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Solving a class of non-convex quadratic problems based on generalized KKT conditions and neurodynamic optimization technique

Alaeddin Malek, Najmeh Hosseinipour-Mahani (2015)

Kybernetika

In this paper, based on a generalized Karush-Kuhn-Tucker (KKT) method a modified recurrent neural network model for a class of non-convex quadratic programming problems involving a so-called Z -matrix is proposed. The basic idea is to express the optimality condition as a mixed nonlinear complementarity problem. Then one may specify conditions for guaranteeing the global solutions of the original problem by using results from the S-lemma. This process is proved by building up a dynamic system from...

Solving non-holonomic Lagrangian dynamics in terms of almost product structures.

Manuel de León, David Martín de Diego (1996)

Extracta Mathematicae

Given a Lagrangian system with non-holonomic constraints we construct an almost product structure on the tangent bundle of the configuration manifold such that the projection of the Euler-Lagrange vector field gives the dynamics of the system. In a degenerate case, we develop a constraint algorithm which determines a final constraint submanifold where a completely consistent dynamics of the initial system exists.

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method

Barari, A., Ghotbi, Abdoul R., Omidvar, M., Ganji, D. D. (2009)

Serdica Journal of Computing

Due to wide range of interest in use of bio-economic models to gain insight into the scientific management of renewable resources like fisheries and forestry,variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting.The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations.

Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains

J. Dedecker, S. Gouëzel, F. Merlevède (2010)

Annales de l'I.H.P. Probabilités et statistiques

We consider a large class of piecewise expanding maps T of [0, 1] with a neutral fixed point, and their associated Markov chains Yi whose transition kernel is the Perron–Frobenius operator of T with respect to the absolutely continuous invariant probability measure. We give a large class of unbounded functions f for which the partial sums of f○Ti satisfy both a central limit theorem and a bounded law of the iterated logarithm. For the same class, we prove that the partial sums of f(Yi) satisfy a...

Some common fixed point results for rational type contraction mappings in partially ordered metric spaces

Sumit Chandok (2013)

Mathematica Bohemica

The purpose of this paper is to establish some common fixed point results for f -nondecreasing mappings which satisfy some nonlinear contractions of rational type in the framework of metric spaces endowed with a partial order. Also, as a consequence, a result of integral type for such class of mappings is obtained. The proved results generalize and extend some of the results of J. Harjani, B. Lopez, K. Sadarangani (2010) and D. S. Jaggi (1977).

Some concepts of regularity for parametric multiple-integral problems in the calculus of variations

M. Crampin, D. J. Saunders (2009)

Czechoslovak Mathematical Journal

We show that asserting the regularity (in the sense of Rund) of a first-order parametric multiple-integral variational problem is equivalent to asserting that the differential of the projection of its Hilbert-Carathéodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter ( m + 1 ) -form are holonomic.

Some constructive applications of Λ 2 -representations to integration of PDEs

A. Popov, S. Zadadaev (2000)

Annales Polonici Mathematici

Two new applications of Λ 2 -representations of PDEs are presented: 1. Geometric algorithms for numerical integration of PDEs by constructing planimetric discrete nets on the Lobachevsky plane Λ 2 . 2. Employing Λ 2 -representations for the spectral-evolutionary problem for nonlinear PDEs within the inverse scattering problem method.

Some dynamical properties of S-unimodal maps

Tomasz Nowicki (1993)

Fundamenta Mathematicae

We study 1) the slopes of central branches of iterates of S-unimodal maps, comparing them to the derivatives on the critical trajectory, 2) the hyperbolic structure of Collet-Eckmann maps estimating the exponents, and under a summability condition 3) the images of the density one under the iterates of the Perron-Frobenius operator, 4) the density of the absolutely continuous invariant measure.

Some examples of cocycles with simple continuous singular spectrum

K. Frączek (2001)

Studia Mathematica

We study spectral properties of Anzai skew products T φ : ² → ² defined by T φ ( z , ω ) = ( e 2 π i α z , φ ( z ) ω ) , where α is irrational and φ: → is a measurable cocycle. Precisely, we deal with the case where φ is piecewise absolutely continuous such that the sum of all jumps of φ equals zero. It is shown that the simple continuous singular spectrum of T φ on the orthocomplement of the space of functions depending only on the first variable is a “typical” property in the above-mentioned class of cocycles, if α admits a sufficiently fast approximation....

Some examples of nonsingular Morse-Smale vector fields on S 3

F. Wesley Wilson Jr (1977)

Annales de l'institut Fourier

One wonders or not whether it is possible to determine the homotopy class of a vector field by examining some algebraic invariants associated with its qualitative behavior. In this paper, we investigate the algebraic invariants which are usually associated with the periodic solutions of non-singular Morse-Smale vector fields on the 3-sphere. We exhibit some examples for which there appears to be no correlation between the algebraic invariants of the periodic solutions and the homotopy classes of...

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