For a quasiregular mapping $$f:{\mathbb {R}}^n \rightarrow {\mathbb {R}}^n$$ , with $$n\ge 2$$ Julia limiting direction $$\theta \in S^{n-1}$$ arises from sequence $$(x_n)_{n=1}^{\infty }$$ contained in the set of f, $$|x_n| \infty $$ and $$x_n/|x_n| \theta . directions have been extensively studied for entire meromorphic functions plane. In this paper, we focus on higher dimensions. First...

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...

For $X(n)$ a Rademacher or Steinhaus random multiplicative function, we consider the polynomials $$ P_N(\theta) = \frac1{\sqrt{N}} \sum_{n\leq N} X(n) e(n\theta), and show that $2k$-th moments on unit circle \int_0^1 \big| \big|^{2k}\, d\theta tend to Gaussian in sense of mean-square convergence, uniformly for $k \ll (\log N / \log N)^{1/3}$, but contrast case i.i.d. coefficients, this behavior...

Recently the author introduced a semidefinite upper bound on the square of the stability number of a graph, the inverse theta number, which is proved here to be multiplicative with respect to the strong graph product, hence to be an upper bound for the square of the Shannon capacity of the graph. We also describe a heuristic algorithm for the stable set problem based on semidefinite programming...

The serine/threonine-specific protein kinase C (PKC)-theta is predominantly expressed in T cells and localizes to the center of the immunological synapse upon T cell receptor (TCR) and CD28 signaling. T cells deficient in PKC-theta exhibit reduced interleukin (IL)-2 production and proliferative responses in vitro, however, its significance in vivo remains unclear. We found that pkc-theta(-/-) m...

The speed of theta brain oscillatory activity is thought to play a key role in determining working memory (WM) capacity. Individual differences in the length of a theta cycle (ranging between 4 and 7 Hz) might determine how many gamma cycles (>30 Hz) can be nested into a theta wave. Gamma cycles are thought to represent single memory items; therefore, this interplay could determine individual m...

glutathione s-transferases (gsts) are encoded by a superfamily of genes and play a role in the detoxification of potential carcinogens. the human gsts are divided into four classes: alpha, mu, pi and theta. previous studies indicated that the absence of the glutathione s-transferase m1 (gstm1) protein correlated with an increased risk of developing some types of cancers. association between spe...