Theta correspondence θ over R was established by Howe in ( [5]). In [10], we proved that θ preserves unitarity under certain restrictions, generalizing the result of Jian-Shu Li ( [16]). The goal of this paper is to elucidate the idea of constructing unitary representation through the propagation of theta correspondences. We show that under a natural condition on the sizes of the related dual p...

In this paper the definition of Location-2-Domination and minimum cardinality of Location-2-Domination are introduced and denoted by R D(G), and a theorem to find Location-2-dominating set for Path, cycle, Theta graph and Trees in different Kinds are introduced. AMS subject classification: 05C69.

Hippocampal place cells that fire together within the same cycle of theta oscillations represent the sequence of positions (movement trajectory) that a rat traverses on a linear track. Furthermore, it has been suggested that the encoding of these and other types of temporal memory sequences is organized by gamma oscillations nested within theta oscillations. Here, we examined whether gamma-rela...

In this article we consider the problem related to positional synthesis and controllability function method more precisely admissible maximum principle. Unlike common approach principle gives discontinuous solutions problem. Let us canonical system of linear equations $\dot{x}_i=x_{i+1}, i=\overline{1,n-1}, \dot{x}_n=u$ with constraints $|u| \le d$. The for an arbitrary $\dot{x} = A x + b u$ ca...

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 1. Notation and terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 2. Modular forms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 3. Discrim...

It is well known that the unitary evolution of a closed $M-$level quantum system can be generated by non-Hermitian Hamiltonian $H$ with real spectrum. Its Hermiticity restored via an amended inner-product metric $\Theta$. In Hermitian cases evaluation spectrum (i.e., bound-state energies) usually achieved diagonalization Hamiltonian. (or, more precisely, in $\Theta-$quasi-Hermitian) mechanics w...

Consider a random vector $(V_{1}, \dots , V_{n})$ where $\{V_{k}\}_{k=1, n}$ are the first $n$ components of two-parameter Poisson-Dirichlet distribution $PD(\alpha \theta )$. In this paper, we derive decomposition for vector, and propose an exact simulation algorithm to sample from vector. Moreover, special case arises when $\theta /\alpha $ is positive integer, which present very fast modifie...

Highly localized neuronal spikes in primate temporal cortex can encode associative memory; however, whether memory formation involves area-wide reorganization of ensemble activity, which often accompanies rhythmicity, or just local microcircuit-level plasticity, remains elusive. Using high-density electrocorticography, we capture local-field potentials spanning the monkey temporal lobes, and sh...

We study a model of proxy voting where the candidates, voters, and proxies are all located on real line, instead directly, each voter delegates its vote to closest proxy. The goal is find set that theta-representative, which entails for any anywhere favorite candidate within distance theta This property guarantees strong form representation as voters not required be fixed in advance, or even fi...