Symmetric Functions in Noncommuting Variables

Consider the algebra Q> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In particular, we define analogs of the monomial, power sum, elementary, complete homogeneous, and Schur symmetric functions as will as investigating their properties.Comment: 16 pages, Latex, see related papers at http://www.math.msu.edu/~sagan, to appear in Transactions of the American Mathematical Societ

Study to determine peening stress profile of rod peened aluminum structural alloys versus shot peened material

The objective of this program was to determine the peening stress profiles of rod peened aluminum structural alloys versus shot peened material to define the effective depth of the compressed surface layer

Modelo analítico para predecir el comportamiento de mechas arteriales

Un análisis matemático para predecir el comportamiento de mechas arteriales, para uso en tubos de calor, es presentado. El estudio está basado en el análisis del problema de penetración capilar bajo las consideraciones de flujo laminar paralelo de un fluido Newtoniano incomprensible en un conducto circular, lo cual conduce a una ecuación diferencial no-lineal cuya integración se obtuvo numéricamente. El análisis es primero restringido a mechas arteriales inclinadas, respecto a la horizontal, trabajando en un medio ambiente de un-g y bajo el efecto adverso de una aceleración constante; enseguida éste es generalizado a mechas arteriales que trabajan horizontalmente, o en un medio ambiente de cero-g. Las soluciones de la ecuación gobernante, la cual depende de los parámetros O, M y N, son presentadas para diferentes situaciones físicas y comparadas con soluciones correspondientes obtenidas a partir de modelos conocidos para el problema de penetración capilar. Finalmente, la aplicabilidad del análisis a mechas arteriales de sección no-circular es discutida

On the growth of Kronecker coefficients (extended abstract)

We present a new stability phenomenon for Kronecker coefficients, that we call hook stability: the Kronecker coefficients stabilize if we add cells to the first row and first column of each of the indexing partitions, simultaneously. We also show that when we increase the sizes of the first two rows of their three indexing partitions, in some appropriate way, the Kronecker coefficients grow linearly, and we are able to give asymptotic estimates

Upper and lower nearly (i, j)-continuous multifunctions

In this paper the authors introduce and study upper and lower nearly (I,J)-continuous multifunctions. Some characterizations and several properties concerning upper (lower) nearly (I,J)-continuous multifunctions are obtained. The results improves many results in Literature

Self-Similarity in Random Collision Processes

Kinetics of collision processes with linear mixing rules are investigated analytically. The velocity distribution becomes self-similar in the long time limit and the similarity functions have algebraic or stretched exponential tails. The characteristic exponents are roots of transcendental equations and vary continuously with the mixing parameters. In the presence of conservation laws, the velocity distributions become universal.Comment: 4 pages, 4 figure

Symmetric functions in noncommuting variables

Consider the algebra Qhhx1, x2, . . .ii of formal power series in countably many noncommuting variables over the rationals. The subalgebra Π(x1, x2, . . .) of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In particular, we define analogs of the monomial, power sum, elementary, complete homogeneous, and Schur symmetric functions as will as investigating their properties