We study pseudospectral and spectral functions for Hamiltonian system J y ′ − B ( t ) = λ Δ $Jy^{\prime }-B(t)=\lambda \Delta (t)y$ differential equation l [ ] $l[y]=\lambda with matrix-valued coefficients defined on an interval I a , b $\mathcal {I}=[a,b)$ the regular endpoint a. It is not assumed that matrix weight ≥ 0 $\Delta (t)\ge 0$ invertible a.e. {I}$ . In this case function always exis...

We consider the non-local Liouville equation $${\left( { - \Delta } \right)^{{1 \over 2}}}u = {h_\varepsilon }{e^u} 1\,\,\,\,\,{\rm{in}}\,\,{\mathbb{S}^1},$$ corresponding to prescription of geodesic curvature on circle. build a family solutions which blow up, when hε approaches function h as ε → 0, at critical point harmonic extension provided some generic assumptions are satisfied.

The sequence of the clathrin heavy chain gene, CHC1, from Saccharomyces cerevisiae is reported. The gene encodes a protein of 1,653 amino acids that is 50% identical to the rat clathrin heavy chain (HC) (Kirchhausen, T., S. C. Harrison, E. P. Chow, R. J. Mattaliano, R. L. Ramachandran, J. Smart, and J. Brosius. 1987. Proc. Natl. Acad. Sci. USA. 84:8805-8809). The alignment extends over the comp...

 The ratio of independent random variables arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice random variables. Ratios of such random variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) a...

BACKGROUND Although I(f), encoded by the hyperpolarization-activated cyclic-nucleotide-modulated (HCN) channel gene family, is known to be functionally important in pacing, its mechanistic action is largely inferential and indeed somewhat controversial. To dissect in detail the role of I(f), we investigated the functional consequences of overexpressing in adult guinea pig left ventricular cardi...

Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. Given two derivations $delta$ and $delta'$ on a $C^*$-algebra $mathfrak A$, we prove that there exists a derivation $Delta$ on $mathfrak A$ such that $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdel...

Selected configuration interaction (SCI) for atomic and molecular electronic structure calculations is reformulated in a general framework encompassing all CI methods. The linked cluster expansion is used as an intermediate device to approximate CI coefficients B(K) of disconnected configurations (those that can be expressed as products of combinations of singly and doubly excited ones) in term...

The function of murine dendritic epidermal cells (dEC) remains largely speculative, probably because of the lack of a suitable in vivo model, although previous studies suggest that gamma/delta+ dEC may have originally evolved to serve as a self-protection mechanism(s). Our previous study demonstrated that the epidermis of mice that had spontaneously recovered from cutaneous graft-vs-host diseas...