In a framework with two parties, deterministic voter preferences and geographical constraints, we propose a set of simple axioms and show that they jointly characterize the districting rule that maximizes the number of districts a party can win, given an electoral outcome (the " optimal gerrymandering rule "). As a corollary, we obtain that no districting rule can satisfy our axioms and treat p...

The idea of extending univariate quadrature formulae to cubature formulae that hold for spaces of polyharmonic functions is employed to obtain in a new way bivariate trapezoidal cubature rules. The notion of univariate monospline is extended to functions of two variables in terms of a solution of Poisson’s equation. This approach allows us to characterize the error of the trapezoidal cubature f...

Linear programming problems with trapezoidal fuzzy variables (FVLP) have recently attracted some interest. Some methods have been developed for solving these problems by introducing and solving certain auxiliary problems. Here, we apply a linear ranking function to order trapezoidal fuzzy numbers. Then, we establish the dual problem of the linear programming problem with trapezoidal fuzzy varia...

Ranking of fuzzy numbers plays a very important role in linguistic decision making and some other fuzzy application systems. Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques has been shown to produce nonintuitive results in certain cases. In this paper, some new approaches for ranking of trapezoidal fuzzy numbers are introduced. Keywords— Magnitude of...

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.

This study presents the numerical simulation of three-dimensional incompressible steady and laminar fluid flow and conjugate heat transfer of a trapezoidal microchannel heat sink using water as a cooling fluid in a silicon substrate. Navier-Stokes equations with conjugate energy equation are discretized by finite-volume method. We perform numerical computations for a range of 50 Re 600, 0.05W ...

The three connected buildings of the former Suffolk Manufacturing Company in Lowell, known as Mills Nos. 5, 6 and 8, were built in 1862 (No. 5) and 1880 (Nos. 6 and 8), at a time when the city of Lowell was one of the predominant centers of the textile industry in the United States. Located within the Locks and Canals National Register Historic District, this impressive complex of mill building...

With respect to multiple attribute group decision making (MAGDM) problems in which the attribute weights and attribute values take the form of the generalized interval-valued trapezoidal fuzzy numbers, a new group decision making analysis method is proposed. Firstly, some operational laws, the distance between two generalized interval-valued trapezoidal fuzzy numbers, and transformation from th...

Network-flow problems can be solved by several methods. Labeling techniques can be used to solve wide variety of network problems. A new algorithm to find the fuzzy maximal flow between source and sink was proposed by Kumar et el. [19]. They have represented normal triangular fuzzy numbers as network flow. It is not possible to restrict the membership function to the normal form and proposed th...

Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^nsubseteqmathbb{C}^n$ given by $$Phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$  where $gammain[0,1/2]$, $z=(z_1,hat{z})in B^n$ and $$Psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$ in which $betain[0,1]$, $f(z_1)neq 0$ a...