A theorem of this paper proves that if the size distribution of random spheres is generalized gamma, its Wicksell transform and other related distributions belong to the domain of attraction of the Gumbel distribution. The theorem also shows the attraction coefficients of the distributions. The fatigue strength of high-strength steel is closely related to the maximum size of nonmetallic inclusi...

JOANNA E. BURDETTE, RACHEL M. OLIVER, VICTORIA ULYANOV, SIGNE M. KILEN, KELLY E. MAYO, AND TERESA K. WOODRUFF Institute for Women’s Health Research (J.E.B., V.U., T.K.W.) Feinberg School of Medicine, Northwestern University, Chicago, IL 60611; Robert H. Lurie Comprehensive Cancer Center of Northwestern University (T.K.W.), Chicago, IL 60611; Department of Biochemistry, Molecular Biology and Cel...

In this article we are interested in the following problem: to find a map u : Ω → R that satisfies { Du ∈ E a.e. in Ω u(x) = φ(x) x ∈ ∂Ω where Ω is an open set of R and E is a compact isotropic set of R2×2. We will show an existence theorem under suitable hypotheses on φ. Mathematics Subject Classification. 34A60, 35F30, 52A30. Received May 14, 2004.

In this paper we study the existence of global weak solutions for a hyperbolic differential inclusion with a discontinuous and nonlinear multivalued term. Also we investigate the asymptotic behavior of solutions.

This paper introduces a second-order differential inclusion for unconstrained convex optimization. In continuous level, solution existence in proper sense is obtained and exponential decay of novel Lyapunov function along with the trajectory derived as well. Then discrete based on numerical discretizations model, two inexact proximal point algorithms are proposed, some new convergence rates est...

We call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it (1) has a product structure, (2) is upper hemi–continuous, (3) always includes a best reply to any mixed strategy profile, and (4) is convexand closed-valued. For each generalized best reply correspondence, we define a generalized best reply dynamics as a differential inclusion...

Considering constrained dynamical systems characterized by a differential inclusion x′ ∈ F (x), we are interested in studying the situation where, for various reasons, the state leaves the constrain domain K either because the initial position does not belong to the Viability Kernel of K for F or it belongs to a “sustainable or tolerable” but not “comfortable” domain. This question appears in n...

A Cauchy problem for a functional-differential inclusion of neutral type with a nonconvex right-hand side is investigated. Questions of the solvability of such a problem are considered, estimates analogous to the Filippov’s estimates are obtained and the density principle is proved. 2000 Mathematics Subject Classification: 34A60, 34G20, 34K35, 49J30, 49K25.