Lötstedt, Erik; Jentschura, Ulrich D
2009-02-01
In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.
The recursive solution of the Schroedinger equation
Haydock, R.
The transformation of an arbitrary quantum model and its subsequent analysis is proposed. The chain expresses mathematically the physical concept of local environment. The recursive transformation yields analytic chains for some systems, but it is also convenient and efficient for constructing numerical chain models enabling the solution of problems which are too big for numerical matrix methods. The chain model sugests new approach to quantum mechanical models. Because of the simple solution of chain models, the qualitative behaviour of different physical properties can be determined. Unlike many methods for solving quantum models, one has rigorous results about the convergence of approximation. Because they are defined recursively, the approsimations are suited to computation. (Ha)
Simple recursion relations for general field theories
Cheung, Clifford; Shen, Chia-Hsien; Trnka, Jaroslav
2015-01-01
On-shell methods offer an alternative definition of quantum field theory at tree-level, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a covering space of recursion relations which naturally generalizes all existing constructions, including those of BCFW and Risager. The validity of each recursion relation hinges on the large momentum behavior of an n-point scattering amplitude under an m-line momentum shift, which we determine solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory are 5-line constructible. Amplitudes are 3-line constructible if an external particle carries spin or if the scalars in the theory carry equal charge under a global or gauge symmetry. Remarkably, this implies the 3-line constructibility of all gauge theories with fermions and complex scalars in arbitrary representations, all supersymmetric theories, and the standard model. Moreover, all amplitudes in non-renormalizable theories without derivative interactions are constructible; with derivative interactions, a subset of amplitudes is constructible. We illustrate our results with examples from both renormalizable and non-renormalizable theories. Our study demonstrates both the power and limitations of recursion relations as a self-contained formulation of quantum field theory.
Model-based dispersive wave processing: A recursive Bayesian solution
Candy, J.V.; Chambers, D.H.
1999-01-01
Wave propagation through dispersive media represents a significant problem in many acoustic applications, especially in ocean acoustics, seismology, and nondestructive evaluation. In this paper we propose a propagation model that can easily represent many classes of dispersive waves and proceed to develop the model-based solution to the wave processing problem. It is shown that the underlying wave system is nonlinear and time-variable requiring a recursive processor. Thus the general solution to the model-based dispersive wave enhancement problem is developed using a Bayesian maximum a posteriori (MAP) approach and shown to lead to the recursive, nonlinear extended Kalman filter (EKF) processor. The problem of internal wave estimation is cast within this framework. The specific processor is developed and applied to data synthesized by a sophisticated simulator demonstrating the feasibility of this approach. copyright 1999 Acoustical Society of America.
Multiphonon theory: generalized Wick's theorem and recursion formulas
Silvestre-Brac, B.; Piepenbring, R.
1982-04-01
Overlaps and matrix elements of one and two-body operators are calculated in a space spanned by multiphonons of different types taking properly the Pauli principle into account. Two methods are developped: a generalized Wick's theorem dealing with new contractions and recursion formulas well suited for numerical applications
Recursive form of general limited memory variable metric methods
Lukšan, Ladislav; Vlček, Jan
2013-01-01
Roč. 49, č. 2 (2013), s. 224-235 ISSN 0023-5954 Institutional support: RVO:67985807 Keywords : unconstrained optimization * large scale optimization * limited memory methods * variable metric updates * recursive matrix formulation * algorithms Subject RIV: BA - General Mathematics Impact factor: 0.563, year: 2013 http://dml.cz/handle/10338.dmlcz/143365
Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang
2006-01-01
This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…
Abadi, Mohammad Tahaye
2015-01-01
A recursive solution method is derived for the transient response of one-dimensional structures subjected to the general form of time dependent boundary conditions. Unlike previous solution methods that assumed the separation of variables, the present method involves formulating and solving the dynamic problems using the summation of two single-argument functions satisfying the motion equation. Based on boundary and initial conditions, a recursive procedure is derived to determine the single-argument functions. Such a procedure is applied to the general form of boundary conditions, and an analytical solution is derived by solving the recursive equation. The present solution method is implemented for base excitation problems, and the results are compared with those of the previous analytical solution and the Finite element (FE) analysis. The FE results converge to the present analytical solution, although considerable error is found in predicting a solution method on the basis of the separation of variables. The present analytical solution predicts the transient response for wave propagation problems in broadband excitation frequencies.
Abadi, Mohammad Tahaye [Aerospace Research Institute, Tehran (Iran, Islamic Republic of)
2015-10-15
A recursive solution method is derived for the transient response of one-dimensional structures subjected to the general form of time dependent boundary conditions. Unlike previous solution methods that assumed the separation of variables, the present method involves formulating and solving the dynamic problems using the summation of two single-argument functions satisfying the motion equation. Based on boundary and initial conditions, a recursive procedure is derived to determine the single-argument functions. Such a procedure is applied to the general form of boundary conditions, and an analytical solution is derived by solving the recursive equation. The present solution method is implemented for base excitation problems, and the results are compared with those of the previous analytical solution and the Finite element (FE) analysis. The FE results converge to the present analytical solution, although considerable error is found in predicting a solution method on the basis of the separation of variables. The present analytical solution predicts the transient response for wave propagation problems in broadband excitation frequencies.
Mueller, A. C.
1977-01-01
An analytical first order solution has been developed which describes the motion of an artificial satellite perturbed by an arbitrary number of zonal harmonics of the geopotential. A set of recursive relations for the solution, which was deduced from recursive relations of the geopotential, was derived. The method of solution is based on Von-Zeipel's technique applied to a canonical set of two-body elements in the extended phase space which incorporates the true anomaly as a canonical element. The elements are of Poincare type, that is, they are regular for vanishing eccentricities and inclinations. Numerical results show that this solution is accurate to within a few meters after 500 revolutions.
Recursive Subspace Identification of AUV Dynamic Model under General Noise Assumption
Zheping Yan
2014-01-01
Full Text Available A recursive subspace identification algorithm for autonomous underwater vehicles (AUVs is proposed in this paper. Due to the advantages at handling nonlinearities and couplings, the AUV model investigated here is for the first time constructed as a Hammerstein model with nonlinear feedback in the linear part. To better take the environment and sensor noises into consideration, the identification problem is concerned as an errors-in-variables (EIV one which means that the identification procedure is under general noise assumption. In order to make the algorithm recursively, propagator method (PM based subspace approach is extended into EIV framework to form the recursive identification method called PM-EIV algorithm. With several identification experiments carried out by the AUV simulation platform, the proposed algorithm demonstrates its effectiveness and feasibility.
Müller, Gert; Sacks, Gerald
1990-01-01
These proceedings contain research and survey papers from many subfields of recursion theory, with emphasis on degree theory, in particular the development of frameworks for current techniques in this field. Other topics covered include computational complexity theory, generalized recursion theory, proof theoretic questions in recursion theory, and recursive mathematics.
Papoyan, V.V.
1989-01-01
A Kerr generalized solution for a stationary axially-symmetric gravitational field of rotating self-gravitational objects is given. For solving the problem Einstein equations and their combinations are used. The particular cases: internal and external Schwarzschild solutions are considered. The external solution of the stationary problem is a Kerr solution generalization. 3 refs
WKB solutions of difference equations and reconstruction by the topological recursion
Marchal, Olivier
2018-01-01
The purpose of this article is to analyze the connection between Eynard-Orantin topological recursion and formal WKB solutions of a \\hbar -difference equation: \\Psi(x+\\hbar)=≤ft(e\\hbar\\fracd{dx}\\right) \\Psi(x)=L(x;\\hbar)\\Psi(x) with L(x;\\hbar)\\in GL_2( ({C}(x))[\\hbar]) . In particular, we extend the notion of determinantal formulas and topological type property proposed for formal WKB solutions of \\hbar -differential systems to this setting. We apply our results to a specific \\hbar -difference system associated to the quantum curve of the Gromov-Witten invariants of {P}1 for which we are able to prove that the correlation functions are reconstructed from the Eynard-Orantin differentials computed from the topological recursion applied to the spectral curve y=\\cosh-1\\frac{x}{2} . Finally, identifying the large x expansion of the correlation functions, proves a recent conjecture made by Dubrovin and Yang regarding a new generating series for Gromov-Witten invariants of {P}1 .
Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
Andersen, Jørgen Ellegaard; Borot, Gaëtan; Orantin, Nicolas
We propose a general theory whose main component are functorial assignments ∑→Ω∑ ∈ E (∑), for a large class of functors E from a certain category of bordered surfaces (∑'s) to a suitable a target category of topological vector spaces. The construction is done by summing appropriate compositions...... as Poisson structures on the moduli space of flat connections. The theory has a wider scope than that and one expects that many functorial objects in low-dimensional geometry and topology should have a GR construction. The geometric recursion has various projections to topological recursion (TR) and we...... in particular show it retrieves all previous variants and applications of TR. We also show that, for any initial data for topological recursion, one can construct initial data for GR with values in Frobenius algebra-valued continuous functions on Teichmueller space, such that the ωg,n of TR are obtained...
Goodstein, R L
2010-01-01
Recursive analysis develops natural number computations into a framework appropriate for real numbers. This text is based upon primary recursive arithmetic and presents a unique combination of classical analysis and intuitional analysis. Written by a master in the field, it is suitable for graduate students of mathematics and computer science and can be read without a detailed knowledge of recursive arithmetic.Introductory chapters on recursive convergence and recursive and relative continuity are succeeded by explorations of recursive and relative differentiability, the relative integral, and
Numerical solution of recirculating flow by a simple finite element recursion relation
Pepper, D W; Cooper, R E
1980-01-01
A time-split finite element recursion relation, based on linear basis functions, is used to solve the two-dimensional equations of motion. Recirculating flow in a rectangular cavity and free convective flow in an enclosed container are analyzed. The relation has the advantage of finite element accuracy and finite difference speed and simplicity. Incorporating dissipation parameters in the functionals decreases numerical dispersion and improves phase lag.
Roberts, Eric S
1986-01-01
Concentrating on the practical value of recursion, this text, the first of its kind, is essential to computer science students' education. In this text, students will learn the concept and programming applications of recursive thinking. This will ultimately prepare students for advanced topics in computer science such as compiler construction, formal language theory, and the mathematical foundations of computer science.
Hansen, Tobias
2015-07-01
This thesis covers two main topics: the tensorial structure of quantum field theory correlators in general spacetime dimensions and a method for computing string theory scattering amplitudes directly in target space. In the first part tensor structures in generic bosonic CFT correlators and scattering amplitudes are studied. To this end arbitrary irreducible tensor representations of SO(d) (traceless mixed-symmetry tensors) are encoded in group invariant polynomials, by contracting with sets of commuting and anticommuting polarization vectors which implement the index symmetries of the tensors. The tensor structures appearing in CFT d correlators can then be inferred by studying these polynomials in a d + 2 dimensional embedding space. It is shown with an example how these correlators can be used to compute general conformal blocks describing the exchange of mixed-symmetry tensors in four-point functions, which are crucial for advancing the conformal bootstrap program to correlators of operators with spin. Bosonic string theory lends itself as an ideal example for applying the same methods to scattering amplitudes, due to its particle spectrum of arbitrary mixed-symmetry tensors. This allows in principle the definition of on-shell recursion relations for string theory amplitudes. A further chapter introduces a different target space definition of string scattering amplitudes. As in the case of on-shell recursion relations, the amplitudes are expressed in terms of their residues via BCFW shifts. The new idea here is that the residues are determined by use of the monodromy relations for open string theory, avoiding the infinite sums over the spectrum arising in on-shell recursion relations. Several checks of the method are presented, including a derivation of the Koba-Nielsen amplitude in the bosonic string. It is argued that this method provides a target space definition of the complete S-matrix of string theory at tree-level in a at background in terms of a small
Jeffrey eWatumull
2014-01-01
Full Text Available It is a truism that conceptual understanding of a hypothesis is required for its empirical investigation. However the concept of recursion as articulated in the context of linguistic analysis has been perennially confused. Nowhere has this been more evident than in attempts to critique and extend Hauser, Chomsky, and Fitch’s (2002 articulation. These authors put forward the hypothesis that what is uniquely human and unique to the faculty of language—the faculty of language in the narrow sense (FLN—is a recursive system that generates and maps syntactic objects to conceptual-intentional and sensory-motor systems. This thesis was based on the standard mathematical definition of recursion as understood by Gödel and Turing, and yet has commonly been interpreted in other ways, most notably and incorrectly as a thesis about the capacity for syntactic embedding. As we explain, the recursiveness of a function is defined independent of such output, whether infinite or finite, embedded or unembedded—existent or nonexistent. And to the extent that embedding is a sufficient, though not necessary, diagnostic of recursion, it has not been established that the apparent restriction on embedding in some languages is of any theoretical import. Misunderstanding of these facts has generated research that is often irrelevant to the FLN thesis as well as to other theories of language competence that focus on its generative power of expression. This essay is an attempt to bring conceptual clarity to such discussions as well as to future empirical investigations by explaining three criterial properties of recursion: computability (i.e., rules in intension rather than lists in extension; definition by induction (i.e., rules strongly generative of structure; and mathematical induction (i.e., rules for the principled—and potentially unbounded—expansion of strongly generated structure. By these necessary and sufficient criteria, the grammars of all natural
Chowdhury, A.R.; Mukherjee, R.
1984-01-01
The authors have made an exhaustive analysis for an equation introduced by Sabatier (1981) which in the special case reduces to the Harry-Dym equation. First they have deduced the Lie point symmetries and the corresponding ordinary differential equation, through the similarity forms. Next the extended Lie-Backlund type generators are deduced. In the second part the cnoidal wave like solutions are considered. From the Fourier spectrum analysis it is shown that a cnoidal wave breaks into several ordinary solitary waves. (Auth.)
Cobham recursive set functions
Beckmann, A.; Buss, S.; Friedman, S.-D.; Müller, M.; Thapen, Neil
2016-01-01
Roč. 167, č. 3 (2016), s. 335-369 ISSN 0168-0072 R&D Projects: GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : set function * polynomial time * Cobham recursion Subject RIV: BA - General Mathematics Impact factor: 0.647, year: 2016 http://www.sciencedirect.com/science/article/pii/S0168007215001293
Recursive automatic classification algorithms
Bauman, E V; Dorofeyuk, A A
1982-03-01
A variational statement of the automatic classification problem is given. The dependence of the form of the optimal partition surface on the form of the classification objective functional is investigated. A recursive algorithm is proposed for maximising a functional of reasonably general form. The convergence problem is analysed in connection with the proposed algorithm. 8 references.
A recursive transfer-matrix solution for a dipole radiating inside and outside a stratified sphere
Moroz, Alexander
2005-01-01
Fast and numerically stable transfer-matrix solution is presented for the classical electromagnetics problem of a dipole radiating inside and outside a stratified sphere consisting of concentric spherical shells. There is no limitation on the dipole position, the number of the concentric shells, the shell medium, or on the sphere radius. Electromagnetic fields are determined anywhere in the space, the time-averaged angular distribution of the radiated power, the total radiated power, Ohmic losses due to an absorbing shell, and Green's function are calculated. An absorbing, optically active, and ultrathin (-bar 10nm) metallic shell (core), characterized by a nonlocal dielectric function, are all allowed. The classical results are then applied to inelastic light scattering (fluorescence and Raman), the radiative and nonradiative normalized decay rates, and frequency shift. Using correspondence principle, the radiative decay rate is calculated from the Poynting vector, whereas the nonradiative decay rate is calculated from the Ohmic losses inside a sphere absorptive shell. Numerical stability of our method and limitations of classical description of decay rates are addressed. The importance of grouping various radiative and nonradiative decay mechanisms into local and nonlocal decay rates is emphasized. Further possible extensions of the theory presented here to the case of an arbitrary multilayered (axially symmetric) particle and to the classical problem of a radiating quadrupole in the presence of a multilayered particle are briefly outlined. Various applications for chemical speciation, LIDAR, fluorescent microscopy, engineering of decay rates, identification of biological particles, and monitoring specific cell functions are envisaged. Computer program is freely available at http://www.wave-scattering.com
Adding Recursive Constructs to Bialgebraic Semantics
Klin, Bartek
2004-01-01
This paper aims at fitting a general class of recursive equations into the framework of ‘well-behaved' structural operational semantics, formalized as bialgebraic semantics by Turi and Plotkin. Rather than interpreting recursive constructs by means of operational rules, separate recursive equatio...
Efficient Integrity Checking for Databases with Recursive Views
Martinenghi, Davide; Christiansen, Henning
2005-01-01
Efficient and incremental maintenance of integrity constraints involving recursive views is a difficult issue that has received some attention in the past years, but for which no widely accepted solution exists yet. In this paper a technique is proposed for compiling such integrity constraints in...... approaches have not achieved comparable optimization with the same level of generality....
Hirata, So; Doran, Alexander E; Knowles, Peter J; Ortiz, J V
2017-07-28
A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.
Axisymmetric solution with charge in general relativity
Arutyunyan, G.G.; Papoyan, V.V.
1989-01-01
The possibility of generating solutions to the equations of general relativity from known solutions of the generalized theory of gravitation and vice versa is proved. An electrovac solution to Einstein's equations that describes a static axisymmetric gravitational field is found. 14 refs
Petersen, Claudio Z. [Universidade Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Bodmann, Bardo E.J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-graduacao em Engenharia Mecanica; Barros, Ricardo C. [Universidade do Estado do Rio de Janeiro, Nova Friburgo, RJ (Brazil). Inst. Politecnico
2014-12-15
In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i.e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.
The Method of Recursive Counting: Can one go further?
Creutz, M.; Horvath, I.
1993-12-01
After a short review of the Method of Recursive Counting we introduce a general algebraic description of recursive lattice building. This provides a rigorous framework for discussion of method's limitations
Recursive-operator method in vibration problems for rod systems
Rozhkova, E. V.
2009-12-01
Using linear differential equations with constant coefficients describing one-dimensional dynamical processes as an example, we show that the solutions of these equations and systems are related to the solution of the corresponding numerical recursion relations and one does not have to compute the roots of the corresponding characteristic equations. The arbitrary functions occurring in the general solution of the homogeneous equations are determined by the initial and boundary conditions or are chosen from various classes of analytic functions. The solutions of the inhomogeneous equations are constructed in the form of integro-differential series acting on the right-hand side of the equation, and the coefficients of the series are determined from the same recursion relations. The convergence of formal solutions as series of a more general recursive-operator construction was proved in [1]. In the special case where the solutions of the equation can be represented in separated variables, the power series can be effectively summed, i.e., expressed in terms of elementary functions, and coincide with the known solutions. In this case, to determine the natural vibration frequencies, one obtains algebraic rather than transcendental equations, which permits exactly determining the imaginary and complex roots of these equations without using the graphic method [2, pp. 448-449]. The correctness of the obtained formulas (differentiation formulas, explicit expressions for the series coefficients, etc.) can be verified directly by appropriate substitutions; therefore, we do not prove them here.
Recursion Relations for Conformal Blocks
Penedones, João; Yamazaki, Masahito
2016-09-12
In the context of conformal field theories in general space-time dimension, we find all the possible singularities of the conformal blocks as functions of the scaling dimension $\\Delta$ of the exchanged operator. In particular, we argue, using representation theory of parabolic Verma modules, that in odd spacetime dimension the singularities are only simple poles. We discuss how to use this information to write recursion relations that determine the conformal blocks. We first recover the recursion relation introduced in 1307.6856 for conformal blocks of external scalar operators. We then generalize this recursion relation for the conformal blocks associated to the four point function of three scalar and one vector operator. Finally we specialize to the case in which the vector operator is a conserved current.
New solutions of Heun's general equation
Ishkhanyan, Artur; Suominen, Kalle-Antti
2003-01-01
We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)
Properties of general relativistic kink solution
Kodama, T.; Oliveira, L.C.S. de; Santos, F.C.
1978-12-01
Properties of the general relativistic kink solution of a nonlinear scalar field recently obtained, are discussed. It has been shown that the kink solution is stable against radical perturbations. Possible applications to Hadron physics from the geometrodynamic point of view are suggested [pt
Oliva, Paulo Borges
2002-01-01
Modified bar recursion is a variant of Spector's bar recursion which can be used to give a realizability interpretation of the classical axiom of dependent choice. This realizability allows for the extraction of witnesses from proofs of forall-exists-formulas in classical analysis. In this talk I...... shall report on results regarding the relationship between modified and Spector's bar recursion. I shall also show that a seemingly weak form of modified bar recursion is as strong as "full" modified bar recursion in higher types....
General solution of string inspired nonlinear equations
Bandos, I.A.; Ivanov, E.; Kapustnikov, A.A.; Ulanov, S.A.
1998-07-01
We present the general solution of the system of coupled nonlinear equations describing dynamics of D-dimensional bosonic string in the geometric (or embedding) approach. The solution is parametrized in terms of two sets of the left- and right-moving Lorentz harmonic variables providing a special coset space realization of the product of two (D-2) dimensional spheres S D-2 = SO(1,D-1)/SO(1,1)xSO(D-2) contained in K D-2 . (author)
General solution of linear vector supersymmetry
Blasi, Alberto; Maggiore, Nicola
2007-01-01
We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such a solution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the cohomology technology, usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example
Generalized solutions of nonlinear partial differential equations
Rosinger, EE
1987-01-01
During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin
General Relativity solutions in modified gravity
Motohashi, Hayato; Minamitsuji, Masato
2018-06-01
Recent gravitational wave observations of binary black hole mergers and a binary neutron star merger by LIGO and Virgo Collaborations associated with its optical counterpart constrain deviation from General Relativity (GR) both on strong-field regime and cosmological scales with high accuracy, and further strong constraints are expected by near-future observations. Thus, it is important to identify theories of modified gravity that intrinsically possess the same solutions as in GR among a huge number of theories. We clarify the three conditions for theories of modified gravity to allow GR solutions, i.e., solutions with the metric satisfying the Einstein equations in GR and the constant profile of the scalar fields. Our analysis is quite general, as it applies a wide class of single-/multi-field scalar-tensor theories of modified gravity in the presence of matter component, and any spacetime geometry including cosmological background as well as spacetime around black hole and neutron star, for the latter of which these conditions provide a necessary condition for no-hair theorem. The three conditions will be useful for further constraints on modified gravity theories as they classify general theories of modified gravity into three classes, each of which possesses i) unique GR solutions (i.e., no-hair cases), ii) only hairy solutions (except the cases that GR solutions are realized by cancellation between singular coupling functions in the Euler-Lagrange equations), and iii) both GR and hairy solutions, for the last of which one of the two solutions may be selected dynamically.
Recursion Operators for Dispersionless KP Hierarchy
Cheng Qiusheng; He Jingsong
2012-01-01
Based on the corresponding theorem between dispersionless KP (dKP) hierarchy and ħ-dependent KP (ħKP) hierarchy, a general formal representation of the recursion operators for dKP hierarchy under n-reduction is given in a systematical way from the corresponding ħKP hierarchy. To illustrate this method, the recursion operators for dKP hierarchy under 2-reduction and 3-reduction are calculated in detail.
Recursion theory computational aspects of definability
Chong, Chi Tat
2015-01-01
This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion theory. These include structure theory, hyperarithmetic determinacy and rigidity, basis theorems, independence results on Turing degrees, as well as applications to higher randomness.
A strange recursion operator demystified
Sergyeyev, A
2005-01-01
We show that a new integrable two-component system of KdV type studied by Karasu (Kalkanli) et al (2004 Acta Appl. Math. 83 85-94) is bi-Hamiltonian, and its recursion operator, which has a highly unusual structure of nonlocal terms, can be written as a ratio of two compatible Hamiltonian operators found by us. Using this we prove that the system in question possesses an infinite hierarchy of local commuting generalized symmetries and conserved quantities in involution, and the evolution systems corresponding to these symmetries are bi-Hamiltonian as well. We also show that upon introduction of suitable nonlocal variables the nonlocal terms of the recursion operator under study can be written in the usual form, with the integration operator D -1 x appearing in each term at most once. (letter to the editor)
Recursion complexity in cognition
Roeper, Thomas
2014-01-01
This volume focuses on recursion, highlighting its central role in modern science. It reveals a host of new theoretical arguments, philosophical perspectives, formal representations and empirical evidence from parsing, acquisition and computer models.
Bouncing solutions from generalized EoS
Contreras, F. [Universidad de Santiago de Chile, Departamento de Matematicas, Santiago (Chile); Cruz, N.; Palma, G. [Universidad de Santiago, Departamento de Fisica, Santiago (Chile)
2017-12-15
We present an exact analytical bouncing solution for a closed universe filled with only one exotic fluid with negative pressure, obeying a generalized equation of state (GEoS) of the form p(ρ) = Aρ+Bρ{sup λ}, where A, B and λ are constants. In our solution A = -1/3, λ = 1/2, and B < 0 is kept as a free parameter. For particular values of the initial conditions, we find that our solution obeys the null energy condition (NEC), which allows us to reinterpret the matter source as that of a real scalar field, φ, with a positive kinetic energy and a potential V(φ). We numerically compute the scalar field as a function of time as well as its potential V(φ), and we find an analytical function for the potential that fits very accurately with the numerical data obtained. The shape of this potential can be well described by a Gaussian-type of function, and hence there is no spontaneous symmetry minimum of V(φ). We show numerically that the bouncing scenario is structurally stable in a small vicinity of the value A = -1/3. We also include the study of the evolution of the linear fluctuations due to linear perturbations in the metric. These perturbations show an oscillatory behavior near the bouncing and approach a constant at large scales. (orig.)
Isotope decay equations solved by means of a recursive method
Grant, Carlos
2009-01-01
The isotope decay equations have been solved using forward finite differences taking small time steps, among other methods. This is the case of the cell code WIMS, where it is assumed that concentrations of all fissionable isotopes remain constant during the integration interval among other simplifications. Even when the problem could be solved running through a logical tree, all algorithms used for resolution of these equations used an iterative programming formulation. That happened because nearly all computer languages used up to a recent past by the scientific programmers did not support recursion, such as the case of the old versions of FORTRAN or BASIC. Nowadays also an integral form of the depletion equations is used in Monte Carlo simulation. In this paper we propose another programming solution using a recursive algorithm, running through all descendants of each isotope and adding their contributions to all isotopes in each generation. The only assumption made for this solution is that fluxes remain constant during the whole time step. Recursive process is interrupted when a stable isotope was attained or the calculated contributions are smaller than a given precision. These algorithms can be solved by means an exact analytic method that can have some problems when circular loops appear for isotopes with alpha decay, and a more general polynomial method. Both methods are shown. (author)
Improved Undecidability Results for Reachability Games on Recursive Timed Automata
Shankara Narayanan Krishna
2014-08-01
Full Text Available We study reachability games on recursive timed automata (RTA that generalize Alur-Dill timed automata with recursive procedure invocation mechanism similar to recursive state machines. It is known that deciding the winner in reachability games on RTA is undecidable for automata with two or more clocks, while the problem is decidable for automata with only one clock. Ouaknine and Worrell recently proposed a time-bounded theory of real-time verification by claiming that restriction to bounded-time recovers decidability for several key decision problem related to real-time verification. We revisited games on recursive timed automata with time-bounded restriction in the hope of recovering decidability. However, we found that the problem still remains undecidable for recursive timed automata with three or more clocks. Using similar proof techniques we characterize a decidability frontier for a generalization of RTA to recursive stopwatch automata.
Recursive representation of Wronskians in confluent supersymmetric quantum mechanics
Contreras-Astorga, Alonso; Schulze-Halberg, Axel
2017-01-01
A recursive form of arbitrary-order Wronskian associated with transformation functions in the confluent algorithm of supersymmetric quantum mechanics (SUSY) is constructed. With this recursive form regularity conditions for the generated potentials can be analyzed. Moreover, as byproducts we obtain new representations of solutions to Schrödinger equations that underwent a confluent SUSY-transformation. (paper)
Lowenthal, Francis
2010-11-01
This paper examines whether the recursive structure imbedded in some exercises used in the Non Verbal Communication Device (NVCD) approach is actually the factor that enables this approach to favor language acquisition and reacquisition in the case of children with cerebral lesions. For that a definition of the principle of recursion as it is used by logicians is presented. The two opposing approaches to the problem of language development are explained. For many authors such as Chomsky [1] the faculty of language is innate. This is known as the Standard Theory; the other researchers in this field, e.g. Bates and Elman [2], claim that language is entirely constructed by the young child: they thus speak of Language Acquisition. It is also shown that in both cases, a version of the principle of recursion is relevant for human language. The NVCD approach is defined and the results obtained in the domain of language while using this approach are presented: young subjects using this approach acquire a richer language structure or re-acquire such a structure in the case of cerebral lesions. Finally it is shown that exercises used in this framework imply the manipulation of recursive structures leading to regular grammars. It is thus hypothesized that language development could be favored using recursive structures with the young child. It could also be the case that the NVCD like exercises used with children lead to the elaboration of a regular language, as defined by Chomsky [3], which could be sufficient for language development but would not require full recursion. This double claim could reconcile Chomsky's approach with psychological observations made by adherents of the Language Acquisition approach, if it is confirmed by researches combining the use of NVCDs, psychometric methods and the use of Neural Networks. This paper thus suggests that a research group oriented towards this problematic should be organized.
Kostov, Ivan
2010-01-01
We study the quasiclassical expansion associated with a complex curve. In a more specific context this is the 1/N expansion in U(N)-invariant matrix integrals. We compare two approaches, the CFT approach and the topological recursion, and show their equivalence. The CFT approach reformulates the problem in terms of a conformal field theory on a Riemann surface, while the topological recursion is based on a recurrence equation for the observables representing symplectic invariants on the complex curve. The two approaches lead to two different graph expansions, one of which can be obtained as a partial resummation of the other.
Exact solution for the generalized Telegraph Fisher's equation
Abdusalam, H.A.; Fahmy, E.S.
2009-01-01
In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 6. Algorithms Procedures and Recursion. R K Shyamasundar. Series Article Volume 1 ... Author Affiliations. R K Shyamasundar1. Computer Science Group, Tata Institute of Fundamental Research, Homi Bhabha Road Mumbai 400 005, India.
Tian Lixin; Yin Jiuli
2004-01-01
In this paper, we introduce the fully nonlinear generalized Camassa-Holm equation C(m,n,p) and by using four direct ansatzs, we obtain abundant solutions: compactons (solutions with the absence of infinite wings), solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions and obtain kink compacton solutions and nonsymmetry compacton solutions. We also study other forms of fully nonlinear generalized Camassa-Holm equation, and their compacton solutions are governed by linear equations
Recursive Trees for Practical ORAM
Moataz Tarik
2015-06-01
Full Text Available We present a new, general data structure that reduces the communication cost of recent tree-based ORAMs. Contrary to ORAM trees with constant height and path lengths, our new construction r-ORAM allows for trees with varying shorter path length. Accessing an element in the ORAM tree results in different communication costs depending on the location of the element. The main idea behind r-ORAM is a recursive ORAM tree structure, where nodes in the tree are roots of other trees. While this approach results in a worst-case access cost (tree height at most as any recent tree-based ORAM, we show that the average cost saving is around 35% for recent binary tree ORAMs. Besides reducing communication cost, r-ORAM also reduces storage overhead on the server by 4% to 20% depending on the ORAM’s client memory type. To prove r-ORAM’s soundness, we conduct a detailed overflow analysis. r-ORAM’s recursive approach is general in that it can be applied to all recent tree ORAMs, both constant and poly-log client memory ORAMs. Finally, we implement and benchmark r-ORAM in a practical setting to back up our theoretical claims.
General classical solutions in the noncommutative CPN-1 model
Foda, O.; Jack, I.; Jones, D.R.T.
2002-01-01
We give an explicit construction of general classical solutions for the noncommutative CP N-1 model in two dimensions, showing that they correspond to integer values for the action and topological charge. We also give explicit solutions for the Dirac equation in the background of these general solutions and show that the index theorem is satisfied
Charged Analogues of Henning Knutsen Type Solutions in General Relativity
Gupta, Y. K.; Kumar, Sachin; Pratibha
2011-11-01
In the present article, we have found charged analogues of Henning Knutsen's interior solutions which join smoothly to the Reissner-Nordstrom metric at the pressure free interface. The solutions are singularity free and analyzed numerically with respect to pressure, energy-density and charge-density in details. The solutions so obtained also present the generalization of A.L. Mehra's solutions.
Approximate Bayesian recursive estimation
Kárný, Miroslav
2014-01-01
Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf
Recursion theory for metamathematics
Smullyan, Raymond M
1993-01-01
This work is a sequel to the author''s Godel''s Incompleteness Theorems, though it can be read independently by anyone familiar with Godel''s incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
A general polynomial solution to convection–dispersion equation ...
Jiao Wang
concentration profiles and optimal solute transport parameters. Furthermore, the general .... requirement; in other words, if Is(t) is cumulated solute added in the column ..... National Natural Science Foundation of China. (Nos. 41530854 and ...
Properties of general classical CPsup(n-1) solutions
Din, A.M.
1980-05-01
The general classical solutions with finite action of the CPsup(n-1) model are displayed. Various properties of the solutions such as topological charge, action, Baecklund like transformations and stability are discussed
A Generalized Deduction of the Ideal-Solution Model
Leo, Teresa J.; Perez-del-Notario, Pedro; Raso, Miguel A.
2006-01-01
A new general procedure for deriving the Gibbs energy of mixing is developed through general thermodynamic considerations, and the ideal-solution model is obtained as a special particular case of the general one. The deduction of the Gibbs energy of mixing for the ideal-solution model is a rational one and viewed suitable for advanced students who…
Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing
Rodriguez, G.; Scheid, R. E., Jr.
1987-01-01
This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.
Cosmology in three dimensions: steps towards the general solution
Barrow, John D; Shaw, Douglas J; Tsagas, Christos G
2006-01-01
We use covariant and first-order formalism techniques to study the properties of general relativistic cosmology in three dimensions. The covariant approach provides an irreducible decomposition of the relativistic equations, which allows for a mathematically compact and physically transparent description of the three-dimensional spacetimes. Using this information we review the features of homogeneous and isotropic 3D cosmologies, provide a number of new solutions and study gauge invariant perturbations around them. The first-order formalism is then used to provide a detailed study of the most general 3D spacetimes containing perfect-fluid matter. Assuming the material content to be dust with comoving spatial 2-velocities, we find the general solution of the Einstein equations with a non-zero (and zero) cosmological constant and generalize known solutions of Kriele and the 3D counterparts of the Szekeres solutions. In the case of a non-comoving dust fluid we find the general solution in the case of one non-zero fluid velocity component. We consider the asymptotic behaviour of the families of 3D cosmologies with rotation and shear and analyse their singular structure. We also provide the general solution for cosmologies with one spacelike Killing vector, find solutions for cosmologies containing scalar fields and identify all the PP-wave 2 + 1 spacetimes
General solution for first order elliptic systems in the plane
Mshimba, A.S.
1990-01-01
It is shown that a system of 2n real-valued partial differential equations of first order, which under certain assumptions can be transformed to the so-called 'complex normal form', admits a general solution. 15 refs
New exact solutions of the generalized Zakharov–Kuznetsov ...
In this paper, new exact solutions, including soliton, rational and elliptic integral function solutions, for the generalized Zakharov–Kuznetsov modified equal-width equation are obtained using a new approach called the extended trial equation method. In this discussion, a new version of the trial equation method for the ...
Minimal solution of general dual fuzzy linear systems
Abbasbandy, S.; Otadi, M.; Mosleh, M.
2008-01-01
Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered
Exact and numerical solutions of generalized Drinfeld-Sokolov equations
Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya36@yahoo.com
2008-04-14
In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)
Exact and numerical solutions of generalized Drinfeld-Sokolov equations
Ugurlu, Yavuz; Kaya, Dogan
2008-01-01
In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)
The ABCD of topological recursion
Andersen, Jorgen Ellegaard; Borot, Gaëtan; Chekhov, Leonid O.
Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of math-ph/0702045, seeing it as a quantization of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial data a quantum Airy structure...... the 2d TQFT partition function as a special case), non-commutative Frobenius algebras, loop spaces of Frobenius algebras and a Z2-invariant version of the latter. This Z2-invariant version in the case of a semi-simple Frobenius algebra corresponds to the topological recursion of math-ph/0702045....
Yang-Mills analogs of general-relativistic solutions
Singlton, D.
1998-01-01
Some solutions of Yang-Mills equations, which can be found with the use of the general relativistic theory and Yang-Mills theory, are discussed. Some notes concerning possible physical sense of these solutions are made. Arguments showing that some of such solutions in the Yang-Mills theory (similar to the general relativistic ones) may be connected with the confinement phenomenon are given in particular. The motion of probe particles located into the phonon potential similar to the Schwarz-Child one is briefly discussed for this purpose [ru
Exact solutions of generalized Zakharov and Ginzburg-Landau equations
Zhang Jinliang; Wang Mingliang; Gao Kequan
2007-01-01
By using the homogeneous balance principle, the exact solutions of the generalized Zakharov equations and generalized Ginzburg-Landau equation are obtained with the aid of a set of subsidiary higher-order ordinary differential equations (sub-equations for short)
Recursive Algorithm For Linear Regression
Varanasi, S. V.
