one of the new topics in dea is the data with integer values. in dea classic models, it is assumed that input and output variables have real values. however, in many cases, some inputs or outputs can have integer values. measuring cost efficiency is another method to evaluate the performance and assess the capabilities of a single decision-making unit for manufacturing current products at a min...

<p>In the realm of convergence spaces, generalisation topological groups is groups, and corresponding extension Pontryagin duality continuous duality. We prove that local quasi-convexity a necessary condition for group to be c-reflexive. Further, we every character locally quasi-convex.</p>

In this article, we present a detailed study of the complex calculus of variations introduced in [4]. This calculus is analogous to the conventional calculus of variations, but is applied here to C functions in C. It is based on new concepts involving the minimum and convexity of a complex function. Such an approach allows us to propose explicit solutions to complex Hamilton-Jacobi equations, i...

We study the stability of traveling wave solutions to a fifth-order water wave model. By solving a constrained minimization problem we show that “ground state” traveling wave solutions exist. Their stability is shown to be determined by the convexity or concavity of a function d(c) of the wave speed c. The analysis makes frequent use of the variational properties of the traveling waves.

Abstract: We consider the problem of the symmetry of the off-diagonal heat-kernel coefficients as well as the coefficients corresponding to the short-distance-divergent part of the Hadamard expansion in general smooth (analytic or not) manifolds. The requirement of such a symmetry played a central rôle in the theory of the point-splitting one-loop renormalization of the stress tensor in either ...

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and en...

We study how convergence of an observer whose state lives in a copy of the given system’s space can be established using a Riemannian metric. We show that the existence of an observer guaranteeing the property that a Riemannian distance between system and observer solutions is nonincreasing implies that the Lie derivative of the Riemannian metric along the system vector field is conditionally n...

Let 2 ≤ p < ∞ and let X be a complex Banach space. It is shown that X is p-uniformly PL-convex if and only if there exists λ > 0 such that ‖f‖Hp(X) ≥ ( ‖f(0)‖p + λ ∫ D (1− |z|2)p−1‖f ′(z)‖pdA(z) )1/p , for all f ∈ Hp(X). Applications to embeddings between vector-valued BMOA spaces defined via Poisson integral or Carleson measures are provided. AMS Subject Class. 46B20,46L52

Let X be a normed linear space, x ∈ X an element of norm one, and ε > 0 and δ(x,ε) the local modulus of convexity of X . We denote by ρ(x,ε) the greatest ρ≥ 0 such that for each closed linear subspace M of X the quotient mapping Q : X → X/M maps the open ε-neighbourhood of x in U onto a set containing the open ρ-neighbourhood of Q(x) in Q(U). It is known that ρ(x,ε) ≥ (2/3)δ(x,ε). We prove that...