provided that f : a, b → is a convex function 1, page 137 , 2, page 1 . This result for convex functions plays an important role in nonlinear analysis. These classical inequalities have been improved and generalized in a number of ways and applied for special means including Stolarsky type, logarithmic, and p-logarithmic means. A generalization of H.H inequalities was obtained in 3–5 , 2, page ...

This article is devoted to define and solve an evolution equation of the form dyt = yt dt + d Xt (yt ), where stands for the Laplace operator on a space of the form L p(Rn), and X is a finite dimensional noisy nonlinearity whose typical form is given by Xt (φ) = ∑N i=1 xi t fi (φ), where each x = (x (1), . . . , x (N ) is a γ -Hölder function generating a rough path and each fi is a smooth enou...

This paper investigates the late-time behaviour of certain cosmological models where oscillations play an essential role. Rigorous results are proved on the asymptotics of homogeneous and isotropic spacetimes with a linear massive scalar field as source. Various generalizations are obtained for nonlinear massive scalar fields, k-essence models and f(R) gravity. The effect of adding ordinary mat...

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent fun...

We discuss two different nonlinear generalizations of the osp(2|2) supersymmetry which arise in superconformal mechanics and fermion-monopole models. Submitted to the Proceedings of the International Workshop “Supersymmetries and Quantum Symmetries” (SQS’03, Dubna, Russia, 24-29 July 2003)

In 1940, Ulam 1 gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems. Among these was the following question concerning the stability of homomorphisms. Let G1 be a group and let G2 be a metric group with metric ρ ·, · . Given > 0, does there exist a δ > 0 such that if f : G1 → G2 satisfies ρ f xy , f x f y < δ for all x, y ∈ ...

We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by Colombeau’s theory of algebras of generalized functions. We show that under some mild conditions on the differential equations, symmetries of classical solutions...

This paper deals with the analysis of a nonlinear dynamical system which characterizes the axons interaction and is based on a generalization of FitzHugh-Nagumo system. The parametric domain of stability is investigated for both the linear and third-order approximation. A further generalization is studied in presence of high-amplitude time-dependent pulse. The corresponding numerical solution f...

The purpose of this paper is to introduce second order (K, F)-pseudoconvex and second order strongly (K, F)pseudoconvex functions which are a generalization of cone-pseudoconvex and strongly cone-pseudoconvex functions. A pair of second order symmetric dual multiobjective nonlinear programs is formulated by using the considered functions. Furthermore, the weak, strong and converse duality theor...

This paper is concerned with continuous-time nonlinear risk-sensitive filters. It is shown that for large classes of nonlinearities entering both the dynamics and measurements, these filters are finitedimensional generalizations of the Benes filters. Specific examples are discussed. The small noise limiting analog is discussed using change of probability measures.