Given a weight of sl(n), we derive a system of variable-coefficient second-order linear partial differential equations that determines the singular vectors in the corresponding Verma module. Moreover, we completely solve the system in a certain space of power series. The polynomial solutions correspond to the singular vectors in the Verma module. The well-known results of Verma, Bernstein-Gel’f...

The increasing request for motor drives with higher power levels is also driving the demand for power modules providing higher currents. The conventional approach to fulfill this requirement is to look for dedicated high current power modules. This article describes the alternative approach of paralleling IGBTs and diodes within one power module to extend its power capability, for example using...

The coefficients of the Pascal triangle were generalized in 1756 by de Moivre [5]. Each row of a Pascal triangle contains a sequence of numbers that are the coefficients of the power series expansion for the binary expression (l + x)^. The de Moivre formula [2], [4], [5], [6] derives the coefficients of the power series for the generalized expansion of (1 + x + x + • • • + x^"^). Thus, for inte...

In [K–K–S] it was shown that fields of generalized power series cannot admit an exponential function. In this paper, we construct fields of generalized power series with bounded support which admit an exponential. We give a natural definition of an exponential, which makes these fields into models of real exponentiation. The method allows to construct for every κ regular uncountable cardinal, 2...

In [K–K–S] it was shown that fields of generalized power series cannot admit an exponential function. In this paper, we construct fields of generalized power series with bounded support which admit an exponential. We give a natural definition of an exponential, which makes these fields into models of real exponentiation. The method allows to construct for every κ regular uncountable cardinal, 2...

In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.

In the Givental’s work on the Gromov-Witten invariants for projective complete intersections, [G1], the principal role is played by certain formal power series connected with the quantum cohomology of a manifold. One has a manifold X with a natural torus action, with the finite number of fixed points, and one has a power series Zw associated with each fixed point xw. The coefficients of these s...