in the paper‎, ‎some new existence theorems of maximal elements for‎ ‎$mathscr{f}_{c,theta}$-mappings and $mathscr{f}_{c,theta}$-majorized mappings are established‎. ‎as applications, ‎some new existence theorems of equilibrium points for‎ ‎one-person games‎, ‎qualitative games and generalized games are obtained‎. ‎our results unify and generalize most known results‎ ‎in recent literature‎.

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...

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 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...

The degree to which electroencephalographic spectral peaks are independent, and the relationships between their frequencies have been debated. A novel fitting method was used to determine peak parameters in the range 2-35 Hz from a large sample of eyes-closed spectra, and their interrelationships were investigated. Findings were compared with a mean-field model of thalamocortical activity, whic...

Given a nondecreasing sequence $$\Lambda =\{\lambda _n>0\}$$ such that $$\displaystyle \lim _{n\rightarrow \infty } \lambda _n=\infty ,$$ we consider the $$\mathcal {N}_\Lambda :=\left\{ _ne^{i\theta _n},n\in \,\mathbb {N}\right\} $$ , where $$\theta _n$$ are independent random variables uniformly distributed on $$[0,2\pi ].$$ We discuss conditions under which N_\Lambda is zero set (a uniqness ...

For $N\geq 3$, by the seminal paper of Brezis and V\'eron (Arch. Rational Mech. Anal. 75(1):1--6, 1980/81), no positive solutions $-\Delta u+u^q=0$ in $\mathbb R^N\setminus \{0\}$ exist if $q\geq N/(N-2)$; for $11$ $\theta\in \mathbb R$, we prove that nonlinear ell...

The main purpose of this paper is to study normed hypervector spaces. We generalize some definitions such as basis, convexity, operator norm, closed set, Cauchy sequences, and continuity in such spaces and prove some theorems about them.