
Szymon Racewicz
2012-09-01
Full Text Available This paper presents an original mathematical model of a synchronous generator using derivatives of fractional order. In contrast to classical models composed of a large number of R-L ladders, it comprises half-order impedances, which enable the accurate description of the electromagnetic induction phenomena in a wide frequency range, while minimizing the order and number of model parameters. The proposed model takes into account the skin eff ect in damper cage bars, the eff ects of eddy currents in rotor solid parts, and the saturation of the machine magnetic circuit. The half-order transfer functions used for modelling these phenomena were verifi ed by simulation of ferromagnetic sheet impedance using the fi nite elements method. The analysed machine’s parameters were identified on the basis of SSFR (StandStill Frequency Response characteristics measured on a gradually magnetised synchronous machine.
Saeed, Muhammad
2012-01-01
The thesis study reveals that the position of bottleneck is a significant importance in supplychain process. The modern supply chain is characterized as having diverse products due tomass customization, dynamic production technology and ever changing customer demand.Usually customized supply chain process consists of an assemble to order (ATO) or make-to-order (MTO) type of operation. By controlling the supply constraints at upstream, a smoothmaterial flow achieved at downstream. Effective ma...
Galindo-Israel, V.; Imbriale, W.; Shogen, K.; Mittra, R.
1990-01-01
In obtaining solutions to the first-order nonlinear partial differential equations (PDEs) for synthesizing offset dual-shaped reflectors, it is found that previously observed computational problems can be avoided if the integration of the PDEs is started from an inner projected perimeter and integrated outward rather than starting from an outer projected perimeter and integrating inward. This procedure, however, introduces a new parameter, the main reflector inner perimeter radius p(o), when given a subreflector inner angle 0(o). Furthermore, a desired outer projected perimeter (e.g., a circle) is no longer guaranteed. Stability of the integration is maintained if some of the initial parameters are determined first from an approximate solution to the PDEs. A one-, two-, or three-parameter optimization algorithm can then be used to obtain a best set of parameters yielding a close fit to the desired projected outer rim. Good low cross-polarization mapping functions are also obtained. These methods are illustrated by synthesis of a high-gain offset-shaped Cassegrainian antenna and a low-noise offset-shaped Gregorian antenna.
Nishitani, Tatsuo
2017-01-01
Combining geometrical and microlocal tools, this monograph gives detailed proofs of many well/ill-posed results related to the Cauchy problem for diﬀerential operators with non-eﬀectively hyperbolic double characteristics. Previously scattered over numerous diﬀerent publications, the results are presented from the viewpoint that the Hamilton map and the geometry of bicharacteristics completely characterizes the well/ill-posedness of the Cauchy problem. A doubly characteristic point of a diﬀerential operator P of order m (i.e. one where Pm = dPm = 0) is eﬀectively hyperbolic if the Hamilton map FPm has real non-zero eigenvalues. When the characteristics are at most double and every double characteristic is eﬀectively hyperbolic, the Cauchy problem for P can be solved for arbitrary lower order terms. If there is a non-eﬀectively hyperbolic characteristic, solvability requires the subprincipal symbol of P to lie between − Pµj and P µj , where iµj are the positive imaginary eigenvalues of FPm ....
Order Denying Petition to Object to Operating Permit for TVA's Shawnee Fossil Plant
This document may be of assistance in applying the Title V air operating permit regulations. This document is part of the Title V Petition Database available at www2.epa.gov/title-v-operating-permits/title-v-petition-database. Some documents in the database are a scanned or retyped version of a paper photocopy of the original. Although we have taken considerable effort to quality assure the documents, some may contain typographical errors. Contact the office that issued the document if you need a copy of the original.
Spectrum of Discrete Second-Order Difference Operator with Sign-Changing Weight and Its Applications
Directory of Open Access Journals (Sweden)
Ruyun Ma
2014-01-01
Full Text Available Let T>1 be an integer, and let=1,2,…,T. We discuss the spectrum of discrete linear second-order eigenvalue problems Δ2ut-1+λmtut=0, t∈, u0=uT+1=0, where λ≠0 is a parameter, m:→ℝ changes sign and mt≠0 on . At last, as an application of this spectrum result, we show the existence of sign-changing solutions of discrete nonlinear second-order problems by using bifurcate technique.
Frames, the Loewner order and eigendecomposition for morphological operators on tensor fields
van de Gronde, Jasper; Roerdink, Jos B. T. M.
2014-01-01
Rotation invariance is an important property for operators on tensor fields, but up to now, most methods for morphology on tensor fields had to either sacrifice rotation invariance, or do without the foundation of mathematical morphology: a lattice structure. Recently, we proposed a framework for
Neuronal Activity in the Visual Cortex Reveals the Temporal Order of Cognitive Operations
Moro, S.I.; Tolboom, M.; Khayat, P.S.; Roelfsema, P.R.
2010-01-01
Most mental processes consist of a number of processing steps that are executed sequentially. The timing of the individual mental operations can usually only be estimated indirectly, from the pattern of reaction times. In vision, however, many processing steps are associated with the modulation of
Neuronal activity in the visual cortex reveals the temporal order of cognitive operations
Moro, Sancho I.; Tolboom, Michiel; Khayat, Paul S.; Roelfsema, Pieter R.
2010-01-01
Most mental processes consist of a number of processing steps that are executed sequentially. The timing of the individual mental operations can usually only be estimated indirectly, from the pattern of reaction times. In vision, however, many processing steps are associated with the modulation of
Czech Academy of Sciences Publication Activity Database
Kyselová, D.; Dubois, D.; Komorníková, M.; Mesiar, Radko
2007-01-01
Roč. 15, č. 6 (2007), s. 1100-1106 ISSN 1063-6706 Institutional research plan: CEZ:AV0Z10750506 Keywords : aggregation operator * multicriteria decision making * preference relation * preorder Subject RIV: BA - General Mathematics Impact factor: 2.137, year: 2007
2012-11-15
... to an extratropical storm that caused widespread power outages, severe flooding, and severe... storm. FAA Analysis Under the FAA's High Density Rule at DCA and Orders limiting operations at LGA, JFK... area or northeastern U.S. affected by the storm. These circumstances may have created a unique hardship...
Directory of Open Access Journals (Sweden)
Jamal Salah
2011-01-01
Full Text Available In this article, we introduce a class of starlike functions of order α by using a fractional operator involving Caputo's fractional which was introduced recently by the authors. The coefficient inequalities and distortion theorems are determined. Further some subordination theorems are given. In addition, results involving Hadamard product are also discussed.
Lorenzo, C F; Hartley, T T; Malti, R
2013-05-13
A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.
Nicholls, David P
2018-04-01
The faithful modelling of the propagation of linear waves in a layered, periodic structure is of paramount importance in many branches of the applied sciences. In this paper, we present a novel numerical algorithm for the simulation of such problems which is free of the artificial singularities present in related approaches. We advocate for a surface integral formulation which is phrased in terms of impedance-impedance operators that are immune to the Dirichlet eigenvalues which plague the Dirichlet-Neumann operators that appear in classical formulations. We demonstrate a high-order spectral algorithm to simulate these latter operators based upon a high-order perturbation of surfaces methodology which is rapid, robust and highly accurate. We demonstrate the validity and utility of our approach with a sequence of numerical simulations.