1988-01-01
Order of model determined easily. Linear-regression algorithhm includes recursive equations for coefficients of model of increased order. Algorithm eliminates duplicative calculations, facilitates search for minimum order of linear-regression model fitting set of data satisfactory.
Tracking of Multiple Moving Sources Using Recursive EM Algorithm
Böhme Johann F
2005-01-01
Full Text Available We deal with recursive direction-of-arrival (DOA estimation of multiple moving sources. Based on the recursive EM algorithm, we develop two recursive procedures to estimate the time-varying DOA parameter for narrowband signals. The first procedure requires no prior knowledge about the source movement. The second procedure assumes that the motion of moving sources is described by a linear polynomial model. The proposed recursion updates the polynomial coefficients when a new data arrives. The suggested approaches have two major advantages: simple implementation and easy extension to wideband signals. Numerical experiments show that both procedures provide excellent results in a slowly changing environment. When the DOA parameter changes fast or two source directions cross with each other, the procedure designed for a linear polynomial model has a better performance than the general procedure. Compared to the beamforming technique based on the same parameterization, our approach is computationally favorable and has a wider range of applications.
Features and Recursive Structure
Kuniya Nasukawa
2015-01-01
Full Text Available Based on the cross-linguistic tendency that weak vowels are realized with a central quality such as ə, ɨ, or ɯ, this paper attempts to account for this choice by proposing that the nucleus itself is one of the three monovalent vowel elements |A|, |I| and |U| which function as the building blocks of melodic structure. I claim that individual languages make a parametric choice to determine which of the three elements functions as the head of a nuclear expression. In addition, I show that elements can be freely concatenated to create melodic compounds. The resulting phonetic value of an element compound is determined by the specific elements it contains and by the head-dependency relations between those elements. This concatenation-based recursive mechanism of melodic structure can also be extended to levels above the segment, thus ultimately eliminating the need for syllabic constituents. This approach reinterprets the notion of minimalism in phonology by opposing the string-based flat structure.
Nikolov, Svetoslav; Gammelmark, Kim; Jensen, Jørgen Arendt
1999-01-01
This paper presents a new imaging method, applicable for both 2D and 3D imaging. It is based on Synthetic Transmit Aperture Focusing, but unlike previous approaches a new frame is created after every pulse emission. The elements from a linear transducer array emit pulses one after another. The same...... transducer element is used after N-xmt emissions. For each emission the signals from the individual elements are beam-formed in parallel for all directions in the image. A new frame is created by adding the new RF lines to the RF lines from the previous frame. The RF data recorded at the previous emission...... with the same element are subtracted. This yields a new image after each pulse emission and can give a frame rate of e.g. 5000 images/sec. The paper gives a derivation of the recursive imaging technique and compares simulations for fast B-mode imaging with measurements. A low value of N-xmt is necessary...
2000-01-01
A method and an apparatus for recursive ultrasound imaging is presented. The method uses a Synthetic Transmit Aperture, but unlike previous approaches a new frame is created at every pulse emission. In receive, parallel beam forming is implemented. The beam formed RF data is added to the previously...... created RF lines. To keep the level of the signal, the RF data obtained previously, when emitting with the same element is subtracted from the RF lines. Up to 5000 frames/sec can be achieved for a tissue depth of 15 cm with a speed of sound of c = 1540 m/s. The high frame rate makes continuous imaging...... data possible, which can significantly enhance flow imaging. A point spread function 2° wide at -6 dB and grating lobes of $m(F) -50 dB is obtained with a 64 elements phased array with a central frequency ƒ¿0? = 3 MHz using a sparse transmit aperture using only 10 elements (N¿xmt? = 10) during pulse...
Hopf algebras and topological recursion
Esteves, João N
2015-01-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293–309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347–452). (paper)
Towards the general solution of the Yang-Mills equations
Helfer, A.D.
1985-01-01
The author presents a new non-perturbative technique for finding arbitrary self-dual solutions to the Yang-Mills equations, and of describing massless fields minimally coupled to them. The approach uses techniques of complex analysis in several variables, and is complementary to Ward's: it is expected that a combination of the two techniques will yield general, non-self-dual solutions to the Yang-Mills equations. This has been verified to first order in perturbation theory
New solutions of Heun's general equation
Ishkhanyan, Artur [Engineering Center of Armenian National Academy of Sciences, Ashtarak (Armenia); Suominen, Kalle-Antti [Helsinki Institute of Physics, PL 64, Helsinki (Finland)
2003-02-07
We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)
Isotropic extensions of the vacuum solutions in general relativity
Molina, C. [Universidade de Sao Paulo (USP), SP (Brazil); Martin-Moruno, Prado [Victoria University of Wellington (New Zealand); Gonzalez-Diaz, Pedro F. [Consejo Superior de Investigaciones Cientificas, Madrid (Spain)
2012-07-01
Full text: Spacetimes described by spherically symmetric solutions of Einstein's equations are of paramount importance both in astrophysical applications and theoretical considerations. And among those, black holes are highlighted. In vacuum, Birkhoff's theorem and its generalizations to non-asymptotically flat cases uniquely fix the metric as the Schwarzschild, Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter geometries, the vacuum solutions of the usual general relativity with zero, positive or negative values for the cosmological constant, respectively. In this work we are mainly interested in black holes in a cosmological environment. Of the two main assumptions of the cosmological principle, homogeneity is lost when compact objects are considered. Nevertheless isotropy is still possible, and we enforce this condition. Within this context, we investigate spatially isotropic solutions close - continuously deformable - to the usual vacuum solutions. We obtain isotropic extensions of the usual spherically symmetric vacuum geometries in general relativity. Exact and perturbative solutions are derived. Maximal extensions are constructed and their causal structures are discussed. The classes of geometries obtained include black holes in compact and non-compact universes, wormholes in the interior region of cosmological horizons, and anti-de Sitter geometries with excess/deficit solid angle. The tools developed here are applicable in more general contexts, with extensions subjected to other constraints. (author)
Analytical Solution of General Bagley-Torvik Equation
William Labecca
2015-01-01
Full Text Available Bagley-Torvik equation appears in viscoelasticity problems where fractional derivatives seem to play an important role concerning empirical data. There are several works treating this equation by using numerical methods and analytic formulations. However, the analytical solutions presented in the literature consider particular cases of boundary and initial conditions, with inhomogeneous term often expressed in polynomial form. Here, by using Laplace transform methodology, the general inhomogeneous case is solved without restrictions in boundary and initial conditions. The generalized Mittag-Leffler functions with three parameters are used and the solutions presented are expressed in terms of Wiman’s functions and their derivatives.
General scalar-tensor cosmology: analytical solutions via noether symmetry
Massaeli, Erfan; Motaharfar, Meysam; Sepangi, Hamid Reza [Shahid Beheshti University, Department of Physics, Tehran (Iran, Islamic Republic of)
2017-02-15
We analyze the cosmology of a general scalar-tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galilean gravity and also the general k-essence type models. Instead of taking into account phenomenological considerations we adopt a Noether symmetry approach, as a physical criterion, to single out the form of undetermined functions in the action. These specified functions symmetrize equations of motion in the simplest possible form which result in exact solutions. Demanding de Sitter, power-law and bouncing universe solutions in the absence and presence of matter density leads to exploring new as well as well-investigated models. We show that there are models for which the dynamics of the system allows a transition from a decelerating phase (matter dominated era) to an accelerating phase (dark energy epoch) and could also lead to general Brans-Dicke with string correction without a self-interaction potential. Furthermore, we classify the models based on a phantom or quintessence dark energy point of view. Finally, we obtain the condition for stability of a de Sitter solution for which the solution is an attractor of the system. (orig.)
The general solution of a Nim-heap game
宋林森; 卢澎涛
2010-01-01
As a combinatorial one,the game Nim turns out to be extremely useful in certain types of combinatorial game analysis.It has given the general solution of the game a Nim-heap game and the result has proved true.
General solution of Bateman equations for nuclear transmutations
Cetnar, Jerzy
2006-01-01
The paper concerns the linear chain method of solving Bateman equations for nuclear transmutation in derivation of the general solution for linear chain with repeated transitions and thus elimination of existing numerical problems. In addition, applications of derived equations for transmutation trajectory analysis method is presented
General analytical shakedown solution for structures with kinematic hardening materials
Guo, Baofeng; Zou, Zongyuan; Jin, Miao
2016-09-01
The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems: a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.
Supersymmetric solutions of N =(1 ,1 ) general massive supergravity
Deger, N. S.; Nazari, Z.; Sarıoǧlu, Ö.
2018-05-01
We construct supersymmetric solutions of three-dimensional N =(1 ,1 ) general massive supergravity (GMG). Solutions with a null Killing vector are, in general, pp-waves. We identify those that appear at critical points of the model, some of which do not exist in N =(1 ,1 ) new massive supergravity (NMG). In the timelike case, we find that many solutions are common with NMG, but there is a new class that is genuine to GMG, two members of which are stationary Lifshitz and timelike squashed AdS spacetimes. We also show that in addition to the fully supersymmetric AdS vacuum, there is a second AdS background with a nonzero vector field that preserves 1 /4 supersymmetry.
The general supersymmetric solution of topologically massive supergravity
Gibbons, G W; Pope, C N; Sezgin, E
2008-01-01
We find the general fully nonlinear solution of topologically massive supergravity admitting a Killing spinor. It is of plane-wave type, with a null Killing vector field. Conversely, we show that all solutions with a null Killing vector are supersymmetric for one or the other choice of sign for the Chern-Simons coupling constant μ. If μ does not take the critical value, μ = ±1, these solutions are asymptotically regular on a Poincare patch, but do not admit a smooth global compactification with boundary S 1 x R. In the critical case, the solutions have a logarithmic singularity on the boundary of the Poincare patch. We derive a Nester-Witten identity, which allows us to identify the associated charges, but we conclude that the presence of the Chern-Simons term prevents us from making a statement about their positivity. The Nester-Witten procedure is applied to the BTZ black hole
A New Solution for Einstein Field Equation in General Relativity
Mousavi, Sadegh
2006-05-01
There are different solutions for Einstein field equation in general relativity that they have been proposed by different people the most important solutions are Schwarzchild, Reissner Nordstrom, Kerr and Kerr Newmam. However, each one of these solutions limited to special case. I've found a new solution for Einstein field equation which is more complete than all previous ones and this solution contains the previous solutions as its special forms. In this talk I will present my new metric for Einstein field equation and the Christofel symbols and Richi and Rieman tensor components for the new metric that I have calculated them by GR TENSOR software. As a result I will determine the actual movement of black holes which is different From Kerr black hole's movement. Finally this new solution predicts, existence of a new and constant field in the nature (that nobody can found it up to now), so in this talk I will introduce this new field and even I will calculate the amount of this field. SADEGH MOUSAVI, Amirkabir University of Technology.
Spherically symmetric solutions of general second-order gravity
Whitt, B.
1988-01-01
The general second-order gravity theory, whose Lagrangian includes higher powers of the curvature, is considered in arbitrary dimensions. It is shown that spherically symmetric solutions are static, except in certain, special, unphysical cases. Spherically symmetric solutions are found and classified. Each theory's solutions fall into a number of distinct branches, which may represent finite space with two singular boundaries, or an asymptotically either flat or (anti--)de Sitter space with one singular boundary. A theory may contain at most one branch of solutions in which all singularities are hidden by event horizons. Such horizons generally emit Hawking radiation, though in certain cases the horizon may have zero temperature. Black holes do not necessarily radiate away all their mass: they may terminate in a zero-temperature black hole, a naked singularity, or a hot black hole in equilibrium with a ''cosmological'' event horizon. The thermodynamics of black-hole solutions is discussed; entropy is found to be an increasing function of horizon area, and the first law is shown to hold
New solutions of the generalized ellipsoidal wave equation
Harold Exton
1999-10-01
Full Text Available Certain aspects and a contribution to the theory of new forms of solutions of an algebraic form of the generalized ellipsoidal wave equation are deduced by considering the Laplace transform of a soluble system of linear differential equations. An ensuing system of non-linear algebraic equations is shown to be consistent and is numerically implemented by means of the computer algebra package MAPLE V. The main results are presented as series of hypergeometric type of there and four variables which readily lend themselves to numerical handling although this does not indicate all of the detailedanalytic properties of the solutions under consideration.
Smooth Gowdy-symmetric generalized Taub–NUT solutions
Beyer, Florian; Hennig, Jörg
2012-01-01
We study a class of S 3 -Gowdy vacuum models with a regular past Cauchy horizon which we call smooth Gowdy-symmetric generalized Taub–NUT solutions. In particular, we prove the existence of such solutions by formulating a singular initial value problem with asymptotic data on the past Cauchy horizon. We prove that also a future Cauchy horizon exists for generic asymptotic data, and derive an explicit expression for the metric on the future Cauchy horizon in terms of the asymptotic data on the past horizon. This complements earlier results about S 1 ×S 2 -Gowdy models. (paper)
Recursive Definitions of Monadic Functions
Alexander Krauss
2010-12-01
Full Text Available Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's imperative programming extension, which results in a convenient definition principle for imperative programs, which were previously hard to define. For such monadic functions, the recursion equation can always be derived without preconditions, even if the function is partial. The construction is easy to automate, and convenient induction principles can be derived automatically.
G. M. N’Guérékata
2018-01-01
Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.
Particular solutions of generalized Euler-Poisson-Darboux equation
Rakhila B. Seilkhanova
2015-01-01
Full Text Available In this article we consider the generalized Euler-Poisson-Darboux equation $$ {u}_{tt}+\\frac{2\\gamma }{t}{{u}_{t}}={u}_{xx}+{u}_{yy} +\\frac{2\\alpha }{x}{{u}_{x}}+\\frac{2\\beta }{y}{{u}_y},\\quad x>0,\\;y>0,\\;t>0. $$ We construct particular solutions in an explicit form expressed by the Lauricella hypergeometric function of three variables. Properties of each constructed solutions have been investigated in sections of surfaces of the characteristic cone. Precisely, we prove that found solutions have singularity $1/r$ at $r\\to 0$, where ${{r}^2}={{( x-{{x}_0}}^2}+{{( y-{{y}_0}}^2}-{{( t-{{t}_0}}^2}$.
On the General Analytical Solution of the Kinematic Cosserat Equations
Michels, Dominik L.
2016-09-01
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
Numerical solution of pipe flow problems for generalized Newtonian fluids
Samuelsson, K.
1993-01-01
In this work we study the stationary laminar flow of incompressible generalized Newtonian fluids in a pipe with constant arbitrary cross-section. The resulting nonlinear boundary value problems can be written in a variational formulation and solved using finite elements and the augmented Lagrangian method. The solution of the boundary value problem is obtained by finding a saddle point of the augmented Lagrangian. In the algorithm the nonlinear part of the equations is treated locally and the solution is obtained by iteration between this nonlinear problem and a global linear problem. For the solution of the linear problem we use the SSOR preconditioned conjugate gradient method. The approximating problem is solved on a sequence of adaptively refined grids. A scheme for adjusting the value of the crucial penalization parameter of the augmented Lagrangian is proposed. Applications to pipe flow and a problem from the theory of capacities are given. (author) (34 refs.)
On the General Analytical Solution of the Kinematic Cosserat Equations
Michels, Dominik L.; Lyakhov, Dmitry; Gerdt, Vladimir P.; Hossain, Zahid; Riedel-Kruse, Ingmar H.; Weber, Andreas G.
2016-01-01
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.
A database for extract solutions in general relativity
Horvath, I.; Horvath, Zs.; Lukacs, B.
1993-07-01
The field of equations of General Relativity are coupled second order partial differential equations. Therefore no general method is known to generate solutions for prescribed initial and boundary conditions. In addition, the meaning of the particular coordinates cannot be known until the metric is not found. Therefore the result must permit arbitrary coordinate transformations, i.e. most kinds of approximating methods are improper. So exact solutions are necessary and each one is an individual product. For storage, retrieval and comparison database handling techniques are needed. A database of 1359 articles is shown (cross-referred at least once) published in 156 more important journals. It can be handled by dBase III plus on IBM PC's. (author) 5 refs.; 5 tabs
Generalized Truncated Methods for an Efficient Solution of Retrial Systems
Ma Jose Domenech-Benlloch
2008-01-01
Full Text Available We are concerned with the analytic solution of multiserver retrial queues including the impatience phenomenon. As there are not closed-form solutions to these systems, approximate methods are required. We propose two different generalized truncated methods to effectively solve this type of systems. The methods proposed are based on the homogenization of the state space beyond a given number of users in the retrial orbit. We compare the proposed methods with the most well-known methods appeared in the literature in a wide range of scenarios. We conclude that the proposed methods generally outperform previous proposals in terms of accuracy for the most common performance parameters used in retrial systems with a moderated growth in the computational cost.
Quantum solutions for Prisoner's Dilemma game with general parameters
Sun, Z.W.; Jin, H.; Zhao, H.
2008-01-01
The quantum game of the Prisoner's Dilemma with general payoff matrix was studied in L. Marinatto and T. Weber's scheme presented in [Phys. Lett. A 272 (2000) 291, so that the results of two schemes of the quantum game can be compared. The Nash equilibria and the solutions of the game are obtained. They are related to initial state, matrix parameters and the intervals among the parameters. It can be concluded from the results that the quantum PD game in Marinatto and Weber's scheme matches the one in Eisert et al.'s scheme, one with general unitary operations.
Automatic computation and solution of generalized harmonic balance equations
Peyton Jones, J. C.; Yaser, K. S. A.; Stevenson, J.
2018-02-01
Generalized methods are presented for generating and solving the harmonic balance equations for a broad class of nonlinear differential or difference equations and for a general set of harmonics chosen by the user. In particular, a new algorithm for automatically generating the Jacobian of the balance equations enables efficient solution of these equations using continuation methods. Efficient numeric validation techniques are also presented, and the combined algorithm is applied to the analysis of dc, fundamental, second and third harmonic response of a nonlinear automotive damper.
A general method for enclosing solutions of interval linear equations
Rohn, Jiří
2012-01-01
Roč. 6, č. 4 (2012), s. 709-717 ISSN 1862-4472 R&D Projects: GA ČR GA201/09/1957; GA ČR GC201/08/J020 Institutional research plan: CEZ:AV0Z10300504 Keywords : interval linear equations * solution set * enclosure * absolute value inequality Subject RIV: BA - General Mathematics Impact factor: 1.654, year: 2012
Analytical Solution of General Bagley-Torvik Equation
William Labecca; Osvaldo Guimarães; José Roberto C. Piqueira
2015-01-01
Bagley-Torvik equation appears in viscoelasticity problems where fractional derivatives seem to play an important role concerning empirical data. There are several works treating this equation by using numerical methods and analytic formulations. However, the analytical solutions presented in the literature consider particular cases of boundary and initial conditions, with inhomogeneous term often expressed in polynomial form. Here, by using Laplace transform methodology, the general inhomoge...
Magnetotail equilibrium theory - The general three-dimensional solution
Birn, J.
1987-01-01
The general magnetostatic equilibrium problem for the geomagnetic tail is reduced to the solution of ordinary differential equations and ordinary integrals. The theory allows the integration of the self-consistent magnetotail equilibrium field from the knowledge of four functions of two space variables: the neutral sheet location, the total pressure, the magnetic field strength, and the z component of the magnetic field at the neutral sheet.
Solution of generalized control system equations at steady state
Vilim, R.B.
1987-01-01
Although a number of reactor systems codes feature generalized control system models, none of the models offer a steady-state solution finder. Indeed, if a transient is to begin from steady-state conditions, the user must provide estimates for the control system initial conditions and run a null transient until the plant converges to steady state. Several such transients may have to be run before values for control system demand signals are found that produce the desired plant steady state. The intent of this paper is (a) to present the control system equations assumed in the SASSYS reactor systems code and to identify the appropriate set of initial conditions, (b) to describe the generalized block diagram approach used to represent these equations, and (c) to describe a solution method and algorithm for computing these initial conditions from the block diagram. The algorithm has been installed in the SASSYS code for use with the code's generalized control system model. The solution finder greatly enhances the effectiveness of the code and the efficiency of the user in running it
Spinning solutions in general relativity with infinite central density
Flammer, P. D.
2018-05-01
This paper presents general relativistic numerical simulations of uniformly rotating polytropes. Equations are developed using MSQI coordinates, but taking a logarithm of the radial coordinate. The result is relatively simple elliptical differential equations. Due to the logarithmic scale, we can resolve solutions with near-singular mass distributions near their center, while the solution domain extends many orders of magnitude larger than the radius of the distribution (to connect with flat space-time). Rotating solutions are found with very high central energy densities for a range of adiabatic exponents. Analytically, assuming the pressure is proportional to the energy density (which is true for polytropes in the limit of large energy density), we determine the small radius behavior of the metric potentials and energy density. This small radius behavior agrees well with the small radius behavior of large central density numerical results, lending confidence to our numerical approach. We compare results with rotating solutions available in the literature, which show good agreement. We study the stability of spherical solutions: instability sets in at the first maximum in mass versus central energy density; this is also consistent with results in the literature, and further lends confidence to the numerical approach.
Proof Rules for Recursive Procedures
Hesselink, Wim H.
1993-01-01
Four proof rules for recursive procedures in a Pascal-like language are presented. The main rule deals with total correctness and is based on results of Gries and Martin. The rule is easier to apply than Martin's. It is introduced as an extension of a specification format for Pascal-procedures, with
Nyvad, Anne Mette; Christensen, Ken Ramshøj; Vikner, Sten
2017-01-01
Based on data from extraction, embedded V2, and complementizer stacking, this paper proposes a cP/CP-analysis of CP-recursion in Danish. Because extraction can be shown to be possible from relative clauses, wh-islands, and adverbial clauses, and given that long extraction is successive......-cyclic, an extra specifier position has to be available as an escape hatch. Consequently, such extractions require a CP-recursion analysis, as has been argued for embedded V2 and for complementizer stacking. Given that CP-recursion in embedded V2 clauses does not allow extraction, whereas other types of CP......-recursion do, we suggest that embedded V2 is fundamentally different, in that main clause V2 and embedded V2 involve a CP (“big CP”), whereas all other clausal projections above IP are instances of cP (“little cP”). The topmost “little” c° has an occurrence feature that enables extraction but bars spell...
Lessons in Contingent, Recursive Humility
Vagle, Mark D.
2011-01-01
In this article, the author argues that critical work in teacher education should begin with teacher educators turning a critical eye on their own practices. The author uses Lesko's conception of contingent, recursive growth and change to analyze a lesson he observed as part of a phenomenological study aimed at understanding more about what it is…
How Learning Logic Programming Affects Recursion Comprehension
Haberman, Bruria
2004-01-01
Recursion is a central concept in computer science, yet it is difficult for beginners to comprehend. Israeli high-school students learn recursion in the framework of a special modular program in computer science (Gal-Ezer & Harel, 1999). Some of them are introduced to the concept of recursion in two different paradigms: the procedural…
Jingtao Shi
2013-01-01
Full Text Available This paper is concerned with the relationship between maximum principle and dynamic programming for stochastic recursive optimal control problems. Under certain differentiability conditions, relations among the adjoint processes, the generalized Hamiltonian function, and the value function are given. A linear quadratic recursive utility portfolio optimization problem in the financial engineering is discussed as an explicitly illustrated example of the main result.
Numerically satisfactory solutions of hypergeometric recursions
A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)
2007-01-01
textabstractEach family of Gauss hypergeometric functions $$ f_n={}_2F_1(a+\\varepsilon_1n, b+\\varepsilon_2n ;c+\\varepsilon_3n; z),\\quad n\\in {\\mathbb Z}\\,, $$ for fixed $\\varepsilon_j=0,\\pm1$ (not all $\\varepsilon_j$ equal to zero) satisfies a second order linear difference equation of the
Numerically satisfactory solutions of hypergeometric recursions
A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)
2006-01-01
textabstractEach family of Gauss hypergeometric functions $f_n = 2F_1(a+epsilon 1n,b+epsilon 2n;c+epsilon 3n;z), nin Z$, for fixed epsilon_j = 0,pm 1$ (not all epsilon j equal to zero) satisfies a second order linear difference equation of the form $A_n f_{n-1} + B_n f_n + C_n f_{n+1} = 0$. Because
On generalized Melvin solution for the Lie algebra E6
Bolokhov, S.V.; Ivashchuk, V.D.
2017-01-01
A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model in D dimensions, D ≥ 4, contains n 2-forms and l ≥ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions H s (z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials H s (z), s = 1,.., 6, for the Lie algebra E 6 are obtained and a corresponding solution for l = n = 6 is presented. The polynomials depend upon integration constants Q s , s = 1,.., 6. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for E 6 -polynomials at large z are governed by the integer-valued matrix ν = A -1 (I + P), where A -1 is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the Z 2 -group of symmetry of the Dynkin diagram. The 2-form fluxes Φ s , s = 1,.., 6, are calculated. (orig.)
Chen, Yong; Shanghai Jiao-Tong Univ., Shangai; Chinese Academy of sciences, Beijing
2005-01-01
A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion
Duda, Piotr; Jaworski, Maciej; Rutkowski, Leszek
2018-03-01
One of the greatest challenges in data mining is related to processing and analysis of massive data streams. Contrary to traditional static data mining problems, data streams require that each element is processed only once, the amount of allocated memory is constant and the models incorporate changes of investigated streams. A vast majority of available methods have been developed for data stream classification and only a few of them attempted to solve regression problems, using various heuristic approaches. In this paper, we develop mathematically justified regression models working in a time-varying environment. More specifically, we study incremental versions of generalized regression neural networks, called IGRNNs, and we prove their tracking properties - weak (in probability) and strong (with probability one) convergence assuming various concept drift scenarios. First, we present the IGRNNs, based on the Parzen kernels, for modeling stationary systems under nonstationary noise. Next, we extend our approach to modeling time-varying systems under nonstationary noise. We present several types of concept drifts to be handled by our approach in such a way that weak and strong convergence holds under certain conditions. Finally, in the series of simulations, we compare our method with commonly used heuristic approaches, based on forgetting mechanism or sliding windows, to deal with concept drift. Finally, we apply our concept in a real life scenario solving the problem of currency exchange rates prediction.
On Recursion Operator of the q -KP Hierarchy
Tian Ke-Lei; Zhu Xiao-Ming; He Jing-Song
2016-01-01
It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy. The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived. (paper)
Analytical Solution of a Generalized Hirota-Satsuma Equation
Kassem, M.; Mabrouk, S.; Abd-el-Malek, M.
A modified version of generalized Hirota-Satsuma is here solved using a two parameter group transformation method. This problem in three dimensions was reduced by Estevez [1] to a two dimensional one through a Lie transformation method and left unsolved. In the present paper, through application of symmetry transformation the Lax pair has been reduced to a system of ordinary equations. Three transformations cases are investigated. The obtained analytical solutions are plotted and show a profile proper to deflagration processes, well described by Degasperis-Procesi equation.
Recursive forgetting algorithms
Parkum, Jens; Poulsen, Niels Kjølstad; Holst, Jan
1992-01-01
In the first part of the paper, a general forgetting algorithm is formulated and analysed. It contains most existing forgetting schemes as special cases. Conditions are given ensuring that the basic convergence properties will hold. In the second part of the paper, the results are applied...... to a specific algorithm with selective forgetting. Here, the forgetting is non-uniform in time and space. The theoretical analysis is supported by a simulation example demonstrating the practical performance of this algorithm...
Exact solutions of (3 + 1-dimensional generalized KP equation arising in physics
Syed Tauseef Mohyud-Din
Full Text Available In this work, we have obtained some exact solutions to (3 + 1-dimensional generalized KP Equation. The improved tanϕ(ξ2-expansion method has been introduced to construct the exact solutions of nonlinear evolution equations. The obtained solutions include hyperbolic function solutions, trigonometric function solutions, exponential solutions, and rational solutions. Our study has added some new varieties of solutions to already available solutions. It is also worth mentioning that the computational work has been reduced significantly. Keywords: Improved tanϕ(ξ2-expansion method, Hyperbolic function solution, Trigonometric function solution, Rational solution, (3 + 1-dimensional generalized KP equation
A generalized trial solution method for solving the aerosol equation
Simons, S.; Simpson, D.R.
1988-01-01
It is shown how the introduction of orthogonal functions together with a time-dependent scaling factor may be used to develop a generalized trial solution method for tackling the aerosol equation. The approach is worked out in detail for the case where the initial particle size spectrum follows a γ-distribution, and it is shown to be a viable technique as long as the initial volume fraction of particulate material is not too large. The method is applied to several situations of interest, and is shown to give more accurate results (with marginally shorter computing times) than are given by the three-parameter log-normal or γ distribution trial functions. (author)
Generalized nonlinear Proca equation and its free-particle solutions
Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)
2016-06-15
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)
On the Relation between Spector's Bar Recursion and Modified Bar Recursion
Oliva, Paulo Borges
2002-01-01
We introduce a variant of Spector's Bar Recursion in finite types to give a realizability interpretation of the classical axiom of dependent choice allowing for the extraction of witnesses from proofs of Sigma_1 formulas in classical analysis. We also give a bar recursive definition of the fan...... functional and study the relationship of our variant of Bar Recursion with others....
Algebraic Optimization of Recursive Database Queries
Hansen, Michael Reichhardt
1988-01-01
Queries are expressed by relational algebra expressions including a fixpoint operation. A condition is presented under which a natural join commutes with a fixpoint operation. This condition is a simple check of attribute sets of sub-expressions of the query. The work may be considered a generali......Queries are expressed by relational algebra expressions including a fixpoint operation. A condition is presented under which a natural join commutes with a fixpoint operation. This condition is a simple check of attribute sets of sub-expressions of the query. The work may be considered...... a generalization of Aho and Ullman, (1979). The result is interpreted in function free logic database terms as a transformation of the recursively defined predicate involving: (a) elimination of an argument, and (b) propagation of selections (instantiations) to the extensionally defined predicates. A collection...
Recursive utility in a Markov environment with stochastic growth.
Hansen, Lars Peter; Scheinkman, José A
2012-07-24
Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron-Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility.
A general solution strategy of modified power method for higher mode solutions
Zhang, Peng; Lee, Hyunsuk; Lee, Deokjung
2016-01-01
A general solution strategy of the modified power iteration method for calculating higher eigenmodes has been developed and applied in continuous energy Monte Carlo simulation. The new approach adopts four features: 1) the eigen decomposition of transfer matrix, 2) weight cancellation for higher modes, 3) population control with higher mode weights, and 4) stabilization technique of statistical fluctuations using multi-cycle accumulations. The numerical tests of neutron transport eigenvalue problems successfully demonstrate that the new strategy can significantly accelerate the fission source convergence with stable convergence behavior while obtaining multiple higher eigenmodes at the same time. The advantages of the new strategy can be summarized as 1) the replacement of the cumbersome solution step of high order polynomial equations required by Booth's original method with the simple matrix eigen decomposition, 2) faster fission source convergence in inactive cycles, 3) more stable behaviors in both inactive and active cycles, and 4) smaller variances in active cycles. Advantages 3 and 4 can be attributed to the lower sensitivity of the new strategy to statistical fluctuations due to the multi-cycle accumulations. The application of the modified power method to continuous energy Monte Carlo simulation and the higher eigenmodes up to 4th order are reported for the first time in this paper. -- Graphical abstract: -- Highlights: •Modified power method is applied to continuous energy Monte Carlo simulation. •Transfer matrix is introduced to generalize the modified power method. •All mode based population control is applied to get the higher eigenmodes. •Statistic fluctuation can be greatly reduced using accumulated tally results. •Fission source convergence is accelerated with higher mode solutions.
New exact solutions of the generalized Zakharov–Kuznetsov ...
years, Liu and other researchers developed the trial equation method and its ... soliton, elliptic integral function and Jacobi elliptic function solutions. ... nonlinearity parameter, is a positive real number. ..... reduce to rational function solution.
Classes of general axisymmetric solutions of Einstein-Maxwell equations
Krori, K.D.; Choudhury, T.
1981-01-01
An exact solution of the Einstein equations for a stationary axially symmetric distribution of mass composed of all types of multipoles is obtained. Following Ernst (1968), from this vacuum solution the corresponding solution of the coupled Einstein-Maxwell equations is derived. A solution of Einstein-Maxwell fields for a static axially symmetric system composed of all types of multipoles is also obtained. (author)
General supersymmetric solutions of five-dimensional supergravity
Gutowski, Jan B.; Sabra, Wafic
2005-01-01
The classification of 1/4-supersymmetric solutions of five dimensional gauged supergravity coupled to arbitrary many abelian vector multiplets, which was initiated elsewhere, is completed. The structure of all solutions for which the Killing vector constructed from the Killing spinor is null is investigated in both the gauged and the ungauged theories and some new solutions are constructed
PARETO OPTIMAL SOLUTIONS FOR MULTI-OBJECTIVE GENERALIZED ASSIGNMENT PROBLEM
S. Prakash
2012-01-01
Full Text Available
ENGLISH ABSTRACT: The Multi-Objective Generalized Assignment Problem (MGAP with two objectives, where one objective is linear and the other one is non-linear, has been considered, with the constraints that a job is assigned to only one worker – though he may be assigned more than one job, depending upon the time available to him. An algorithm is proposed to find the set of Pareto optimal solutions of the problem, determining assignments of jobs to workers with two objectives without setting priorities for them. The two objectives are to minimise the total cost of the assignment and to reduce the time taken to complete all the jobs.
AFRIKAANSE OPSOMMING: ‘n Multi-doelwit veralgemeende toekenningsprobleem (“multi-objective generalised assignment problem – MGAP” met twee doelwitte, waar die een lineêr en die ander nielineêr is nie, word bestudeer, met die randvoorwaarde dat ‘n taak slegs toegedeel word aan een werker – alhoewel meer as een taak aan hom toegedeel kan word sou die tyd beskikbaar wees. ‘n Algoritme word voorgestel om die stel Pareto-optimale oplossings te vind wat die taaktoedelings aan werkers onderhewig aan die twee doelwitte doen sonder dat prioriteite toegeken word. Die twee doelwitte is om die totale koste van die opdrag te minimiseer en om die tyd te verminder om al die take te voltooi.
Primitive recursive realizability and basic propositional logic
Plisko, Valery
2007-01-01
Two notions of primitive recursive realizability for arithmetic sentences are considered. The first one is strictly primitive recursive realizability introduced by Z. Damnjanovic in 1994. We prove that intuitionistic predicate logic is not sound with this kind of realizability. Namely there
Conjugate gradient algorithms using multiple recursions
Barth, T.; Manteuffel, T.
1996-12-31
Much is already known about when a conjugate gradient method can be implemented with short recursions for the direction vectors. The work done in 1984 by Faber and Manteuffel gave necessary and sufficient conditions on the iteration matrix A, in order for a conjugate gradient method to be implemented with a single recursion of a certain form. However, this form does not take into account all possible recursions. This became evident when Jagels and Reichel used an algorithm of Gragg for unitary matrices to demonstrate that the class of matrices for which a practical conjugate gradient algorithm exists can be extended to include unitary and shifted unitary matrices. The implementation uses short double recursions for the direction vectors. This motivates the study of multiple recursion algorithms.
Wronskians, generalized Wronskians and solutions to the Korteweg-de Vries equation
Ma Wenxiu
2004-01-01
A bridge going from Wronskian solutions to generalized Wronskian solutions of the Korteweg-de Vries (KdV) equation is built. It is then shown that generalized Wronskian solutions can be viewed as Wronskian solutions. The idea is used to generate positons, negatons and their interaction solutions to the KdV equation. Moreover, general positons and negatons are constructed through the Wronskian formulation. A few new exact solutions to the KdV equation are explicitly presented as examples of Wronskian solutions
Bounded queries in recursion theory
Gasarch, William I
1999-01-01
One of the major concerns of theoretical computer science is the classifi cation of problems in terms of how hard they are. The natural measure of difficulty of a function is the amount of time needed to compute it (as a function of the length of the input). Other resources, such as space, have also been considered. In recursion theory, by contrast, a function is considered to be easy to compute if there exists some algorithm that computes it. We wish to classify functions that are hard, i.e., not computable, in a quantitative way. We cannot use time or space, since the functions are not even computable. We cannot use Turing degree, since this notion is not quantitative. Hence we need a new notion of complexity-much like time or spac~that is quantitative and yet in some way captures the level of difficulty (such as the Turing degree) of a function.
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....
Solitary wave solution to a singularly perturbed generalized Gardner ...
2017-03-24
Mar 24, 2017 ... Abstract. This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the ...
Recursive Bayesian recurrent neural networks for time-series modeling.
