We construct linear operators factorizing the three bases of symmetric polynomials: monomial symmetric functions mλ(x), elementary symmetric polynomials Eλ(x), and Schur functions sλ(x), into products of univariate polynomials.

Nowadays, observing and understanding the performance of a multithreaded application is untrivial, especially within a complex thread environment (multilevel scheduling). Thanks to our environment, the run of a multithreaded application can be precisely analyzed. In particular, our environment allows the programmer to measure the number of CPU cycles used by a given function or the precise sche...

Vol. 9 No. 1 1997 27 In computing, a cluster is loosely defined as a parallel system comprising a collection of stand-alone computers (each called a node) connected by a network. Each node runs its own copy of the operating system, and cluster software coordinating the entire parallel system attempts to provide users with a unified system view. Since each node in the cluster is an off-the-shelf...

Encryption algorithms are known to be computationally intensive. They consume a significant amount of computing resources such as CPU time, memory, and battery power. A wireless device, usually with very limited resources, especially battery power, is subject to the problem of energy consumption due to encryption algorithms. Designing energy efficient security protocols first requires an unders...

Traffic monitoring and analysis based on general purpose systems with high speed interfaces, such as Gigabit Ethernet and 10 Gigabit Ethernet, requires carefully designed software in order to achieve the needed performance. One approach to attain such a performance relies on deploying multiple processors. This work analyses some general issues in multiprocessor systems that are particularly cri...

for a symmetric group $g:=sym(n)$ and a conjugacy class $mathcal{x}$ of involutions in $g$, it is known that if the class of involutions does not have a unique fixed point, then - with a few small exceptions - given two elements $a,x in mathcal{x}$, either $angbrac{a,x}$ is isomorphic to the dihedral group $d_{8}$, or there is a further element $y in mathcal{x}$ such that $angbrac{a,y} cong ang...

A central problem in Diophantine geometry is to uniformly bound the number of $K$-rational points on a smooth curve $X/K$ terms $K$ and its genus $g$. recent paper by Stoll proved uniform bounds for hyperelliptic $X$ provided that rank Jacobian at most $g - 3$. Katz, Rabinoff Zureick-Brown generalized his result arbitrary curves satisfying same condition. In this paper, we prove conditional r...

In this paper, Burr-type XII ̄X synthetic schemes are proposed as an alternative to the classical ̄X synthetic schemes when the assumption of normality fails to hold. First, the basic design of the Burr-type XII ̄X synthetic scheme is developed and its performance investigated using exact formulae. Secondly, the non-side-sensitive and side-sensitive Burr-type XII ̄X synthetic schemes are int...

I n 1998, I. G. Macdonald (1) introduced a remarkable new basis for the space of symmetric functions. The elements of this basis are denoted P (x ; q, t), where is a partition and p, q are two free parameters. The P (x ; q, t)’s, which are now called ‘‘Macdonald polynomials,’’ specialize to many of the well known bases for the symmetric functions, by suitable choices of the parameters q and t. ...