In this paper we study motion of surfaces of revolution under the mean curvature flow. For an open set of initial conditions close to cylindrical surfaces we show that the solution forms a “neck” which pinches in a finite time at a single point. We also obtain a detailed description of the neck pinching process.

with A a diagonal matrix. Appropriate boundary and initial conditions are given. The amplification matrix Q(£) need not be diagonal. However, he required that |Q(£)| ^ 1We use certain results in matrix theory and Wiener-Hopf factorization to replace this restrictive assumption by certain reasonable assumptions on accuracy of Q(£) and smoothness of an associated positive-definite symmetric matri...

The detection of insu ciently resolved or ill-conditioned integrand structures is critical for the reliability assessment of the quadrature rule outputs. We discuss a method of analysis of the pro le of the integrand at the quadrature knots which allows inferences approaching the theoretical 100% rate of success, under error estimate sharpening. The proposed procedure is of the highest interest...

We study the Q evolution of parton distributions at small x values, obtained in the case of flat initial conditions. The contributions of twist-two and (renormalontype) higher-twist operators of the Wilson operator product expansion are taken into account. The results are in good agreement with deep inelastic scattering experimental data from HERA.

The Ulam sequence is defined as a1 = 1, a2 = 2 and an being the smallest integer that can be written as the sum of two distinct earlier elements in a unique way. This gives 1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47, . . . Ulam remarked that understanding the sequence, which has been described as ’quite erratic’, seems difficult and indeed nothing is known. We report the empirical dis...

Solution of homogeneous fuzzy partial differential equations with specific fuzzy boundary and initial conditions are proposed. Using Adomian Decomposition method, we solve the heat equations for which it is difficult to find the solution by classical methods. We extend the crisp solution in the fuzzy form as a Seikkala solution. MSC: 34A07 • 35K51

We study a setting where imitative players are matched into pairs to play a Prisoners’ Dilemma game. A well known result in such setting is that under random matching cooperation vanishes for any interior initial condition. The novelty of this paper is that we consider partial rematching: players that belong to a pair where both parties cooperate repeat partner next period whilst all other play...

An inhomogeneous version of pre–Big Bang cosmology emerges, within string theory, from quite generic initial conditions, provided they lie deeply inside the weak-coupling, lowcurvature regime. Large-scale homogeneity, flatness, and isotropy appear naturally as latetime outcomes of such an evolution. CERN-TH/97-42 March 1997

We prove that any hyperplane H in a CAT(0) cubical complex X has no self-intersections and separates X into two convex complementary components. These facts were originally proved by Sageev. Our argument shows that his theorem (or this direction of his theorem) is a corollary of Gromov’s link condition. We also give new arguments establishing some combinatorial properties of hyperplanes. We sho...

A rebutting counterargument is considered a very effective strategy to make one’s own argument more persuasive; however, the possible reasons behind this are not clear. In this study, we investigated the effects of rebutting counterarguments on persuasiveness in written arguments. One hundred undergraduate students were assigned randomly to two conditions: a “non-rebuttal condition” and a “rebu...