Mirikitani, Derrick T; Nikolaev, Nikolay
2010-02-01
This paper develops a probabilistic approach to recursive second-order training of recurrent neural networks (RNNs) for improved time-series modeling. A general recursive Bayesian Levenberg-Marquardt algorithm is derived to sequentially update the weights and the covariance (Hessian) matrix. The main strengths of the approach are a principled handling of the regularization hyperparameters that leads to better generalization, and stable numerical performance. The framework involves the adaptation of a noise hyperparameter and local weight prior hyperparameters, which represent the noise in the data and the uncertainties in the model parameters. Experimental investigations using artificial and real-world data sets show that RNNs equipped with the proposed approach outperform standard real-time recurrent learning and extended Kalman training algorithms for recurrent networks, as well as other contemporary nonlinear neural models, on time-series modeling.
Parallelizable approximate solvers for recursions arising in preconditioning
Shapira, Y. [Israel Inst. of Technology, Haifa (Israel)
1996-12-31
For the recursions used in the Modified Incomplete LU (MILU) preconditioner, namely, the incomplete decomposition, forward elimination and back substitution processes, a parallelizable approximate solver is presented. The present analysis shows that the solutions of the recursions depend only weakly on their initial conditions and may be interpreted to indicate that the inexact solution is close, in some sense, to the exact one. The method is based on a domain decomposition approach, suitable for parallel implementations with message passing architectures. It requires a fixed number of communication steps per preconditioned iteration, independently of the number of subdomains or the size of the problem. The overlapping subdomains are either cubes (suitable for mesh-connected arrays of processors) or constructed by the data-flow rule of the recursions (suitable for line-connected arrays with possibly SIMD or vector processors). Numerical examples show that, in both cases, the overhead in the number of iterations required for convergence of the preconditioned iteration is small relatively to the speed-up gained.
Abdou, M.A.
2008-01-01
The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics
Data harmonization of environmental variables: from simple to general solutions
Baume, O.
2009-04-01
European data platforms often contain measurements from different regional or national networks. As standards and protocols - e.g. type of measurement devices, sensors or measurement site classification, laboratory analysis and post-processing methods, vary between networks, discontinuities will appear when mapping the target variable at an international scale. Standardisation is generally a costly solution and does not allow classical statistical analysis of previously reported values. As an alternative, harmonization should be envisaged as an integrated step in mapping procedures across borders. In this paper, several harmonization solutions developed under the INTAMAP FP6 project are presented. The INTAMAP FP6 project is currently developing an interoperable framework for real-time automatic mapping of critical environmental variables by extending spatial statistical methods to web-based implementations. Harmonization is often considered as a pre-processing step in statistical data analysis workflow. If biases are assessed with little knowledge about the target variable - in particular when no explanatory covariate is integrated, a harmonization procedure along borders or between regionally overlapping networks may be adopted (Skøien et al., 2007). In this case, bias is estimated as the systematic difference between line or local predictions. On the other hand, when covariates can be included in spatial prediction, the harmonization step is integrated in the whole model estimation procedure, and, therefore, is no longer an independent pre-processing step of the automatic mapping process (Baume et al., 2007). In this case, bias factors become integrated parameters of the geostatistical model and are estimated alongside the other model parameters. The harmonization methods developed within the INTAMAP project were first applied within the field of radiation, where the European Radiological Data Exchange Platform (EURDEP) - http://eurdep.jrc.ec.europa.eu/ - has
Some recursive formulas for Selberg-type integrals
Iguri, Sergio [Instituto de AstronomIa y Fisica del Espacio (CONICET-UBA). C. C. 67, Suc. 28, 1428 Buenos Aires (Argentina); Mansour, Toufik, E-mail: siguri@iafe.uba.a, E-mail: toufik@math.haifa.ac.i [Department of Mathematics, University of Haifa, Haifa 31905 (Israel)
2010-02-12
A set of recursive relations satisfied by Selberg-type integrals involving monomial symmetric polynomials are derived, generalizing previous results in Aomoto (1987) SIAM J. Math. Anal. 18 545-49 and Iguri (2009) Lett. Math. Phys. 89 141-58. These formulas provide a well-defined algorithm for computing Selberg-Schur integrals whenever the Kostka numbers relating Schur functions and the corresponding monomial polynomials are explicitly known. We illustrate the usefulness of our results discussing some interesting examples.
Institutional Problems and Solutions of General Education in Chinese Universities
Meng, Weiqing; Huang, Wei
2018-01-01
Embedding general education in the Chinese university education system is a considerably complex systemic project, and a lack of institutional arrangements beneficial to general education has always been a key barrier in implementation. Currently, the main institutional restricting factors for university general education include substantial…
Exact solutions of strong gravity in generalized metrics
Hojman, R.; Smailagic, A.
1981-05-01
We consider classical solutions for the strong gravity theory of Salam and Strathdee in a wider class of metrics with positive, zero and negative curvature. It turns out that such solutions exist and their relevance for quark confinement is explored. Only metrics with positive curvature (spherical symmetry) give a confining potential in a simple picture of the scalar hadron. This supports the idea of describing the hadron as a closed microuniverse of the strong metric. (author)
Recursion relations for AdS/CFT correlators
Raju, Suvrat
2011-01-01
We expand on the results of our recent letter [Phys. Rev. Lett. 106, 091601 (2011)], where we presented new recursion relations for correlation functions of the stress-tensor and conserved currents in conformal field theories with an AdS d+1 dual for d≥4. These recursion relations are derived by generalizing the Britto-Cachazo-Feng-Witten (BCFW) relations to amplitudes in anti-de Sitter space (AdS) that are dual to boundary correlators, and are usually computed perturbatively by Witten diagrams. Our results relate vacuum-correlation functions to integrated products of lower-point transition amplitudes, which correspond to correlators calculated between states dual to certain normalizable modes. We show that the set of ''polarization vectors'' for which amplitudes behave well under the BCFW extension is smaller than in flat-space. We describe how transition amplitudes for more general external polarizations can be constructed by combining answers obtained by different pairs of BCFW shifts. We then generalize these recursion relations to supersymmetric theories. In AdS, unlike flat-space, even maximal supersymmetry is insufficient to permit the computation of all correlators of operators in the same multiplet as a stress-tensor or conserved current. Finally, we work out some simple examples to verify our results.
Recursive sequences in first-year calculus
Krainer, Thomas
2016-02-01
This article provides ready-to-use supplementary material on recursive sequences for a second-semester calculus class. It equips first-year calculus students with a basic methodical procedure based on which they can conduct a rigorous convergence or divergence analysis of many simple recursive sequences on their own without the need to invoke inductive arguments as is typically required in calculus textbooks. The sequences that are accessible to this kind of analysis are predominantly (eventually) monotonic, but also certain recursive sequences that alternate around their limit point as they converge can be considered.
The Generalized Wronskian Solution to a Negative KdV-mKdV Equation
Liu Yu-Qing; Chen Deng-Yuan; Hu Chao
2012-01-01
A negative KdV-mKdV hierarchy is presented through the KdV-mKdV operator. The generalized Wronskian solution to the negative KdV-mKdV equation is obtained. Some soliton-like solutions and a complexiton solution are presented explicitly as examples. (general)
General classical solutions in the noncommutative CP{sup N-1} model
Foda, O.; Jack, I.; Jones, D.R.T
2002-10-31
We give an explicit construction of general classical solutions for the noncommutative CP{sup N-1} model in two dimensions, showing that they correspond to integer values for the action and topological charge. We also give explicit solutions for the Dirac equation in the background of these general solutions and show that the index theorem is satisfied.
New explicit spike solutions-non-local component of the generalized Mixmaster attractor
Lim, Woei Chet
2008-01-01
By applying a standard solution-generating transformation to an arbitrary vacuum Bianchi type II solution, one generates a new solution with spikes commonly observed in numerical simulations. It is conjectured that the spike solutions are part of the generalized Mixmaster attractor
Solving the AKNS Hierarchy by Its Bilinear Form: Generalized Double Wronskian Solutions
Yin Fumei; Sun Yepeng; Cai Fuqing; Chen Dengyuan
2008-01-01
Through the Wronskian technique, a simple and direct proof is presented that the AKNS hierarchy in the bilinear form has generalized double Wronskian solutions. Moreover, by using a unified way, soliton solutions, rational solutions, Matveev solutions and complexitons in double Wronskian form for it are constructed.
Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation
Pandir, Yusuf; Gurefe, Yusuf; Misirli, Emine
2013-01-01
In this paper, we study the Kadomtsev-Petviashvili equation with generalized evolution and derive some new results using the approach called the trial equation method. The obtained results can be expressed by the soliton solutions, rational function solutions, elliptic function solutions and Jacobi elliptic function solutions. In the discussion, we give a new version of the trial equation method for nonlinear differential equations.
Elastic stars in general relativity: III. Stiff ultrarigid exact solutions
Karlovini, Max; Samuelsson, Lars
2004-01-01
We present an equation of state for elastic matter which allows for purely longitudinal elastic waves in all propagation directions, not just principal directions. The speed of these waves is equal to the speed of light whereas the transversal type speeds are also very high, comparable to but always strictly less than that of light. Clearly such an equation of state does not give a reasonable matter description for the crust of a neutron star, but it does provide a nice causal toy model for an extremely rigid phase in a neutron star core, should such a phase exist. Another reason for focusing on this particular equation of state is simply that it leads to a very simple recipe for finding stationary rigid motion exact solutions to the Einstein equations. In fact, we show that a very large class of stationary spacetimes with constant Ricci scalar can be interpreted as rigid motion solutions with this matter source. We use the recipe to derive a static spherically symmetric exact solution with constant energy density, regular centre and finite radius, having a nontrivial parameter that can be varied to yield a mass-radius curve from which stability can be read off. It turns out that the solution is stable down to a tenuity R/M slightly less than 3. The result of this static approach to stability is confirmed by a numerical determination of the fundamental radial oscillation mode frequency. We also present another solution with outwards decreasing energy density. Unfortunately, this solution only has a trivial scaling parameter and is found to be unstable
Xu Guiqiong; Li Zhibin
2005-01-01
It is proven that generalized coupled higher-order nonlinear Schroedinger equations possess the Painleve property for two particular choices of parameters, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests
ETHICS AND KNOWLEDGE OF RECURSIVITY IN PSYCHOLOGISTS TRAINING
Ramón Sanz Ferramola
2008-07-01
Full Text Available This work deals with the characterization of psychology as a science and profession. Thisfeature is part of the Argentine academic tradition which goes from the origins of psychology as an undergraduate program by the end of the 1950s to the present day. In relation to this topic, four issues are analysed: a the knowledges of psychology showing the necessity of two epistemic dimensions closely related, namely the discursivity and recursivity, or knowledge and metaknowledge, b the role of psychology as a profession within the praxis, rather than in the poiesis, according to the Greek distinction between the implications of these two modalities of the “doing”, c the concurrence and difference of ethics and deontology, their roles, bounds and potentialities within the psychological field in general, and that of scientific-professional morality in particular, and d the definition and characterization of ethics and epistemology as knowledge of recursivity in psychologists’ training.
One loop integration with hypergeometric series by using recursion relations
Watanabe, Norihisa; Kaneko, Toshiaki
2014-01-01
General one-loop integrals with arbitrary mass and kinematical parameters in d-dimensional space-time are studied. By using Bernstein theorem, a recursion relation is obtained which connects (n + 1)-point to n-point functions. In solving this recursion relation, we have shown that one-loop integrals are expressed by a newly defined hypergeometric function, which is a special case of Aomoto-Gelfand hypergeometric functions. We have also obtained coefficients of power series expansion around 4-dimensional space-time for two-, three- and four-point functions. The numerical results are compared with ''LoopTools'' for the case of two- and three-point functions as examples
The generalized tanh method to obtain exact solutions of nonlinear partial differential equation
Gómez, César
2007-01-01
In this paper, we present the generalized tanh method to obtain exact solutions of nonlinear partial differential equations, and we obtain solitons and exact solutions of some important equations of the mathematical physics.
Travelling Solitary Wave Solutions for Generalized Time-delayed Burgers-Fisher Equation
Deng Xijun; Han Libo; Li Xi
2009-01-01
In this paper, travelling wave solutions for the generalized time-delayed Burgers-Fisher equation are studied. By using the first-integral method, which is based on the ring theory of commutative algebra, we obtain a class of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation. A minor error in the previous article is clarified. (general)
Recursive relations for a quiver gauge theory
Park, Jaemo; Sim, Woojoo
2006-01-01
We study the recursive relations for a quiver gauge theory with the gauge group SU(N 1 ) x SU(N 2 ) with bifundamental fermions transforming as (N 1 , N-bar 2 ). We work out the recursive relation for the amplitudes involving a pair of quark and antiquark and gluons of each gauge group. We realize directly in the recursive relations the invariance under the order preserving permutations of the gluons of the first and the second gauge group. We check the proposed relations for MHV, 6-point and 7-point amplitudes and find the agreements with the known results and the known relations with the single gauge group amplitudes. The proposed recursive relation is much more efficient in calculating the amplitudes than using the known relations with the amplitudes of the single gauge group
A general solution to some plane problems of micropolar elasticity
Warren, William E.; Byskov, Esben
2008-01-01
functions, the solution is obtained in terms of two analytic functions and a third function satisfying the modified homogeneous Helmholtz equation. Expressions for the two-dimensional components of displacement, stress, and couple stress, along with the resultant force on a contour, are presented.We observe...
Vicari, Giuseppe; Adenzato, Mauro
2014-05-01
In their 2002 seminal paper Hauser, Chomsky and Fitch hypothesize that recursion is the only human-specific and language-specific mechanism of the faculty of language. While debate focused primarily on the meaning of recursion in the hypothesis and on the human-specific and syntax-specific character of recursion, the present work focuses on the claim that recursion is language-specific. We argue that there are recursive structures in the domain of motor intentionality by way of extending John R. Searle's analysis of intentional action. We then discuss evidence from cognitive science and neuroscience supporting the claim that motor-intentional recursion is language-independent and suggest some explanatory hypotheses: (1) linguistic recursion is embodied in sensory-motor processing; (2) linguistic and motor-intentional recursions are distinct and mutually independent mechanisms. Finally, we propose some reflections about the epistemic status of HCF as presenting an empirically falsifiable hypothesis, and on the possibility of testing recursion in different cognitive domains. Copyright © 2014 Elsevier Inc. All rights reserved.
A Study for Obtaining New and More General Solutions of Special-Type Nonlinear Equation
Zhao Hong
2007-01-01
The generalized algebraic method with symbolic computation is extended to some special-type nonlinear equations for constructing a series of new and more general travelling wave solutions in terms of special functions. Such equations cannot be directly dealt with by the method and require some kinds of pre-processing techniques. It is shown that soliton solutions and triangular periodic solutions can be established as the limits of the Jacobi doubly periodic wave solutions.
Recursive tridiagonalization of infinite dimensional Hamiltonians
Haydock, R.; Oregon Univ., Eugene, OR
1989-01-01
Infinite dimensional, computable, sparse Hamiltonians can be numerically tridiagonalized to finite precision using a three term recursion. Only the finite number of components whose relative magnitude is greater than the desired precision are stored at any stage in the computation. Thus the particular components stored change as the calculation progresses. This technique avoids errors due to truncation of the orbital set, and makes terminators unnecessary in the recursion method. (orig.)
Explicit Solutions for Generalized (2+1)-Dimensional Nonlinear Zakharov-Kuznetsov Equation
Sun Yuhuai; Ma Zhimin; Li Yan
2010-01-01
The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equation are explored by the method of the improved generalized auxiliary differential equation. Many explicit analytic solutions of the Z-K equation are obtained. The methods used to solve the Z-K equation can be employed in further work to establish new solutions for other nonlinear partial differential equations. (general)
M. Arshad
Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method
A theory of general solutions of 3D problems in 1D hexagonal quasicrystals
Gao Yang; Xu Sipeng; Zhao Baosheng
2008-01-01
A theory of general solutions of three-dimensional (3D) problems is developed for the coupled equilibrium equations in 1D hexagonal quasicrystals (QCs), and two new general solutions, which are called generalized Lekhnitskii-Hu-Nowacki (LHN) and Elliott-Lodge (E-L) solutions, respectively, are presented based on three theorems. As a special case, the generalized LHN solution is obtained from our previous general solution by introducing three high-order displacement functions. For further simplification, considering three cases in which three characteristic roots are distinct or possibly equal to each other, the generalized E-L solution shall take different forms, and be expressed in terms of four quasi-harmonic functions which are very simple and useful. It is proved that the general solution presented by Peng and Fan is consistent with one case of the generalized E-L solution, while does not include the other two cases. It is important to note that generalized LHN and E-L solutions are complete in z-convex domains, while incomplete in the usual non-z-convex domains
Efficient Implementation of the Riccati Recursion for Solving Linear-Quadratic Control Problems
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration....... In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky...... factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver....
A recursive Monte Carlo method for estimating importance functions in deep penetration problems
Goldstein, M.
1980-04-01
A pratical recursive Monte Carlo method for estimating the importance function distribution, aimed at importance sampling for the solution of deep penetration problems in three-dimensional systems, was developed. The efficiency of the recursive method was investigated for sample problems including one- and two-dimensional, monoenergetic and and multigroup problems, as well as for a practical deep-penetration problem with streaming. The results of the recursive Monte Carlo calculations agree fairly well with Ssub(n) results. It is concluded that the recursive Monte Carlo method promises to become a universal method for estimating the importance function distribution for the solution of deep-penetration problems, in all kinds of systems: for many systems the recursive method is likely to be more efficient than previously existing methods; for three-dimensional systems it is the first method that can estimate the importance function with the accuracy required for an efficient solution based on importance sampling of neutron deep-penetration problems in those systems
Approximation solutions for indifference pricing under general utility functions
Chen, An; Pelsser, Antoon; Vellekoop, M.H.
2008-01-01
With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners
Approximate Solutions for Indifference Pricing under General Utility Functions
Chen, A.; Pelsser, A.; Vellekoop, M.
2007-01-01
With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners
Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion
Alexandrov, A.; Chapuy, G.; Eynard, B.; Harnad, J.
2018-06-01
A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2 D Toda {τ} -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel-Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers.
Recursive regularization step for high-order lattice Boltzmann methods
Coreixas, Christophe; Wissocq, Gauthier; Puigt, Guillaume; Boussuge, Jean-François; Sagaut, Pierre
2017-09-01
A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from 104 to 106, and where a thorough analysis of the case at Re=3 ×104 is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.
Fermionic Approach to Weighted Hurwitz Numbers and Topological Recursion
Alexandrov, A.; Chapuy, G.; Eynard, B.; Harnad, J.
2017-12-01
A fermionic representation is given for all the quantities entering in the generating function approach to weighted Hurwitz numbers and topological recursion. This includes: KP and 2D Toda {τ} -functions of hypergeometric type, which serve as generating functions for weighted single and double Hurwitz numbers; the Baker function, which is expanded in an adapted basis obtained by applying the same dressing transformation to all vacuum basis elements; the multipair correlators and the multicurrent correlators. Multiplicative recursion relations and a linear differential system are deduced for the adapted bases and their duals, and a Christoffel-Darboux type formula is derived for the pair correlator. The quantum and classical spectral curves linking this theory with the topological recursion program are derived, as well as the generalized cut-and-join equations. The results are detailed for four special cases: the simple single and double Hurwitz numbers, the weakly monotone case, corresponding to signed enumeration of coverings, the strongly monotone case, corresponding to Belyi curves and the simplest version of quantum weighted Hurwitz numbers.
Yusuf Pandir
2013-01-01
Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.
Cho, Pyeong Whan; Szkudlarek, Emily; Tabor, Whitney
2016-01-01
Learning is typically understood as a process in which the behavior of an organism is progressively shaped until it closely approximates a target form. It is easy to comprehend how a motor skill or a vocabulary can be progressively learned-in each case, one can conceptualize a series of intermediate steps which lead to the formation of a proficient behavior. With grammar, it is more difficult to think in these terms. For example, center embedding recursive structures seem to involve a complex interplay between multiple symbolic rules which have to be in place simultaneously for the system to work at all, so it is not obvious how the mechanism could gradually come into being. Here, we offer empirical evidence from a new artificial language (or "artificial grammar") learning paradigm, Locus Prediction, that, despite the conceptual conundrum, recursion acquisition occurs gradually, at least for a simple formal language. In particular, we focus on a variant of the simplest recursive language, a (n) b (n) , and find evidence that (i) participants trained on two levels of structure (essentially ab and aabb) generalize to the next higher level (aaabbb) more readily than participants trained on one level of structure (ab) combined with a filler sentence; nevertheless, they do not generalize immediately; (ii) participants trained up to three levels (ab, aabb, aaabbb) generalize more readily to four levels than participants trained on two levels generalize to three; (iii) when we present the levels in succession, starting with the lower levels and including more and more of the higher levels, participants show evidence of transitioning between the levels gradually, exhibiting intermediate patterns of behavior on which they were not trained; (iv) the intermediate patterns of behavior are associated with perturbations of an attractor in the sense of dynamical systems theory. We argue that all of these behaviors indicate a theory of mental representation in which recursive
A note on the solution of general Falkner-Skan problem by two novel semi-analytical techniques
Ahmed Khidir
2015-12-01
Full Text Available The aim of this paper is to give a presentation of two new iterative methods for solving non-linear differential equations, they are successive linearisation method and spectral homotopy perturbation method. We applied these techniques on the non-linear boundary value problems of Falkner-Skan type. The methods used to find a recursive former for higher order equations that are solved using the Chebyshev spectral method to find solutions that are accurate and converge rapidly to the full numerical solution. The methods are illustrated by progressively applying the technique to the Blasius boundary layer equation, the Falkner-Skan equation and finally, the magnetohydrodynamic (MHD Falkner-Skan equation. The solutions are compared to other methods in the literature such as the homotopy analysis method and the spectral-homotopy analysis method with focus on the accuracy and convergence of this new techniques.
van den Bos, E.; de Rooij, M.; Sumter, S.R.; Westenberg, P.M.
2016-01-01
The present study adds to the emerging literature on the development of social cognition in adolescence by investigating the development of recursive thinking (i.e., thinking about thinking). Previous studies have indicated that the development of recursive thinking is not completed during
Thirukkanesh, S. [Eastern University, Department of Mathematics, Chenkalady (Sri Lanka); Ragel, F.C. [Eastern University, Department of Physics, Chenkalady (Sri Lanka); Sharma, Ranjan; Das, Shyam [P.D. Women' s College, Department of Physics, Jalpaiguri (India)
2018-01-15
We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as an anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular solution is taken up to show its physical acceptability. Making use of the current estimate of mass and radius of a known pulsar, the effects of anisotropic stress on the gross physical behaviour of a relativistic compact star is also highlighted. (orig.)
Exact solutions of nonlinear generalizations of the Klein Gordon and Schrodinger equations
Burt, P.B.
1978-01-01
Exact solutions of sine Gordon and multiple sine Gordon equations are constructed in terms of solutions of a linear base equation, the Klein Gordon equation and also in terms of nonlinear base equations where the nonlinearity is polynomial in the dependent variable. Further, exact solutions of nonlinear generalizations of the Schrodinger equation and of additional nonlinear generalizations of the Klein Gordon equation are constructed in terms of solutions of linear base equations. Finally, solutions with spherical symmetry, of nonlinear Klein Gordon equations are given. 14 references
Chain of matrices, loop equations and topological recursion
Orantin, Nicolas
2009-01-01
Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. These two definitions, perturbative and non-perturbative, are discussed in this chapter as well as their relation. The so-called loop equations satisfied by integrals over random matrices coupled in chain is discussed as well as their recursive solution in the perturbative case when the matrices are Hermitean.
Optimally eating a stochastic cake. A recursive utility approach
Epaulard, Anne; Pommeret, Aude
2003-01-01
In this short paper, uncertainties on resource stock and on technical progress are introduced into an intertemporal equilibrium model of optimal extraction of a non-renewable resource. The representative consumer maximizes a recursive utility function which disentangles between intertemporal elasticity of substitution and risk aversion. A closed-form solution is derived for both the optimal extraction and price paths. The value of the intertemporal elasticity of substitution relative to unity is then crucial in understanding extraction. Moreover, this model leads to a non-renewable resource price following a geometric Brownian motion
Tisdell, C. C.
2017-01-01
Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…
Travelling wave solutions of the generalized Benjamin-Bona-Mahony equation
Estevez, P.G.; Kuru, S.; Negro, J.; Nieto, L.M.
2009-01-01
A class of particular travelling wave solutions of the generalized Benjamin-Bona-Mahony equation is studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and of its modified version, are also recovered.
Kuo-Shou Chiu
2011-11-01
Full Text Available We examine scalar differential equations with a general piecewise constant argument, in short DEPCAG, that is, the argument is a general step function. Criteria of existence of the oscillatory and nonoscillatory solutions of such equations are proposed. Necessary and sufficient conditions for stability of the zero solution are obtained. Appropriate examples are given to show our results.
Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation
Ma Zhi-Min; Sun Yu-Huai; Liu Fu-Sheng
2013-01-01
In this paper, the generalized Boussinesq wave equation u tt — u xx + a(u m ) xx + bu xxxx = 0 is investigated by using the bifurcation theory and the method of phase portraits analysis. Under the different parameter conditions, the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained. (general)
General solution of the Bagley-Torvik equation with fractional-order derivative
Wang, Z. H.; Wang, X.
2010-05-01
This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.
Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy's law
Khan, M.; Hayat, T.; Asghar, S.
2005-12-01
This paper deals with an exact solution for the magnetohydrodynamic (MHD) flow of a generalized Oldroyd-B fluid in a circular pipe. For the description of such a fluid, the fractional calculus approach has been used throughout the analysis. Based on modified Darcy's law for generalized Oldroyd-B fluid, the velocity field is calculated analytically. Several known solutions can be recovered as the limiting cases of our solution. (author)
General solutions of second-order linear difference equations of Euler type
Akane Hongyo
2017-01-01
Full Text Available The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \\(y^{\\prime\\prime}+(\\lambda/t^2y=0\\ or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.
Exact solutions of the one-dimensional generalized modified complex Ginzburg-Landau equation
Yomba, Emmanuel; Kofane, Timoleon Crepin
2003-01-01
The one-dimensional (1D) generalized modified complex Ginzburg-Landau (MCGL) equation for the traveling wave systems is analytically studied. Exact solutions of this equation are obtained using a method which combines the Painleve test for integrability in the formalism of Weiss-Tabor-Carnevale and Hirota technique of bilinearization. We show that pulses, fronts, periodic unbounded waves, sources, sinks and solution as collision between two fronts are the important coherent structures that organize much of the dynamical properties of these traveling wave systems. The degeneracies of the 1D generalized MCGL equation are examined as well as several of their solutions. These degeneracies include two important equations: the 1D generalized modified Schroedinger equation and the 1D generalized real modified Ginzburg-Landau equation. We obtain that the one parameter family of traveling localized source solutions called 'Nozaki-Bekki holes' become a subfamily of the dark soliton solutions in the 1D generalized modified Schroedinger limit
Solution of generalized shifted linear systems with complex symmetric matrices
Sogabe, Tomohiro; Hoshi, Takeo; Zhang, Shao-Liang; Fujiwara, Takeo
2012-01-01
We develop the shifted COCG method [R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara, Linear algebraic calculation of Green’s function for large-scale electronic structure theory, Phys. Rev. B 73 (165108) (2006) 1–9] and the shifted WQMR method [T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems, Electron. Trans. Numer. Anal. 31 (2008) 126–140] for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory. The complex symmetric Lanczos process with a suitable bilinear form plays an important role in the development of the methods. The numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved.
Recursions of Symmetry Orbits and Reduction without Reduction
Andrei A. Malykh
2011-04-01
Full Text Available We consider a four-dimensional PDE possessing partner symmetries mainly on the example of complex Monge-Ampère equation (CMA. We use simultaneously two pairs of symmetries related by a recursion relation, which are mutually complex conjugate for CMA. For both pairs of partner symmetries, using Lie equations, we introduce explicitly group parameters as additional variables, replacing symmetry characteristics and their complex conjugates by derivatives of the unknown with respect to group parameters. We study the resulting system of six equations in the eight-dimensional space, that includes CMA, four equations of the recursion between partner symmetries and one integrability condition of this system. We use point symmetries of this extended system for performing its symmetry reduction with respect to group parameters that facilitates solving the extended system. This procedure does not imply a reduction in the number of physical variables and hence we end up with orbits of non-invariant solutions of CMA, generated by one partner symmetry, not used in the reduction. These solutions are determined by six linear equations with constant coefficients in the five-dimensional space which are obtained by a three-dimensional Legendre transformation of the reduced extended system. We present algebraic and exponential examples of such solutions that govern Legendre-transformed Ricci-flat Kähler metrics with no Killing vectors. A similar procedure is briefly outlined for Husain equation.
General predictive control using the delta operator
Jensen, Morten Rostgaard; Poulsen, Niels Kjølstad; Ravn, Ole
1993-01-01
This paper deals with two-discrete-time operators, the conventional forward shift-operator and the δ-operator. Both operators are treated in view of construction of suitable solutions to the Diophantine equation for the purpose of prediction. A general step-recursive scheme is presented. Finally...... a general predictive control (GPC) is formulated and applied adaptively to a continuous-time plant...
General solution to the E-B mixing problem
Smith, Kendrick M.; Zaldarriaga, Matias
2007-01-01
We derive a general ansatz for optimizing pseudo-C l estimators used to measure cosmic microwave background anisotropy power spectra, and apply it to the recently proposed pure pseudo-C l formalism, to obtain an estimator which achieves near-optimal B-mode power spectrum errors for any specified noise distribution while minimizing leakage from ambiguous modes. Our technique should be relevant for upcoming cosmic microwave background polarization experiments searching for B-mode polarization. We compare our technique both to the theoretical limits based on a full Fisher matrix calculation and to the standard pseudo-C l technique. We demonstrate it by applying it to a fiducial survey with realistic inhomogeneous noise, complex boundaries, point source masking, and a noise level comparable to what is expected for next-generation experiments (∼5.75 μK-arcmin). For such an experiment our technique could improve the constraints on the amplitude of a gravity wave background by over a factor of 10 compared to what could be obtained using ordinary pseudo-C l , coming quite close to saturating the theoretical limit. Constraints on the amplitude of the lensing B-modes are improved by about a factor of 3
A General Solution Framework for Component-Commonality Problems
Nils Boysen
2009-05-01
Full Text Available Component commonality - the use of the same version of a component across multiple products - is being increasingly considered as a promising way to offer high external variety while retaining low internal variety in operations. However, increasing commonality has both positive and negative cost effects, so that optimization approaches are required to identify an optimal commonality level. As components influence to a greater or lesser extent nearly every process step along the supply chain, it is not surprising that a multitude of diverging commonality problems is being investigated in literature, each of which are developing a specific algorithm designed for the respective commonality problem being considered. The paper on hand aims at a general framework which is flexible and efficient enough to be applied to a wide range of commonality problems. Such a procedure based on a two-stage graph approach is presented and tested. Finally, flexibility of the procedure is shown by customizing the framework to account for different types of commonality problems.
Updating Recursive XML Views of Relations
Choi, Byron; Cong, Gao; Fan, Wenfei
2009-01-01
This paper investigates the view update problem for XML views published from relational data. We consider XML views defined in terms of mappings directed by possibly recursive DTDs compressed into DAGs and stored in relations. We provide new techniques to efficiently support XML view updates...... specified in terms of XPath expressions with recursion and complex filters. The interaction between XPath recursion and DAG compression of XML views makes the analysis of the XML view update problem rather intriguing. Furthermore, many issues are still open even for relational view updates, and need...... to be explored. In response to these, on the XML side, we revise the notion of side effects and update semantics based on the semantics of XML views, and present effecient algorithms to translate XML updates to relational view updates. On the relational side, we propose a mild condition on SPJ views, and show...
Sabry, R.; Zahran, M.A.; Fan Engui
2004-01-01
A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found
Adaptable Iterative and Recursive Kalman Filter Schemes
Zanetti, Renato
2014-01-01
Nonlinear filters are often very computationally expensive and usually not suitable for real-time applications. Real-time navigation algorithms are typically based on linear estimators, such as the extended Kalman filter (EKF) and, to a much lesser extent, the unscented Kalman filter. The Iterated Kalman filter (IKF) and the Recursive Update Filter (RUF) are two algorithms that reduce the consequences of the linearization assumption of the EKF by performing N updates for each new measurement, where N is the number of recursions, a tuning parameter. This paper introduces an adaptable RUF algorithm to calculate N on the go, a similar technique can be used for the IKF as well.
Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation
Sun Chengfeng; Gao Hongjun
2009-01-01
The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.
Computer local construction of a general solution for the Chew-Low equations
Gerdt, V.P.
1980-01-01
General solution of the dynamic form of the Chew-Low equations in the vicinity of the restpoint is considered. A method for calculating coefficients of series being members of such solution is suggested. The results of calculations, coefficients of power series and expansions carried out by means of the SCHOONSCHIP and SYMBAL systems are given. It is noted that the suggested procedure of the Chew-Low equation solutions basing on using an electronic computer as an instrument for analytical calculations permits to obtain detail information on the local structure of general solution
Fernandes, Julio C.L.; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: julio.lombaldo@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada; Dulla, Sandra; Ravetto, Piero, E-mail: sandra.dulla@polito.it, E-mail: piero.ravetto@polito.it [Dipartimento di Energia, Politecnico di Torino, Piemonte (Italy)
2015-07-01
In this work we generalize the solution of the one-dimensional neutron transport equation to a multi- group approach in planar geometry. The basic idea of this work consists in consider the hierarchical construction of a solution for a generic number G of energy groups, starting from a mono-energetic solution. The hierarchical method follows the reasoning of the decomposition method. More specifically, the additional terms from adding energy groups is incorporated into the recursive scheme as source terms. This procedure leads to an analytical representation for the solution with G energy groups. The recursion depth is related to the accuracy of the solution, that may be evaluated after each recursion step. The authors present a heuristic analysis of stability for the results. Numerical simulations for a specific example with four energy groups and a localized pulsed source. (author)
Exact solution of the generalized Peierls equation for arbitrary n-fold screw dislocation
Wang, Shaofeng; Hu, Xiangsheng
2018-05-01
The exact solution of the generalized Peierls equation is presented and proved for arbitrary n-fold screw dislocation. The displacement field, stress field and the energy of the n-fold dislocation are also evaluated explicitly. It is found that the solution defined on each individual fold is given by the tail cut from the original Peierls solution. In viewpoint of energetics, a screw dislocation has a tendency to spread the distribution on all possible slip planes which are contained in the dislocation line zone. Based on the exact solution, the approximated solution of the improved Peierls equation is proposed for the modified γ-surface.
Deformation of the three-term recursion relation and generation of new orthogonal polynomials
Alhaidari, A D
2002-01-01
We find solutions for a linear deformation of the three-term recursion relation. The orthogonal polynomials of the first and second kind associated with the deformed relation are obtained. The new density (weight) function is written in terms of the original one and the deformation parameters
A foundation for real recursive function theory
J.F. Costa; B. S. Loff Barreto (Bruno Serra); J. Mycka
2009-01-01
htmlabstractThe class of recursive functions over the reals, denoted by REC(R), was introduced by Cristopher Moore in his seminal paper written in 1995. Since then many subsequent investigations brought new results: the class REC(R) was put in relation with the class of functions generated by the
Decidability and Expressiveness of Recursive Weighted Logic
Xue, Bingtian; Larsen, Kim Guldstrand; Mardare, Radu Iulian
2014-01-01
Labelled weighted transition systems (LWSs) are transition systems labelled with actions and real numbers. The numbers represent the costs of the corresponding actions in terms of resources. RecursiveWeighted Logic (RWL) is a multimodal logic that expresses qualitative and quantitative properties...
Adaptable recursive binary entropy coding technique
Kiely, Aaron B.; Klimesh, Matthew A.
2002-07-01
We present a novel data compression technique, called recursive interleaved entropy coding, that is based on recursive interleaving of variable-to variable length binary source codes. A compression module implementing this technique has the same functionality as arithmetic coding and can be used as the engine in various data compression algorithms. The encoder compresses a bit sequence by recursively encoding groups of bits that have similar estimated statistics, ordering the output in a way that is suited to the decoder. As a result, the decoder has low complexity. The encoding process for our technique is adaptable in that each bit to be encoded has an associated probability-of-zero estimate that may depend on previously encoded bits; this adaptability allows more effective compression. Recursive interleaved entropy coding may have advantages over arithmetic coding, including most notably the admission of a simple and fast decoder. Much variation is possible in the choice of component codes and in the interleaving structure, yielding coder designs of varying complexity and compression efficiency; coder designs that achieve arbitrarily small redundancy can be produced. We discuss coder design and performance estimation methods. We present practical encoding and decoding algorithms, as well as measured performance results.
Certified higher-order recursive path ordering
Koprowski, A.; Pfenning, F.
