A new block method of order two for the numerical solution of initial value problems is derived. This method is similar to the block Trapezoidal rule [12] , where the low power of the block size appear in the principal local truncation error. Direct comparison with result relating to the block Trapezoidal rule results obtained in [1] is made.

We present a construction and basic properties of a class of continuous distributions of an arbitrary form defined on a compact (bounded) set by concatenating in a continuous manner three probability density functions with bounded support using a modified mixture technique. These three distributions may represent growth, stability and decline stages of a physical or mental phenomenon.

Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and...

This paper proposes a new approach based on Bonferroni mean operator and possibility degree to solve fuzzy multi-attribute decision making (FMADM) problems in which the attribute value takes the form of interval type-2 fuzzy numbers. We introduce the concepts of interval possibility mean value and present a new method for calculating the possibility degree of two interval trapezoidal type-2 fuz...

The diffraction efficiency behavior of reflection gratings with an asymmetrical trapezoidal groove profile has been studied. Theoretical calculations predict that at certain grating parameters superior efficiency compared to the conventional ruled gratings can be achieved.

We prove a Murnaghan–Nakayama rule for k-Schur functions of Lapointe and Morse. That is, we give an explicit formula for the expansion of the product of a power sum symmetric function and a k-Schur function in terms of k-Schur functions. This is proved using the noncommutative k-Schur functions in terms of the nilCoxeter algebra introduced by Lam and the affine analogue of noncommutative symmet...

We study a division problem which allocates resources to agents with single-peaked preferences, who have a right to decide for the participation. We introduce the generalized uniform rule which assigns resources to agent as equally as possible subject to the participation constraints. We present various characterizations of the generalized uniform rule on the basis of separability principle.

Using Hayashi's inequality, an Iyengar type inequality for functions with bounded second derivative is obtained. This result improves a similar result from [N. Elezovi´c, J. Pečari´c, Steffensen's inequality and estimates of error in trapezoidal rule, Appl. In 1938 Iyengar proved the following inequality in [1]: Theorem 1. Let function f be differentiable on [a, b] and | f (x)| ≤ M. Then 1 b − ...

If Visser’s rules are admissible for an intermediate logic, they form a basis for the admissible rules of the logic. How to characterize the admissible rules of intermediate logics for which not all of Visser’s rules are admissible is not known. Here we study the situation for specific intermediate logics. We provide natural examples of logics for which Visser’s rule are derivable, admissible b...