This paper studies the large time behavior of solutions to semi-linear Cauchy problems with quadratic nonlinearity in gradients. The Cauchy problem considered has a general state space and may degenerate on the boundary of the state space. Two types of large time behavior are obtained: i) pointwise convergence of the solution and its gradient; ii) convergence of solutions to associated backward...

The definition of lacunary strong convergence is extended to a definition of lacunary strong convergence with respect to a sequence of modulus functions in a Banach space. We study some connections between lacunary statistical convergence and lacunary strong convergence with respect to a sequence of modulus functions in a Banach space.

Integrating various suppliers to satisfy market demand is of great importance for e ective supply chain management. In this paper, we consider the ODE-PDE model of supply chain and apply a classical explicit fourth-order Runge-Kutta scheme for the related ODE model of suppliers. Also, the convergence of the proposed method is proved. Finally a numerical example is studied to demonstrate the acc...

Curvature Scale Space (CSS) representations have been shown to be very useful for recognition of noisy curves of arbitrary shapes at unknown orientations and scales [10,14]. This paper contains a number of important results on the convergence properties of CSS representations and on the evolution and arc length evolution of planar curves [6,12]. The processes which convolve arc length parametri...

The goal of this paper is to present a local convergence analysis of Newton’s method for approximating a locally unique solution of an equation in a Banach space setting. Using the gauge function theory and our new idea of restricted convergence regions we present an extended and unified convergence theory. Key–Words: Newton’s method, Banach space, semilocal convergence, gauge function, converg...

A. Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models....

Sufficient conditions are given under which a sequence of independent random elements taking values in a Banach space satisfy the Hsu and Robbins law of large numbers. The complete convergence of random indexed sums of random elements is also considered.

Abstract. The aim of this paper is to study the notion of lacunary I-convergence in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary I-limit points and lacunary I-cluster points have been defined and the relation between them has been established. Furthermore, lacunary Cauchy and lacunary I-Cauchy sequences are introduced and studied. Finally, we provid...

The convergence of Fourier series of trigonometric functions is easy to see, but the same question for general functions is not simple to answer. We study the convergence of Fourier series in Lp spaces. This result gives us a criterion that determines whether certain partial differential equations have solutions or not.We will follow closely the ideas from Schlag and Muscalu’s Classical and Mul...

The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of...