in this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. the differential operator is taken in the riemann-liouville sense. applying the schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system d^{alpha}_{0+}x(t)=fleft(t,y(t),d^{p}_{0+}y(t)right), t in (0,...

‎let $g$ be a finite group and $d_2(g)$ denotes the probability ‎that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $g$‎. ‎we ‎will obtain lower and upper bounds for $d_2(g)$ in the case where ‎the sets $e_g(x)={yin g:[y,x,x]=1}$ are subgroups of $g$ for ‎all $xin g$‎. ‎also the given examples illustrate that all the ‎bounds are sharp.

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.

Formation micro imager (FMI) can directly reflect changes of wall stratums and rock structures. Conventionally, FMI images mainly are analyzed with manual processing, which is extremely inefficient and incurs a heavy workload for experts. Iranian reservoirs are mainly carbonate reservoirs, in which the fractures have an important effect on permeability and petroleum production. In this paper, a...

In  this paper, we investigate the generalizedHyers-Ulam-Rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{Z}-{0,pm1}$) in $p-$Banach spaces.

In this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the Hermitian matrix expression $$‎ ‎f(X,Y)=C_{4}-B_{4}Y-(B_{4}Y)^{*}-A_{4}XA_{4}^{*},$$ where $C_{4}$ is‎ ‎Hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$X$ and $Y$ satisfy‎ ‎the following consistent system of matrix equations $A_{3}Y=C_{3}‎, ‎A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2},X=X^{*}.$ As‎ ‎consequences‎, ‎we g...

The gene MIC2 is located in the pseudoautosomal region at the ends of the short arms of the X and Y chromosomes. In females MIC2 escapes X inactivation. We have analyzed the methylation pattern of MIC2 on the active X, the inactive X chromosomes, and the Y chromosome. The 5' end of the gene contains a GC rich region which is unmethylated on the active X, the inactive X and on the Y. The body of...