All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 6 Next

Displaying 101 – 120 of 137

Showing per page

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Andries, Erik, Umarov, Sabir, Steinberg, Stanly (2006)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step) of the Cauchy problem for...

More on the Continuity of Real Functions

Keiko Narita, Artur Kornilowicz, Yasunari Shidama (2011)

Formalized Mathematics

In this article we demonstrate basic properties of the continuous functions from R to Rn which correspond to state space equations in control engineering.

Morse-Sard theorem for delta-convex curves

D. Pavlica (2008)

Mathematica Bohemica

Let f : I → X be a delta-convex mapping, where I ⊂ ℝ is an open interval and X a Banach space. Let C f be the set of critical points of f . We prove that f ( C f ) has zero 1 / 2 -dimensional Hausdorff measure.

Moser's Inequality for a class of integral operators

Finbarr Holland, David Walsh (1995)

Studia Mathematica

Let 1 < p < ∞, q = p/(p-1) and for f ∈ L p ( 0 , ∞ ) define F ( x ) = ( 1 / x ) ʃ 0 x f ( t ) d t , x > 0. Moser’s Inequality states that there is a constant C p such that s u p a ≤ 1 s u p f ∈ B p ʃ 0 ∞ e x p [ a x q | F ( x ) | q - x ] d x = C p where B p is the unit ball of L p . Moreover, the value a = 1 is sharp. We observe that F = K 1 f where the integral operator K 1 has a simple kernel K. We consider the question of for what kernels K(t,x), 0 ≤ t, x < ∞, this result can be extended, and proceed to discuss this when K is non-negative and homogeneous of degree -1. A sufficient condition on K is found for the analogue...

Moser-Trudinger and logarithmic HLS inequalities for systems

Itai Shafrir, Gershon Wolansky (2005)

Journal of the European Mathematical Society

We prove several optimal Moser–Trudinger and logarithmic Hardy–Littlewood–Sobolev inequalities for systems in two dimensions. These include inequalities on the sphere S 2 , on a bounded domain Ω ⊂ ℝ 2 and on all of ℝ 2 . In some cases we also address the question of existence of minimizers.

Multidimensional Opial inequalities for functions vanishing at an interior point

George A. Anastassiou, Gisèle Ruiz Goldstein, Jerome A. Goldstein (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we generalize Opial inequalities in the multidimensional case over balls. The inequalities carry weights and are proved to be sharp. The functions under consideration vanish at the center of the ball.

Multifunctions of two variables: examples and counterexamples

Jürgen Appell (1996)

Banach Center Publications

A brief account of the connections between Carathéodory multifunctions, Scorza-Dragoni multifunctions, product-measurable multifunctions, and superpositionally measurable multifunctions of two variables is given.

Currently displaying 101 – 120 of 137