2006-01-01
The paper reports on a formalization of a proof of wellfoundedness of the higher-order recursive path ordering (HORPO) in the proof checker Coq. The development is axiom-free and fully constructive. Three substantive parts that could be used also in other developments are the formalizations of the
Exact solution of the N-dimensional generalized Dirac-Coulomb equation
Tutik, R.S.
1992-01-01
An exact solution to the bound state problem for the N-dimensional generalized Dirac-Coulomb equation, whose potential contains both the Lorentz-vector and Lorentz-scalar terms of the Coulomb form, is obtained. 24 refs. (author)
Global existence of a generalized solution for the radiative transfer equations
Golse, F.; Perthame, B.
1984-01-01
We prove global existence of a generalized solution of the radiative transfer equations, extending Mercier's result to the case of a layer with an initially cold area. Our Theorem relies on the results of Crandall and Ligett [fr
A Survey on Teaching and Learning Recursive Programming
Rinderknecht, Christian
2014-01-01
We survey the literature about the teaching and learning of recursive programming. After a short history of the advent of recursion in programming languages and its adoption by programmers, we present curricular approaches to recursion, including a review of textbooks and some programming methodology, as well as the functional and imperative…
Analytical approximate solutions for a general class of nonlinear delay differential equations.
Căruntu, Bogdan; Bota, Constantin
2014-01-01
We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.
Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation
Rasmussen, Kim; Henning, D.; Gabriel, H.
1996-01-01
We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interes...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.......We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...
Particular transcendent solution of the Ernst system generalized on n fields
Leaute, B.; Marcilhacy, G.
1986-01-01
A particular solution, a function of a particular form of the fifth Painleve transcendent, of the Ernst system generalized to n fields is determined, which characterizes both the stationary axially symmetric fields, the solution of the Einstein (n-1) Maxwell equations, and one class of axially symmetric static self-dual SU(n+1) Yang--Mills fields
A general solution of the plane problem in thermoelasticity in polar coordinates
Tabakman, H.D.; Lin, Y.J.
1977-01-01
A general solution, in polar coordinates, of the plane problem in thermoelasticity is obtained in terms of a stress and displacement function. The solution is valid for arbitrary temperature distribution T(r,theta). The characteristic feature of the paper is the forthright determination of the displacement components brought about by the introduction of a displacement function. (Auth.)
A general solution of the plane problem thermoelasticity in polar coordinates
Tabakman, H.D.; Lin, Y.J.
1977-01-01
A general solution, in polar coordinates, of the plane problem in thermoelasticity is obtained in terms of a stress and displacement function. The solution is valid for arbitrary temperature distribution T(r, theta). The characteristic feature of the paper is the forthright determination of the displacement components brought about by the introduction of a displacement function
General solution of Poisson equation in three dimensions for disk-like galaxies
Tong, Y.; Zheng, X.; Peng, O.
1982-01-01
The general solution of the Poisson equation is solved by means of integral transformations for Vertical BarkVertical Barr>>1 provided that the perturbed density of disk-like galaxies distributes along the radial direction according to the Hankel function. This solution can more accurately represent the outer spiral arms of disk-like galaxies
Generalized Sturmian Solutions for Many-Particle Schrödinger Equations
Avery, John; Avery, James Emil
2004-01-01
The generalized Sturmian method for obtaining solutions to the many-particle Schrodinger equation is reviewed. The method makes use of basis functions that are solutions of an approximate Schrodinger equation with a weighted zeroth-order potential. The weighting factors are especially chosen so...
Peakons, solitary patterns and periodic solutions for generalized Camassa-Holm equations
Zheng Yin; Lai Shaoyong
2008-01-01
This Letter deals with a generalized Camassa-Holm equation and a nonlinear dispersive equation by making use of a mathematical technique based on using integral factors for solving differential equations. The peakons, solitary patterns and periodic solutions are expressed analytically under various circumstances. The conditions that cause the qualitative change in the physical structures of the solutions are highlighted
Tables of generalized Airy functions for the asymptotic solution of the differential equation
Nosova, L N
1965-01-01
Tables of Generalized Airy Functions for the Asymptotic Solution of the Differential Equations contains tables of the special functions, namely, the generalized Airy functions, and their first derivatives, for real and pure imaginary values. The tables are useful for calculations on toroidal shells, laminae, rode, and for the solution of certain other problems of mathematical physics. The values of the functions were computed on the ""Strela"" highspeed electronic computer.This book will be of great value to mathematicians, researchers, and students.
Zhang Liang; Zhang Lifeng; Li Chongyin
2008-01-01
By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions
On the structure of generalized monopole solutions in gauge-theories
Horvath, Z.; Palla, L.
1976-01-01
A method is presented for constructing generalized 't Hooft monopole solutions in a gauge theory with an arbitrary gauge group. Restrictions arising from the condition of finite energy are derived. The radial oscillation of the solution is discussed. Using this method all the SU(3) solutions known in the literature are reproduced. Finite energy monopoles possessing magnetic charge in the range g 0 0 0 are found in SU(N) gauge theories. Different charge quantization conditions are analyzed to understand the structure of the solutions. (Auth.)
Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation
Said-Houari, Belkacem
2014-01-01
In this paper, we study the decay rates of solutions for the generalized Benjamin-Bona-Mahony equation in multi-dimensional space. For initial data in some L1-weighted spaces, we prove faster decay rates of the solutions. More precisely, using the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J. Differential Equations 158(2) (1999), 314-340 and Nonlinear Anal. 75(7) (2012), 3385-3392. © 2014-IOS Press.
Abundant general solitary wave solutions to the family of KdV type equations
Md. Azmol Huda
2017-03-01
Full Text Available This work explores the construction of more general exact traveling wave solutions of some nonlinear evolution equations (NLEEs through the application of the (G′/G, 1/G-expansion method. This method is allied to the widely used (G′/G-method initiated by Wang et al. and can be considered as an extension of the (G′/G-expansion method. For effectiveness, the method is applied to the family of KdV type equations. Abundant general form solitary wave solutions as well as periodic solutions are successfully obtained through this method. Moreover, in the obtained wider set of solutions, if we set special values of the parameters, some previously known solutions are revived. The approach of this method is simple and elegantly standard. Having been computerized it is also powerful, reliable and effective.
Nemeth, Michael P.; Schultz, Marc R.
2012-01-01
A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.
General classical solutions of the complex Grassmannian and CP sub(N-1) sigma models
Sasaki, Ryu.
1983-05-01
General classical solutions are constructed for the complex Grassmannian non-linear sigma models in two euclidean dimensions in terms of holomorphic functions. The Grassmannian sigma models are a simple generalization of the well known CP sup(N-1) model in two dimensions and they share various interesting properties; existence of (anti-) instantons, an infinite number of conserved quantities and complete integrability. (author)
Buurma, NJ; Blandamer, MJ; Engberts, JBFN; Buurma, Niklaas J.
The reactivity of 1-benzoyl-3-phenyl-1,2,4-triazole (1a) was studied in the presence of a range of weak bases in aqueous solution. A change in mechanism is observed from general-base catalysed hydrolysis to nucleophilic substitution and general-base catalysed nucleophilic substitution. A slight
A new algorithm for recursive estimation of ARMA parameters in reactor noise analysis
Tran Dinh Tri
1992-01-01
In this paper a new recursive algorithm for estimating the parameters of the Autoregressive Moving Average (ARMA) model from measured data is presented. The Yule-Walker equations for the case of the ARMA model are derived from the ARMA equation with innovations. The recursive algorithm is based on choosing an appropriate form of the operator functions and suitable representation of the (n + 1)-th order operator functions according to those with lower order. Two cases, when the order of the AR part is equal to that of the MA part, and the general case, were considered. (Author)
Olga Lucia Quintero
2008-05-01
Full Text Available This work presents a state estimator for a continuous bioprocess. To this aim, the Non Linear Filtering theory based on the recursive application of Bayes rule and Monte Carlo techniques is used. Recursive Bayesian Filters Sampling Importance Resampling (SIR is employed, including different kinds of resampling. Generally, bio-processes have strong non-linear and non-Gaussian characteristics, and this tool becomes attractive. The estimator behavior and performance are illustrated with the continuous process of alcoholic fermentation of Zymomonas mobilis. Not too many applications with this tool have been reported in the biotechnological area.
Zhu, Chaoyuan; Lin, Sheng Hsien
2006-07-28
Unified semiclasical solution for general nonadiabatic tunneling between two adiabatic potential energy surfaces is established by employing unified semiclassical solution for pure nonadiabatic transition [C. Zhu, J. Chem. Phys. 105, 4159 (1996)] with the certain symmetry transformation. This symmetry comes from a detailed analysis of the reduced scattering matrix for Landau-Zener type of crossing as a special case of nonadiabatic transition and nonadiabatic tunneling. Traditional classification of crossing and noncrossing types of nonadiabatic transition can be quantitatively defined by the rotation angle of adiabatic-to-diabatic transformation, and this rotational angle enters the analytical solution for general nonadiabatic tunneling. The certain two-state exponential potential models are employed for numerical tests, and the calculations from the present general nonadiabatic tunneling formula are demonstrated in very good agreement with the results from exact quantum mechanical calculations. The present general nonadiabatic tunneling formula can be incorporated with various mixed quantum-classical methods for modeling electronically nonadiabatic processes in photochemistry.
Approximate solution of generalized Ginzburg-Landau-Higgs system via homotopy perturbation method
Lu Juhong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Dept. of Information Engineering, Coll. of Lishui Professional Tech., Zhejiang (China); Zheng Chunlong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Shanghai Inst. of Applied Mathematics and Mechanics, Shanghai Univ., SH (China)
2010-04-15
Using the homotopy perturbation method, a class of nonlinear generalized Ginzburg-Landau-Higgs systems (GGLH) is considered. Firstly, by introducing a homotopic transformation, the nonlinear problem is changed into a system of linear equations. Secondly, by selecting a suitable initial approximation, the approximate solution with arbitrary degree accuracy to the generalized Ginzburg-Landau-Higgs system is derived. Finally, another type of homotopic transformation to the generalized Ginzburg-Landau-Higgs system reported in previous literature is briefly discussed. (orig.)
On semantics and applications of guarded recursion
Bizjak, Aleš
2016-01-01
denotational model and a logic for reasoning about program equivalence. In the last three chapters we study syntax and semantics of a dependent type theory with a family of later modalities indexed by the set of clocks, and clock quantifiers. In the fourth and fifth chapters we provide two model constructions......In this dissertation we study applications and semantics of guarded recursion, which is a method for ensuring that self-referential descriptions of objects define a unique object. The first two chapters are devoted to applications. We use guarded recursion, first in the form of explicit step......-indexing and then in the form of the internal language of particular sheaf topos, to construct logical relations for reasoning about contextual approximation of probabilistic and nondeterministic programs. These logical relations are sound and complete and useful for showing a range of example equivalences. In the third...
a Recursive Approach to Compute Normal Forms
HSU, L.; MIN, L. J.; FAVRETTO, L.
2001-06-01
Normal forms are instrumental in the analysis of dynamical systems described by ordinary differential equations, particularly when singularities close to a bifurcation are to be characterized. However, the computation of a normal form up to an arbitrary order is numerically hard. This paper focuses on the computer programming of some recursive formulas developed earlier to compute higher order normal forms. A computer program to reduce the system to its normal form on a center manifold is developed using the Maple symbolic language. However, it should be stressed that the program relies essentially on recursive numerical computations, while symbolic calculations are used only for minor tasks. Some strategies are proposed to save computation time. Examples are presented to illustrate the application of the program to obtain high order normalization or to handle systems with large dimension.
A recursive reduction of tensor Feynman integrals
Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.
2009-07-01
We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)
Interpretations of Recursive Type Definitions
Schwartzbach, Michael Ignatieff
1992-01-01
A system of hierarchical imperative types is extended to allow infinite values. The general structure of value assignments to types in the context of a hierarchy is considered, and it is shown that both a minimal and a maximal value assignment exist. We give two different characterizations...... of intermediate value assignments: In terms of the predicates that describe them as subsets of the maximal values, and in terms of computational stability. As an application we introduce rational infinite values in our system. Programs can then work on infinite imperative data structures which are allocated...
A recursive algorithm for trees and forests
Guo, Song; Guo, Victor J. W.
2017-01-01
Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on $\\{1,2,\\ldots,n\\}$. Classical formulas for counting various trees such as rooted trees, bipartite trees, tripartite trees, plane trees, $k$-ary plane trees, $k$-edge colored trees follow immediately from our recursive relations.
Lu, Chao; Li, Xubin; Wu, Dongsheng; Zheng, Lianqing; Yang, Wei
2016-01-12
In aqueous solution, solute conformational transitions are governed by intimate interplays of the fluctuations of solute-solute, solute-water, and water-water interactions. To promote molecular fluctuations to enhance sampling of essential conformational changes, a common strategy is to construct an expanded Hamiltonian through a series of Hamiltonian perturbations and thereby broaden the distribution of certain interactions of focus. Due to a lack of active sampling of configuration response to Hamiltonian transitions, it is challenging for common expanded Hamiltonian methods to robustly explore solvent mediated rare conformational events. The orthogonal space sampling (OSS) scheme, as exemplified by the orthogonal space random walk and orthogonal space tempering methods, provides a general framework for synchronous acceleration of slow configuration responses. To more effectively sample conformational transitions in aqueous solution, in this work, we devised a generalized orthogonal space tempering (gOST) algorithm. Specifically, in the Hamiltonian perturbation part, a solvent-accessible-surface-area-dependent term is introduced to implicitly perturb near-solute water-water fluctuations; more importantly in the orthogonal space response part, the generalized force order parameter is generalized as a two-dimension order parameter set, in which essential solute-solvent and solute-solute components are separately treated. The gOST algorithm is evaluated through a molecular dynamics simulation study on the explicitly solvated deca-alanine (Ala10) peptide. On the basis of a fully automated sampling protocol, the gOST simulation enabled repetitive folding and unfolding of the solvated peptide within a single continuous trajectory and allowed for detailed constructions of Ala10 folding/unfolding free energy surfaces. The gOST result reveals that solvent cooperative fluctuations play a pivotal role in Ala10 folding/unfolding transitions. In addition, our assessment
On exact solutions for some oscillating motions of a generalized Oldroyd-B fluid
Khan, M.; Anjum, Asia; Qi, Haitao; Fetecau, C.
2010-02-01
This paper deals with exact solutions for some oscillating motions of a generalized Oldroyd-B fluid. The fractional calculus approach is used in the constitutive relationship of fluid model. Analytical expressions for the velocity field and the corresponding shear stress for flows due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient are determined using Fourier sine and Laplace transforms. The obtained solutions are presented under integral and series forms in terms of the Mittag-Leffler functions. For α = β = 1, our solutions tend to the similar solutions for ordinary Oldroyd-B fluid. A comparison between generalized and ordinary Oldroyd-B fluids is shown by means of graphical illustrations.
On the stability of soliton solution in NLS-type general field model
Chakrabarti, S.; Nayyar, A.H.
1982-08-01
A model incorporating the nonlinear Schroedinger equation and its generalizations is considered and the stability of its periodic-in-time solutions under the restriction of a fixed charge Q is analysed. It is shown that the necessary condition for the stability is given by the inequality deltaQ/deltaν<0, where ν is the parameter of periodicity of the solution in time. In particular, one specific class of Lagrangians is considered and, in addition, the sufficient conditions for the stability of the soliton solutions are also determined. This study thus examines both the necessary and the sufficient conditions for the stability of the solutions of nonlinear Schroedinger equation and some of its generalizations. (author)
Interacting via the Heap in the Presence of Recursion
Jurriaan Rot
2012-12-01
Full Text Available Almost all modern imperative programming languages include operations for dynamically manipulating the heap, for example by allocating and deallocating objects, and by updating reference fields. In the presence of recursive procedures and local variables the interactions of a program with the heap can become rather complex, as an unbounded number of objects can be allocated either on the call stack using local variables, or, anonymously, on the heap using reference fields. As such a static analysis is, in general, undecidable. In this paper we study the verification of recursive programs with unbounded allocation of objects, in a simple imperative language for heap manipulation. We present an improved semantics for this language, using an abstraction that is precise. For any program with a bounded visible heap, meaning that the number of objects reachable from variables at any point of execution is bounded, this abstraction is a finitary representation of its behaviour, even though an unbounded number of objects can appear in the state. As a consequence, for such programs model checking is decidable. Finally we introduce a specification language for temporal properties of the heap, and discuss model checking these properties against heap-manipulating programs.
Qiying Wei
2009-01-01
Full Text Available By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an -point singular -Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential (=ℝ and difference equations (=ℤ, as well as in general time scales setting. As an application, an example is given to illustrate the results.
Centennial of General Relativity (1915-2015); The Schwarzschild Solution and Black Holes
Blinder, S. M.
2015-01-01
This year marks the 100th anniversary of Einstein's General Theory of Relativity (1915-2015). The first nontrivial solution of the Einstein field equations was derived by Karl Schwarzschild in 1916. This Note will focus mainly on the Schwarzschild solution and the remarkable developments which it inspired, the most dramatic being the prediction of black holes. Later extensions of Schwarzschild's spacetime structure has led to even wilder conjectures, such as white holes and passages to other ...
Fundamental solutions for Schrödinger operators with general inverse square potentials
Chen, Huyuan
2017-03-17
In this paper, we clarify the fundamental solutions for Schrödinger operators given as (Formula presented.), where the potential V is a general inverse square potential in (Formula presented.) with (Formula presented.). In particular, letting (Formula presented.),(Formula presented.) where (Formula presented.), we discuss the existence and nonexistence of positive fundamental solutions for Hardy operator (Formula presented.), which depend on the parameter t.
Fundamental solutions for Schrödinger operators with general inverse square potentials
Chen, Huyuan; Alhomedan, Suad; Hajaiej, Hichem; Markowich, Peter A.
2017-01-01
In this paper, we clarify the fundamental solutions for Schrödinger operators given as (Formula presented.), where the potential V is a general inverse square potential in (Formula presented.) with (Formula presented.). In particular, letting (Formula presented.),(Formula presented.) where (Formula presented.), we discuss the existence and nonexistence of positive fundamental solutions for Hardy operator (Formula presented.), which depend on the parameter t.
Kuo-Shou Chiu
2010-08-01
Full Text Available In this paper we investigate the existence of the periodic solutions of a quasilinear differential equation with piecewise constant argument of generalized type. By using some fixed point theorems and some new analysis technique, sufficient conditions are obtained for the existence and uniqueness of periodic solutions of these systems. A new Gronwall type lemma is proved. Some examples concerning biological models as Lasota-Wazewska, Nicholson's blowflies and logistic models are treated.
Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation
Mi, Yuzhen
2016-01-01
This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-v)v+ϵf(ϵ,v,vx,u,ux), uxx=-(1-u-a1v)u+ϵg(ϵ,v,vx,u,ux). By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.
Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation
Yuzhen Mi
2016-01-01
Full Text Available This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-vv+ϵf(ϵ,v,vx,u,ux, uxx=-(1-u-a1vu+ϵg(ϵ,v,vx,u,ux. By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.
Serva, M.
1986-01-01
In this paper we give probabilistic solutions to the equations describing non-relativistic quantum electrodynamical systems. These solutions involve, besides the usual diffusion processes, also birth and death processes corresponding to the 'photons number' variables. We state some inequalities and in particular we establish bounds to the ground state energy of systems composed by a non relativistic particle interacting with a field. The result is general and it is applied as an example to the polaron problem. (orig.)
On global structure of general solution of the Chew-Sow equations
Gerdt, V.P.
1981-01-01
The Chew-Low equations for static p-wave πN-scattering are considered. The equations are formulated in the form of a system of three nonlinear difference equations of the first order which have the general solution depending on three arbitrary periodic functions. An approach to the global construction of the general solution is suggested which is based on the series expansion in powers of one of the arbitrary functions C(ω) determining the structure of the invariant curve for the Chew-Low equations. It is shown that the initial nonlinear problem is reduced to the linear one in every order in C(ω). By means of solving the linear problem the general solution is found in the first-order approximation in C(ω) [ru
Fischer, E.
1977-01-01
Various families of exact solutions to the Einstein and Einstein--Maxwell field equations of general relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations. The physical situations in which such equations arise include: the external gravitational field of an axisymmetric, uncharged steadily rotating body, cylindrical gravitational waves with two degrees of freedom, colliding plane gravitational waves, the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein--Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa. The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables
Batcho, P.F.; Karniadakis, G.E.
1994-01-01
The present study focuses on the solution of the incompressible Navier-Stokes equations in general, non-separable domains, and employs a Galerkin projection of divergence-free vector functions as a trail basis. This basis is obtained from the solution of a generalized constrained Stokes eigen-problem in the domain of interest. Faster convergence can be achieved by constructing a singular Stokes eigen-problem in which the Stokes operator is modified to include a variable coefficient which vanishes at the domain boundaries. The convergence properties of such functions are advantageous in a least squares sense and are shown to produce significantly better approximations to the solution of the Navier-Stokes equations in post-critical states where unsteadiness characterizes the flowfield. Solutions for the eigen-systems are efficiently accomplished using a combined Lanczos-Uzawa algorithm and spectral element discretizations. Results are presented for different simulations using these global spectral trial basis on non-separable and multiply-connected domains. It is confirmed that faster convergence is obtained using the singular eigen-expansions in approximating stationary Navier-Stokes solutions in general domains. It is also shown that 100-mode expansions of time-dependent solutions based on the singular Stokes eigenfunctions are sufficient to accurately predict the dynamics of flows in such domains, including Hopf bifurcations, intermittency, and details of flow structures
General solution of the Dirac equation for quasi-two-dimensional electrons
Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2016-06-15
The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.
Semiclassical series solution of the generalized phase shift atom--diatom scattering equations
Squire, K.R.; Curtiss, C.F.
1980-01-01
A semiclassical series solution of the previously developed operator form of the generalized phase shift equations describing atom--diatom scattering is presented. This development is based on earlier work which led to a double series in powers of Planck's constant and a scaling parameter of the anisotropic portion of the intermolecular potential. The present solution is similar in that it is a double power series in Planck's constant and in the difference between the spherical radial momentum and a first order approximation. The present series solution avoids difficulties of the previous series associated with the classical turning point
Generalized dynamics of soft-matter quasicrystals mathematical models and solutions
Fan, Tian-You
2017-01-01
The book systematically introduces the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (SMQ). It provides methods for solving the initial-boundary value problems in these systems. The solutions obtained demonstrate the distribution, deformation and motion of the soft-matter quasicrystals, and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. Mathematical solutions for solid and soft-matter quasicrystals are compared, to help readers to better understand the featured properties of SMQ.
Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems
Misha V. Feigin
2009-09-01
Full Text Available We consider trigonometric solutions of WDVV equations and derive geometric conditions when a collection of vectors with multiplicities determines such a solution. We incorporate these conditions into the notion of trigonometric Veselov system (v-system and we determine all trigonometric v-systems with up to five vectors. We show that generalized Calogero-Moser-Sutherland operator admits a factorized eigenfunction if and only if it corresponds to the trigonometric v-system; this inverts a one-way implication observed by Veselov for the rational solutions.
A Recursive Formula for the Evaluation of Earth Return Impedance on Buried Cables
Reynaldo Iracheta
2015-09-01
Full Text Available This paper presents an alternative solution based on infinite series for the accurate and efficient evaluation of cable earth return impedances. This method uses Wedepohl and Wilcox’s transformation to decompose Pollaczek’s integral in a set of Bessel functions and a definite integral. The main feature of Bessel functions is that they are easy to compute in modern mathematical software tools such as Matlab. The main contributions of this paper are the approximation of the definite integral by an infinite series, since it does not have analytical solution; and its numerical solution by means of a recursive formula. The accuracy and efficiency of this recursive formula is compared against the numerical integration method for a broad range of frequencies and cable configurations. Finally, the proposed method is used as a subroutine for cable parameter calculation in the inverse Numerical Laplace Transform (NLT to obtain accurate transient responses in the time domain.
LAGRANGE SOLUTIONS TO THE DISCRETE-TIME GENERAL THREE-BODY PROBLEM
Minesaki, Yukitaka
2013-01-01
There is no known integrator that yields exact orbits for the general three-body problem (G3BP). It is difficult to verify whether a numerical procedure yields the correct solutions to the G3BP because doing so requires knowledge of all 11 conserved quantities, whereas only six are known. Without tracking all of the conserved quantities, it is possible to show that the discrete general three-body problem (d-G3BP) yields the correct orbits corresponding to Lagrange solutions of the G3BP. We show that the d-G3BP yields the correct solutions to the G3BP for two special cases: the equilateral triangle and collinear configurations. For the triangular solution, we use the fact that the solution to the three-body case is a superposition of the solutions to the three two-body cases, and we show that the three bodies maintain the same relative distances at all times. To obtain the collinear solution, we assume a specific permutation of the three bodies arranged along a straight rotating line, and we show that the d-G3BP maintains the same distance ratio between two bodies as in the G3BP. Proving that the d-G3BP solutions for these cases are equivalent to those of the G3BP makes it likely that the d-G3BP and G3BP solutions are equivalent in other cases. To our knowledge, this is the first work that proves the equivalence of the discrete solutions and the Lagrange orbits.
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
A Note about the General Meromorphic Solutions of the Fisher Equation
Jian-ming Qi
2014-01-01
Full Text Available We employ the complex method to obtain the general meromorphic solutions of the Fisher equation, which improves the corresponding results obtained by Ablowitz and Zeppetella and other authors (Ablowitz and Zeppetella, 1979; Feng and Li, 2006; Guo and Chen, 1991, and wg,i(z are new general meromorphic solutions of the Fisher equation for c=±5i/6. Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics.
The General Traveling Wave Solutions of the Fisher Equation with Degree Three
Wenjun Yuan
2013-01-01
degree three and the general meromorphic solutions of the integrable Fisher equations with degree three, which improves the corresponding results obtained by Feng and Li (2006, Guo and Chen (1991, and Ağırseven and Öziş (2010. Moreover, all wg,1(z are new general meromorphic solutions of the Fisher equations with degree three for c=±3/2. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.
A nested recursive logit model for route choice analysis
Mai, Tien; Frejinger, Emma; Fosgerau, Mogens
2015-01-01
choices and the model does not require any sampling of choice sets. Furthermore, the model can be consistently estimated and efficiently used for prediction.A key challenge lies in the computation of the value functions, i.e. the expected maximum utility from any position in the network to a destination....... The value functions are the solution to a system of non-linear equations. We propose an iterative method with dynamic accuracy that allows to efficiently solve these systems.We report estimation results and a cross-validation study for a real network. The results show that the NRL model yields sensible......We propose a route choice model that relaxes the independence from irrelevant alternatives property of the logit model by allowing scale parameters to be link specific. Similar to the recursive logit (RL) model proposed by Fosgerau et al. (2013), the choice of path is modeled as a sequence of link...
Xingwei Wang
2014-01-01
Full Text Available Due to the uneven distribution of pollutions and blur edge of pollutant area, there will exist uncertainty of source term shape in advective-diffusion equation model of contaminant transport. How to generalize those irregular source terms and deal with those uncertainties is very critical but rarely studied in previous research. In this study, the fate and transport of contaminant from rectangular and elliptic source geometry were simulated based on a three-dimensional analytical solute transport model, and the source geometry generalization guideline was developed by comparing the migration of contaminant. The result indicated that the variation of source area size had no effect on pollution plume migration when the plume migrated as far as five times of source side length. The migration of pollution plume became slower with the increase of aquifer thickness. The contaminant concentration was decreasing with scale factor rising, and the differences among various scale factors became smaller with the distance to field increasing.
Solutions to the maximal spacelike hypersurface equation in generalized Robertson-Walker spacetimes
Henrique F. de Lima
2018-03-01
Full Text Available We apply some generalized maximum principles for establishing uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker (GRW spacetime, which is supposed to obey the so-called timelike convergence condition (TCC. As application, we study the uniqueness and nonexistence of entire solutions of a suitable maximal spacelike hypersurface equation in GRW spacetimes obeying the TCC.
Exact solutions of the Navier-Stokes equations generalized for flow in porous media
Daly, Edoardo; Basser, Hossein; Rudman, Murray
2018-05-01
Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.
New and More General Rational Formal Solutions to (2+1)-Dimensional Toda System
Bai Chenglin
2007-01-01
With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to (2+1)-dimensional Toda system are obtained. The method used here can also be applied to solve other nonlinear differential-difference equation or equations.
Maxim Olegovich Korpusov
2012-07-01
Full Text Available In this article the initial-boundary-value problem for generalized dissipative high-order equation of Klein-Gordon type is considered. We continue our study of nonlinear hyperbolic equations and systems with arbitrary positive energy. The modified concavity method by Levine is used for proving blow-up of solutions.
Generalized Couette flow of a third-grade fluid with slip. The exact solutions
Ellahi, Rahmat [IIUI, Islamabad (Pakistan). Dept. of Mathematics; Hayat, Tasawar [Quaid-i-Azam Univ., Islamabad (Pakistan). Dept. of Mathematics; King Saud Univ., Riyadh (Saudi Arabia). Dept. of Mathematics; Mahomed, Fazal Mahmood [Univ. of the Witwatersrand, Wits (South Africa). Centre for Differential Equations, Continuum, Mechanics and Applications
2010-12-15
The present note investigates the influence of slip on the generalized Couette flows of a third-grade fluid. Two flow problems are considered. The resulting equations and the boundary conditions are nonlinear. Analytical solutions of the governing nonlinear problems are found in closed form. (orig.)
General thermo-elastic solution of radially heterogeneous, spherically isotropic rotating sphere
Bayat, Yahya; EkhteraeiToussi, THamid [Ferdowsi University of Mashhad, Mashhad (Iran, Islamic Republic of)
2015-06-15
A thick walled rotating spherical object made of transversely isotropic functionally graded materials (FGMs) with general types of thermo-mechanical boundary conditions is studied. The thermo-mechanical governing equations consisting of decoupled thermal and mechanical equations are represented. The centrifugal body forces of the rotation are considered in the modeling phase. The unsymmetrical thermo-mechanical boundary conditions and rotational body forces are expressed in terms of the Legendre series. The series method is also implemented in the solution of the resulting equations. The solutions are checked with the known literature and FEM based solutions of ABAQUS software. The effects of anisotropy and heterogeneity are studied through the case studies and the results are represented in different figures. The newly developed series form solution is applicable to the rotating FGM spherical transversely isotropic vessels having nonsymmetrical thermo-mechanical boundary condition.
Recursive definition of global cellular-automata mappings
Feldberg, Rasmus; Knudsen, Carsten; Rasmussen, Steen
1994-01-01
A method for a recursive definition of global cellular-automata mappings is presented. The method is based on a graphical representation of global cellular-automata mappings. For a given cellular-automaton rule the recursive algorithm defines the change of the global cellular-automaton mapping...... as the number of lattice sites is incremented. A proof of lattice size invariance of global cellular-automata mappings is derived from an approximation to the exact recursive definition. The recursive definitions are applied to calculate the fractal dimension of the set of reachable states and of the set...
Recursive definition of global cellular-automata mappings
Feldberg, R.; Knudsen, C.; Rasmussen, S.
1994-01-01
A method for a recursive definition of global cellular-automata mappings is presented. The method is based on a graphical representation of global cellular-automata mappings. For a given cellular-automaton rule the recursive algorithm defines the change of the global cellular-automaton mapping as the number of lattice sites is incremented. A proof of lattice size invariance of global cellular-automata mappings is derived from an approximation to the exact recursive definition. The recursive definitions are applied to calculate the fractal dimension of the set of reachable states and of the set of fixed points of cellular automata on an infinite lattice
Chen Huaitang; Zhang Hongqing
2004-01-01
A generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions. More new multiple soliton solutions are obtained for the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation
Recursive deconvolution of combinatorial chemical libraries.
Erb, E; Janda, K D; Brenner, S
1994-01-01
A recursive strategy that solves for the active members of a chemical library is presented. A pentapeptide library with an alphabet of Gly, Leu, Phe, and Tyr (1024 members) was constructed on a solid support by the method of split synthesis. One member of this library (NH2-Tyr-Gly-Gly-Phe-Leu) is a native binder to a beta-endorphin antibody. A variation of the split synthesis approach is used to build the combinatorial library. In four vials, a member of the library's alphabet is coupled to a...
The Lehmer Matrix and Its Recursive Analogue
2010-01-01
LU factorization of matrix A by considering det A = det U = ∏n i=1 2i−1 i2 . The nth Catalan number is given in terms of binomial coefficients by Cn...for failing to comply with a collection of information if it does not display a currently valid OMB control number . 1. REPORT DATE 2010 2. REPORT...TYPE 3. DATES COVERED 00-00-2010 to 00-00-2010 4. TITLE AND SUBTITLE The Lehmer matrix and its recursive analogue 5a. CONTRACT NUMBER 5b
A general solution to the material performance index for bending strength design
Burgess, S.C.; Pasini, D.; Smith, D.J.; Alemzadeh, K.
2006-01-01
This paper presents a general solution to the material performance index for the bending strength design of beams. In general, the performance index for strength design is ρ f q /ρ where σ f is the material strength, ρ is the material density and q is a function of the direction of scaling. Previous studies have only solved q for three particular cases: proportional scaling of width and height (q=2/3), constrained height (q=1) and constrained width (q=1/2). This paper presents a general solution to the exponent q for any arbitrary direction of scaling. The index is used to produce performance maps that rank relative material performance for particular design cases. The performance index and the performance maps are applied to a design case study
Montani, Giovanni; Ruffini, Remo; Zalaletdinov, Roustam
2003-01-01
A model for the static weak-field macroscopic medium is analysed and the equation for the macroscopic gravitational potential is derived. This is a biharmonic equation which is a non-trivial generalization of the Poisson equation of Newtonian gravity. In the case of strong gravitational quadrupole polarization, it essentially holds inside a macroscopic matter source. Outside the source the gravitational potential fades away exponentially. The equation is equivalent to a system of the Poisson equation and the non-homogeneous modified Helmholtz equations. The general solution to this system is obtained by using the Green function method and it is not limited to Newtonian gravity. In the case of insignificant gravitational quadrupole polarization, the equation for macroscopic gravitational potential becomes the Poisson equation with the matter density renormalized by a factor including the value of the quadrupole gravitational polarization of the source. The general solution to this equation obtained by using the Green function method is limited to Newtonian gravity
Syntactic Recursion Facilitates and Working Memory Predicts Recursive Theory of Mind
Arslan, Burcu; Hohenberger, Annette; Verbrugge, Rineke
2017-01-01
In this study, we focus on the possible roles of second-order syntactic recursion and working memory in terms of simple and complex span tasks in the development of second-order false belief reasoning. We tested 89 Turkish children in two age groups, one younger (4;6-6;5 years) and one older
Source localization using recursively applied and projected (RAP) MUSIC
Mosher, J.C. [Los Alamos National Lab., NM (United States); Leahy, R.M. [Univ. of Southern California, Los Angeles, CA (United States). Signal and Image Processing Inst.
1998-03-01
A new method for source localization is described that is based on a modification of the well known multiple signal classification (MUSIC) algorithm. In classical MUSIC, the array manifold vector is projected onto an estimate of the signal subspace, but errors in the estimate can make location of multiple sources difficult. Recursively applied and projected (RAP) MUSIC uses each successively located source to form an intermediate array gain matrix, and projects both the array manifold and the signal subspace estimate into its orthogonal complement. The MUSIC projection is then performed in this reduced subspace. Using the metric of principal angles, the authors describe a general form of the RAP-MUSIC algorithm for the case of diversely polarized sources. Through a uniform linear array simulation, the authors demonstrate the improved Monte Carlo performance of RAP-MUSIC relative to MUSIC and two other sequential subspace methods, S and IES-MUSIC.
Chen, Po-Chia; Chuang, Mo-Hsiung; Tan, Yih-Chi
2014-05-01
In recent years the urban and industrial developments near the coastal area are rapid and therefore the associated population grows dramatically. More and more water demand for human activities, agriculture irrigation, and aquaculture relies on heavy pumping in coastal area. The decline of groundwater table may result in the problems of seawater intrusion and/or land subsidence. Since the 1950s, numerous studies focused on the effect of tidal fluctuation on the groundwater flow in the coastal area. Many studies concentrated on the developments of one-dimensional (1D) and two-dimensional (2D) analytical solutions describing the tide-induced head fluctuations. For example, Jacob (1950) derived an analytical solution of 1D groundwater flow in a confined aquifer with a boundary condition subject to sinusoidal oscillation. Jiao and Tang (1999) derived a 1D analytical solution of a leaky confined aquifer by considered a constant groundwater head in the overlying unconfined aquifer. Jeng et al. (2002) studied the tidal propagation in a coupled unconfined and confined costal aquifer system. Sun (1997) presented a 2D solution for groundwater response to tidal loading in an estuary. Tang and Jiao (2001) derived a 2D analytical solution in a leaky confined aquifer system near open tidal water. This study aims at developing a general analytical solution describing the head fluctuations in a 2D estuarine aquifer system consisted of an unconfined aquifer, a confined aquifer, and an aquitard between them. Both the confined and unconfined aquifers are considered to be anisotropic. The predicted head fluctuations from this solution will compare with the simulation results from the MODFLOW program. In addition, the solutions mentioned above will be shown to be special cases of the present solution. Some hypothetical cases regarding the head fluctuation in costal aquifers will be made to investigate the dynamic effects of water table fluctuation, hydrogeological conditions, and
Generalized Langevin Theory Of The Brownian Motion And The Dynamics Of Polymers In Solution
Tothova, J.; Lisy, V.
