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...

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...

Different properties of general linear descriptor systems are reviewed (existence of solution, consistency of initial condition, impulse controllability and controllability) and structurally characterized. The invariants are associated to a known feedback canonical form of descriptor systems. The aim is to sort the systems by inclusion properties depending on these characterizations.

for all z0 ∈ D(A). Here T (t) is the C0-semigroup generated by A. A system (1) that satisfies the above conditions will be denoted by Σ(A,C). The admissibility of C, eqn. (2), implies that we can extend the mapping z0 → CT (·)z0 to a bounded linear mapping from Z to L2(0,∞). We denote this mapping by C. Thus we have that for any initial condition z0 the solution of (1) is given by z(t) = T (t)z...

A geometrical model which captures the main ingredients governing atom-diatom collinear chemical reactions is proposed. This model is neither near-integrable nor hyperbolic, yet it is amenable to analysis using a combination of the recently developed tools for studying systems with steep potentials and the study of the phase space structure near a center-saddle equilibrium. The nontrivial depen...

For a set of masses having positive measure, excepting eventually a negligible set of initial conditions, every noncollinear bounded solution of the planar three-body problem that has a syzygy configuration encounters an infinity of such configurations. Along a noncollinear syzygy solution, the set of syzygy configuration instants is discrete.

with initial conditions r(0) = do and ṙ(0) = vo. If the system is un-damped (C = 0N×N), the free response of the system will not decay with time, and a suitable trial solution to the differential equation (1) is r(t) = r̄ sin(ωnt), where r̄ is a constant vector of dimension N . Differentiating r(t) twice, r̈(t) = −ω2 nr̄ sin(ωnt), and substituting the trial solution into equation (1) we obtain − ω2...