The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by Özkoç and Aslım [10] called weakly $eR$-open functions and $e$-$theta$-open functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topolo...

Let $(X, \tau)$ and $(Y, \sigma)$ be topological spaces in which no separation axioms are assumed, unless explicitly stated if $\mathcal{I}$ is an ideal on $X$.Given a multifunction $F\colon (X, \tau)\rightarrow (Y, \sigma)$, $\alpha,\beta$ operators \tau)$, $\theta,\delta$ proper $X$. We introduce study upper lower $(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous multifunctions.A said to...

We study the spanning properties of Theta-Theta graphs. Similar in spirit with the Yao-Yao graphs, Theta-Theta graphs partition the space around each vertex into a set of k cones, for some fixed integer k > 1, and select at most one edge per cone. The difference is in the way edges are selected. Yao-Yao graphs select an edge of minimum length, whereas Theta-Theta graphs select an edge of minimu...

We prove the reducibility of 1-D quantum harmonic oscillators in $\mathbb R$ perturbed by a quasi-periodic time potential $V(x,\omega t)$ under following conditions, namely there is $C>0$ such that \begin{equation*} |V(x,\theta)|\le C,\quad|x\partial_xV(x,\theta)|\le C,\quad\forall~(x,\theta)\in\mathbb R\times\mathbb T_\sigma^n. \end{equation*} The corresponding perturbation matrix $(P_i^j(\the...

The medial septum/vertical limb of diagonal band complex (MS/vDB) consists of cholinergic, GABAergic, and glutamatergic neurons that project to the hippocampus and functionally regulate attention, memory, and cognitive processes. Using tyrosine hydroxlase (TH) immunocytochemistry and dark-field light microscopy, we found that the MS/vDB is innervated by a sparse network of TH-immunoreactive (pu...

The aim of this paper is to introduce fuzzy ($e$, almost) $e^{*}$-regular spaces in $check{S}$ostak's fuzzy topological spaces. Using the $r$-fuzzy $e$-closed sets, we define $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points and their properties. Moreover, we investigate the relations among $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points, $r$-fuzzy ($e$, almost) $e^{*}$-regular spaces a...

objectives: autism spectrum disorder (asd) is a group of neurodevelopment syndromes with impairments in social communications and restrictive or repetitive behaviors. neurofeedback is a new method that may regulate neuro and metabolic function in brain. this study is semi-experimental, with pre and post test.  methods: in 26 children with asd, 40 sessions of neurofeedback were done. brain waves...