2015-01-01
The review deals with a generalization of the Rouse and Zimm bead-spring models of the dynamics of flexible polymers in dilute solutions. As distinct from these popular theories, the memory in the polymer motion is taken into account. The memory naturally arises as a consequence of the fluid and bead inertia within the linearized Navier-Stokes hydrodynamics. We begin with a generalization of the classical theory of the Brownian motion, which forms the basis of any theory of the polymer dynamics. The random force driving the Brownian particles is not the white one as in the Langevin theory, but “colored”, i.e., statistically correlated in time, and the friction force on the particles depends on the history of their motion. An efficient method of solving the resulting generalized Langevin equations is presented and applied to the solution of the equations of motion of polymer beads. The memory effects lead to several peculiarities in the time correlation functions used to describe the dynamics of polymer chains. So, the mean square displacement of the polymer coils contains algebraic long-time tails and at short times it is ballistic. It is shown how these features reveal in the experimentally observable quantities, such as the dynamic structure factors of the scattering or the viscosity of polymer solutions. A phenomenological theory is also presented that describes the dependence of these quantities on the polymer concentration in solution. (author)
Chirped self-similar solutions of a generalized nonlinear Schroedinger equation
Fei Jin-Xi [Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Zheng Chun-Long [Shaoguan Univ., Guangdong (China). School of Physics and Electromechanical Engineering; Shanghai Univ. (China). Shanghai Inst. of Applied Mathematics and Mechanics
2011-01-15
An improved homogeneous balance principle and an F-expansion technique are used to construct exact chirped self-similar solutions to the generalized nonlinear Schroedinger equation with distributed dispersion, nonlinearity, and gain coefficients. Such solutions exist under certain conditions and impose constraints on the functions describing dispersion, nonlinearity, and distributed gain function. The results show that the chirp function is related only to the dispersion coefficient, however, it affects all of the system parameters, which influence the form of the wave amplitude. As few characteristic examples and some simple chirped self-similar waves are presented. (orig.)
General-purpose chemical analyzer for on-line analyses of radioactive solutions
Spencer, W.A.; Kronberg, J.W.
1983-01-01
An automated analyzer is being developed to perform analytical measurements on radioactive solutions on-line in a hostile environment. This General Purpose Chemical Analyzer (GPCA) samples a process stream, adds reagents, measures solution absorbances or electrode potentials, and automatically calculates the results. The use of modular components, under microprocessor control, permits a single analyzer design to carry out many types of analyses. This paper discusses the more important design criteria for the GPCA, and describes the equipment being tested in a prototype unit
Elliptic solutions of generalized Brans-Dicke gravity with a non-universal coupling
Alimi, J.M.; Reverdy, V. [Observatoire de Paris, Laboratoire Univers et Theories (LUTh), Meudon (France); Golubtsova, A.A. [Observatoire de Paris, Laboratoire Univers et Theories (LUTh), Meudon (France); Peoples' Friendship University of Russia, Institute of Gravitation and Cosmology, Moscow (Russian Federation)
2014-10-15
We study a model of the generalized Brans-Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics equations on the target space of the nonlinear sigma model. The analytical solutions in elliptical functions are obtained when the conformal couplings are given by reciprocal exponential functions. The behavior of the scale factor in the Jordan frame is studied using numerical computations. For certain parameters the solutions can describe an accelerated expansion. We also derive an analytical approximation in exponential functions. (orig.)
Travelling wave solutions in a class of generalized Korteweg-de Vries equation
Shen Jianwei; Xu Wei
2007-01-01
In this paper, we consider a new generalization of KdV equation u t = u x u l-2 + α[2u xxx u p + 4pu p-1 u x u xx + p(p - 1)u p-2 (u x ) 3 ] and investigate its bifurcation of travelling wave solutions. From the above analysis, we know that there exists compacton and cusp waves in the system. We explain the reason that these non-smooth travelling wave solution arise by using the bifurcation theory
First general solutions for unidirectional motions of rate type fluids over an infinite plate
Constantin Fetecau
2015-09-01
Full Text Available Based on a simple but important remark regarding the governing equation for the non-trivial shear stress corresponding to the motion of a fluid over an infinite plate, exact solutions are established for the motion of Oldroyd-B fluids due to the plate that applies an arbitrary time-dependent shear stress to the fluid. These solutions, that allow us to provide the first exact solutions for motions of rate type fluids produced by an infinite plate that applies constant, constantly accelerating or oscillating shears stresses to the fluid, can easily be reduced to the similar solutions for Maxwell, second grade or Newtonian fluids performing the same motion. Furthermore, the obtained solutions are used to develop general solutions for the motion induced by a moving plate and to correct or recover as special cases different known results from the existing literature. Consequently, the motion problem of such fluids over an infinite plate that is moving in its plane or applies a shear stress to the fluid is completely solved.
Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation
Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei
2018-03-01
The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.
Zhang Weiguo; Dong Chunyan; Fan Engui
2006-01-01
In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.
Recursive Monte Carlo method for deep-penetration problems
Goldstein, M.; Greenspan, E.
1980-01-01
The Recursive Monte Carlo (RMC) method developed for estimating importance function distributions in deep-penetration problems is described. Unique features of the method, including the ability to infer the importance function distribution pertaining to many detectors from, essentially, a single M.C. run and the ability to use the history tape created for a representative region to calculate the importance function in identical regions, are illustrated. The RMC method is applied to the solution of two realistic deep-penetration problems - a concrete shield problem and a Tokamak major penetration problem. It is found that the RMC method can provide the importance function distributions, required for importance sampling, with accuracy that is suitable for an efficient solution of the deep-penetration problems considered. The use of the RMC method improved, by one to three orders of magnitude, the solution efficiency of the two deep-penetration problems considered: a concrete shield problem and a Tokamak major penetration problem. 8 figures, 4 tables
Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model
Nikola V. Georgiev
2003-01-01
Full Text Available An analytic time series in the form of numerical solution (in an appropriate finite time interval of the Hodgkin-Huxley current clamped (HHCC system of four differential equations, well known in the neurophysiology as an exact empirical model of excitation of a giant axon of Loligo, is presented. Then we search for a second-order differential equation of generalized Fitzhugh-Nagumo (GFN type, having as a solution the given single component (action potential of the numerical solution. The given time series is used as a basis for reconstructing orders, powers, and coefficients of the polynomial right-hand sides of GFN equation approximately governing the process of action potential. For this purpose, a new geometrical method for determining phase space dimension of the unknown dynamical system (GFN equation and a specific modification of least squares method for identifying unknown coefficients are developed and applied.
General exact solution for homogeneous time-dependent self-gravitating perfect fluids
Gaete, P.; Hojman, R.
1988-01-01
A procedure to obtain the general exact solution of Einstein equations for a self-gravitating spherically-symmetric static perfect fluid obeying an arbitrary equation of state, is applied to time-dependent Kantowsky-Sachs line elements (with spherical, planar and hyperbolic symmetry). As in the static case, the solution is generated by an arbitrary function of the independent variable and its first derivative. To illustrate the results, the whole family of (plane-symmetric) solutions with a ''gamma-law'' equation of state is explicity obtained in terms of simple known functions. It is also shown that, while in the static plane-symmtric line elements, every metric is in one to one correspondence with a ''partner-metric'' (both originated from the same generatrix function), in this case every generatrix function univocally determines one metric. (author) [pt
O, Hyong-Chol; Jo, Jong-Jun; Kim, Ji-Sok
2016-02-01
We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and study such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security pricing. In particular, we focus on finding representation of the gradient (with respect to the stock price variable) of solutions to the terminal value problems with discontinuous terminal payoffs or inhomogeneous terms. Such terminal value problems are often encountered in pricing problems of compound-like options such as Bermudan options or defaultable bonds with discrete default barrier, default intensity and endogenous default recovery. Our results can be used in pricing real defaultable bonds under consideration of existence of discrete coupons or taxes on coupons.
Black holes in the Universe: Generalized Lemaitre-Tolman-Bondi solutions
Gao Changjun; Chen Xuelei; Shen Yougen; Faraoni, Valerio
2011-01-01
We present new exact solutions which presumably describe black holes in the background of a spatially flat, pressureless dark-matter- or dark matter plus dark energy (DM+DE)- or quintom-dominated Universe. These solutions generalize Lemaitre-Tolman-Bondi metrics. For a dark-matter- or (DM+DE)-dominated universe, the area of the black hole apparent horizon (AH) decreases with the expansion of the Universe while that of the cosmic AH increases. However, for a quintom-dominated universe, the black hole AH first shrinks and then expands, while the cosmic AH first expands and then shrinks. A (DM+DE)-dominated universe containing a black hole will evolve to the Schwarzschild-de Sitter solution with both AHs approaching constant size. In a quintom-dominated universe, the black hole and cosmic AHs will coincide at a certain time, after which the singularity becomes naked, violating cosmic censorship.
Asymptotics for Large Time of Global Solutions to the Generalized Kadomtsev-Petviashvili Equation
Hayashi, Nakao; Naumkin, Pavel I.; Saut, Jean-Claude
We study the large time asymptotic behavior of solutions to the generalized Kadomtsev-Petviashvili (KP) equations where σ= 1 or σ=- 1. When ρ= 2 and σ=- 1, (KP) is known as the KPI equation, while ρ= 2, σ=+ 1 corresponds to the KPII equation. The KP equation models the propagation along the x-axis of nonlinear dispersive long waves on the surface of a fluid, when the variation along the y-axis proceeds slowly [10]. The case ρ= 3, σ=- 1 has been found in the modeling of sound waves in antiferromagnetics [15]. We prove that if ρ>= 3 is an integer and the initial data are sufficiently small, then the solution u of (KP) satisfies the following estimates: for all t∈R, where κ= 1 if ρ= 3 and κ= 0 if ρ>= 4. We also find the large time asymptotics for the solution.
Regular Bulk Solutions in Brane-Worlds with Inhomogeneous Dust and Generalized Dark Radiation
Rocha, Roldão da; Kuerten, A. M.; Herrera-Aguilar, A.
2015-01-01
From the dynamics of a brane-world with matter fields present in the bulk, the bulk metric and the black string solution near the brane are generalized, when both the dynamics of inhomogeneous dust/generalized dark radiation on the brane-world and inhomogeneous dark radiation in the bulk as well are considered as exact dynamical collapse solutions. Based on the analysis on the inhomogeneous static exterior of a collapsing sphere of homogeneous dark radiation on the brane, the associated black string warped horizon is studied, as well as the 5D bulk metric near the brane. Moreover, the black string and the bulk are shown to be more regular upon time evolution, for suitable values for the dark radiation parameter in the model, by analyzing the soft physical singularities
Sukjung Hwang
2015-11-01
Full Text Available Here we generalize quasilinear parabolic p-Laplacian type equations to obtain the prototype equation $$ u_t - \\hbox{div} \\Big(\\frac{g(|Du|}{|Du|} Du\\Big = 0, $$ where g is a nonnegative, increasing, and continuous function trapped in between two power functions $|Du|^{g_0 -1}$ and $|Du|^{g_1 -1}$ with $1
General solution of superconvergent sum rules for scattering of I=1 reggeons on baryons
Grigoryan, A.A.; Khachatryan, G.N.
1986-01-01
Superconvergent sum rules for reggeon-particle scattering are applied to scattering of reggeons α i (i=π, ρ, A 2 ) with isospin I=1 on baryons with strangeness S=-1. The saturation scheme of these sum rules is determined on the basis of experimental data. Two series of baryon resonances with arbitrary isospins I and spins J=I+1/2 and J=I-1/2 are predicted. A general solution for vertices of interaction of these resonances with α i is found. Predictions for coupling vertices B α i B'(B, B'=Λ, Σ, Σ * ) agree well with the experiment. It is shown that the condition of sum rules saturation by minimal number of resonances brings to saturation schemes resulting from experimental data. A general solution of sum rules for scattering of α i reggeons on Ξ and Ω hyperons is analyzed
Active control versus recursive backstepping control of a chaotic ...
... than for the recursive backstepping controllers. However, the flexibility in the choice of the control laws for recursive backstepping design gives room for further improvement in its performance and enables it to achieve the goals of stabilization and tracking. Journal of the Nigerian Association of Mathematical Physics Vol.
Language, Mind, Practice: Families of Recursive Thinking in Human Reasoning
Josephson, Marika
2011-01-01
In 2002, Chomsky, Hauser, and Fitch asserted that recursion may be the one aspect of the human language faculty that makes human language unique in the narrow sense--unique to language and unique to human beings. They also argue somewhat more quietly (as do Pinker and Jackendoff 2005) that recursion may be possible outside of language: navigation,…
Recursive smoothers for hidden discrete-time Markov chains
Lakhdar Aggoun
2005-01-01
Full Text Available We consider a discrete-time Markov chain observed through another Markov chain. The proposed model extends models discussed by Elliott et al. (1995. We propose improved recursive formulae to update smoothed estimates of processes related to the model. These recursive estimates are used to update the parameter of the model via the expectation maximization (EM algorithm.
An approximate JKR solution for a general contact, including rough contacts
Ciavarella, M.
2018-05-01
In the present note, we suggest a simple closed form approximate solution to the adhesive contact problem under the so-called JKR regime. The derivation is based on generalizing the original JKR energetic derivation assuming calculation of the strain energy in adhesiveless contact, and unloading at constant contact area. The underlying assumption is that the contact area distributions are the same as under adhesiveless conditions (for an appropriately increased normal load), so that in general the stress intensity factors will not be exactly equal at all contact edges. The solution is simply that the indentation is δ =δ1 -√{ 2 wA‧ /P″ } where w is surface energy, δ1 is the adhesiveless indentation, A‧ is the first derivative of contact area and P‧‧ the second derivative of the load with respect to δ1. The solution only requires macroscopic quantities, and not very elaborate local distributions, and is exact in many configurations like axisymmetric contacts, but also sinusoidal waves contact and correctly predicts some features of an ideal asperity model used as a test case and not as a real description of a rough contact problem. The solution permits therefore an estimate of the full solution for elastic rough solids with Gaussian multiple scales of roughness, which so far was lacking, using known adhesiveless simple results. The result turns out to depend only on rms amplitude and slopes of the surface, and as in the fractal limit, slopes would grow without limit, tends to the adhesiveless result - although in this limit the JKR model is inappropriate. The solution would also go to adhesiveless result for large rms amplitude of roughness hrms, irrespective of the small scale details, and in agreement with common sense, well known experiments and previous models by the author.
A general solution of the BV-master equation and BRST field theories
Dayi, O.F.
1993-05-01
For a class of first order gauge theories it was shown that the proper solution of the BV-master equation can be obtained straightforwardly. Here we present the general condition which the gauge generators should satisfy to conclude that this construction is relevant. The general procedure is illustrated by its application to the Chern-Simons theory in any odd-dimension. Moreover, it is shown that this formalism is also applicable to BRST field theories, when one replaces the role of the exterior derivative with the BRST charge of first quantization. (author). 17 refs
Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method
Ying Wang
2014-06-01
Full Text Available We give a more generalized treatment of the 1D generalized Gross-Pitaevskii equation (GGPE with variable term coefficients. External harmonic trapping potential is fully considered and the nonlinear interaction term is of arbitrary polytropic index of superfluid wave function. We also eliminate the interdependence between variable coefficients of the equation terms avoiding the restrictions that occur in some other works. The exact soliton solutions of the GGPE are obtained through the delicate combined utilization of modified lens-type transformation and F-expansion method with dominant features like soliton type properties highlighted.
Wang, Yu-Zhu; Wei, Changhua
2018-04-01
In this paper, we investigate the initial value problem for the generalized double dispersion equation in R^n. Weighted decay estimate and asymptotic profile of global solutions are established for n≥3 . The global existence result was already proved by Kawashima and the first author in Kawashima and Wang (Anal Appl 13:233-254, 2015). Here, we show that the nonlinear term plays an important role in this asymptotic profile.
Conservation Laws and Traveling Wave Solutions of a Generalized Nonlinear ZK-BBM Equation
Khadijo Rashid Adem
2014-01-01
Full Text Available We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the (G'/G-expansion method.
Exact periodic solutions of the sixth-order generalized Boussinesq equation
Kamenov, O Y
2009-01-01
This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u tt = u xx + 3(u 2 ) xx + u xxxx + αu xxxxxx , α in R, depending on the positive parameter α. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.
On exact solutions for oscillatory flows in a generalized Burgers fluid with slip condition
Hayat, Tasawar [Dept. of Mathematics, Quaid-i-Azam Univ., Islamabad (Pakistan); Dept. of Mathematics, Coll. of Sciences, KS Univ., Riyadh (Saudi Arabia); Najam, Saher [Theoretical Plasma Physics Div., PINSTECH, P.O. Nilore, Islamabad (Pakistan); Sajid, Muhammad; Mesloub, Said [Dept. of Mathematics, Coll. of Sciences, KS Univ., Riyadh (Saudi Arabia); Ayub, Muhammad [Dept. of Mathematics, Quaid-i-Azam Univ., Islamabad (Pakistan)
2010-05-15
An analysis is performed for the slip effects on the exact solutions of flows in a generalized Burgers fluid. The flow modelling is based upon the magnetohydrodynamic (MHD) nature of the fluid and modified Darcy law in a porous space. Two illustrative examples of oscillatory flows are considered. The results obtained are compared with several limiting cases. It has been shown here that the derived results hold for all values of frequencies including the resonant frequency. (orig.)
A General Construction of Linear Differential Equations with Solutions of Prescribed Properties
Neuman, František
2004-01-01
Roč. 17, č. 1 (2004), s. 71-76 ISSN 0893-9659 R&D Projects: GA AV ČR IAA1019902; GA ČR GA201/99/0295 Institutional research plan: CEZ:AV0Z1019905 Keywords : construction of linear differential equations * prescribed qualitative properties of solutions Subject RIV: BA - General Mathematics Impact factor: 0.414, year: 2004
Exact solutions of generalized Calogero-Sutherland models: BCN and CN cases
Kojima, M.; Ohta, N.
1996-01-01
Using a collective field method, we obtain explicit solutions of the generalized Calogero-Sutherland models that are characterized by the roots of the classical groups B N and C N . Starting from the explicit wave functions for the A N-1 type expressed in terms of the singular vectors of the W N algebra, we give a systematic method to construct wave functions and derive energy eigenvalues for other types of theories. (orig.)
Cosymmetries and Nijenhuis recursion operators for difference equations
Mikhailov, Alexander V; Xenitidis, Pavlos; Wang, Jing Ping
2011-01-01
In this paper we discuss the concept of cosymmetries and co-recursion operators for difference equations and present a co-recursion operator for the Viallet equation. We also discover a new type of factorization for the recursion operators of difference equations. This factorization enables us to give an elegant proof that the pseudo-difference operator R presented in Mikhailov et al 2011 Theor. Math. Phys. 167 421–43 is a recursion operator for the Viallet equation. Moreover, we show that the operator R is Nijenhuis and thus generates infinitely many commuting local symmetries. The recursion operator R and its factorization into Hamiltonian and symplectic operators have natural applications to Yamilov's discretization of the Krichever–Novikov equation
Schwinghammer, Jan; Birkedal, Lars; Støvring, Kristian
2011-01-01
´eraud and Pottier’s type and capability system including both frame and anti-frame rules. The model is a possible worlds model based on the operational semantics and step-indexed heap relations, and the worlds are constructed as a recursively defined predicate on a recursively defined metric space. We also extend...
Birkedal, Lars; Schwinghammer, Jan; Støvring, Kristian
2010-01-01
for Chargu´eraud and Pottier’s type and capability system including frame and anti-frame rules, based on the operational semantics and step-indexed heap relations. The worlds are constructed as a recursively defined predicate on a recursively defined metric space, which provides a considerably simpler...
Cao Rui; Zhang Jian
2013-01-01
In this paper, the trial function method is extended to study the generalized nonlinear Schrödinger equation with time-dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrödinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrödinger equation with time-dependent coefficients under constraint conditions. (general)
Locating one pairwise interaction: Three recursive constructions
Charles J. Colbourn
2016-09-01
Full Text Available In a complex component-based system, choices (levels for components (factors may interact tocause faults in the system behaviour. When faults may be caused by interactions among few factorsat specific levels, covering arrays provide a combinatorial test suite for discovering the presence offaults. While well studied, covering arrays do not enable one to determine the specific levels of factorscausing the faults; locating arrays ensure that the results from test suite execution suffice to determinethe precise levels and factors causing faults, when the number of such causes is small. Constructionsfor locating arrays are at present limited to heuristic computational methods and quite specific directconstructions. In this paper three recursive constructions are developed for locating arrays to locateone pairwise interaction causing a fault.
Shock-jump conditions in a general medium: weak-solution approach
Forbes, L. K.; Krzysik, O. A.
2017-05-01
General conservation laws are considered, and the concept of a weak solution is extended to the case of an equation involving three space variables and time. Four-dimensional vector calculus is used to develop general jump conditions at a shock wave in the material. To illustrate the use of this result, jump conditions at a shock in unsteady three-dimensional compressible gas flow are presented. It is then proved rigorously that these reduce to the commonly assumed conditions in coordinates normal and tangential to the shock face. A similar calculation is also outlined for an unsteady three-dimensional shock in magnetohydrodynamics, and in a chemically reactive fluid. The technique is available for determining shock-jump conditions in quite general continuous media.
Syntactic Recursion Facilitates and Working Memory Predicts Recursive Theory of Mind.
Burcu Arslan
Full Text Available In this study, we focus on the possible roles of second-order syntactic recursion and working memory in terms of simple and complex span tasks in the development of second-order false belief reasoning. We tested 89 Turkish children in two age groups, one younger (4;6-6;5 years and one older (6;7-8;10 years. Although second-order syntactic recursion is significantly correlated with the second-order false belief task, results of ordinal logistic regressions revealed that the main predictor of second-order false belief reasoning is complex working memory span. Unlike simple working memory and second-order syntactic recursion tasks, the complex working memory task required processing information serially with additional reasoning demands that require complex working memory strategies. Based on our results, we propose that children's second-order theory of mind develops when they have efficient reasoning rules to process embedded beliefs serially, thus overcoming a possible serial processing bottleneck.
Syntactic Recursion Facilitates and Working Memory Predicts Recursive Theory of Mind
Arslan, Burcu; Hohenberger, Annette; Verbrugge, Rineke
2017-01-01
In this study, we focus on the possible roles of second-order syntactic recursion and working memory in terms of simple and complex span tasks in the development of second-order false belief reasoning. We tested 89 Turkish children in two age groups, one younger (4;6–6;5 years) and one older (6;7–8;10 years). Although second-order syntactic recursion is significantly correlated with the second-order false belief task, results of ordinal logistic regressions revealed that the main predictor of second-order false belief reasoning is complex working memory span. Unlike simple working memory and second-order syntactic recursion tasks, the complex working memory task required processing information serially with additional reasoning demands that require complex working memory strategies. Based on our results, we propose that children’s second-order theory of mind develops when they have efficient reasoning rules to process embedded beliefs serially, thus overcoming a possible serial processing bottleneck. PMID:28072823
On generalized Melvin solution for the Lie algebra E{sub 6}
Bolokhov, S.V. [Peoples' Friendship University of Russia (RUDN University), Moscow (Russian Federation); Ivashchuk, V.D. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia (RUDN University), Moscow (Russian Federation)
2017-10-15
A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model in D dimensions, D ≥ 4, contains n 2-forms and l ≥ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions H{sub s}(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials H{sub s}(z), s = 1,.., 6, for the Lie algebra E{sub 6} are obtained and a corresponding solution for l = n = 6 is presented. The polynomials depend upon integration constants Q{sub s}, s = 1,.., 6. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for E{sub 6}-polynomials at large z are governed by the integer-valued matrix ν = A{sup -1}(I + P), where A{sup -1} is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the Z{sub 2}-group of symmetry of the Dynkin diagram. The 2-form fluxes Φ{sup s}, s = 1,.., 6, are calculated. (orig.)
Rosenfeld, M.; Kwak, D.; Vinokur, M.
1988-01-01
A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method. 23 references
Borhanifar, A.; Kabir, M.M.; Maryam Vahdat, L.
2009-01-01
In this paper, the Exp-function method is used to obtain generalized solitonary solutions and periodic solutions of the Generalized Zakharov system and (2 + 1)-dimensional Nizhnik-Novikov-Veselov system. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
Kim, Myong-Ha; Ri, Guk-Chol; O, Hyong-Chol
2013-01-01
This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.
Recursive estimation of the claim rates and sizes in an insurance model
Lakhdar Aggoun
2004-01-01
Full Text Available It is a common fact that for most classes of general insurance, many possible sources of heterogeneity of risk exist. Premium rates based on information from a heterogeneous portfolio might be quite inadequate. One way of reducing this danger is by grouping policies according to the different levels of the various risk factors involved. Using measure change techniques, we derive recursive filters and predictors for the claim rates and claim sizes for the different groups.
On Recursive Modification in Child L1 French
Yves Roberge
2018-03-01
Full Text Available This paper investigates nominal recursive modification (RM in the L1 acquisition of French. Although recursion is considered the fundamental property of human languages, recursive self-embedding is found to be difficult for children in a variety of languages and constructions. Despite these challenges, the acquisition of RM proves to be resilient; acquirable even under severely degraded input conditions. From a minimalist perspective on the operations of narrow syntax, recursive embedding is essentially the application of a sequence of Merge operations (Chomsky 1995; Trotzke and Zwart 2014; therefore, given the universality of Merge, we do not expect to find cross-linguistic differences in how difficult recursion is. But if the challenging nature of recursion stems from factors which might differ from language to language, we expect different outcomes cross-linguistically. We compare new data from French to existing English data (Pérez-Leroux et al. 2012 in order to examine to what extent language-specific properties of RM structures determine the acquisition path. While children’s production differs significantly from their adult’s counterparts, we find no differences between French-speaking and English-speaking children. Our findings suggest that the challenging nature of recursion does not stem from the grammar itself and that what shapes the acquisition path is the interaction between universal properties of language and considerations not specific to language, namely computational efficiency.
Holographic thermalization and generalized Vaidya-AdS solutions in massive gravity
Hu, Ya-Peng; Zeng, Xiao-Xiong; Zhang, Hai-Qing
2017-02-01
We investigate the effect of massive graviton on the holographic thermalization process. Before doing this, we first find out the generalized Vaidya-AdS solutions in the de Rham-Gabadadze-Tolley (dRGT) massive gravity by directly solving the gravitational equations. Then, we study the thermodynamics of these Vaidya-AdS solutions by using the Misner-Sharp energy and unified first law, which also shows that the massive gravity is in a thermodynamic equilibrium state. Moreover, we adopt the two-point correlation function at equal time to explore the thermalization process in the dual field theory, and to see how the graviton mass parameter affects this process from the viewpoint of AdS/CFT correspondence. Our results show that the graviton mass parameter will increase the holographic thermalization process.
Holographic thermalization and generalized Vaidya-AdS solutions in massive gravity
Hu, Ya-Peng, E-mail: huyp@nuaa.edu.cn [College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Instituut-Lorentz for Theoretical Physics, Leiden University, Niels Bohrweg 2, Leiden 2333 CA (Netherlands); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190 (China); Zeng, Xiao-Xiong, E-mail: xxzengphysics@163.com [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190 (China); School of Science, Chongqing Jiaotong University, Chongqing 400074 (China); Zhang, Hai-Qing, E-mail: H.Q.Zhang@uu.nl [Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands)
2017-02-10
We investigate the effect of massive graviton on the holographic thermalization process. Before doing this, we first find out the generalized Vaidya-AdS solutions in the de Rham–Gabadadze–Tolley (dRGT) massive gravity by directly solving the gravitational equations. Then, we study the thermodynamics of these Vaidya-AdS solutions by using the Misner–Sharp energy and unified first law, which also shows that the massive gravity is in a thermodynamic equilibrium state. Moreover, we adopt the two-point correlation function at equal time to explore the thermalization process in the dual field theory, and to see how the graviton mass parameter affects this process from the viewpoint of AdS/CFT correspondence. Our results show that the graviton mass parameter will increase the holographic thermalization process.
Inverse planning for x-ray rotation therapy: a general solution of the inverse problem
Oelfke, U.; Bortfeld, T.
1999-01-01
Rotation therapy with photons is currently under investigation for the delivery of intensity modulated radiotherapy (IMRT). An analytical approach for inverse treatment planning of this radiotherapy technique is described. The inverse problem for the delivery of arbitrary 2D dose profiles is first formulated and then solved analytically. In contrast to previously applied strategies for solving the inverse problem, it is shown that the most general solution for the fluence profiles consists of two independent solutions of different parity. A first analytical expression for both fluence profiles is derived. The mathematical derivation includes two different strategies, an elementary expansion of fluence and dose into polynomials and a more practical approach in terms of Fourier transforms. The obtained results are discussed in the context of previous work on this problem. (author)
Analytical general solutions for static wormholes in f(R,T) gravity
Moraes, P. H. R. S.; Correa, R. A. C.; Lobato, R. V.
2017-07-01
Originally proposed as a tool for teaching the general theory of relativity, wormholes are today approached in many different ways and are seeing as an efficient alternative for interstellar and time travel. Attempts to achieve observational signatures of wormholes have been growing as the subject has become more and more popular. In this article we investigate some f(R,T) theoretical predictions for static wormholes, i.e., wormholes whose throat radius can be considered a constant. Since the T-dependence in f(R,T) gravity is due to the consideration of quantum effects, a further investigation of wormholes in such a theory is well motivated. We obtain the energy conditions of static wormholes in f(R,T) gravity and apply an analytical approach to find their physical and geometrical solutions. We highlight that our results are in agreement with previous solutions and assumptions presented in the literature.
Holographic thermalization and generalized Vaidya-AdS solutions in massive gravity
Hu, Ya-Peng; Zeng, Xiao-Xiong; Zhang, Hai-Qing
2017-01-01
We investigate the effect of massive graviton on the holographic thermalization process. Before doing this, we first find out the generalized Vaidya-AdS solutions in the de Rham–Gabadadze–Tolley (dRGT) massive gravity by directly solving the gravitational equations. Then, we study the thermodynamics of these Vaidya-AdS solutions by using the Misner–Sharp energy and unified first law, which also shows that the massive gravity is in a thermodynamic equilibrium state. Moreover, we adopt the two-point correlation function at equal time to explore the thermalization process in the dual field theory, and to see how the graviton mass parameter affects this process from the viewpoint of AdS/CFT correspondence. Our results show that the graviton mass parameter will increase the holographic thermalization process.
Analytical Solution of Displacements Around Circular Openings in Generalized Hoek-Brown Rocks
Huang Houxu
2017-09-01
Full Text Available The rock in plastic region is divided into numbers of elements by the slip lines, resulted from shear localization. During the deformation process, the elements will slip along the slip lines and the displacement field is discontinuous. Slip lines around circular opening in isotropic rock, subjected to hydrostatic stress are described by the logarithmic spirals. Deformation of the plastic region is mainly attributed to the slippage. Relationship between the shear stresses and slippage on slip lines is presented, based on the study of Revuzhenko and Shemyakin. Relations between slippage and rock failure are described, based on the elastic-brittle-plastic model. An analytical solution is presented for the plane strain analysis of displacements around circular openings in the Generalized Hoek-Brown rock. With properly choosing of slippage parameters, results obtained by using the proposed solution agree well with those presented in published sources.
Analytical general solutions for static wormholes in f ( R , T ) gravity
Moraes, P.H.R.S.; Correa, R.A.C.; Lobato, R.V., E-mail: moraes.phrs@gmail.com, E-mail: fis04132@gmail.com, E-mail: ronaldo.lobato@icranet.org [ITA-Instituto Tecnológico de Aeronáutica, 12228-900, São José dos Campos, SP (Brazil)
2017-07-01
Originally proposed as a tool for teaching the general theory of relativity, wormholes are today approached in many different ways and are seeing as an efficient alternative for interstellar and time travel. Attempts to achieve observational signatures of wormholes have been growing as the subject has become more and more popular. In this article we investigate some f ( R , T ) theoretical predictions for static wormholes, i.e., wormholes whose throat radius can be considered a constant. Since the T -dependence in f ( R , T ) gravity is due to the consideration of quantum effects, a further investigation of wormholes in such a theory is well motivated. We obtain the energy conditions of static wormholes in f ( R , T ) gravity and apply an analytical approach to find their physical and geometrical solutions. We highlight that our results are in agreement with previous solutions and assumptions presented in the literature.
Existence of solution for a general fractional advection-dispersion equation
Torres Ledesma, César E.
2018-05-01
In this work, we consider the existence of solution to the following fractional advection-dispersion equation -d/dt ( p {_{-∞}}It^{β }(u'(t)) + q {t}I_{∞}^{β }(u'(t))) + b(t)u = f(t, u(t)),t\\in R where β \\in (0,1) , _{-∞}It^{β } and tI_{∞}^{β } denote left and right Liouville-Weyl fractional integrals of order β respectively, 0continuous functions. Due to the general assumption on the constant p and q, the problem (0.1) does not have a variational structure. Despite that, here we study it performing variational methods, combining with an iterative technique, and give an existence criteria of solution for the problem (0.1) under suitable assumptions.
S. C. Oukouomi Noutchie
2014-01-01
Full Text Available We make use of Laplace transform techniques and the method of characteristics to solve fragmentation equations explicitly. Our result is a breakthrough in the analysis of pure fragmentation equations as this is the first instance where an exact solution is provided for the fragmentation evolution equation with general fragmentation rates. This paper is the key for resolving most of the open problems in fragmentation theory including “shattering” and the sudden appearance of infinitely many particles in some systems with initial finite particles number.
Lie group classification and exact solutions of the generalized Kompaneets equations
Oleksii Patsiuk
2015-04-01
Full Text Available We study generalized Kompaneets equations (GKEs with one functional parameter, and using the Lie-Ovsiannikov algorithm, we carried out the group classification. It is shown that the kernel algebra of the full groups of the GKEs is the one-dimensional Lie algebra. Using the direct method, we find the equivalence group. We obtain six non-equivalent (up to transformations from the equivalence group GKEs that allow wider invariance algebras than the kernel one. We find a number of exact solutions of the non-linear GKE which has the maximal symmetry properties.
N=1 domain wall solutions of massive type II supergravity as generalized geometries
Louis, J.
2006-05-01
We study N=1 domain wall solutions of type IIB supergravity compactified on a Calabi-Yau manifold in the presence of RR and NS electric and magnetic fluxes. We show that the dynamics of the scalar fields along the direction transverse to the domain wall is described by gradient flow equations controlled by a superpotential W. We then provide a geometrical interpretation of the gradient flow equations in terms of the mirror symmetric compactification of type IIA. They correspond to a set of generalized Hitchin flow equations of a manifold with SU(3) x SU(3)structure which is fibered over the direction transverse to the domain wall. (Orig.)
Classic tests of General Relativity described by brane-based spherically symmetric solutions
Cuzinatto, R.R. [Universidade Federal de Alfenas, Instituto de Ciencia e Tecnologia, Pocos de Caldas, MG (Brazil); Pompeia, P.J. [Departamento de Ciencia e Tecnologia Aeroespacial, Instituto de Fomento e Coordenacao Industrial, Sao Jose dos Campos, SP (Brazil); Departamento de Ciencia e Tecnologia Aeroespacial, Instituto Tecnologico de Aeronautica, Sao Jose dos Campos, SP (Brazil); De Montigny, M. [University of Alberta, Theoretical Physics Institute, Edmonton, AB (Canada); University of Alberta, Campus Saint-Jean, Edmonton, AB (Canada); Khanna, F.C. [University of Alberta, Theoretical Physics Institute, Edmonton, AB (Canada); TRIUMF, Vancouver, BC (Canada); University of Victoria, Department of Physics and Astronomy, PO box 1700, Victoria, BC (Canada); Silva, J.M.H. da [Universidade Estadual Paulista, Departamento de Fisica e Quimica, Guaratingueta, SP (Brazil)
2014-08-15
We discuss a way to obtain information about higher dimensions from observations by studying a brane-based spherically symmetric solution. The three classic tests of General Relativity are analyzed in detail: the perihelion shift of the planet Mercury, the deflection of light by the Sun, and the gravitational redshift of atomic spectral lines. The braneworld version of these tests exhibits an additional parameter b related to the fifth-coordinate. This constant b can be constrained by comparison with observational data for massive and massless particles. (orig.)
