We study a family of the generalized principal series and obtain necessary and sufficient conditions under which the induced representation of studied form contains a discrete series subquotient. Furthermore, we show that if the generalized principal series which belongs to the studied family has a discrete series subquotient, then it has a discrete series subrepresentation.

Continuous, wherein observations are made at every instant of time, for example electrocardiograms, lie detectors, etc. A continuous time series can be denoted as [x(t)]. Continuous time series are sampled (measured) at discrete time points and are ultimately treated as discrete series. Discrete, wherein observations are made at (usually) equispaced intervals. A discrete time series can be repr...

Let G be a connected semisimple real Lie group with compact Cartan subgroup. Harish-Chandra gave formulas for discrete series characters which are completely explicit except for certain interger constants appearing in the numerators. The main result of this paper is a new formula for these constants using two-structures. The new formula avoids endoscopy and stable discrete series entirely, expr...

This paper describes a novel approach to representing experimental biological data in metabolic networks. The aim is to allow biologists to visualise and analyse the data in the context of the underlying processes. Biological networks can be modelled as graphs and visualised using graph drawing methods. We present a general method for mapping experimental data onto nodes and edges of a graph an...

We consider the modulated harmonic wave in discrete series connected Josephson transmission line (JTL). formulate approach to modulation problems for equations based on calculus. check up by applying it Fermi-Pasta-Ulam-Tsingou type problem. Applying JTL, we obtain equation describing amplitude, which turns out be defocusing nonlinear Schr\"odinger (NLS) equation. compare profile of single soli...