Biological diversity and species richness have been declined throughout the world as a result of human activities. Measuring species richness is important in rangeland conservation to evaluate the status and trends of native plant species, detecting non-native species invasion and monitoring rare species. However, heterogeneity in plant distribution makes inventories difficult. In this study tw...

We study generalized and degenerate Whittaker models for reductive groups over local fields of characteristic zero (archimedean or non-archimedean). Our main result is the construction of epimorphisms from the generalized Whittaker model corresponding to a nilpotent orbit to any degenerate Whittaker model corresponding to the same orbit, and to certain degenerate Whittaker models corresponding ...

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The propagation of torsional waves in a prestressed fiber-reinforced half-space under the effect of magnetic field and gravity has been discussed. The problem has been solved analytically using Whittaker function to obtain the exact solution frequency equations. Numerical results for stress, gravity and magnetic field are given and illustrated graphically. Comparisons are made with the results ...

We classify irreducible Whittaker modules for generalized Heisenberg Lie algebra t and irreducible Whittaker modules for Lie algebra t̃ obtained by adjoining m degree derivations d1, d2, . . . , dm to t. Using these results, we construct imaginary Whittaker modules for non-twisted extended affine Lie algebras and prove that the imaginary Whittaker modules of Z-independent level are always irredu...

In this paper, Whittaker modules for the W -algebra W (2, 2) are studied. We obtain analogues to several results from the classical setting and the case of the Virasoro algebra, including a classification of simple Whittaker modules by central characters and composition series for general Whittaker modules.

In this paper, we obtain the extended Wright generalized Hypergeometric function using extended Beta function. We also obtain certain integral representations, Mellin transform and some derivative properties of extended Wright generalized Hypergeometric function. Further, we represent extended Wright generalized Hypergeometric function in the form of Laguerre polynomials and Whittaker function.

We provide formulas for various bases of spherical Whittaker functions on the n-fold metaplectic cover of GLr over a p-adic field and show that there is a basis of symmetric functions in the complex parameter. In addition we relate a specific spherical Whittaker function to the p-power part of the Weyl group multiple Dirichlet series for the root system of type Ar−1 constructed from nth order G...