A. OPTIMAL DIVISION OF SURPLUS: SUFFICIENT CONDITION IN THIS SECTION, we show that the function β∗(j) in equation (15) of the main text, characterizing the optimal division of surplus at stage j, indeed satisfies a sufficient condition for the associated profit-maximization problem of the firm. Our approach builds on recasting this as a dynamic programming problem. Remember that in the main tex...

Let {X,Xn; n ? 0} be a sequence of independent and identically distributed random variables in sub-linear expectation space (?,H,?). We establish complete convergence theorem the maximum partial sums max1?j?n |?j i=1 Xi| under optimal moment condition space. Our result generalizes improves corresponding results.

By imposing a structural criterion on a graph, we generalize the well-known Chvátal’s sufficient condition for hamiltonicity (J. Combin. Theory Ser. B 12 (1972) 163–168). Using this result, we describe a new class of hamiltonian degree sequenceswhich contains the sequences given byChvátal’s condition, as well as a class of degree sequences described by Fan and Liu (J. Systems Sci. Math. Sci. 4 ...

A second look at the authors' [BDR1], [BDR2] characterization of the approximation order of a Finitely generated Shift-Invariant (FSI) subspace S(() of L 2 (R d) results in a more explicit formulation entirely in terms of the (Fourier transform of the) generators ϕ ∈ of the subspace. Further, when the generators satisfy a certain technical condition, then, under the mild assumption that the set...

A second look at the authors' (BDR1], BDR2]) characterization of the approximation order of a Finitely generated Shift-Invariant subspace S(() of L 2 (IR d) results in a more explicit formulation entirely in terms of the (Fourier transform of the) generators ' 2 of the subspace. Further, when the generators satisfy a certain technical condition, then, under the mild assumption that the set of 1...

The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of ...

Abstract We consider integral functionals $$ \mathcal {F}^{(j)}_{\varepsilon } F ε ( j ) , doubly indexed by \varepsilon > 0 > 0 and $$j \in \mathbb N...

This paper deals with conservation laws on networks, represented by graphs. Entropy-type conditions are considered to determine dynamics at nodes. Since entropy dispersion is a local concept, we consider a network composed by a single node J with n incoming and m outgoing arcs. We extend at J the classical Kružkov entropy obtaining two conditions, denoted by (E1) and (E2): the first requiring e...

We consider the class of quadratically-constrained quadratic-programming methods in the framework extended from optimization to more general variational problems. Previously, in the optimization case, Anitescu (SIAM J. Optim. 12, 949–978, 2002) showed superlinear convergence of the primal sequence under the Mangasarian-Fromovitz constraint qualification and the quadratic growth condition. Quadr...