We consider a bounded domain \(\Omega\) of \(\mathbb{R}^N\), \(N \geq 3\), \(h\) and \(b\) continuous functions on \(\Omega\). Let \(\Gamma\) be closed curve contained in study existence positive solutions \(u \in H^1_0(\Omega)\) to the perturbed Hardy-Sobolev equation: \[-\Delta u+hu+bu^{1+\delta}=\rho^{-\sigma}_{\Gamma} u^{2^*_{\sigma}-1} \quad \textrm{ } \Omega,\] where \(2^*_{\sigma}:=\frac...

The 180-amino acid core of the TATA-binding protein (TBPcore) is conserved from Archae bacteria to man. Vertebrate TBPs contain, in addition, a large and highly conserved N-terminal region that is not found in other phyla. We have generated a line of mice in which the tbp allele is replaced with a version, tbp(Delta N), which lacks 111 of 135 N-terminal amino acid residues. Most tbp(Delta N/Del...

We derive the multi-scaling of probability distributions of multi-particle configurations for the binary reaction-diffusion system in A + A --> O in d < or =2 and for the ternary system in 3A --> O in d=1. For the binary reaction we find that the probability Pt(N, Delta V) of finding N particles in a fixed volume element Delta V at time t decays in the limit of large time as (ln t/t)N(ln t)-N(N...

The clock synchronization problem is to determine the time difference Delta between two spatially separated clocks. When message delivery times between the two clocks are uncertain, O(2(2n)) classical messages must be exchanged between the clocks to determine n digits of Delta. On the other hand, as we show, there exists a quantum algorithm to obtain n digits of Delta while communicating only O...

Three cytokinin-over-producing mutants of the moss, Physcomitrella patens, have been shown to convert [8-(14)C]adenine to N(6)-[(14)C](Delta(2)-isopentenyl)adenine, the presence of which was confirmed by thin layer chromatography, high performance liquid chromatography, and recrystallization to constant specific radioactivity. The labeled cytokinin was detected in the culture medium within 6 ho...

Over the years, different types of hyperideals have been introduced in order to let us fully realize structures hyperrings general. The aim this research work is define and characterize a new class Krasner $(m,n)$-hyperring that we call n-ary $J$-hyperideals. A proper hyperideal $Q$ with scalar identity $1_R$ said be an $J$-hyperideal if whenever $x_1^n \in R$ such $g(x_1^n) Q$ $x_i \notin J_{(...

We consider the quasilinear Kirchhoff's problem$$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$with the initial conditions  $ u(x,0) = u_0 (x)$  and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ;  f(u)=|u|^{a}u$ and $(phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} )$ is a positive function. The purpose of our work is to ...

The absolute, average, and differential phase shifts that p- and s-polarized light experience in total internal reflection (TIR) at the planar interface between two transparent media are considered as functions of the angle of incidence phi. Special angles at which quarter-wave phase shifts are achieved are determined as functions of the relative refractive index N. When the average phase shift...