In applied investigations, the invariance of the Lyapunov dimension under a diffeomorphism is often used. However, in the case of irregular linearization, this fact was not strictly considered in the classical works. In the present work, the invariance of the Lyapunov dimension under diffeomorphism is demonstrated in the general case. This fact is used to obtain the analytic exact upper bound o...

This paper investigates the implementation of Variational Iteration Method (VIM) to practical and higher order nonlinear equations in kind of Korteweg-de-Vries (KdV) equation. The obtained solutions from thirdand fourth-order modified KdV are compared with the exact and Homotopy Perturbation Method (HPM) solutions. Results illustrate the efficiency and capability of VIM to solve high order nonl...

The paper is dedicated to analytical and algebraic approaches to the problem of the integration of ordinary differential equations. The first part is devoted to linear ordinary differential equations of the second and nth orders, while the second deals with nonlinear ordinary differential equations. Factorization of nonlinear equations of the second and the third orders both through commutative...

We present a method to linearize, without approximation, specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the are expressed by scalar functions that defined quotient linear eigenvector. The exact linearization relies on an equivalent multiparameter problem (MEP) contains solutions NEPv. Due characterization MEPs in terms generalized this provides direct way co...

It is generally known that Lie symmetries of differential equations can lead to a reduction the governing equation(s), exact solutions these and, in best case scenario, linearization original equation. In this paper, we consider model from optimal investment theory where show equation possesses an extensive contact symmetry through this, it linearizable. Several are provided including solution ...

Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. A Global Symbol for the Small b-Calculus on Manifolds With Boundary Thesis directed by Prof. Markus Pflaum Starting with the normal symbold of M. Pflaum ([Pfl98]), we generalize the mac...

We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing numerical schemes in order to make them locally exact. The resulting schemes preserve all fixed points and are A-stable. The most promising results concern the...

‎Assume that $A$ is a Banach algebra‎. ‎We define the‎ ‎$beta-$topology and the $gamma-$topology on the space $QM_{el}(A^{*})$ of all bounded extended left quasi-multipliers of $A^{*}.$‎ ‎We establish further properties of $(QM_{el}(A^{*}),gamma)$ when $A$ is a $C^{*}-$algebra‎. ‎In particular‎, ‎we characterize the $gamma-$dual‎ ‎of $QM_{el}(A^{*})$ and prove that $(QM_{el}(A^{*}),gamma)^{*},$...

Belief Propagation (BP) is a widely used approximation for exact probabilistic inference in graphical models, such as Markov Random Fields (MRFs). In graphs with cycles, however, no exact convergence guarantees for BP are known, in general. For the case when all edges in the MRF carry the same symmetric, doubly stochastic potential, recent works have proposed to approximate BP by linearizing th...