Analytic solutions for Burgers equations with source terms, possibly stiff, represent an important element to assess numerical schemes. Here we present a procedure, based on the characteristic technique to obtain analytic solutions for these equations with smooth initial conditions.

This paper considers the problem of how to price a conspicuous product while maintaining liquidity during a recession, which both reduces demand and freezes credit markets. Reducing price would help maintain cash flow, but low prices can erode brand image and, hence, long-term sales. The paper extends earlier work of the same authors by explicitly deriving a firm’s optimal cash management behav...

Article history: Received 2 April 2013 Received in revised form 17 November 2013 Accepted 13 January 2014 Available online 21 January 2014

and Applied Analysis 3 where bi t , rj t , aik t , cil t , djk t , ejl t , ejl t i, k 1, 2, . . . ,N; j, l 1, 2, . . . ,M are assumed to be continuous ω-periodic functions and the delays τik, δjk, ηil, ξjl are assumed to be positive constants. The system 1.3 is supplemented with the initial condition: xi θ φi θ , yj θ ψi θ , θ ∈ −τ, 0 , φi 0 > 0, ψi 0 > 0, 1.4

of the results and conclusions are found in section 5.

An elevated Schröder path is a lattice path that uses the steps (1, 1), (1,−1), and (2, 0), that begins and ends on the x-axis, and that remains strictly above the x-axis otherwise. The total area of elevated Schröder paths of length 2n + 2 satisfies the recurrence fn+1 = 6fn − fn−1, n ≥ 2, with the initial conditions f0 = 1, f1 = 7. A combinatorial interpretation of this recurrence is given, b...

For endofunctors F of many-sorted sets the iterative construction of initial algebras is proved to converge whenever F has an initial algebra. In case of one-sorted sets the convergence takes n steps where either n is an infinite regular cardinal or it is at most 3. Dually, the existence of a terminal coalgebra implies that the iterative construction of a terminal coalgebra converges. As demons...

It was conjectured that for every integer m 3 the unique equilibrium c = 1 of the generalized Putnam equation xn+1 = ∑m−2 i=0 xn−i + xn−m+1xn−m xnxn−1 + ∑m i=2 xn−i , n= 0,1,2, . . . , with positive initial conditions is globally asymptotically stable. In this paper, we prove this conjecture. © 2005 Elsevier Inc. All rights reserved.

I study derivative expansions of effective actions at finite temperature, illustrating how the standard methods are badly defined at finite temperature. I then show that by setting up the initial conditions at a finite time, these problems are solved. 1.1 Zero temperature I will work with a simple model of two real fields φ and η 1 L[φ, η] = 1 2 η∆ −1 η − 1 2 gφη 2 + L 0 [φ], (1) and integratin...

There are games with a unique Nash equilibrium but such that, for almost all initial conditions, all strategies in the support of this equilibrium are eliminated by the replicator dynamics and the bestreply dynamics. MSC classification. Primary: 91A22 ; Secondary: 34A34, 34A60.