For simplicity, we adopt the following rules: a, b, x, y, z, X, Y , Z denote sets, n denotes a natural number, i denotes an integer, r, r1, r2, r3, s denote real numbers, c, c1, c2 denote complex numbers, and p denotes a point of En T. Let us observe that every element of IQ is irrational. Next we state a number of propositions: (1) If 0 ≤ r and 0 ≤ s and r2 = s2, then r = s. (2) If frac r ≥ fr...

Matrix metalloproteinases (MMPs) are widely hypothesized to regulate signaling events through processing of extracellular matrix (ECM) molecules. We previously demonstrated that membrane-associated Mmp2 is expressed in exit glia and contributes to motor axon targeting. To identify possible substrates, we undertook a yeast interaction screen for Mmp2-binding proteins and identified the novel ECM...

The Plurality problem - introduced by Aigner \cite{A2004} - has many variants. In this article we deal with the following version: suppose we are given $n$ balls, each of them colored by one of three colors. A \textit{plurality ball} is one such that its color class is strictly larger than any other color class. Questioner wants to find a plurality ball as soon as possible or state there is no,...

Brownian motion with drift is constructed on the real line as the almost sure limit of a sequence of random walks. Central to the construction is an embedded varying environment branching process, which encodes the sample path behaviour of the limiting diiusion. We show how a single small time bound on the normed limit of the branching process leads to diierent small and large time bounds on th...

PURPOSE To determine the appropriateness of statistical models using the truncated Gaussian distribution and gamma distribution for diffusion signal decay, and to assess the correlation between the parameters obtained from the statistical models and estimated glomerular filtration rate (eGFR). METHODS Twenty-nine patients with chronic kidney disease and 21 healthy volunteers were included and...

Background: Ionizing radia on causes cogni ve impairment in adult brain. However, the effects of various irradia on protocols with frac onated fixed total dose on hippocampal func on have not yet been studied. Materials and Methods: Frac onated whole brain irradia on with a total dose of 36 Gy was performed according to the following protocols: 2Gy-18 frac ons (2Gy*18), 4Gy-9 frac on (4Gy*9) an...

Shifting markets can cause unexpected, stochastic changes in rural landscapes that may take local communities by surprise. Preferential siting of new industrial facilities in poor areas or in areas with few regulatory restrictions can have implications for environmental sustainability, human health, and social justice. This study focuses on frac sand mining-the mining of high-quality silica san...

Hydraulic fracturing is used to increase the permeability of shale gas formations and involves pumping large volumes of fluids into these formations. A portion of the frac fluid remains in the formation after the fracturing process is complete, which could potentially contribute to deleterious microbially induced processes in natural gas wells. Here, we report on the geochemical and microbiolog...

The Food Research and Action Center (FRAC) is pleased to re-launch FRAC Focus: Obesity and Poverty. This periodical e-newsletter focuses on obesity as it relates to lowincome children and adults, looking at the intersection of obesity, income, food insecurity, the federal nutrition programs, and federal food and nutrition policy. Each issue highlights relevant research and reports recently rele...

The harmonic index of a graph $G$, denoted by $H(G)$, is defined asthe sum of weights $2/[d(u)+d(v)]$ over all edges $uv$ of $G$, where$d(u)$ denotes the degree of a vertex $u$. Hu and Zhou [Y. Hu and X. Zhou, WSEAS Trans. Math. {bf 12} (2013) 716--726] proved that for any bicyclic graph $G$ of order $ngeq 4$, $H(G)le frac{n}{2}-frac{1}{15}$ and characterize all extremal bicyclic graphs.In this...