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.

Hanging to the trapezoidal sheet by a very widespread solution used in civil engineering to lead the distribution of energy, sanitary, air distribution system etc. under the roof or floor structure. The trapezoidal decking part of the whole installation system for specific distribution medium. The leading companies offer installation systems for each specific distribution e.g. pipe rings, sprin...

In some cases, our uncertainty about about a quantity can be described by an interval of its possible values. If we have two or more pieces of interval information about the same quantity, then we can conclude that the actual value belongs to the intersection of these intervals. In general, we may need a fuzzy number to represent our partial knowledge. A fuzzy number can be viewed as a collecti...

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 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.

We propose a novel SAS macro to utilize PROC NLMIXED in SAS to estimate the standard error for AUC when the AUC estimator is based on the trapezoidal rule. Our method accounts for the trapezoidal region-by-region correlation structure. An example is provided for the standard error of the AUC under the ROC curve.

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...