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...

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.

There are a few facts that can be read off from this expression immediately. We consider t > 0 here; t < 0 is similar. First, for t0 > 0, u(x0, t0) depends on the initial data φ just at the two points x0± ct0, while it depends on the values of ψ in the whole interval [x0 − ct0, x0 + ct0]. Thus, we call the interval [x0 − ct0, x0 + ct0] the domain of dependence of (x0, t0): if the initial condit...

We study in detail the possibility that the flat directions of the minimal supersymmetric standard model ~MSSM! could act as a curvaton and generate the observed adiabatic density perturbations. For that the flat direction energy density has to dominate the Universe at the time when it decays. We point out that this is not possible if the inflaton decays into MSSM degrees of freedom. If the inf...