In this paper, the exact distribution of largest eigenvalue a singular random matrix for multivariate analysis variance (MANOVA) is discussed. The key to developing theory eigenvalues use heterogeneous hypergeometric functions with two arguments. study, we define beta [Formula: see text]-matrix and extend distributions nonsingular case. We also give joint density in terms functions.

The aim of this paper is to introduce and study two new classes of functions called weakly $e^{*}$-open functions and weakly $e^{*}$-closed functions via the concept of $e^{*}$-open set defined by Ekici cite{erd1}. The notions of weakly $e^{*}$-open and weakly $e^{*}$-closed functions are weaker than the notions of weakly $beta$-open and weakly $beta$-closed functions defined by Caldas and Nava...

This paper deals with the study of global analysis following $(1,2)-$type system non-linear difference equations:\[ u_{n+1}=\frac{\alpha v_{n-1}}{\beta +\gamma v_{n}^{p}v_{n-2}^{q}},\ \ v_{n+1}=\frac{\alpha _{1}u_{n-1}}{\beta _{1}+\gamma _{1}u_{n}^{p}u_{n-2}^{q}},\ n=0,1,... \] where parameters $\alpha ,\beta ,\gamma ,\alpha _{1},\beta _{1},\gamma _{1,}p,q$ and initial conditions $u_{i},v_{i},$...

CaMK-II (the (type II) multifunctional Ca2+/CaM-dependent protein kinase) has been implicated in diverse neuronal and non-neuronal functions, including cell growth control. CaMKII expression was evaluated in a variety of human tumor cell lines using RT-PCR (reverse transcriptase coupled polymerase chain reaction). PCR primers which flanked the CaMK-II variable domain were used so that all possi...

Consider the nearest-neighbor Ising model on $$\Lambda _n:=[-n,n]^d\cap {\mathbb {Z}}^d$$ at inverse temperature $$\beta \ge 0$$ with free boundary conditions, and let $$Y_n(\sigma ):=\sum _{u\in \Lambda _n}\sigma _u$$ be its total magnetization. Let $$X_n$$ magnetization perturbed by a critical Curie–Weiss interaction, i.e., $$\begin{aligned} \frac{d F_{X_n}}{d F_{Y_n}}(x):=\frac{\exp [x^2/\le...

An in situ 35S-labeled guanosine 5'-3-O-(thio)triphosphate (GTP gamma S) binding procedure was developed to assay light-stimulated G protein activity in Drosophila compound eyes. We found that Drosophila with mutations in G beta e, an abundant photoreceptor-specific G protein beta subunit essential for photoexcitation, are defective in light-stimulated [35S]GTP gamma S binding. We confirmed tha...

Aims/ Objectives: Recently, it has been shown by Ighachane and Akkouchi [1] that using binomial coefficients, one can derive some new refinements of Holder’s inequalities. This inequalities then be applied to a wide class special functions such as the Nielsen’s beta function extended gamma functions. In this paper, we have derived generalizations previously known number theoretic Furthermore, b...

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...

introduction genetic evaluation and estimation of breeding value are one of the most fundamental elements of breeding programmes for genetic improvement. recently, genomic selection has become an efficient method to approach this aim. the accuracy of estimated genomic breeding value is the most important factor in genomic selection. different studies have been performed addressing the factors a...