The General Analytic Solution of a Functional Equation of Addition Type
Braden, H. W.; Buchstaber, V. M.
1995-01-01
The general analytic solution to the functional equation $$ \\phi_1(x+y)= { { \\biggl|\\matrix{\\phi_2(x)&\\phi_2(y)\\cr\\phi_3(x)&\\phi_3(y)\\cr}\\biggr|} \\over { \\biggl|\\matrix{\\phi_4(x)&\\phi_4(y)\\cr\\phi_5(x)&\\phi_5(y)\\cr}\\biggr|} } $$ is characterised. Up to the action of the symmetry group, this is described in terms of Weierstrass elliptic functions. We illustrate our theory by applying it to the classical addition theorems of the Jacobi elliptic functions and the functional equations $$ \\phi_1(x+...
General Series Solutions for Stresses and Displacements in an Inner-fixed Ring
Jiao, Yongshu; Liu, Shuo; Qi, Dexuan
2018-03-01
The general series solution approach is provided to get the stress and displacement fields in the inner-fixed ring. After choosing an Airy stress function in series form, stresses are expressed by infinite coefficients. Displacements are obtained by integrating the geometric equations. For an inner-fixed ring, the arbitrary loads acting on outer edge are extended into two sets of Fourier series. The zero displacement boundary conditions on inner surface are utilized. Then the stress (and displacement) coefficients are expressed by loading coefficients. A numerical example shows the validity of this approach.
Exact periodic solutions of the sixth-order generalized Boussinesq equation
Kamenov, O Y [Department of Applied Mathematics and Informatics, Technical University of Sofia, PO Box 384, 1000 Sofia (Bulgaria)], E-mail: okam@abv.bg
2009-09-18
This paper examines a class of nonlinear sixth-order generalized Boussinesq-like equations (SGBE): u{sub tt} = u{sub xx} + 3(u{sup 2}){sub xx} + u{sub xxxx} + {alpha}u{sub xxxxxx}, {alpha} in R, depending on the positive parameter {alpha}. Hirota's bilinear transformation method is applied to the above class of non-integrable equations and exact periodic solutions have been obtained. The results confirmed the well-known nonlinear superposition principle.
The general Klein-Gordon-Schroedinger system: modulational instability and exact solutions
Tang Xiaoyan; Ding Wei
2008-01-01
The general Klein-Gordon-Schroedinger (gKGS) system is studied where the cubic auto-interactions are introduced in both the nonlinear Schroedinger and the nonlinear Klein-Gordon fields. We first investigate the modulational instability (MI) of the system, and thus derive the general dispersion relation between the frequency and wavenumber of the modulating perturbations, which demonstrates many possibilities for the MI regions. Using the travelling wave reduction, the gKGS system is greatly simplified. Via a simple function expansion method, we obtain some exact travelling wave solutions. Under some special parameter values, some representative wave structures are graphically displayed including the kink, anti-kink, bright, dark, grey and periodic solitons
Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng
2018-03-01
In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.
Nakata, Toshihiko; Ninomiya, Takanori
2006-10-10
A general solution of undersampling frequency conversion and its optimization for parallel photodisplacement imaging is presented. Phase-modulated heterodyne interference light generated by a linear region of periodic displacement is captured by a charge-coupled device image sensor, in which the interference light is sampled at a sampling rate lower than the Nyquist frequency. The frequencies of the components of the light, such as the sideband and carrier (which include photodisplacement and topography information, respectively), are downconverted and sampled simultaneously based on the integration and sampling effects of the sensor. A general solution of frequency and amplitude in this downconversion is derived by Fourier analysis of the sampling procedure. The optimal frequency condition for the heterodyne beat signal, modulation signal, and sensor gate pulse is derived such that undesirable components are eliminated and each information component is converted into an orthogonal function, allowing each to be discretely reproduced from the Fourier coefficients. The optimal frequency parameters that maximize the sideband-to-carrier amplitude ratio are determined, theoretically demonstrating its high selectivity over 80 dB. Preliminary experiments demonstrate that this technique is capable of simultaneous imaging of reflectivity, topography, and photodisplacement for the detection of subsurface lattice defects at a speed corresponding to an acquisition time of only 0.26 s per 256 x 256 pixel area.
Cusping, transport and variance of solutions to generalized Fokker-Planck equations
Carnaffan, Sean; Kawai, Reiichiro
2017-06-01
We study properties of solutions to generalized Fokker-Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker-Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.
General N-Dark Soliton Solutions of the Multi-Component Mel'nikov System
Han, Zhong; Chen, Yong; Chen, Junchao
2017-07-01
A general form of N-dark soliton solutions of the multi-component Mel'nikov system are presented. Taking the coupled Mel'nikov system comprised of two-component short waves and one-component long wave as an example, its general N-dark-dark soliton solutions in Gram determinant form are constructed through the KP hierarchy reduction method. The dynamics of single dark-dark soliton and two dark-dark solitons are discussed in detail. It can be shown that the collisions of dark-dark solitons are elastic and energies of the solitons in different components completely transmit through. In addition, the dark-dark soliton bound states including both stationary and moving cases are also investigated. An interesting feature for the coupled Mel'nikov system is that the stationary dark-dark soliton bound states can exist for all possible combinations of nonlinearity coefficients including positive, negative and mixed types, while the moving case are possible when nonlinearity coefficients take opposite signs or they are both negative.
Appleby, N J; Dunt, D; Southern, D M; Young, D
1999-08-01
To identify practical examples of barriers and possible solutions to improve general practice integration with other health service providers. Twelve focus groups, including one conducted by teleconference, were held across Australia with GPs and non GP primary health service providers between May and September, 1996. Focus groups were embedded within concept mapping sessions, which were used to conceptually explore the meaning of integration in general practice. Data coding, organising and analysis were based on the techniques documented by Huberman and Miles. Barriers to integration were perceived to be principally due to the role and territory disputes between the different levels of government and their services, the manner in which the GP's role is currently defined, and the system of GP remuneration. Suggestions on ways to improve integration involved two types of strategies. The first involves initiatives implemented 'top down' through major government reform to service structures, including the expansion of the role of divisions of general practice, and structural changes to the GP remuneration systems. The second type of strategy suggested involves initiatives implemented from the 'bottom up' involving services such as hospitals (e.g. additional GP liaison positions) and the use of information technology to link services and share appropriate patient data. The findings support the need for further research and evaluation of initiatives aimed at achieving general practice integration at a systems level. There is little evidence to suggest which types of initiatives improve integration. However, general practice has been placed in the centre of the health care debate and is likely to remain central to the success of such initiatives. Clarification of the future role and authority of general practice will therefore be required if such integrative strategies are to be successful at a wider health system level.
Recursive approach for non-Markovian time-convolutionless master equations
Gasbarri, G.; Ferialdi, L.
2018-02-01
We consider a general open system dynamics and we provide a recursive method to derive the associated non-Markovian master equation in a perturbative series. The approach relies on a momenta expansion of the open system evolution. Unlike previous perturbative approaches of this kind, the method presented in this paper provides a recursive definition of each perturbative term. Furthermore, we give an intuitive diagrammatic description of each term of the series, which provides a useful analytical tool to build them and to derive their structure in terms of commutators and anticommutators. We eventually apply our formalism to the evolution of the observables of the reduced system, by showing how the method can be applied to the adjoint master equation, and by developing a diagrammatic description of the associated series.
Snezhana Georgieva Gocheva-Ilieva
2013-01-01
Full Text Available There are obtained integral form and recurrence representations for some Fourier series and connected with them Favard constants. The method is based on preliminary integration of Fourier series which permits to establish general recursion formulas for Favard constants. This gives the opportunity for effective summation of infinite series and calculation of some classes of multiple singular integrals by the Favard constants.
Recursive recovery of Markov transition probabilities from boundary value data
Patch, Sarah Kathyrn [Univ. of California, Berkeley, CA (United States)
1994-04-01
In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requires finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.
Inner and Outer Recursive Neural Networks for Chemoinformatics Applications.
Urban, Gregor; Subrahmanya, Niranjan; Baldi, Pierre
2018-02-26
Deep learning methods applied to problems in chemoinformatics often require the use of recursive neural networks to handle data with graphical structure and variable size. We present a useful classification of recursive neural network approaches into two classes, the inner and outer approach. The inner approach uses recursion inside the underlying graph, to essentially "crawl" the edges of the graph, while the outer approach uses recursion outside the underlying graph, to aggregate information over progressively longer distances in an orthogonal direction. We illustrate the inner and outer approaches on several examples. More importantly, we provide open-source implementations [available at www.github.com/Chemoinformatics/InnerOuterRNN and cdb.ics.uci.edu ] for both approaches in Tensorflow which can be used in combination with training data to produce efficient models for predicting the physical, chemical, and biological properties of small molecules.
Convolution of second order linear recursive sequences II.
Szakács Tamás
2017-12-01
Full Text Available We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]. In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.
Recursive stochastic effects in valley hybrid inflation
Levasseur, Laurence Perreault; Vennin, Vincent; Brandenberger, Robert
2013-10-01
Hybrid inflation is a two-field model where inflation ends because of a tachyonic instability, the duration of which is determined by stochastic effects and has important observational implications. Making use of the recursive approach to the stochastic formalism presented in [L. P. Levasseur, preceding article, Phys. Rev. D 88, 083537 (2013)], these effects are consistently computed. Through an analysis of backreaction, this method is shown to converge in the valley but points toward an (expected) instability in the waterfall. It is further shown that the quasistationarity of the auxiliary field distribution breaks down in the case of a short-lived waterfall. We find that the typical dispersion of the waterfall field at the critical point is then diminished, thus increasing the duration of the waterfall phase and jeopardizing the possibility of a short transition. Finally, we find that stochastic effects worsen the blue tilt of the curvature perturbations by an O(1) factor when compared with the usual slow-roll contribution.
Recursive relations for processes with n photons of noncommutative QED
Jafari, Abolfazl
2007-01-01
Recursion relations are derived in the sense of Berends-Giele for the multi-photon processes of noncommutative QED. The relations concern purely photonic processes as well as the processes with two fermions involved, both for arbitrary number of photons at tree level. It is shown that despite of the dependence of noncommutative vertices on momentum, in contrast to momentum-independent color factors of QCD, the recursion relation method can be employed for multi-photon processes of noncommutative QED
COMPARISON OF RECURSIVE ESTIMATION TECHNIQUES FOR POSITION TRACKING RADIOACTIVE SOURCES
Muske, K.; Howse, J.
2000-01-01
This paper compares the performance of recursive state estimation techniques for tracking the physical location of a radioactive source within a room based on radiation measurements obtained from a series of detectors at fixed locations. Specifically, the extended Kalman filter, algebraic observer, and nonlinear least squares techniques are investigated. The results of this study indicate that recursive least squares estimation significantly outperforms the other techniques due to the severe model nonlinearity
Quantum rings and recursion relations in 2D quantum gravity
Kachru, S.
1992-01-01
This paper discusses tachyon condensate perturbations to the action of the two-dimensional string theory corresponding to the c + 1 matrix model. These are shown to deform the action of the ground ring on the tachyon modules, confirming a conjecture of Witten. The ground ring structure is used to derive recursion relations which relate (N + 1) and N tachyon bulk scattering amplitudes. These recursion relations allow one to compute all bulk amplitudes
Zhenguo Luo
2014-01-01
Full Text Available By using a fixed point theorem of strict-set-contraction, which is different from Gaines and Mawhin's continuation theorem and abstract continuation theory for k-set contraction, we established some new criteria for the existence of positive periodic solution of the following generalized neutral delay functional differential equation with impulse: x'(t=x(t[a(t-f(t,x(t,x(t-τ1(t,x(t,…,x(t-τn(t,x(t,x'(t-γ1(t,x(t,…,x'(t-γm(t,x(t], t≠tk, k∈Z+; x(tk+=x(tk-+θk(x(tk, k∈Z+. As applications of our results, we also give some applications to several Lotka-Volterra models and new results are obtained.
A Generalized Measure for the Optimal Portfolio Selection Problem and its Explicit Solution
Zinoviy Landsman
2018-03-01
Full Text Available In this paper, we offer a novel class of utility functions applied to optimal portfolio selection. This class incorporates as special cases important measures such as the mean-variance, Sharpe ratio, mean-standard deviation and others. We provide an explicit solution to the problem of optimal portfolio selection based on this class. Furthermore, we show that each measure in this class generally reduces to the efficient frontier that coincides or belongs to the classical mean-variance efficient frontier. In addition, a condition is provided for the existence of the a one-to-one correspondence between the parameter of this class of utility functions and the trade-off parameter λ in the mean-variance utility function. This correspondence essentially provides insight into the choice of this parameter. We illustrate our results by taking a portfolio of stocks from National Association of Securities Dealers Automated Quotation (NASDAQ.
Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem
Alchalabi, R.M. [BOC Group, Murray Hill, NJ (United States); Turinsky, P.J. [North Carolina State Univ., Raleigh, NC (United States)
1996-12-31
The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.
On flux integrals for generalized Melvin solution related to simple finite-dimensional Lie algebra
Ivashchuk, V.D. [VNIIMS, Center for Gravitation and Fundamental Metrology, Moscow (Russian Federation); Peoples' Friendship University of Russia (RUDN University), Institute of Gravitation and Cosmology, Moscow (Russian Federation)
2017-10-15
A generalized Melvin solution for an arbitrary simple finite-dimensional Lie algebra G is considered. The solution contains a metric, n Abelian 2-forms and n scalar fields, where n is the rank of G. It is governed by a set of n moduli functions H{sub s}(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials - the so-called fluxbrane polynomials. These polynomials depend upon integration constants q{sub s}, s = 1,.., n. In the case when the conjecture on the polynomial structure for the Lie algebra G is satisfied, it is proved that 2-form flux integrals Φ{sup s} over a proper 2d submanifold are finite and obey the relations q{sub s} Φ{sup s} = 4πn{sub s}h{sub s}, where the h{sub s} > 0 are certain constants (related to dilatonic coupling vectors) and the n{sub s} are powers of the polynomials, which are components of a twice dual Weyl vector in the basis of simple (co-)roots, s = 1,.., n. The main relations of the paper are valid for a solution corresponding to a finite-dimensional semi-simple Lie algebra G. Examples of polynomials and fluxes for the Lie algebras A{sub 1}, A{sub 2}, A{sub 3}, C{sub 2}, G{sub 2} and A{sub 1} + A{sub 1} are presented. (orig.)
Mohamed Abdalla Darwish
2014-01-01
Full Text Available We study a generalized fractional quadratic functional-integral equation of Erdélyi-Kober type in the Banach space BC(ℝ+. We show that this equation has at least one asymptotically stable solution.
Recursion to food plants by free-ranging Bornean elephant
Megan English
2015-08-01
Full Text Available Plant recovery rates after herbivory are thought to be a key factor driving recursion by herbivores to sites and plants to optimise resource-use but have not been investigated as an explanation for recursion in large herbivores. We investigated the relationship between plant recovery and recursion by elephants (Elephas maximus borneensis in the Lower Kinabatangan Wildlife Sanctuary, Sabah. We identified 182 recently eaten food plants, from 30 species, along 14 × 50 m transects and measured their recovery growth each month over nine months or until they were re-browsed by elephants. The monthly growth in leaf and branch or shoot length for each plant was used to calculate the time required (months for each species to recover to its pre-eaten length. Elephant returned to all but two transects with 10 eaten plants, a further 26 plants died leaving 146 plants that could be re-eaten. Recursion occurred to 58% of all plants and 12 of the 30 species. Seventy-seven percent of the re-eaten plants were grasses. Recovery times to all plants varied from two to twenty months depending on the species. Recursion to all grasses coincided with plant recovery whereas recursion to most browsed plants occurred four to twelve months before they had recovered to their previous length. The small sample size of many browsed plants that received recursion and uneven plant species distribution across transects limits our ability to generalise for most browsed species but a prominent pattern in plant-scale recursion did emerge. Plant recovery time was a good predictor of time to recursion but varied as a function of growth form (grass, ginger, palm, liana and woody and differences between sites. Time to plant recursion coincided with plant recovery time for the elephant’s preferred food, grasses, and perhaps also gingers, but not the other browsed species. Elephants are bulk feeders so it is likely that they time their returns to bulk feed on these grass species when
Recursion to food plants by free-ranging Bornean elephant.
English, Megan; Gillespie, Graeme; Goossens, Benoit; Ismail, Sulaiman; Ancrenaz, Marc; Linklater, Wayne
2015-01-01
Plant recovery rates after herbivory are thought to be a key factor driving recursion by herbivores to sites and plants to optimise resource-use but have not been investigated as an explanation for recursion in large herbivores. We investigated the relationship between plant recovery and recursion by elephants (Elephas maximus borneensis) in the Lower Kinabatangan Wildlife Sanctuary, Sabah. We identified 182 recently eaten food plants, from 30 species, along 14 × 50 m transects and measured their recovery growth each month over nine months or until they were re-browsed by elephants. The monthly growth in leaf and branch or shoot length for each plant was used to calculate the time required (months) for each species to recover to its pre-eaten length. Elephant returned to all but two transects with 10 eaten plants, a further 26 plants died leaving 146 plants that could be re-eaten. Recursion occurred to 58% of all plants and 12 of the 30 species. Seventy-seven percent of the re-eaten plants were grasses. Recovery times to all plants varied from two to twenty months depending on the species. Recursion to all grasses coincided with plant recovery whereas recursion to most browsed plants occurred four to twelve months before they had recovered to their previous length. The small sample size of many browsed plants that received recursion and uneven plant species distribution across transects limits our ability to generalise for most browsed species but a prominent pattern in plant-scale recursion did emerge. Plant recovery time was a good predictor of time to recursion but varied as a function of growth form (grass, ginger, palm, liana and woody) and differences between sites. Time to plant recursion coincided with plant recovery time for the elephant's preferred food, grasses, and perhaps also gingers, but not the other browsed species. Elephants are bulk feeders so it is likely that they time their returns to bulk feed on these grass species when quantities have
V. Rukavishnikov
2014-01-01
Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.
[Burnout of general practitioners in Belgium: societal consequences and paths to solutions].
Kacenelenbogen, N; Offermans, A M; Roland, M
2011-09-01
corollary a questioning of the viability of the health care system as we know it. At the time of writing this article, the Belgian Health Care Knowledge Centre (KCE) is completing, at the request of the Belgian Ministry (SPF) of Health a study entitled "Burn Out of General Practitioners: which prevention, which solutions" whose goal is to make recommendations for the prevention and support of this issue. To measure the real impact of the solutions eventually implemented, we need to create a tool for a regular assessment of the prevalence of this problem in our country.
Categorical Semantics for Functional Reactive Programming with Temporal Recursion and Corecursion
Wolfgang Jeltsch
2014-06-01
Full Text Available Functional reactive programming (FRP makes it possible to express temporal aspects of computations in a declarative way. Recently we developed two kinds of categorical models of FRP: abstract process categories (APCs and concrete process categories (CPCs. Furthermore we showed that APCs generalize CPCs. In this paper, we extend APCs with additional structure. This structure models recursion and corecursion operators that are related to time. We show that the resulting categorical models generalize those CPCs that impose an additional constraint on time scales. This constraint boils down to ruling out ω-supertasks, which are closely related to Zeno's paradox of Achilles and the tortoise.
Huanhe Dong
2014-01-01
Full Text Available We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.
A novel noncommutative KdV-type equation, its recursion operator, and solitons
Carillo, Sandra; Lo Schiavo, Mauro; Porten, Egmont; Schiebold, Cornelia
2018-04-01
A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived.
Parallel Implementation of Riccati Recursion for Solving Linear-Quadratic Control Problems
Frison, Gianluca; Jørgensen, John Bagterp
2013-01-01
In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is usually the main computational effort. In this paper...... an alternative version of the Riccati recursion solver for LQ control problems is presented. The performance of both the classical and the alternative version is analyzed from a theoretical as well as a numerical point of view, and the alternative version is found to be approximately 50% faster than...
Yingwei Li
2013-01-01
Full Text Available The global exponential stability issues are considered for almost periodic solution of the neural networks with mixed time-varying delays and discontinuous neuron activations. Some sufficient conditions for the existence, uniqueness, and global exponential stability of almost periodic solution are achieved in terms of certain linear matrix inequalities (LMIs, by applying differential inclusions theory, matrix inequality analysis technique, and generalized Lyapunov functional approach. In addition, the existence and asymptotically almost periodic behavior of the solution of the neural networks are also investigated under the framework of the solution in the sense of Filippov. Two simulation examples are given to illustrate the validity of the theoretical results.
Ribeiro, F B
1999-01-01
Solutions of the diffusion equation in cylindrical coordinates are presented for a radionuclide produced by the decay of a not diffusing parent isotope with arbitrary activity distribution. General initial and Dirichlet boundary conditions are considered and the diffusion equation is solved for a finite cylinder. Solutions corresponding to two particular boundary conditions that can be imposed in laboratory diffusion coefficient measurements are presented. An analysis of the speed of convergence and of the series truncation error is done for these particular solutions. An example of the escape to production ratio derived from one of the solutions is also presented.
Ribeiro, Fernando Brenha
1999-01-01
Solutions of the diffusion equation in cylindrical coordinates are presented for a radionuclide produced by the decay of a not diffusing parent isotope with arbitrary activity distribution. General initial and Dirichlet boundary conditions are considered and the diffusion equation is solved for a finite cylinder. Solutions corresponding to two particular boundary conditions that can be imposed in laboratory diffusion coefficient measurements are presented. An analysis of the speed of convergence and of the series truncation error is done for these particular solutions. An example of the escape to production ratio derived from one of the solutions is also presented
Amm, O.; Fujii, R.; VanhamäKi, H.; Yoshikawa, A.; Ieda, A.
2013-05-01
We devise an approach to calculate the polarization electric field in the ionosphere, when the ionospheric conductances, the primary (modeled) or the total (measured) electric field, and the Cowling efficiency are given. In contrast to previous studies, our approach is a general solution which is not limited to specific geometrical setups, and all parameters may have any kind of spatial dependence. The solution technique is based on spherical elementary current (vector) systems (SECS). This way, we avoid the need to specify explicit boundary conditions for the searched polarization electric field of its potential which would be required if the problem was solved in a differential equation approach. Instead, we solve an algebraic matrix equation, and the implicit boundary condition that the divergence of the polarization electric field vanishes outside our analysis area is sufficient. In order to illustrate our theory, we then apply it to two simple models of auroral electrodynamic situations, the first being a mesoscale strong conductance enhancement in the early morning sector within a relatively weak southward primary electric field, and a morning sector auroral arc with only a weak conductance enhancement, but a large southward primary electric field at the poleward flank of the arc. While the significance of the polarization electric field for maximum Cowling efficiency is large for the first case, it is rather minor for the second one. Both models show that the polarization electric field effect may not only change the magnitude of the current systems but also their overall geometry. Furthermore, the polarization electric field may extend into regions where the primary electric field is small, thus even dominating the total electric field in these regions. For the first model case, the total Joule heating integrated over the analysis area decreases by a factor of about 4 for maximum Cowling efficiency as compared to the case of vanishing Cowling efficiency
Video game for learning and metaphorization of recursive algorithms
Ricardo Inacio Alvares Silva
2013-09-01
Full Text Available The learning of recursive algorithms in computer programming is problematic, because its execution and resolution is not natural to the thinking way people are trained and used to since young. As with other topics in algorithms, we use metaphors to make parallels between the abstract and the concrete to help in understanding the operation of recursive algorithms. However, the classic metaphors employed in this area, such as calculating factorial recursively and Towers of Hanoi game, may just confuse more or be insufficient. In this work, we produced a computer game to assist students in computer courses in learning recursive algorithms. It was designed to have regular video game characteristics, with narrative and classical gameplay elements, commonly found in this kind of product. Aiding to education occurs through metaphorization, or in other words, through experiences provided by game situations that refer to recursive algorithms. To this end, we designed and imbued in the game four valid metaphors related to the theory, and other minor references to the subject.
Recursion method in the k-space representation
Anlage, S.M.; Smith, D.L.
1986-01-01
We show that by using a unitary transformation to k space and the special-k-point method for evaluating Brillouin-zone sums, the recursion method can be very effectively applied to translationally invariant systems. We use this approach to perform recursion calculations for realistic tight-binding Hamiltonians which describe diamond- and zinc-blende-structure semiconductors. Projected densities of states for these Hamiltonians have band gaps and internal van Hove singularities. We calculate coefficients for 63 recursion levels exactly and for about 200 recursion levels to a good approximation. Comparisons are made for materials with different magnitude band gaps (diamond, Si, α-Sn). Comparison is also made between materials with one (e.g., diamond) and two (e.g., GaAs) band gaps. The asymptotic behavior of the recursion coefficients is studied by Fourier analysis. Band gaps in the projected density of states dominate the asymptotic behavior. Perturbation analysis describes the asymptotic behavior rather well. Projected densities of states are calculated using a very simple termination scheme. These densities of states compare favorably with the results of Gilat-Raubenheimer integration
Hoshyargar, Vahid; Fadaei, Farzad; Ashrafizadeh, Seyed Nezameddin
2015-01-01
A comprehensive mathematical model is developed for simulation of ion transport through nanofiltration membranes. The model is based on the Maxwell-Stefan approach and takes into account steric, Donnan, and dielectric effects in the transport of mono and divalent ions. Theoretical ion rejection for multi-electrolyte mixtures was obtained by numerically solving the 'hindered transport' based on the generalized Maxwell-Stefan equation for the flux of ions. A computer simulation has been developed to predict the transport in the range of nanofiltration, a numerical procedure developed linearization and discretization form of the governing equations, and the finite volume method was employed for the numerical solution of equations. The developed numerical method is capable of solving equations for multicomponent systems of n species no matter to what extent the system shows stiffness. The model findings were compared and verified with the experimental data from literature for two systems of Na 2 SO 4 +NaCl and MgCl 2 +NaCl. Comparison showed great agreement for different concentrations. As such, the model is capable of predicting the rejection of different ions at various concentrations. The advantage of such a model is saving costs as a result of minimizing the number of required experiments, while it is closer to a realistic situation since the adsorption of ions has been taken into account. Using this model, the flux of permeates and rejections of multi-component liquid feeds can be calculated as a function of membrane properties. This simulation tool attempts to fill in the gap in methods used for predicting nanofiltration and optimization of the performance of charged nanofilters through generalized Maxwell-Stefan (GMS) approach. The application of the current model may weaken the latter gap, which has arisen due to the complexity of the fundamentals of ion transport processes via this approach, and may further facilitate the industrial development of
Jarsjoe, Jerker; Destouni, Georgia; Persson, Klas; Prieto, Carmen
2007-12-01
We formulate a general theoretical conceptualisation of solute transport from inland sources to downstream recipients, considering main recipient load contributions from all different nutrient and pollutant sources that may exist within any catchment. Since the conceptualisation is model independent, its main hydrological factors and mass delivery factors can be quantified on the basis of inputs to and outputs from any considered analytical or numerical model. Some of the conceptually considered source contribution and transport pathway combinations are however commonly neglected in catchment-scale solute transport and attenuation modelling, in particular those related to subsurface sources, diffuse sources at the land surface and direct groundwater transport into the recipient. The conceptual framework provides a possible tool for clarification of underlying and often implicit model assumptions, which can be useful for e.g. inter-model comparisons. In order to further clarify and explain research questions that may be of particular importance for transport pathways from deep groundwater surrounding a repository, we concretise and interpret some selected transport scenarios for model conditions in the Forsmark area. Possible uncertainties in coastal discharge predictions, related to uncertain spatial variation of evapotranspiration within the catchment, were shown to be small for the relatively large, focused surface water discharges from land to sea, because local differences were averaged out along the length of the main water flow paths. In contrast, local flux values within the diffuse groundwater flow field from land to sea are more uncertain, although estimates of mean values and total sums of submarine groundwater discharge (SGD) along some considerable coastline length may be robust. The present results show that 80% to 90% of the total coastal discharge of Forsmark occurred through focused flows in visible streams, whereas the remaining 10% to 20% was
Multipolar electromagnetic fields around neutron stars: general-relativistic vacuum solutions
Pétri, J.
2017-12-01
Magnetic fields inside and around neutron stars are at the heart of pulsar magnetospheric activity. Strong magnetic fields are responsible for quantum effects, an essential ingredient to produce leptonic pairs and the subsequent broad-band radiation. The variety of electromagnetic field topologies could lead to the observed diversity of neutron star classes. Thus, it is important to include multipolar components to a presumably dominant dipolar magnetic field. Exact analytical solutions for these multipoles in Newtonian gravity have been computed in recent literature. However, flat space-time is not adequate to describe physics in the immediate surroundings of neutron stars. We generalize the multipole expressions to the strong gravity regime by using a slowly rotating metric approximation such as the one expected around neutron stars. Approximate formulae for the electromagnetic field including frame dragging are computed from which we estimate the Poynting flux and the braking index. Corrections to leading order in compactness and spin parameter are presented. As far as spin-down luminosity is concerned, it is shown that frame dragging remains irrelevant. For high-order multipoles starting from the quadrupole, the electric part can radiate more efficiently than the magnetic part. Both analytical and numerical tools are employed.
D'Ambra, Pasqua; Tartaglione, Gaetano
2015-04-01
Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.
Solution of Ambrosio-Tortorelli model for image segmentation by generalized relaxation method
D'Ambra, Pasqua; Tartaglione, Gaetano
2015-03-01
Image segmentation addresses the problem to partition a given image into its constituent objects and then to identify the boundaries of the objects. This problem can be formulated in terms of a variational model aimed to find optimal approximations of a bounded function by piecewise-smooth functions, minimizing a given functional. The corresponding Euler-Lagrange equations are a set of two coupled elliptic partial differential equations with varying coefficients. Numerical solution of the above system often relies on alternating minimization techniques involving descent methods coupled with explicit or semi-implicit finite-difference discretization schemes, which are slowly convergent and poorly scalable with respect to image size. In this work we focus on generalized relaxation methods also coupled with multigrid linear solvers, when a finite-difference discretization is applied to the Euler-Lagrange equations of Ambrosio-Tortorelli model. We show that non-linear Gauss-Seidel, accelerated by inner linear iterations, is an effective method for large-scale image analysis as those arising from high-throughput screening platforms for stem cells targeted differentiation, where one of the main goal is segmentation of thousand of images to analyze cell colonies morphology.
Numerical solutions of the aerosol general dynamic equation for nuclear reactor safety studies
Park, J.W.
1988-01-01
Methods and approximations inherent in modeling of aerosol dynamics and evolution for nuclear reactor source term estimation have been investigated. Several aerosol evolution problems are considered to assess numerical methods of solving the aerosol dynamic equation. A new condensational growth model is constructed by generalizing Mason's formula to arbitrary particle sizes, and arbitrary accommodation of the condensing vapor and background gas at particle surface. Analytical solution is developed for the aerosol growth equation employing the new condensation model. The space-dependent aerosol dynamic equation is solved to assess implications of spatial homogenization of aerosol distributions. The results of our findings are as follows. The sectional method solving the aerosol dynamic equation is quite efficient in modeling of coagulation problems, but should be improved for simulation of strong condensation problems. The J-space transform method is accurate in modeling of condensation problems, but is very slow. For the situation considered, the new condensation model predicts slower aerosol growth than the corresponding isothermal model as well as Mason's model, the effect of partial accommodation is considerable on the particle evolution, and the effect of the energy accommodation coefficient is more pronounced than that of the mass accommodation coefficient. For the initial conditions considered, the space-dependent aerosol dynamics leads to results that are substantially different from those based on the spatially homogeneous aerosol dynamic equation
Generalization of the Numerov method for solution of N-d breakup problem in configuration space
Suslov, V.M.; Vlahovic, B.
2004-01-01
A new computational method for solving the configuration-space Faddeev equations for three-nucleon systems has been developed. This method is based on the spline decomposition in the angular variable and a generalization of the Numerov method for the hyperradius. The s-wave calculations of the inelasticity and phase shift as well as breakup amplitudes for n-d and p-d breakup scatterings for lab energies 14.1 and 42.0 MeV were performed with the Malfliet-Tjon I-III potential. In the case of n-d breakup scattering the results are in good agreement with those of the benchmark solution [J. L. Friar, B. F. Gibson, G. Berthold, W. Gloeckle, Th. Cornelius, H. Witala, J. Haidenbauer, Y. Koike, G. L. Payne, J. A. Tjon, and W. M. Kloet, Phys. Rev. C 42, 1838 (1990); J. L. Friar, G. L. Payne, W. Gloeckle, D. Hueber, and H. Witala, Phys. Rev. C 51, 2356 (1995)]. In the case of p-d quartet breakup scattering disagreement for the inelasticities reaches up to 6% as compared with those of the Pisa group [A. Kievsky, M. Viviani, and S. Rosati, Phys. Rev. C 64, 024002 (2001)]. The calculated p-d amplitudes fulfill the optical theorem with a good precision
Analytic study of the Migdal-Kadanoff recursion formula
Ito, K.R.
1984-01-01
After proposing lattice gauge field models in which the Migdal renormalization group recursion formulas are exact, we study the recursion formulas analytically. If D is less than 4, it is shown that the effective actions of D-dimensional U(1) lattice gauge models are uniformly driven to the high temperature region no matter how low the initial temperature is. If the initial temperature is large enough, this holds for any D and gauge group G. These are also the cases for the recursion formulas of Kadanoff type. It turns out, however, that the string tension for D=3 obtained by these methods is rather big compared with the one already obtained by Mack, Goepfert and by the present author. The reason is clarified. (orig.)
Darmani, G.; Setayeshi, S.; Ramezanpour, H.
2012-01-01
In this paper an efficient computational method based on extending the sensitivity approach (SA) is proposed to find an analytic exact solution of nonlinear differential difference equations. In this manner we avoid solving the nonlinear problem directly. By extension of sensitivity approach for differential difference equations (DDEs), the nonlinear original problem is transformed into infinite linear differential difference equations, which should be solved in a recursive manner. Then the exact solution is determined in the form of infinite terms series and by intercepting series an approximate solution is obtained. Numerical examples are employed to show the effectiveness of the proposed approach. (general)
Recursive B-spline approximation using the Kalman filter
Jens Jauch
2017-02-01
Full Text Available This paper proposes a novel recursive B-spline approximation (RBA algorithm which approximates an unbounded number of data points with a B-spline function and achieves lower computational effort compared with previous algorithms. Conventional recursive algorithms based on the Kalman filter (KF restrict the approximation to a bounded and predefined interval. Conversely RBA includes a novel shift operation that enables to shift estimated B-spline coefficients in the state vector of a KF. This allows to adapt the interval in which the B-spline function can approximate data points during run-time.
Jarsjoe, Jerker; Destouni, Georgia; Persson, Klas; Prieto, Carmen (Dept. of Physical Geography, Quaternary Geology, Stockholm Univ., Stockholm (Sweden))
2007-12-15
We formulate a general theoretical conceptualisation of solute transport from inland sources to downstream recipients, considering main recipient load contributions from all different nutrient and pollutant sources that may exist within any catchment. Since the conceptualisation is model independent, its main hydrological factors and mass delivery factors can be quantified on the basis of inputs to and outputs from any considered analytical or numerical model. Some of the conceptually considered source contribution and transport pathway combinations are however commonly neglected in catchment-scale solute transport and attenuation modelling, in particular those related to subsurface sources, diffuse sources at the land surface and direct groundwater transport into the recipient. The conceptual framework provides a possible tool for clarification of underlying and often implicit model assumptions, which can be useful for e.g. inter-model comparisons. In order to further clarify and explain research questions that may be of particular importance for transport pathways from deep groundwater surrounding a repository, we concretise and interpret some selected transport scenarios for model conditions in the Forsmark area. Possible uncertainties in coastal discharge predictions, related to uncertain spatial variation of evapotranspiration within the catchment, were shown to be small for the relatively large, focused surface water discharges from land to sea, because local differences were averaged out along the length of the main water flow paths. In contrast, local flux values within the diffuse groundwater flow field from land to sea are more uncertain, although estimates of mean values and total sums of submarine groundwater discharge (SGD) along some considerable coastline length may be robust. The present results show that 80% to 90% of the total coastal discharge of Forsmark occurred through focused flows in visible streams, whereas the remaining 10% to 20% was
Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-
2014-01-01
Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.
System Simulation by Recursive Feedback: Coupling a Set of Stand-Alone Subsystem Simulations
Nixon, D. D.
