and |g′′(x)| = M. We will show that |f(x)| ≤ g(x) on [0, 1]. The desired conclusion follows. Suppose however that this is false, that there is a number q ∈ [0, 1] for which f(q) > g(q). (The other case, f(q) < −g(q), is similar.) Our strategy will be to show that there are real numbers s and t with s < t such that f ′(s) > g′(s) and f ′(t) < g′(t). See figure. We will then apply the Mean Value ...

We systematically study wreath product Schur functions and give a combinatorial construction using colored partitions and tableaux. The Pieri rule and the Littlewood-Richardson rule are studied. We also discuss the connection with representations of generalized symmetric groups.

This paper provides a characterization of dominant strategy mechanisms with quasi-linear utilities and multi-dimensional types for a variety of preference domains. These characterizations are in terms of a monotonicity property on the underlying allocation rule.

In this paper, we want represented a method for ranking of two exponential trapezoidal fuzzy numbers with TRD distance. The main advantage of the proposed approach is that the proposed approach provide the correct ordering of exponential trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems.

A new algorithm namely, fuzzy zero point method is proposed for finding a fuzzy optimal solution for a fuzzy transportation problem where the transportation cost, supply and demand are trapezoidal fuzzy numbers. The optimal solution for the fuzzy transportation problem by the fuzzy zero point method is a trapezoidal fuzzy number. The solution procedure is illustrated with numerical example. Mat...

In the current presentation, we suggest a very simple and effective post-processing procedure to increase the order of accuracy in time for numerical results obtained at time integration of linear elastodynamics problems by the trapezoidal rule. This technique is based on a new exact, closed-form, a-priori error estimator for time integration of linear elastodynamics equations by the trapezoida...

To make the analysis more consistent and logical according to real life situations, in thispaper, the concept of trapezoidal vague set is extended by the idea of trapezoidal vaguesets of type-II. Also we have introduced: definition of trapezoidal vague set of type-IIand arithmetic operations between two trapezoidal vague sets of type-II. Further, a newmethod has been developed f...

In this study, a new proposed multi-generation system as a promising integrated energy conversion system is studied, and its performance is investigated thermodynamically. The system equipped with parabolic trough collectors and biomass combustor to generate electricity, heating and cooling loads, hydrogen and potable water. A double effect absorption chiller to provide cooling demand, a proton...