An increasing sequence $(x_i)_{i=1}^n$ of positive integers is an $n$-term Egyptian underapproximation $\theta \in (0,1]$ if $\sum_{i=1}^n \frac{1}{x_i} < \theta$. A greedy algorithm constructs $\theta$. For some but not all numbers $\theta$, the gives a unique best for $n$. infinite set rational constructed which underapproximations are best, and also studied.

in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

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...

In this article, we consider the misspecified optimization problem of minimizing a convex function $f(x;\theta ^*)$ in notation="LaTeX">$x$ over conic constraint set represented by notation="LaTeX">$h(x;\thet...

We define a constructive topos to be a locally cartesian closed pretopos. The terminology is supported by the fact that constructive toposes enjoy a relationship with constructive set theory similar to the relationship between elementary toposes and (impredicative) intuitionistic set theory. This paper elaborates upon one aspect of the relationship between constructive toposes and constructive ...

‎We use of two notions functionally convex (briefly‎, ‎F--convex) and functionally closed (briefly‎, ‎F--closed) in functional analysis and obtain more results‎. ‎We show that if $lbrace A_{alpha} rbrace _{alpha in I}$ is a family $F$--convex subsets with non empty intersection of a Banach space $X$‎, ‎then $bigcup_{alphain I}A_{alpha}$ is F--convex‎. ‎Moreover‎, ‎we introduce new definition o...

In the present explorative experimental study, we examined the diversity of electroencephalographic (EEG) short-term spectral patterns (SPs) within a broad frequency band (1.5-30Hz) for healthy adult subjects during closed eyes and open eyes resting conditions. The types of EEG SPs were assessed by counting all identical SPs with peaks in the same frequency bins from the pools of SPs, which wer...

BACKGROUND In this study, the magnitude and spatial distribution of theta power in the resting EEG were examined to explore the changes in the neurophysiological status of the alcoholic brain. Some state- and trait-related issues of theta power increases in the EEG of alcoholics were also examined. METHODS Absolute theta (3-7 Hz) power in eyes-closed EEGs of 307 alcohol-dependent subjects and...

OBJECTIVE This study investigated differences in EEG coherence measures between two groups of children with Attention-Deficit/Hyperactivity Disorder (AD/HD) - one with the more common EEG profile (increased theta), and a group with excess alpha activity as the dominant EEG abnormality. METHODS 26 children (aged 9-13years) with AD/HD were included in each of the excess-theta and excess-alpha g...