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...

Throughout this report, polling systems play a central role. Polling systems are queueing systems consisting of multiple queues, attended by a single server. The server can only serve one queue at a time. Whenever the server moves from one queue to another, a stochastic, non-zero switch-over time is incurred. The server never idles; even when there are no customers waiting in the system, the se...

We explore an intimate connection between Young tableaux and representations of the symmetric group. We describe the construction of Specht modules which are irreducible representations of Sn, and also highlight some interesting results such as the branching rule and Young’s rule.

Following the ideas of Liniger and Willoughby (although acting along different lines), a new family of schemes, derived from the trapezoidal rule, is developed, which enables the fitting of the scheme to arbitrary sets of equations.

Objective This study aims at determining the prevalence of little finger brachymesophalangia (BMP-V) in Chinese ethnic population. Methods A retrospective reviewing hand radiographs taken United Christian Hospital from January 2011 to July 2016. Exclusion criteria included previous trauma, background history genetic syndromes and non-Chinese origin. The were assessed with objective measurement ...

the leopard moth, zeuzera pyrina (l.) (lepidoptera: cossidae) is a serious pest of walnut and apple trees in iran. one of the control methods for this pest is the mass trapping of males using pheromone traps. to determine the best size and color of traps, four different colors (green, yellow, white, gray) and two different sizes (delta shape with standard adhesive surface, 19 × 22 cm and trapez...