background and purpose: sample size and its determination is one of the most important problems in health researches. calculating sample size for prevalence studies is one of the common questions of sample size topics. minimum sample size with least complexity is desirable in order to achieve the basic goal of these studies. this study aims to compare two formulas of sample size calculation for...

Abstract Virtual reality has great potential to enable remote collaborative work from anywhere in the world. Developing virtual into a platform suitable for natural interaction and immersive collaboration requires experience be reliably stable. For networked environment, perceived smoothness of motion is limited by tick rate, that is, frequency at which information distributed. As rate increase...

Given a set A $\mathbb {A}$ consisting of positive integers 1 < 2 ⋯ k $a_1<a_2<\cdots <a_k$ and k-term partition P : n + = $P: n_1+n_2 \cdots n_k=n$ , find the extremal denominators regular semi-regular continued fraction [ 0 ; x … ] $[0;x_1,x_2,\ldots ,x_n]$ with partial quotients i ∈ $x_i\in \mathbb where each $a_i$ occurs precisely $n_i$ times in sequence $x_1,x_2,\ldots ,x_n$ . In 1983, G. ...

In this paper we give a geometric condition which ensures that (q, p)-Poincaré-Sobolev inequalities are implied from generalized (1, 1)-Poincaré related to L1 norms in the context of product spaces. The concept eccentricity plays central role paper. We provide several type adapted different geometries and then show our self-improving method can be applied obtain special interesting Poincaré-Sob...

We establish an asymptotic formula for the number of lattice points in sets $$\begin{aligned} {\textbf{S}}_{h_1, h_2, h_3}(\lambda ): =\left\{ x\in {\mathbb {Z}}_+^3:\lfloor h_1(x_1)\rfloor +\lfloor h_2(x_2)\rfloor h_3(x_3)\rfloor =\lambda \right\} \quad \text {with}\quad \lambda \in {Z}}_+; \end{aligned}$$ where functions $$h_1, h_3$$ are constant multiples regularly varying form $$h(x):=x^c\e...

We present a search for RR Lyrae stars using the full six-year data set from Dark Energy Survey (DES) covering ~5,000 sq. deg. of southern sky. Using multi-stage multi-variate classification and light curve template-fitting scheme, we identify candidates with median 35 observations per candidate. detect 6,971 out to ~335 kpc, estimate that our sample is >70% complete at ~150 kpc. find excellent...

The Maxwell-Boltzmann speed distribution is the probability that describes speeds of particles ideal gases. valid for both un-mixed (one type particle) and mixed (two types particles). For particles, follow distribution. Also, most probable inversely proportional to square root mass.&#x0D; &#x0D; This paper proves ratio using computer-generated data based on Newton&amp;rsquo;s law motion. To ac...