On Exact Polya and Putinar's Representations

On the Exact Solution of a Generalized Polya Process

There are two types of master equations in describing nonequilibrium phenomena with memory effect: i the memory function type and ii the nonstationary type. A generalized Polya process is studied within the framework of a non-stationary type master equation approach. For a transitionrate with an arbitrary time-dependent relaxation function, the exact solution of a generalized Polya process is o...

Some exact inequalities of Hardy-Littlewood-Polya type for periodic functions

The Representations and Positive Type Functions of Some Homogenous Spaces

‎For a homogeneous spaces ‎$‎G/H‎$‎, we show that the convolution on $L^1(G/H)$ is the same as convolution on $L^1(K)$, where $G$ is semidirect product of a closed subgroup $H$ and a normal subgroup $K $ of ‎$‎G‎$‎. ‎Also we prove that there exists a one to one correspondence between nondegenerat $ast$-representations of $L^1(G/H)$ and representations of ...

An Autoregressive Approach to Nonparametric Hierarchical Dependent Modeling

We propose a conditional autoregression framework for a collection of random probability measures. Under this framework, we devise a conditional autoregressive Dirichlet process (DP) that we call one-parameter dependent DP (ω-DDP). The appealing properties of this specification are that it has two equivalent representations and its inference can be implemented in a conditional Polya urn scheme....

Brain-specific polyA- transcripts are detected in polyA+ RNA: do complex polyA- brain RNAs really exist?

Transcripts encoded by 2 different rat genomic clones, rg13 and rg100, appear to be typical brain-specific polyA- RNAs, as defined by previous criteria (rare, polysomal, and postnatally expressed from single-copy genes). However, we have found by using a sensitive nuclease protection assay that low levels of these transcripts (10% and 3%, respectively) are detected in polyA+ RNA. To determine i...