2001-01-01
Conventional construction of digital dynamic system simulations often involves collecting differential equations that model each subsystem, arran g them to a standard form, and obtaining their numerical gin solution as a single coupled, total-system simultaneous set. Simulation by numerical coupling of independent stand-alone subsimulations is a fundamentally different approach that is attractive because, among other things, the architecture naturally facilitates high fidelity, broad scope, and discipline independence. Recursive feedback is defined and discussed as a candidate approach to multidiscipline dynamic system simulation by numerical coupling of self-contained, single-discipline subsystem simulations. A satellite motion example containing three subsystems (orbit dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Distributed and centralized implementations of coupling have been considered. Numerical results are evaluated by direct comparison with a standard total-system, simultaneous-solution approach.
Li Jiangfan; Jiang Zongfu; Xiao Fuliang; Huang Chunjia
2005-01-01
The dynamics of a generalized non-degenerate optical parametric down-conversion interaction whose Hamiltonian includes an arbitrary time-dependent driving part and a two-mode coupled part is studied by adopting the Lewis-Riesenfeld invariant theory. The closed formulae for the evolution of the quantum states and the evolution operators of the system are obtained. It is shown that various generalized squeezed states arise naturally in the process, and the two-mode squeezed effect is independent of the driving part. An explicitly analytical solution of the Schroedinger equation is further derived as the classical generalized force acting on each mode and the coupling of the two modes both have harmonic time dependences. This solution is found to be in agreement with previous research in special cases
Embedded class solutions compatible for physical compact stars in general relativity
Newton Singh, Ksh.; Pant, Neeraj; Tewari, Neeraj; Aria, Anil K.
2018-05-01
We have explored a family of new solutions satisfying Einstein's field equations and Karmarkar condition. We have assumed an anisotropic stress-tensor with no net electric charge. Interestingly, the new solutions yield zero values of all the physical quantities for all even integer n > 0. However, for all n >0 (n ≠ even numbers) they yield physically possible solutions. We have tuned the solution for neutron star Vela X-1 so that the solutions matches the observed mass and radius. For the same star we have extensively discussed the behavior of the solutions. The solutions yield a stiffer equation of state for larger values of n since the adiabatic index increases and speed of sound approaches the speed of light. It is also found that the solution is physically possible for Vela X-1 if 1.8 ≤ n < 7 (with n≠ 2,4,6). All the solutions for n ≥ 7 violates the causality condition and all the solutions with 0 < n < 1.8 lead to complex values of transverse sound speed vt. The range of well-behaved n depends on the mass and radius of compact stars.
Fernandes, L.; Friedlander, A.; Guedes, M.; Judice, J.
2001-01-01
This paper addresses a General Linear Complementarity Problem (GLCP) that has found applications in global optimization. It is shown that a solution of the GLCP can be computed by finding a stationary point of a differentiable function over a set defined by simple bounds on the variables. The application of this result to the solution of bilinear programs and LCPs is discussed. Some computational evidence of its usefulness is included in the last part of the paper
Shang Yadong
2005-01-01
In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Lienard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long-short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions
Tupper, B.O.J.
1976-01-01
In a previous article (Gen. Rel. Grav.; 6 : 345 (1975)) the Einstein-Maxwell field equations for non-null electromagnetic fields were studied under the conditions that the null tetrad is parallel-propagated along both principal null congruences. A solution with twist and shear, but no expansion, was found and was conjectured to be the only expansion-free solution. Here it is shown that this conjecture is false; the general expansion-free solution is found to be a family of space-times depending on a single constant parameter which is the ratio of the (constant) twists of the two principal null congruences. (author)
Interpretation and further properties of general classical CPsup(n-1) solutions
Din, A.M.
1980-11-01
We present arguments suggesting that non-(anti)selfdual classical solutions to the equations of motion of the euclidean CPsup(n-1) model can be interpreted as unstable non-interacting mixtures of instantons and anti-instantons. Fermionic modes in the background of these solutions are discussed. We determine the modes explicitly for the case of an embedded O(3) solution and point out that they give rise to a non-trivial illustration of the Atiyah-Singer index theorem
Recruitment and retention of general practitioners in the UK: what are the problems and solutions?
Young, R; Leese, B
1999-10-01
Recruitment and retention of general practitioners (GPs) has become an issue of major concern in recent years. However, much of the evidence is anecdotal and some commentators continue to question the scale of workforce problems. Hence, there is a need to establish a clear picture of those instabilities (i.e. imbalances between demand and supply) that do exist in the GP labour market in the UK. Based on a review of the published literature, we identify problems that stem from: (i) the changing social composition of the workforce and the fact that a large proportion of qualified GPs are significantly underutilized within traditional career structures; and (ii) the considerable differences in the ability of local areas to match labour demand and supply. We argue that one way to address these problems would be to encourage greater flexibility in a number of areas highlighted in the literature: (i) time commitment across the working day and week; (ii) long-term career paths; (iii) training and education; and (iv) remuneration and contract conditions. Overall, although the evidence suggests that the predicted 'crisis' has not yet occurred in the GP labour market as a whole, there is no room for lack of imagination in planning terms. Workforce planners continue to emphasize national changes to the medical school intake as the means to balance labour demand and supply between the specialities; however, better retention and deployment of existing GP labour would arguably produce more effective supply-side solutions. In this context, current policy and practice developments (e.g. Primary Care Groups and Primary Care Act Pilot Sites) offer a unique learning base upon which to move forward.
Shaw-Yang Yang Hund-Der Yeh
2012-01-01
Full Text Available This note develops a general mathematical model for describing the transient hydraulic head response for constant-head test, constant-flux test, and slug test in a radial confined aquifer system with a partially penetrating well. The Laplace-domain solution for the model is derived by applying the Laplace transform with respect to time and finite Fourier cosine transform with respect to the z-direction. This new solution has been shown to reduce to the constant-head test when discounting the wellbore storage and maintaining a constant well water level. This solution can also be reduced to the constant-flux test solution when discounting the wellbore storage and keeping a constant pumping rate in the well. Moreover, the solution becomes the slug test solution when there is no pumping in the well. This general solution can be used to develop a single computer code to estimate aquifer parameters if coupled with an optimization algorithm or to assess the effect of well partial penetration on hydraulic head distribution for three types of aquifer tests.
Chang, Chein-I
2017-01-01
This book explores recursive architectures in designing progressive hyperspectral imaging algorithms. In particular, it makes progressive imaging algorithms recursive by introducing the concept of Kalman filtering in algorithm design so that hyperspectral imagery can be processed not only progressively sample by sample or band by band but also recursively via recursive equations. This book can be considered a companion book of author’s books, Real-Time Progressive Hyperspectral Image Processing, published by Springer in 2016. Explores recursive structures in algorithm architecture Implements algorithmic recursive architecture in conjunction with progressive sample and band processing Derives Recursive Hyperspectral Sample Processing (RHSP) techniques according to Band-Interleaved Sample/Pixel (BIS/BIP) acquisition format Develops Recursive Hyperspectral Band Processing (RHBP) techniques according to Band SeQuential (BSQ) acquisition format for hyperspectral data.
A recursion relation for coefficients of fractional parentage in the seniority scheme
Evans, T.
1985-01-01
A recursion relations for coefficients as fractional parentage in the seniority scheme are discussed. Determinated dependence of recursion relations from the particle number permit to evaluate matrix elements of creation and annihilation operators for fermions or bosons. 10 refs. (author)
Yomba, Emmanuel
2008-01-01
With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schroedinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons
Generalized Solutions of the Dirac Equation, W Bosons, and Beta Decay
Okniński, Andrzej
2016-01-01
We study the 7×7 Hagen-Hurley equations describing spin 1 particles. We split these equations, in the interacting case, into two Dirac equations with nonstandard solutions. It is argued that these solutions describe decay of a virtual W boson in beta decay.
Reuss, J.D.
1967-08-01
We recall the algebraic statement that can be done for Petrov's classification. We determine Petrov's class in some points of the axial symmetric stationary solution given in 1953 by Papapetrou. We complete the determination of the Papapetrou non stationary cylindric solution. (author) [fr
Two general classes of self dual, Minkowski propagating wave solutions in Yang Mills gauge theory
Kovacs, E.; Lo, S.Y.
1979-01-01
Two classes of self dual propogating wave solutions to the sourceless field equations in Minkowski space are presented. Some of these solutions can be linearly superposed. These waves can propogate at either the speed of light or at a speed less than that of light
Traversable intra-Universe wormholes and timeholes in General Relativity: two new solutions
Smirnov, Alexey L.
2016-11-01
Using thin shell formalism we construct two solutions of intra-Universe wormholes. The first model is a cosmological analog of the Aichelburg-Schein timehole, while another one is an intra-Universe form of the Bronnikov-Ellis solution.
Traversable intra-Universe wormholes and timeholes in General Relativity: two new solutions
Smirnov, Alexey L
2016-01-01
Using thin shell formalism we construct two solutions of intra-Universe wormholes. The first model is a cosmological analog of the Aichelburg–Schein timehole, while another one is an intra-Universe form of the Bronnikov–Ellis solution. (paper)
Improved decay rates for solutions for a multidimensional generalized Benjamin-Bona-Mahony equation
Said-Houari, Belkacem
2014-01-01
the Fourier transform and the energy method, we show the global existence and the convergence rates of the solutions under the smallness assumption on the initial data and we give better decay rates of the solutions. This result improves early works in J
Active control versus recursive backstepping control of a chaotic ...
In this paper active controllers and recursive backstepping controllers are designed for a third order chaotic system. The performances of these controllers in the control of the dynamics of the chaotic system are investigated numerically and are found to be effective. Comparison of their transient performances show that the ...
Recursive representation of the torus 1-point conformal block
Hadasz, Leszek; Jaskólski, Zbigniew; Suchanek, Paulina
2010-01-01
The recursive relation for the 1-point conformal block on a torus is derived and used to prove the identities between conformal blocks recently conjectured by Poghossian in [1]. As an illustration of the efficiency of the recurrence method the modular invariance of the 1-point Liouville correlation function is numerically analyzed.
The Free Energy in the Derrida-Retaux Recursive Model
Hu, Yueyun; Shi, Zhan
2018-05-01
We are interested in a simple max-type recursive model studied by Derrida and Retaux (J Stat Phys 156:268-290, 2014) in the context of a physics problem, and find a wide range for the exponent in the free energy in the nearly supercritical regime.
Recursive subspace identification for in flight modal analysis of airplanes
De Cock , Katrien; Mercère , Guillaume; De Moor , Bart
2006-01-01
International audience; In this paper recursive subspace identification algorithms are applied to track the modal parameters of airplanes on-line during test flights. The ability to track changes in the damping ratios and the influence of the forgetting factor are studied through simulations.
Differential constraints for bounded recursive identification with multivariate splines
De Visser, C.C.; Chu, Q.P.; Mulder, J.A.
2011-01-01
The ability to perform online model identification for nonlinear systems with unknown dynamics is essential to any adaptive model-based control system. In this paper, a new differential equality constrained recursive least squares estimator for multivariate simplex splines is presented that is able
Predicate Transformers for Recursive Procedures with Local Variables
Hesselink, Wim H.
1999-01-01
The weakest precondition semantics of recursive procedures with local variables are developed for an imperative language with demonic and angelic operators for unbounded nondeterminate choice. This does not require stacking of local variables. The formalism serves as a foundation for a proof rule
Denotational semantics of recursive types in synthetic guarded domain theory
Møgelberg, Rasmus Ejlers; Paviotti, Marco
2016-01-01
typed lambda calculus with fixed points). This model was intensional in that it could distinguish between computations computing the same result using a different number of fixed point unfoldings. In this work we show how also programming languages with recursive types can be given denotational...
A bijection between phylogenetic trees and plane oriented recursive trees
Prodinger, Helmut
2017-01-01
Phylogenetic trees are binary nonplanar trees with labelled leaves, and plane oriented recursive trees are planar trees with an increasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the respective representations a 2-partitions and trapezoidal words.
Step-indexed Kripke models over recursive worlds
Birkedal, Lars; Reus, Bernhard; Schwinghammer, Jan
2011-01-01
worlds that are recursively defined in a category of metric spaces. In this paper, we broaden the scope of this technique from the original domain-theoretic setting to an elementary, operational one based on step indexing. The resulting method is widely applicable and leads to simple, succinct models...
Theory of Mind, linguistic recursion and autism spectrum disorder
Polyanskaya, Irina; Blackburn, Patrick Rowan; Braüner, Torben
2017-01-01
In this paper we give the motivation for and discuss the design of an experiment investigating whether the acquisition of linguistic recur-sion helps children with Autism Spectrum Disorder (ASD) develop second-order false belief skills. We first present the relevant psycho-logical concepts (in...
A metric model of lambda calculus with guarded recursion
Birkedal, Lars; Schwinghammer, Jan; Støvring, Kristian
2010-01-01
We give a model for Nakano’s typed lambda calculus with guarded recursive definitions in a category of metric spaces. By proving a computational adequacy result that relates the interpretation with the operational semantics, we show that the model can be used to reason about contextual equivalence....
Symbolic Reachability for Process Algebras with Recursive Data Types
Blom, Stefan; van de Pol, Jan Cornelis; Fitzgerald, J.S.; Haxthausen, A.E.; Yenigun, H.
2008-01-01
In this paper, we present a symbolic reachability algorithm for process algebras with recursive data types. Like the various saturation based algorithms of Ciardo et al, the algorithm is based on partitioning of the transition relation into events whose influence is local. As new features, our
Recursivity: A Working Paper on Rhetoric and "Mnesis"
Stormer, Nathan
2013-01-01
This essay proposes the genealogical study of remembering and forgetting as recursive rhetorical capacities that enable discourse to place itself in an ever-changing present. "Mnesis" is a meta-concept for the arrangements of remembering and forgetting that enable rhetoric to function. Most of the essay defines the materiality of "mnesis", first…
Consumption-Portfolio Optimization with Recursive Utility in Incomplete Markets
Kraft, Holger; Seifried, Frank Thomas; Steffensen, Mogens
2013-01-01
In an incomplete market, we study the optimal consumption-portfolio decision of an investor with recursive preferences of Epstein–Zin type. Applying a classical dynamic programming approach, we formulate the associated Hamilton–Jacobi–Bellman equation and provide a suitable verification theorem...
Exploiting fine-grain parallelism in recursive LU factorization
Dongarra, Jack; Faverge, Mathieu; Ltaief, Hatem; Luszczek, Piotr R.
2012-01-01
is the panel factorization due to its memory-bound characteristic and the atomicity of selecting the appropriate pivots. We remedy this in our new approach to LU factorization of (narrow and tall) panel submatrices. We use a parallel fine-grained recursive
Pedestrian Path Prediction with Recursive Bayesian Filters: A Comparative Study
Schneider, N.; Gavrila, D.M.
2013-01-01
In the context of intelligent vehicles, we perform a comparative study on recursive Bayesian filters for pedestrian path prediction at short time horizons (< 2s). We consider Extended Kalman Filters (EKF) based on single dynamical models and Interacting Multiple Models (IMM) combining several such
A Recursive Semantics for Defeasible Reasoning
Pollock, John L.
One of the most striking characteristics of human beings is their ability to function successfully in complex environments about which they know very little. Reflect on how little you really know about all the individual matters of fact that characterize the world. What, other than vague generalizations, do you know about the apples on the trees of China, individual grains of sand, or even the residents of Cincinnati? But that does not prevent you from eating an apple while visiting China, lying on the beach in Hawaii, or giving a lecture in Cincinnati. Our ignorance of individual matters of fact is many orders of magnitude greater than our knowledge. And the situation does not improve when we turn to knowledge of general facts. Modern science apprises us of some generalizations, and our experience teaches us numerous higher-level although less precise general truths, but surely we are ignorant of most general truths.
Parallel Recursive State Compression for Free
Laarman, Alfons; van de Pol, Jan Cornelis; Weber, M.; Groce, Alex; Musuvathi, Madanlal
2011-01-01
State space exploration is a basic solution to many verification problems, but is limited by time and memory usage. Due to physical limits in modern CPUs, sequential exploration algorithms do not benefit automatically from the next generation of processors anymore, hence the need for multi-core
Çeliksular, M Cem; Saraçoğlu, Ayten; Yentür, Ercüment
2016-06-01
The effects of oral carbohydrate solutions, ingested 2 h prior to operation, on stress response were studied in patients undergoing general or epidural anaesthesia. The study was performed on 80 ASA I-II adult patients undergoing elective total hip replacement, which were randomized to four groups (n=20). Group G patients undergoing general anaesthesia fasted for 8 h preoperatively; Group GN patients undergoing general anaesthesia drank oral carbohydrate solutions preoperatively; Group E patients undergoing epidural anaesthesia fasted for 8 h and Group EN patients undergoing epidural anaesthesia drank oral carbohydrate solutions preoperatively. Groups GN and EN drank 800 mL of 12.5% oral carbohydrate solution at 24:00 preoperatively and 400 mL 2 h before the operation. Blood samples were taken for measurements of glucose, insulin, cortisol and IL-6 levels. The effect of preoperative oral carbohydrate ingestion on blood glucose levels was not significant. Insulin levels 24 h prior to surgery were similar; however, insulin levels measured just before surgery were 2-3 times higher in groups GN and EN than in groups G and E. Insulin levels at the 24(th) postoperative hour in epidural groups were increased compared to those at basal levels, although general anaesthesia groups showed a decrease. From these measurements, only the change in Group EN was statistically significant (poral carbohydrate nutrition did not reveal a significant effect on surgical stress response.
Wang, Xin; Chen, Yong; Cao, Jianli
2015-01-01
In this paper, we utilize generalized Darboux transformation to study higher-order rogue wave solutions of the three-wave resonant interaction equation, which describes the propagation and mixing of waves with different frequencies in weakly nonlinear dispersive media. A general Nth-order rogue wave solution with two characteristic velocities structural parameters and 3N independent parameters under a determined plane-wave background and a specific parameter condition is derived. As an application, we show that four fundamental rogue waves with fundamental, two kinds of line and quadrilateral patterns, or six fundamental rogue waves with fundamental, triangular, two kinds of quadrilateral and circular patterns can emerge in the second-order rogue waves. Moreover, several important wave characteristics including the maximum values, the corresponding coordinate positions of the humps, and the stability problem for some special higher-order rogue wave solutions such as the fundamental and quadrilateral cases are discussed. (paper)
New exact solutions to the generalized KdV equation with ...
is reduced to an ordinary differential equation with constant coefficients ... Application to generalized KdV equation with generalized evolution ..... [12] P F Byrd and M D Friedman, Handbook of elliptic integrals for engineers and physicists.
A Simple General Solution for Maximal Horizontal Range of Projectile Motion
Busic, Boris
2005-01-01
A convenient change of variables in the problem of maximizing the horizontal range of the projectile motion, with an arbitrary initial vertical position of the projectile, provides a simple, straightforward solution.
A generalized exp-function method for multiwave solutions of sine ...
With the development of soliton theory, finding multiwave solutions has ... transmission, self-transparency due to nonlinear effects of optical pulses, ..... Secondly, expanding each new dependent variable in infinite series of a formal expansion.
Zulfiqar Ali
2013-01-01
Full Text Available We find exact solutions of the Generalized Modified Boussinesq (GMB equation, the Kuromoto-Sivashinsky (KS equation the and, Camassa-Holm (CH equation by utilizing the double reduction theory related to conserved vectors. The fourth order GMB equation involves the arbitrary function and mixed derivative terms in highest derivative. The partial Noether’s approach yields seven conserved vectors for GMB equation and one conserved for vector KS equation. Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. The extra terms that constitute the trivial part of conserved vectors are adjusted and the resulting conserved vectors satisfy the divergence property. The double reduction theory yields two independent solutions and one reduction for GMB equation and one solution for KS equation. For CH equation two independent solutions are obtained elsewhere by double reduction theory with the help of conserved Vectors.
Variable depth recursion algorithm for leaf sequencing
Siochi, R. Alfredo C.
2007-01-01
The processes of extraction and sweep are basic segmentation steps that are used in leaf sequencing algorithms. A modified version of a commercial leaf sequencer changed the way that the extracts are selected and expanded the search space, but the modification maintained the basic search paradigm of evaluating multiple solutions, each one consisting of up to 12 extracts and a sweep sequence. While it generated the best solutions compared to other published algorithms, it used more computation time. A new, faster algorithm selects one extract at a time but calls itself as an evaluation function a user-specified number of times, after which it uses the bidirectional sweeping window algorithm as the final evaluation function. To achieve a performance comparable to that of the modified commercial leaf sequencer, 2-3 calls were needed, and in all test cases, there were only slight improvements beyond two calls. For the 13 clinical test maps, computation speeds improved by a factor between 12 and 43, depending on the constraints, namely the ability to interdigitate and the avoidance of the tongue-and-groove under dose. The new algorithm was compared to the original and modified versions of the commercial leaf sequencer. It was also compared to other published algorithms for 1400, random, 15x15, test maps with 3-16 intensity levels. In every single case the new algorithm provided the best solution
Markos, P; Schweitzer, L; Weyrauch, M
2004-01-01
In a recent publication, Kuzovkov et al (2002 J. Phys.: Condens. Matter. 14 13777) announced an analytical solution of the two-dimensional Anderson localization problem via the calculation of a generalized Lyapunov exponent using signal theory. Surprisingly, for certain energies and small disorder strength they observed delocalized states. We study the transmission properties of the same model using well-known transfer matrix methods. Our results disagree with the findings obtained using signal theory. We point to the possible origin of this discrepancy and comment on the general strategy of using a generalized Lyapunov exponent for studying Anderson localization. (comment)
Schilder, J.; Ellenbroek, M.; de Boer, A.
2017-12-01
In this work, the floating frame of reference formulation is used to create a flexible multibody model of slender offshore structures such as pipelines and risers. It is shown that due to the chain-like topology of the considered structures, the equation of motion can be expressed in terms of absolute interface coordinates. In the presented form, kinematic constraint equations are satisfied explicitly and the Lagrange multipliers are eliminated from the equations. Hence, the structures can be conveniently coupled to finite element or multibody models of for example seabed and vessel. The chain-like topology enables the efficient use of recursive solution procedures for both transient dynamic analysis and equilibrium analysis. For this, the transfer matrix method is used. In order to improve the convergence of the equilibrium analysis, the analytical solution of an ideal catenary is used as an initial configuration, reducing the number of required iterations.
A new recursion operator for Adler's equation in the Viallet form
Mikhailov, A.V.; Wang, J.P.
2011-01-01
For Adler's equation in the Viallet form and Yamilov's discretisation of the Krichever-Novikov equation we present new recursion and Hamiltonian operators. This new recursion operator and the recursion operator found in [A.V. Mikhailov, et al., Theor. Math. Phys. 167 (2011) 421, (arXiv:1004.5346)] satisfy the spectral curve associated with the equation. -- Highlights: → We present new recursion and Hamiltonian operators for the equation. → We establish the relation between this recursion operator and the known one. → The relation is given by the spectral curve associated with the equation.
Panov, E Yu
1999-01-01
We consider a hyperbolic system of conservation laws on the space of symmetric second-order matrices. The right-hand side of this system contains the functional calculus operator f-bar(U) generated in the general case only by a continuous scalar function f(u). For these systems we define and describe the set of singular entropies, introduce the concept of generalized entropy solutions of the corresponding Cauchy problem, and investigate the properties of generalized entropy solutions. We define the class of strong generalized entropy solutions, in which the Cauchy problem has precisely one solution. We suggest a condition on the initial data under which any generalized entropy solution is strong, which implies its uniqueness. Under this condition we establish that the 'vanishing viscosity' method converges. An example shows that in the general case there can be more than one generalized entropy solution
On а Recursive-Parallel Algorithm for Solving the Knapsack Problem
Vladimir V. Vasilchikov
2018-01-01
Full Text Available In this paper, we offer an efficient parallel algorithm for solving the NP-complete Knapsack Problem in its basic, so-called 0-1 variant. To find its exact solution, algorithms belonging to the category ”branch and bound methods” have long been used. To speed up the solving with varying degrees of efficiency, various options for parallelizing computations are also used. We propose here an algorithm for solving the problem, based on the paradigm of recursive-parallel computations. We consider it suited well for problems of this kind, when it is difficult to immediately break up the computations into a sufficient number of subtasks that are comparable in complexity, since they appear dynamically at run time. We used the RPM ParLib library, developed by the author, as the main tool to program the algorithm. This library allows us to develop effective applications for parallel computing on a local network in the .NET Framework. Such applications have the ability to generate parallel branches of computation directly during program execution and dynamically redistribute work between computing modules. Any language with support for the .NET Framework can be used as a programming language in conjunction with this library. For our experiments, we developed some C# applications using this library. The main purpose of these experiments was to study the acceleration achieved by recursive-parallel computing. A detailed description of the algorithm and its testing, as well as the results obtained, are also given in the paper.
Hernandez-Walls, R; Martín-Atienza, B; Salinas-Matus, M; Castillo, J
2017-01-01
When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations. (paper)
Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.
2017-11-01
When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.
Twenty Years of General Education in China: Progress, Problems, and Solutions
Wang, Hongcai; Xie, Debo
2018-01-01
General education is a subject with rich contents and that is highly contested in the field of higher education studies. It has been highly praised for its core concepts such as broad educational targets, liberating educational objectives, and balanced educational content. Looking back at the course of general education in China over the past 20…
The Role of General Physical Education in Solution of Health Problem of Russia’s Population
V.P. Lykyanenko
2012-06-01
Full Text Available The educational concept, worked out by the author rests on the ideas of fundamentalization of school physical educational process, basing on the unique general educational potential of this subject, acquiring the character of fundamental, backbone principle of general secondary education, reflecting its essence, goal and objectives in modern society with its core.
Nyasulu, Frazier; Stevanov, Kelly; Barlag, Rebecca
2010-01-01
Using a conductivity sensor, a temperature sensor, and a datalogger, fundamental factors that affect conductivity are explored. These factors are (i) concentration, (ii) temperature, (iii) ion charge, and (iv) size and or mass of anion. In addition, the conductivities of a number of other solutions are measured. This lab has been designed to…
Algebraic computability and enumeration models recursion theory and descriptive complexity
Nourani, Cyrus F
2016-01-01
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic type...
EEG and MEG source localization using recursively applied (RAP) MUSIC
Mosher, J.C. [Los Alamos National Lab., NM (United States); Leahy, R.M. [University of Southern California, Los Angeles, CA (United States). Signal and Image Processing Inst.
1996-12-31
The multiple signal characterization (MUSIC) algorithm locates multiple asynchronous dipolar sources from electroencephalography (EEG) and magnetoencephalography (MEG) data. A signal subspace is estimated from the data, then the algorithm scans a single dipole model through a three-dimensional head volume and computes projections onto this subspace. To locate the sources, the user must search the head volume for local peaks in the projection metric. Here we describe a novel extension of this approach which we refer to as RAP (Recursively APplied) MUSIC. This new procedure automatically extracts the locations of the sources through a recursive use of subspace projections, which uses the metric of principal correlations as a multidimensional form of correlation analysis between the model subspace and the data subspace. The dipolar orientations, a form of `diverse polarization,` are easily extracted using the associated principal vectors.
BPSK Receiver Based on Recursive Adaptive Filter with Remodulation
N. Milosevic
2011-12-01
Full Text Available This paper proposes a new binary phase shift keying (BPSK signal receiver intended for reception under conditions of significant carrier frequency offsets. The recursive adaptive filter with least mean squares (LMS adaptation is used. The proposed receiver has a constant, defining the balance between the recursive and the nonrecursive part of the filter, whose proper choice allows a simple construction of the receiver. The correct choice of this parameter could result in unitary length of the filter. The proposed receiver has performance very close to the performance of the BPSK receiver with perfect frequency synchronization, in a wide range of frequency offsets (plus/minus quarter of the signal bandwidth. The results obtained by the software simulation are confirmed by the experimental results measured on the receiver realized with the universal software radio peripheral (USRP, with the baseband signal processing at personal computer (PC.
Recursive Neural Networks in Quark/Gluon Tagging
CERN. Geneva
2018-01-01
Vidyo contribution Based on the natural tree-like structure of jet sequential clustering, the recursive neural networks (RecNNs) embed jet clustering history recursively as in natural language processing. We explore the performance of RecNN in quark/gluon discrimination. The results show that RecNNs work better than the baseline BDT by a few percent in gluon rejection at the working point of 50\\% quark acceptance. We also experimented on some relevant aspects which might influence the performance of networks. It shows that even only particle flow identification as input feature without any extra information on momentum or angular position is already giving a fairly good result, which indicates that most of the information for q/g discrimination is already included in the tree-structure itself.
Topological recursion for Gaussian means and cohomological field theories
Andersen, J. E.; Chekhov, L. O.; Norbury, P.; Penner, R. C.
2015-12-01
We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich-Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M g,s disc (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M g,1 for all g in three ways: using the refined Harer-Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly.
Study of recursive model for pole-zero cancellation circuit
Zhou Jianbin; Zhou Wei; Hong Xu; Hu Yunchuan; Wan Xinfeng; Du Xin; Wang Renbo
2014-01-01
The output of charge sensitive amplifier (CSA) is a negative exponential signal with long decay time which will result in undershoot after C-R differentiator. Pole-zero cancellation (PZC) circuit is often applied to eliminate undershoot in many radiation detectors. However, it is difficult to use a zero created by PZC circuit to cancel a pole in CSA output signal accurately because of the influences of electronic components inherent error and environmental factors. A novel recursive model for PZC circuit is presented based on Kirchhoff's Current Law (KCL) in this paper. The model is established by numerical differentiation algorithm between the input and the output signal. Some simulation experiments for a negative exponential signal are carried out using Visual Basic for Application (VBA) program and a real x-ray signal is also tested. Simulated results show that the recursive model can reduce the time constant of input signal and eliminate undershoot. (authors)
Functional Dual Adaptive Control with Recursive Gaussian Process Model
Prüher, Jakub; Král, Ladislav
2015-01-01
The paper deals with dual adaptive control problem, where the functional uncertainties in the system description are modelled by a non-parametric Gaussian process regression model. Current approaches to adaptive control based on Gaussian process models are severely limited in their practical applicability, because the model is re-adjusted using all the currently available data, which keeps growing with every time step. We propose the use of recursive Gaussian process regression algorithm for significant reduction in computational requirements, thus bringing the Gaussian process-based adaptive controllers closer to their practical applicability. In this work, we design a bi-criterial dual controller based on recursive Gaussian process model for discrete-time stochastic dynamic systems given in an affine-in-control form. Using Monte Carlo simulations, we show that the proposed controller achieves comparable performance with the full Gaussian process-based controller in terms of control quality while keeping the computational demands bounded. (paper)
Exact solution of an electroosmotic flow for generalized Burgers fluid in cylindrical domain
Masood Khan
Full Text Available The present paper reports a theoretical study of the dynamics of an electroosmotic flow (EOF in cylindrical domain. The Cauchy momentum equation is first simplified by incorporating the electrostatic body force in the electric double layer and the generalized Burgers fluid constitutive model. The electric potential distribution is given by the linearized Poisson–Boltzmann equation. After solving the linearized Poisson–Boltzmann equation, the Cauchy momentum equation with electrostatic body force is solved analytically by using the temporal Fourier and finite Hankel transforms. The effects of important involved parameters are examined and presented graphically. The results obtained reveal that the magnitude of velocity increases with increase of the Debye–Huckel and electrokinetic parameters. Further, it is shown that the results presented for generalized Burgers fluid are quite general so that results for the Burgers, Oldroyd-B, Maxwell and Newtonian fluids can be obtained as limiting cases. Keywords: Generalized Burgers fluid, Electroosmotic flow, Fourier and Hankel transform
Classification and Recursion Operators of Dark Burgers' Equation
Chen, Mei-Dan; Li, Biao
2018-01-01
With the help of symbolic computation, two types of complete scalar classification for dark Burgers' equations are derived by requiring the existence of higher order differential polynomial symmetries. There are some free parameters for every class of dark Burgers' systems; so some special equations including symmetry equation and dual symmetry equation are obtained by selecting the free parameter. Furthermore, two kinds of recursion operators for these dark Burgers' equations are constructed by two direct assumption methods.
A RECURSIVE ALGORITHM SUITABLE FOR REAL-TIME MEASUREMENT
Giovanni Bucci
1995-12-01
Full Text Available This paper deals with a recursive algorithm suitable for realtime measurement applications, based on an indirect technique, useful in those applications where the required quantities cannot be measured in a straightforward way. To cope with time constraints a parallel formulation of it, suitable to be implemented on multiprocessor systems, is presented. The adopted concurrent implementation is based on factorization techniques. Some experimental results related to the application of the system for carrying out measurements on synchronous motors are included.
Model-based Recursive Partitioning for Subgroup Analyses
Seibold, Heidi; Zeileis, Achim; Hothorn, Torsten
2016-01-01
The identification of patient subgroups with differential treatment effects is the first step towards individualised treatments. A current draft guideline by the EMA discusses potentials and problems in subgroup analyses and formulated challenges to the development of appropriate statistical procedures for the data-driven identification of patient subgroups. We introduce model-based recursive partitioning as a procedure for the automated detection of patient subgroups that are identifiable by...
A Decidable Recursive Logic for Weighted Transition Systems
Xue, Bingtian; Larsen, Kim Guldstrand; Mardare, Radu Iulian
2014-01-01
In this paper we develop and study the Recursive Weighted Logic (RWL), a multi-modal logic that expresses qualitative and quantitative properties of labelled weighted transition systems (LWSs). LWSs are transition systems labelled with actions and real-valued quantities representing the costs of ...... extends previous results that we have demonstrated for a similar but much more restrictive logic that can only use one variable for each type of resource to encode logical properties....
Exact, E = 0, classical and quantum solutions for general power-law oscillators
Nieto, M.M.; Daboul, J.
1994-01-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -γ/r ν , γ > 0 and -∞ 0 (t))] 1/μ , with μ = ν/2 - 1 ≠ 0. For ν > 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when ν > 2 the solutions are normalizable (bound), as in the classical case. Also, there are normalizable discrete, yet unbound, state which correspond to unbound classical particles which reach infinity in a finite time. These and other interesting comparisons to the classical system will be discussed
On the Exact Solution Explaining the Accelerate Expanding Universe According to General Relativity
Rabounski D.
2012-04-01
Full Text Available A new method of calculation is applied to the frequency of a photon according to the tra- velled distance. It consists in solving the scalar geodesic equation (equation of energy of the photon, and manifests gravitation, non-holonomity, and deformation of space as the intrinsic geometric factors affecting the photon’s frequency. The solution obtained in the expanding space of Friedmann’s metric manifests the exponential cosmological redshift: its magnitude increases, exponentially, with distance. This explains the acce- lerate expansion of the Universe registered recently by the astronomers. According to the obtained solution, the redshift reaches the ultimately high value z = e π − 1 = 22 . 14 at the event horizon.
C. Avramescu
2003-07-01
Full Text Available Let $f:\\mathbb{R}\\times \\mathbb{R}^{N}\\rightarrow \\mathbb{R}^{N}$ be a continuous function and let $h:\\mathbb{R}\\rightarrow \\mathbb{R}$ be a continuous and strictly positive function. A sufficient condition such that the equation $\\dot{x}=f\\left( t,x\\right $ admits solutions $x:\\mathbb{R}\\rightarrow \\mathbb{R}^{N}$ satisfying the inequality $\\left| x\\left( t\\right \\right| \\leq k\\cdot h\\left( t\\right ,$ $t\\in \\mathbb{R},$ $k>0$, where $\\left| \\cdot \\right| $ is the euclidean norm in $\\mathbb{R}^{N},$ is given. The proof of this result is based on the use of a special function of Lyapunov type, which is often called guiding function. In the particular case $h\\equiv 1$, one obtains known results regarding the existence of bounded solutions.
Yu, Shengqi
2018-05-01
This work studies a generalized μ-type integrable equation with both quadratic and cubic nonlinearities; the μ-Camassa-Holm and modified μ-Camassa-Holm equations are members of this family of equations. It has been shown that the Cauchy problem for this generalized μ-Camassa-Holm integrable equation is locally well-posed for initial data u0 ∈ Hs, s > 5/2. In this work, we further investigate the continuity properties to this equation. It is proved in this work that the data-to-solution map of the proposed equation is not uniformly continuous. It is also found that the solution map is Hölder continuous in the Hr-topology when 0 ≤ r < s with Hölder exponent α depending on both s and r.
General solution of the aerosol dynamic equation: growth and diffusion processes
Elgarayhi, A.; Elhanbaly, A.
2004-01-01
The dispersion of aerosol particles in a fluid media is studied considering the main mechanism for condensation and diffusion. This has been done when the technique of Lie is used for solving the aerosol dynamic equation. This method is very useful in sense that it reduces the partial differential equation to some ordinary differential equations. So, different classes of similarity solutions have been obtained. The quantity of well-defined physical interest is the mean particle volume has been calculated
Kiknadze, N.A.; Khelashvili, A.A.
1990-01-01
The problem on stability of classical soliton solutions is studied from the unique point of view: the Legendre condition - necessary condition of existence of weak local minimum for energy functional (term soliton is used here in the wide sense) is used. Limits to parameters of the model Lagrangians are obtained; it is shown that there is no soliton stabilization in some of them despite the phenomenological achievements. The Jacoby sufficient condition is discussed
Complete factorisation and analytic solutions of generalized Lotka-Volterra equations
Brenig, L.
