Infinitesimal holomorphic realizations for the Schrödinger-Weil representation and the discrete series representations of the Jacobi group are constructed. Explicit expressions of the basic differential operators are obtained. The squeezed states for the unitary irreducible representation of the Jacobi group are introduced. Matrix elements of the squeezed operators, expectation values of polyno...

Recently Delorme and Opdam have generalized the theory of Rgroups towards affine Hecke algebras with unequal labels. We apply their results in the case where the affine Hecke algebra is of type B, for an induced discrete series representation with real central character. We calculate the R-group of such an induced representation, and show that it decomposes multiplicity free into 2 irreducible ...

In the series of papers [FL1, FL2] we approach quaternionic analysis from the point of view of representation theory of the conformal group SL(2,HC) ' SL(4,C) and its real forms. This approach has proven very fruitful and pushed further the parallel with complex analysis and develop a rich theory. In [FL2] we study the counterparts of Cauchy-Fueter and Poisson formulas on the spaces of split qu...

A linear-like discrete-time fuzzy controller was designed to control and stabilize a single-pool irrigation canal. Saint Venant equations for open-channel flow were linearized using the Taylor series and a finite-difference approximation of the original nonlinear partial differential equations. Using the linear optimal control theory, a traditional linear quadratic regulator (LQR) was first dev...

In this paper, we consider the fuzzy fixed-charge transportation problem (FFCTP). Both of fixed and transportation cost are fuzzy numbers. Contrary to previous works, Electromagnetism-like Algorithms (EM) is firstly proposed in this research area to solve the problem. Three types of EM; original EM, revised EM, and hybrid EM are firstly employed for the given problem. The latter is being firstl...