map is the most important tool for cognizance in the field of geography and is the best instrument for presentation of geographic information. the study of ecology in general, which means the study of relationship between man and his environment, is only possible by means of maps. as a tool for ecology and manifestation of human sovereignty over environment, the map has served political power-h...

Convex models in each optimization class are then developed in parallel for a variety of practical applications such as unit commitment, generation and transmission planning, and nodal pricing. Presenting classical approximations and modern convex relaxations side-by-side, and a selection of problems and worked examples, this book is an invaluable resource for students and researchers from indu...

Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this result. In recent years, some authors applied these generalizations to solve several special integral equations and some of the...

The problem considered is as follows: given C ⊂ R and F : C → R differentiable, find f : C → R differentiable such that ‖∇f(x)‖−1∇f(x) = ‖F (x)‖−1F (x) for all x ∈ C. Conditions for f to be pseudoconvex or convex are given. The results are applied to the differentiable case of the revealed preference problem.

The operation of air-cooled chillers accounts for significant energy consumption in local commercial buildings, and low operational efficiency especially under partial load conditions and poor control are part of reasons for such huge energy consumption. Chiller efficiency can be improved by enhancing heat transfer rate in condensers. This paper considers how the chiller performance can be impr...

The purpose of this paper is to obtain an existence result for the integral equation u (t) = φ (t, u (t)) + ∫ b a ψ (t, s, u (s)) ds, t ∈ [a, b] where φ : [a, b]×R → R and ψ : [a, b]× [a, b]×R → R are continuous functions which satisfy some special growth conditions. The main idea is to transform the integral equation into a fixed point problem for a condensing map T : C [a, b] → C [a, b]. The ...

The purpose of this paper is to characterize the Banach spaces and the locally convex spaces E for which bounded additive measures or bounded σadditive measures with values in L(E, F ), the space of continuous linear maps from E into F , are of bounded semi-variation for any Banach space or locally convex space F . This paper gives an answer to a problem posed by D.H. Tucker in [6].

The notion of a generalized convex space we work with in this paper was introduced by Park and Kim in [10]. In generalized convex spaces, many results on fixed points, coincidence points, equilibrium problems, variational inequalities, continuous selections, saddle points, and others have been obtained, see, for example, [6, 8, 10–13]. In this paper, we obtain an almost coincidence point theore...

The convex dimension of a graph G = (V, E) is the smallest dimension d for which G admits an injective map f : V −→ R of its vertices into d-space, such that the barycenters of the images of the edges of G are in convex position. The strong convex dimension of G is the smallest d for which G admits a map as above such that the images of the vertices of G are also in convex position. In this pap...