1988-11-01
It is shown that many systems of nonlinear differential equations of interest in various fields are naturally imbedded in a new family of differential equations. This family is invariant under nonlinear transformations based on the concept of matrix power of a vector. Each equation belonging to that family can be brought into a factorized canonical form for which integrable cases can be easily identified and solutions can be found by quadratures.
Bing, Xue; Yicai, Ji
2018-06-01
In order to understand directly and analyze accurately the detected magnetotelluric (MT) data on anisotropic infinite faults, two-dimensional partial differential equations of MT fields are used to establish a model of anisotropic infinite faults using the Fourier transform method. A multi-fault model is developed to expand the one-fault model. The transverse electric mode and transverse magnetic mode analytic solutions are derived using two-infinite-fault models. The infinite integral terms of the quasi-analytic solutions are discussed. The dual-fault model is computed using the finite element method to verify the correctness of the solutions. The MT responses of isotropic and anisotropic media are calculated to analyze the response functions by different anisotropic conductivity structures. The thickness and conductivity of the media, influencing MT responses, are discussed. The analytic principles are also given. The analysis results are significant to how MT responses are perceived and to the data interpretation of the complex anisotropic infinite faults.
Suheel Abdullah Malik
Full Text Available In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE through substitution is converted into a nonlinear ordinary differential equation (NODE. The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM, homotopy perturbation method (HPM, and optimal homotopy asymptotic method (OHAM, show that the suggested scheme is fairly accurate and viable for solving such problems.
Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul
2015-01-01
In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.
Recursion Of Binary Space As A Foundation Of Repeatable Programs
Jeremy Horne
2006-10-01
Full Text Available Every computation, including recursion, is based on natural philosophy. Our world may be expressed in terms of a binary logical space that contains functions that act simultaneously as objects and processes (operands and operators. This paper presents an outline of the results of research about that space and suggests routes for further inquiry. Binary logical space is generated sequentially from an origin in a standard coordinate system. At least one method exists to show that each of the resulting 16 functions repeats itself by repeatedly forward-feeding outputs of a function operating over two others as new operands of the original function until the original function appears as an output, thus behaving as an apparent homeostatic automaton. As any space of any dimension is composed of one or more of these functions, so the space is recursive, as well. Semantics gives meaning to recursive structures, computer programs and fundamental constituents of our universe being two examples. Such thoughts open inquiry into larger philosophical issues as free will and determinism.
Koeppel, T.; Harvey, M.
1984-06-01
A new numerical method is applied to solving the equations of motion of the Friedberg-Lee Soliton model for both ground and spherically symmetric excited states. General results have been obtained over a wide range of parameters. Critical coupling constants and critical particle numbers have been determined below which soliton solutions cease to exist. The static properties of the proton are considered to show that as presently formulated the model fails to fit all experimental data for any set of parameters
Biswas, Anjan
2009-01-01
In this Letter, the 1-soliton solution of the Zakharov-Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.
Dauda GuliburYAKUBU
2012-12-01
Full Text Available Accurate solutions to initial value systems of ordinary differential equations may be approximated efficiently by Runge-Kutta methods or linear multistep methods. Each of these has limitations of one sort or another. In this paper we consider, as a middle ground, the derivation of continuous general linear methods for solution of stiff systems of initial value problems in ordinary differential equations. These methods are designed to combine the advantages of both Runge-Kutta and linear multistep methods. Particularly, methods possessing the property of A-stability are identified as promising methods within this large class of general linear methods. We show that the continuous general linear methods are self-starting and have more ability to solve the stiff systems of ordinary differential equations, than the discrete ones. The initial value systems of ordinary differential equations are solved, for instance, without looking for any other method to start the integration process. This desirable feature of the proposed approach leads to obtaining very high accuracy of the solution of the given problem. Illustrative examples are given to demonstrate the novelty and reliability of the methods.
Badia, Santiago; Martín, Alberto F.; Planas, Ramon
2014-10-01
The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 × 2 block matrix, and consider an LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknowns, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.
From twistor string theory to recursion relations
Spradlin, Marcus; Volovich, Anastasia
2009-01-01
Witten's twistor string theory gives rise to an enigmatic formula 1 known as the 'connected prescription' for tree-level Yang-Mills scattering amplitudes. We derive a link representation for the connected prescription by Fourier transforming it to mixed coordinates in terms of both twistor and dual twistor variables. We show that it can be related to other representations of amplitudes by applying the global residue theorem to deform the contour of integration. For six and seven particles we demonstrate explicitly that certain contour deformations rewrite the connected prescription as the Britto-Cachazo-Feng-Witten representation, thereby establishing a concrete link between Witten's twistor string theory and the dual formulation for the S matrix of the N=4 SYM recently proposed by Arkani-Hamed et al. Other choices of integration contour also give rise to 'intermediate prescriptions'. We expect a similar though more intricate structure for more general amplitudes.
Recursive structures in the multispecies TASEP
Arita, Chikashi; Ayyer, Arvind; Mallick, Kirone; Prolhac, Sylvain
2011-01-01
We consider a multispecies generalization of the totally asymmetric simple exclusion process (TASEP) with the simple hopping rule: for the α and βth-class particles (α < β), the transition αβ → βα occurs with a rate independent from the values α and β. Ferrari and Martin (2007 Ann. Prob. 35 807) obtained the stationary state of this model thanks to a combinatorial algorithm, which was subsequently interpreted as a matrix product representation by Evans et al (2009 J. Stat. Phys. 135 217). This 'matrix ansatz' shows that the stationary state of the multispecies TASEP with N classes of particles (N-TASEP) can be constructed algebraically by the action of an operator on the (N - 1)-TASEP stationary state. Besides, Arita et al (2009 J. Phys. A. Math Theor. 45 345002) analyzed the spectral structure of the Markov matrix: they showed that the set of eigenvalues of the N-TASEP contains those of the (N - 1)-TASEP and that the various spectral inclusions can be encoded in a hierarchical set-theoretic structure known as the Hasse diagram. Inspired by these works, we define nontrivial operators that allow us to construct eigenvectors of the N-TASEP by lifting the eigenvectors of the (N - 1)-TASEP. This goal is achieved by generalizing the matrix product representation and the Ferrari-Martin algorithm. In particular, we show that the matrix ansatz is not only a convenient tool to write the stationary state but in fact intertwines Markov matrices of different values of N.
Recursive structures in the multispecies TASEP
Arita, Chikashi [Faculty of Mathematics, Kyushu University, Fukuoka 819-0395 (Japan); Ayyer, Arvind [University of California Davis, One Shields Avenue Davis, CA 95616 (United States); Mallick, Kirone [Institut de Physique Theorique CEA, F-91191 Gif-sur-Yvette (France); Prolhac, Sylvain, E-mail: arita@math.kyushu-u.ac.jp, E-mail: ayyer@math.ucdavis.edu, E-mail: kirone.mallick@cea.fr, E-mail: prolhac@ma.tum.de [Zentrum Mathematik, Technische Universitaet Muenchen (Germany)
2011-08-19
We consider a multispecies generalization of the totally asymmetric simple exclusion process (TASEP) with the simple hopping rule: for the {alpha} and {beta}th-class particles ({alpha} < {beta}), the transition {alpha}{beta} {yields} {beta}{alpha} occurs with a rate independent from the values {alpha} and {beta}. Ferrari and Martin (2007 Ann. Prob. 35 807) obtained the stationary state of this model thanks to a combinatorial algorithm, which was subsequently interpreted as a matrix product representation by Evans et al (2009 J. Stat. Phys. 135 217). This 'matrix ansatz' shows that the stationary state of the multispecies TASEP with N classes of particles (N-TASEP) can be constructed algebraically by the action of an operator on the (N - 1)-TASEP stationary state. Besides, Arita et al (2009 J. Phys. A. Math Theor. 45 345002) analyzed the spectral structure of the Markov matrix: they showed that the set of eigenvalues of the N-TASEP contains those of the (N - 1)-TASEP and that the various spectral inclusions can be encoded in a hierarchical set-theoretic structure known as the Hasse diagram. Inspired by these works, we define nontrivial operators that allow us to construct eigenvectors of the N-TASEP by lifting the eigenvectors of the (N - 1)-TASEP. This goal is achieved by generalizing the matrix product representation and the Ferrari-Martin algorithm. In particular, we show that the matrix ansatz is not only a convenient tool to write the stationary state but in fact intertwines Markov matrices of different values of N.
Exact solution of the generalized time-dependent Jaynes-Cummings Hamiltonian
Gruver, J.L.; Aliaga, J.; Cerdeira, H.A.; Proto, A.N.
1993-04-01
A time-dependent generalization of the Jaynes-Cummings Hamiltonian is studied using the maximum entropy formalism. The approach, related to a semi-Lie algebra, allows to find three different sets of physical relevant operators which describe the dynamics of the system for any temporal dependence. It is shown how the initial conditions of the operators are determined via the maximum entropy principle density operator, where the inclusion of the temperature turns the description of the problem into a thermodynamical one. The generalized time-independent Jaynes-Cummings Hamiltonian is exactly solved as a particular example. (author). 14 refs
Solution of the generalized Emden-Fowler equations by the hybrid functions method
Tabrizidooz, H R; Marzban, H R; Razzaghi, M
2009-01-01
In this paper, we present a numerical algorithm for solving the generalized Emden-Fowler equations, which have many applications in mathematical physics and astrophysics. The method is based on hybrid functions approximations. The properties of hybrid functions, which consist of block-pulse functions and Lagrange interpolating polynomials, are presented. These properties are then utilized to reduce the computation of the generalized Emden-Fowler equations to a system of nonlinear equations. The method is easy to implement and yields very accurate results.
Generalized Analytical Treatment Of The Source Strength In The Solution Of The Diffusion Equation
Essa, Kh.S.M.; EI-Otaify, M.S.
2007-01-01
The source release strength (which is an integral part of the mathematical formulation of the diffusion equation) together with the boundary conditions leads to three different forms of the diffusion equation. The obtained forms have been solved analytically under different boundary conditions, by using transformation of axis, cosine, and Fourier transformation. Three equivalent alternative mathematical formulations of the problem have been obtained. The estimated solution of the concentrations at the ground source has been used for comparison with observed concentrations data for SF 6 tracer experiments in low wind and unstable conditions at lIT Delhi sports ground. A good agreement between estimated and observed concentrations is found
Gang-Ling Hou
2018-04-01
Full Text Available This article concerns the fractional Schrodinger type equations $$ (-\\Delta^\\alpha u+V(xu =f(x,u \\quad\\text{in } \\mathbb{R}^N, $$ where $N\\geq 2$, $\\alpha\\in(0,1$, $(-\\Delta^\\alpha$ stands for the fractional Laplacian, $V$ is a positive continuous potential, $f\\in C(\\mathbb{R}^N\\times\\mathbb{R},\\mathbb{R}$. We establish criteria that guarantee the existence of infinitely many solutions by using the genus properties in critical point theory.
Solution of the General Helmholtz Equation Starting from Laplace’s Equation
2002-11-01
infinity for the two dimensional case. For the 3D the general form case, this term does not exist, as the potential at infinity is zero. Hence the Green’s...companies. She has assisted the Comisi6n the Living System Laboratory, Interministerial de Ciencia y Tecnologia (National LG Electronics, From 1998 to 2000
Exact solutions of the generalized Lane–Emden equations of the ...
the mutual attraction of its molecules and subject to the classical laws of thermodynamics. This equation was proposed ... was investigated for first integrals by Leach [31]. Moreover, transformation properties of a more general Emden–Fowler equation were considered in Mellin et al [5]. A review paper by Wong [32] contains ...
Akkerman, Erik M.
2010-01-01
Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional
Expanding the class of general exact solutions for interacting two field kinks
Souza Dutra, A. de; Amaro de Faria, A.C.
2006-01-01
In this work we extend the range of applicability of a method recently introduced where coupled first-order nonlinear equations can be put into a linear form, and consequently be solved completely. Some general consequences of the present extension are then commented
Panov, E Yu
2000-01-01
Many-dimensional non-strictly hyperbolic systems of conservation laws with a radially degenerate flux function are considered. For such systems the set of entropies is defined and described, the concept of generalized entropy solution of the Cauchy problem is introduced, and the properties of generalized entropy solutions are studied. The class of strong generalized entropy solutions is distinguished, in which the Cauchy problem in question is uniquely soluble. A condition on the initial data is described that ensures that the generalized entropy solution is strong and therefore unique. Under this condition the convergence of the 'vanishing viscosity' method is established. An example presented in the paper shows that a generalized entropy solution is not necessarily unique in the general case
Rogério Luizari Guedes
2015-08-01
Full Text Available The measurement of serum parameters during general anesthesia procedures are subject to variations due to differences in protocol, splenic storage, and by the instituted fluid therapy. The aim of this study was to assess the hematocrit changes promoted by controlled fluid therapy and general anesthesia. Six mongrel female dogs underwent an anesthetic protocol with acepromazine (0.03 mg kg-1 and tramadol (5 mg kg-1 for premedication, induction with propofol (3 mg kg-1, and maintained with isoflurane and mechanical ventilation for 120 minutes. After induction, they were infused with 10 ml kg hr-1 of Ringer’s lactate solution. Hematocrit measurements were performed from the start until 72 hours from anesthesia and evaluated statistically to check if there were significant changes over time. The fluid therapy, the acepromazine and propofol in the anesthetic protocol promotes a significant reduction of hematocrit up to four hours after general anesthesia.
General Exact Solution to the Problem of the Probability Density for Sums of Random Variables
Tribelsky, Michael I.
2002-07-01
The exact explicit expression for the probability density pN(x) for a sum of N random, arbitrary correlated summands is obtained. The expression is valid for any number N and any distribution of the random summands. Most attention is paid to application of the developed approach to the case of independent and identically distributed summands. The obtained results reproduce all known exact solutions valid for the, so called, stable distributions of the summands. It is also shown that if the distribution is not stable, the profile of pN(x) may be divided into three parts, namely a core (small x), a tail (large x), and a crossover from the core to the tail (moderate x). The quantitative description of all three parts as well as that for the entire profile is obtained. A number of particular examples are considered in detail.
A case of generalized argyria after ingestion of colloidal silver solution.
Kim, Yangho; Suh, Ho Seok; Cha, Hee Jeong; Kim, Suk Hwan; Jeong, Kyoung Sook; Kim, Dong Hoon
2009-03-01
A 58-year-old woman was referred to our hospital due to progressive skin darkening, which began 5 months previously. The patient had strikingly diffuse blue-gray discoloration of the skin, most prominent in sun-exposed areas, especially her face and hands. The oral mucosa, tongue, gums, eye conjunctiva, ears, nail beds, and trunk were also involved. Bluish-gray discoloration of all nails was aggravated by cold weather. She had ingested 1 L of colloidal silver solution daily for approximately 16 months as a traditional remedy. Her serum silver concentration was 381 ng/ml which was a very high (reference level: silver and sulfur in the dense black deposits. The ingestion of colloidal silver appears to be an increasing practice among patients using alternative health practices. All silver-containing products including colloidal silver should be labeled with a clear warning to prevent argyria, especially in alternative health practices.
Ben Ambridge
Full Text Available Participants aged 5;2-6;8, 9;2-10;6 and 18;1-22;2 (72 at each age rated verb argument structure overgeneralization errors (e.g., *Daddy giggled the baby using a five-point scale. The study was designed to investigate the feasibility of two proposed construction-general solutions to the question of how children retreat from, or avoid, such errors. No support was found for the prediction of the preemption hypothesis that the greater the frequency of the verb in the single most nearly synonymous construction (for this example, the periphrastic causative; e.g., Daddy made the baby giggle, the lower the acceptability of the error. Support was found, however, for the prediction of the entrenchment hypothesis that the greater the overall frequency of the verb, regardless of construction, the lower the acceptability of the error, at least for the two older groups. Thus while entrenchment appears to be a robust solution to the problem of the retreat from error, and one that generalizes across different error types, we did not find evidence that this is the case for preemption. The implication is that the solution to the retreat from error lies not with specialized mechanisms, but rather in a probabilistic process of construction competition.
Anti-Authoritarian Metrics: Recursivity as a strategy for post-capitalism
David Adam Banks
2016-12-01
Full Text Available This essay proposes that those seeking to build counter-power institutions and communities learn to think in terms of what I call “recursivity.” Recursivity is an anti-authoritarian metric that helps bring about a sensitivity to feedback loops at multiple levels of organization. I begin by describing how technological systems and the socio-economic order co-constitute one-another around efficiency metrics. I then go on to define recursivity as social conditions that contain within them all of the parts and practices for their maturation and expansion, and show how organizations that demonstrate recursivity, like the historical English commons, have been marginalized or destroyed all together. Finally, I show how the ownership of property is inherently antithetical to the closed loops of recursivity. All of this is bookended by a study of urban planning’s recursive beginnings.
Li, Mu; Wang, Weiyu; Yin, Panchao
2018-05-02
Herein, we reported a general protocol for an ab initio modeling approach to deduce structure information of polyoxometalates (POMs) in solutions from scattering data collected by the small-angle X-ray scattering (SAXS) technique. To validate the protocol, the morphologies of a serious of known POMs in either aqueous or organic solvents were analyzed. The obtained particle morphologies were compared and confirmed with previous reported crystal structures. To extend the feasibility of the protocol to an unknown system of aqueous solutions of Na 2 MoO 4 with the pH ranging from -1 to 8.35, the formation of {Mo 36 } clusters was probed, identified, and confirmed by SAXS. The approach was further optimized with a multi-processing capability to achieve fast analysis of experimental data, thereby, facilitating in situ studies of formations of POMs in solutions. The advantage of this approach is to generate intuitive 3D models of POMs in solutions without confining information such as symmetries and possible sizes. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Iterative approximation of a solution of a general variational-like inclusion in Banach spaces
Chidume, C.E.; Kazmi, K.R.; Zegeye, H.
2002-07-01
In this paper, we introduce a class of η-accretive mappings in a real Banach space, and show that the η-proximal point mapping for η-m-accretive mapping is Lipschitz continuous. Further we develop an iterative algorithm for a class of general variational-like inclusions involving η-accretive mappings in real Banach space, and discuss its convergence criteria. The class of η-accretive mappings includes several important classes of operators that have been studied by various authors. (author)
Sweilam, N. H.; Abou Hasan, M. M.
2017-05-01
In this paper, the weighted-average non-standard finite-difference (WANSFD) method is used to study numerically the general time-fractional nonlinear, one-dimensional problem of thermoelasticity. This model contains the standard system arising in thermoelasticity as a special case. The stability of the proposed method is analyzed by a procedure akin to the standard John von Neumann technique. Moreover, the accuracy of the proposed scheme is proved. Numerical results are presented graphically, which reveal that the WANSFD method is easy to implement, effective and convenient for solving the proposed system. The proposed method could also be easily extended to solve other systems of fractional partial differential equations.
A generalization of the quantum Rabi model: exact solution and spectral structure
Eckle, Hans-Peter; Johannesson, Henrik
2017-01-01
We consider a generalization of the quantum Rabi model where the two-level system and the single-mode cavity oscillator are coupled by an additional Stark-like term. By adapting a method recently introduced by Braak (2011 Phys. Rev. Lett . 107 100401), we solve the model exactly. The low-lying spectrum in the experimentally relevant ultrastrong and deep strong regimes of the Rabi coupling is found to exhibit two striking features absent from the original quantum Rabi model: avoided level crossings for states of the same parity and an anomalously rapid onset of two-fold near-degenerate levels as the Rabi coupling increases. (paper)
Global solutions in lower order Sobolev spaces for the generalized Boussinesq equation
Luiz G. Farah
2012-03-01
Full Text Available We show that the Cauchy problem for the defocusing generalized Boussinesq equation $$ u_{tt}-u_{xx}+u_{xxxx}-(|u|^{2k}u_{xx}=0, quad kgeq 1, $$ on the real line is globally well-posed in $H^s(mathbb{R}$ with s>1-(1/(3k. To do this, we use the I-method, introduced by Colliander, Keel, Staffilani, Takaoka and Tao [8,9], to define a modification of the energy functional that is almost conserved in time. Our result extends a previous result obtained by Farah and Linares [16] for the case k=1.
General solution of an exact correlation function factorization in conformal field theory
Simmons, Jacob J H; Kleban, Peter
2009-01-01
The correlation function factorization with K a boundary operator product expansion coefficient, is known to hold for certain scaling operators at the two-dimensional percolation point and in a few other cases. Here the correlation functions are evaluated in the upper half-plane (or any conformally equivalent region) with x 1 and x 2 arbitrary points on the real axis, and z an arbitrary point in the interior. This type of result is of interest because it is both exact and universal, relates higher-order correlation functions to lower-order ones and has a simple interpretation in terms of cluster or loop probabilities in several statistical models. This motivated us to use the techniques of conformal field theory to determine the general conditions for its validity. Here, we discover that either (see display) factorizes in this way for any central charge c, generalizing previous results. In particular, the factorization holds for either FK (Fortuin–Kasteleyn) or spin clusters in the Q-state Potts models; it also applies to either the dense or dilute phases of the O(n) loop models. Further, only one other non-trivial set of highest-weight operators (in an irreducible Verma module) factorizes in this way. In this case the operators have negative dimension (for c<1) and do not seem to have a physical realization
Colaiori, Francesca; Castellano, Claudio; Cuskley, Christine F.; Loreto, Vittorio; Pugliese, Martina; Tria, Francesca
2015-01-01
Empirical evidence shows that the rate of irregular usage of English verbs exhibits discontinuity as a function of their frequency: the most frequent verbs tend to be totally irregular. We aim to qualitatively understand the origin of this feature by studying simple agent-based models of language dynamics, where each agent adopts an inflectional state for a verb and may change it upon interaction with other agents. At the same time, agents are replaced at some rate by new agents adopting the regular form. In models with only two inflectional states (regular and irregular), we observe that either all verbs regularize irrespective of their frequency, or a continuous transition occurs between a low-frequency state, where the lemma becomes fully regular, and a high-frequency one, where both forms coexist. Introducing a third (mixed) state, wherein agents may use either form, we find that a third, qualitatively different behavior may emerge, namely, a discontinuous transition in frequency. We introduce and solve analytically a very general class of three-state models that allows us to fully understand these behaviors in a unified framework. Realistic sets of interaction rules, including the well-known naming game (NG) model, result in a discontinuous transition, in agreement with recent empirical findings. We also point out that the distinction between speaker and hearer in the interaction has no effect on the collective behavior. The results for the general three-state model, although discussed in terms of language dynamics, are widely applicable.
Generalized solution of design optimization and failure analysis of composite drive shaft
Kollipalli, K.; Shivaramakrishna, K.V.S.; Prabhakaran, R.T.D. [Birla Institute of Technology and Science, Goa (India)
2012-07-01
Composites have an edge over conventional metals like steel and aluminum due to higher stiffness-to-weight ratio and strength-to-weight ratio. Due to these advantages, composites can bring out a revolutionary change in materials used in automotive engineering, as weight savings has positive impacts on other attributes like fuel economy and possible noise, vibration and harshness (NVH). In this paper, the drive line system of an automotive system is targeted for use of composites by keeping constraints in view such as such as torque transmission, torsional buckling load and fundamental natural frequency. Composite drive shafts made of three different composites ('HM Carbon/HS Carbon/E-glass'-epoxy) was modeled using Catia V5R16 CPD workbench and a finite element analysis with boundary conditions, fiber orientation and stacking sequence was performed using ANSYS Composite module. Results obtained were compared to theoretical results and were found to be accurate and in the limits. This paper also speaks on drive shaft modeling and analysis generalization i.e., changes in stacking sequence in the future can be incorporated directly into ANSYS model without modeling it again in Catia. Hence the base model and analysis method made up in this analysis generalization facilitated by CAD/CAE can be used to carry out any composite shaft design optimization process. (Author)
Lipparini, Filippo; Scalmani, Giovanni; Frisch, Michael J.; Lagardère, Louis; Stamm, Benjamin; Cancès, Eric; Maday, Yvon; Piquemal, Jean-Philip; Mennucci, Benedetta
2014-01-01
We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute
Lipparini, Filippo, E-mail: flippari@uni-mainz.de [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris (France); Sorbonne Universités, UPMC Univ. Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris (France); Sorbonne Universités, UPMC Univ. Paris 06, Institut du Calcul et de la Simulation, F-75005 Paris (France); Scalmani, Giovanni; Frisch, Michael J. [Gaussian, Inc., 340 Quinnipiac St. Bldg. 40, Wallingford, Connecticut 06492 (United States); Lagardère, Louis [Sorbonne Universités, UPMC Univ. Paris 06, Institut du Calcul et de la Simulation, F-75005 Paris (France); Stamm, Benjamin [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris (France); CNRS, UMR 7598 and 7616, F-75005 Paris (France); Cancès, Eric [Université Paris-Est, CERMICS, Ecole des Ponts and INRIA, 6 and 8 avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2 (France); Maday, Yvon [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris (France); Institut Universitaire de France, Paris, France and Division of Applied Maths, Brown University, Providence, Rhode Island 02912 (United States); Piquemal, Jean-Philip [Sorbonne Universités, UPMC Univ. Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris (France); CNRS, UMR 7598 and 7616, F-75005 Paris (France); Mennucci, Benedetta [Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Via Risorgimento 35, 56126 Pisa (Italy)
2014-11-14
We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.
On the asymptotic form of the recursion method basis vectors for periodic Hamiltonians
O'Reilly, E.P.; Weaire, D.
1984-01-01
The authors present the first detailed study of the recursion method basis vectors for the case of a periodic Hamiltonian. In the examples chosen, the probability density scales linearly with n as n → infinity, whenever the local density of states is bounded. Whenever it is unbounded and the recursion coefficients diverge, different scaling behaviour is found. These findings are explained and a scaling relationship between the asymptotic forms of the recursion coefficients and basis vectors is proposed. (author)
Kuhlmann, Arne; Herd, Daniel; Röβler, Benjamin; Gallmann, Eva; Jungbluth, Thomas
In pig production software and electronic systems are widely used for process control and management. Unfortunately most devices on farms are proprietary solutions and autonomically working. To unify data communication of devices in agricultural husbandry, the international standard ISOagriNET (ISO 17532:2007) was developed. It defines data formats and exchange protocols, to link up devices like climate controls, feeding systems and sensors, but also management software. The aim of the research project, "Information and Data Collection in Livestock Systems" is to develop an ISOagriNET compliant IT system, a so called Farming Cell. It integrates all electronic components to acquire the available data and information for pig fattening. That way, an additional benefit to humans, animals and the environment regarding process control and documentation, can be generated. Developing the Farming Cell is very complex; in detail it is very difficult and long-winded to integrate hardware and software by various vendors into an ISOagriNET compliant IT system. This ISOagriNET prototype shows as a test environment the potential of this new standard.
Lacey, E [Commonwealth Scientific and Industrial Research Organization, Glebe, NSW (Australia). Div. of Animal Health, McMaster Lab.; Dawson, M [Sydney Univ. (Australia). Dept. of Pharmacy; Long, M A; Than, C [New South Wales Univ., Kensington (Australia). School of Chemistry
1989-12-01
Benzimidazole carbamates (BZCs) act as inhibitors of the tubulin-microtubule equilibria in eukaryotic organisms. Recently drug resistance to this class of compounds in helminth parasites has been shown to be due to a reduced ability of resistant tubulin to bind BZCs. In order to quantitate the nature of the tubulin-BZC interaction a general method for the specific tritium labelling of BZCs has been developed. The BZCs: mebendazole, oxfendazole, parbendazole, oxibendazole, albendazole and fenbendazole were labelled by catalytic exchange using palladium on calcium carbonate in pure dioxane at 60{sup 0}C under tritium gas. The position of label incorporation for tritiated albendazole was determined by tritium-NMR as the 4-position of benzimadazole nucleus. The yields for individual BZCs varied from 8 to 68% for a range of specific activity of 0.44 to 13.4 Ci/mmole. (author).
Lacey, E.; Dawson, M.; Long, M.A.; Than, C.
1989-01-01
Benzimidazole carbamates (BZCs) act as inhibitors of the tubulin-microtubule equilibria in eukaryotic organisms. Recently drug resistance to this class of compounds in helminth parasites has been shown to be due to a reduced ability of resistant tubulin to bind BZCs. In order to quantitate the nature of the tubulin-BZC interaction a general method for the specific tritium labelling of BZCs has been developed. The BZCs: mebendazole, oxfendazole, parbendazole, oxibendazole, albendazole and fenbendazole were labelled by catalytic exchange using palladium on calcium carbonate in pure dioxane at 60 0 C under tritium gas. The position of label incorporation for tritiated albendazole was determined by tritium-NMR as the 4-position of benzimadazole nucleus. The yields for individual BZCs varied from 8 to 68% for a range of specific activity of 0.44 to 13.4 Ci/mmole. (author)
Friedberg, R.; Lee, T.D.
2003-01-01
We present a new and simpler proof for the convergent iterative solution of the one-dimensional degenerate double-well potential. This new proof depends on a general theorem, called the hierarchy theorem, that shows the successive stages in the iteration to form a monotonically increasing sequence of approximations to the energy and to the wavefunction at any point x. This important property makes possible a much simpler proof of convergence than the one given before in the literature. The hierarchy theorem proven in this paper is applicable to a much wider class of potentials which includes the quartic potential
Agalarov, Agalar; Zhulego, Vladimir; Gadzhimuradov, Telman
2015-04-01
The reduction procedure for the general coupled nonlinear Schrödinger (GCNLS) equations with four-wave mixing terms is proposed. It is shown that the GCNLS system is equivalent to the well known integrable families of the Manakov and Makhankov U(n,m)-vector models. This equivalence allows us to construct bright-bright and dark-dark solitons and a quasibreather-dark solution with unconventional dynamics: the density of the first component oscillates in space and time, whereas the density of the second component does not. The collision properties of solitons are also studied.
A model of guarded recursion with clock synchronisation
Bizjak, Aleš; Møgelberg, Rasmus Ejlers
2015-01-01
productivity to be captured in types. The calculus uses clocks representing time streams and clock quantifiers which allow limited and controlled elimination of modalities. The calculus has since been extended to dependent types by Møgelberg. Both works give denotational semantics but no rewrite semantics....... In previous versions of this calculus, different clocks represented separate time streams and clock synchronisation was prohibited. In this paper we show that allowing clock synchronisation is safe by constructing a new model of guarded recursion and clocks. This result will greatly simplify the type theory...... by removing freshness restrictions from typing rules, and is a necessary step towards defining rewrite semantics, and ultimately implementing the calculus....
Recursive inter-generational utility in global climate risk modeling
Minh, Ha-Duong [Centre International de Recherche sur l' Environnement et le Developpement (CIRED-CNRS), 75 - Paris (France); Treich, N. [Institut National de Recherches Agronomiques (INRA-LEERNA), 31 - Toulouse (France)
2003-07-01
This paper distinguishes relative risk aversion and resistance to inter-temporal substitution in climate risk modeling. Stochastic recursive preferences are introduced in a stylized numeric climate-economy model using preliminary IPCC 1998 scenarios. It shows that higher risk aversion increases the optimal carbon tax. Higher resistance to inter-temporal substitution alone has the same effect as increasing the discount rate, provided that the risk is not too large. We discuss implications of these findings for the debate upon discounting and sustainability under uncertainty. (author)
Recursive Neural Networks Based on PSO for Image Parsing
Guo-Rong Cai
2013-01-01
Full Text Available This paper presents an image parsing algorithm which is based on Particle Swarm Optimization (PSO and Recursive Neural Networks (RNNs. State-of-the-art method such as traditional RNN-based parsing strategy uses L-BFGS over the complete data for learning the parameters. However, this could cause problems due to the nondifferentiable objective function. In order to solve this problem, the PSO algorithm has been employed to tune the weights of RNN for minimizing the objective. Experimental results obtained on the Stanford background dataset show that our PSO-based training algorithm outperforms traditional RNN, Pixel CRF, region-based energy, simultaneous MRF, and superpixel MRF.
Structural properties of recursively partitionable graphs with connectivity 2
Baudon, Olivier; Bensmail, Julien; Foucaud, Florent
2017-01-01
, namely the ones of being online arbitrarily partitionable and recursively arbitrarily partitionable (OL-AP and R-AP for short, respectively), in which the subgraphs induced by a partition of G must not only be con-nected but also ful_l additional conditions. In this paper, we point out some structural...... properties of OL-AP and R-AP graphs with connectivity 2. In particular, we show that deleting a cut pair of these graphs results in a graph with a bounded number of components, some of whom have a small number of vertices. We obtain these results by studying a simple class of 2-connected graphs called...
General solution of the multigroup spherical harmonics equations in R-Z geometry
Matausek, M.
1983-01-01
In the present paper the generalization is performed of the procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed foe one-dimensional systems in cylindrical or spherical geometry, and later extended for special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r and z directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. The analysis is performed of the possibilities to satisfy the boundary conditions in the case when the system considered represents an elementary reactor lattice cell and in the case when the system represents a reactor as a whole. The computational effort is estimated for system of a given configuration. (author)
A new Bayesian recursive technique for parameter estimation
Kaheil, Yasir H.; Gill, M. Kashif; McKee, Mac; Bastidas, Luis
2006-08-01
The performance of any model depends on how well its associated parameters are estimated. In the current application, a localized Bayesian recursive estimation (LOBARE) approach is devised for parameter estimation. The LOBARE methodology is an extension of the Bayesian recursive estimation (BARE) method. It is applied in this paper on two different types of models: an artificial intelligence (AI) model in the form of a support vector machine (SVM) application for forecasting soil moisture and a conceptual rainfall-runoff (CRR) model represented by the Sacramento soil moisture accounting (SAC-SMA) model. Support vector machines, based on statistical learning theory (SLT), represent the modeling task as a quadratic optimization problem and have already been used in various applications in hydrology. They require estimation of three parameters. SAC-SMA is a very well known model that estimates runoff. It has a 13-dimensional parameter space. In the LOBARE approach presented here, Bayesian inference is used in an iterative fashion to estimate the parameter space that will most likely enclose a best parameter set. This is done by narrowing the sampling space through updating the "parent" bounds based on their fitness. These bounds are actually the parameter sets that were selected by BARE runs on subspaces of the initial parameter space. The new approach results in faster convergence toward the optimal parameter set using minimum training/calibration data and fewer sets of parameter values. The efficacy of the localized methodology is also compared with the previously used BARE algorithm.
Recursive estimation of the parts production process quality indicator
Filipovich Oleg
2017-01-01
Full Text Available Consideration is given to a mathematical representation for manufacturing of batch parts on a metal-cutting machine tool. Linear dimensions of machined parts are assumed to be the major quality indicator, deviation from these dimensions is determined by size setting of machine tool and ensemble of random factors. It is allowed to have absolutely precise pre-setting of machine tool, effects from setup level offsetting due to deformation in process equipment on the specified indicator are disregarded. Consideration is given to factors which affect the tool wear, with two definitions of tool wear being provided. Reasons for development of random error in processing, dependence of measurement results on error as well as distribution laws and some parameters of random values are provided. To evaluate deviation of size setting value in each cycle, it is proposed to apply a recursive algorithm in description of investigated dynamic discrete process in the space state. Kalman filter equations are used in description of process model by means of first-order difference equations. The algorithm of recursive estimation is implemented in the mathematical software Maple. Simulation results which prove effectiveness of algorithm application to investigate the given dynamic system are provided. Variants of algorithm application and opportunities of further research are proposed.
Exploiting fine-grain parallelism in recursive LU factorization
Dongarra, Jack
2012-01-01
The LU factorization is an important numerical algorithm for solving system of linear equations. This paper proposes a novel approach for computing the LU factorization in parallel on multicore architectures. It improves the overall performance and also achieves the numerical quality of the standard LU factorization with partial pivoting. While the update of the trailing submatrix is computationally intensive and highly parallel, the inherently problematic portion of the LU factorization is the panel factorization due to its memory-bound characteristic and the atomicity of selecting the appropriate pivots. We remedy this in our new approach to LU factorization of (narrow and tall) panel submatrices. We use a parallel fine-grained recursive formulation of the factorization. It is based on conflict-free partitioning of the data and lock-less synchronization mechanisms. Our implementation lets the overall computation naturally flow with limited contention. Our recursive panel factorization provides the necessary performance increase for the inherently problematic portion of the LU factorization of square matrices. A large panel width results in larger Amdahl\\'s fraction as our experiments have revealed which is consistent with related efforts. The performance results of our implementation reveal superlinear speedup and far exceed what can be achieved with equivalent MKL and/or LAPACK routines. © 2012 The authors and IOS Press. All rights reserved.
Alam, Md Nur; Akbar, M Ali
2013-01-01
The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.