Decomposability of matrix polynomials with coefficients possessing quasi-simple structure

The decomposability of matrix polynomials with commuting coefficients of quasi-simple structure into regular factors and the solvability of the corresponding matrix polynomial one-sided equations are investigated.Translated from Ukrainskii Matematicheskie Zhurnal, Vol. 44, No. 12, pp. 1716–1718, December, 1992.     

Selective saturation and inversion of multiple resonances in high-resolution solid-state 13C experiments using slow spinning CP/MAS and tailored DANTE pulse sequences.

Taking advantage of the long 13C T1 values generally encountered in solids, selective saturation and inversion of more than one resonance in 13C CP/MAS experiments can be achieved by sequentially applying several DANTE pulse sequences centered at different transmitter frequency offsets. A new selective saturation pulse sequence is introduced composed of a series of 90 degrees DANTE sequences separated by interrupted decoupling periods during which the selected resonance is destroyed. Applications of this method, including the simplification of the measurement of the principal values of the 13C chemical shift tensor under slow MAS conditions, are described. The determination of the aromaticity of coal using a relatively slow MAS rate is also described.     

Faddeev-Noble Versus Sasakawa-Sawada Equations for the Nuclear Three-Body Coulomb Problem

We compare the efficiency of two Faddeev-type approaches for the nuclear three-body Coulomb problem. The first one is a modification of Noble’s approach, the second one is due to Sasakawa and Sawada. In an integral-equation formulation both of these methods rely on the same Green’s operators and driving terms. The differences lie in the treatment of the long-range Coulomb potentials. Numerical examples show that the modified Faddeev-Noble approach provides for faster convergence.     

A Lower Bound for the Differences of Powers of Linear Operators

Let T be a bounded linear operator in a Banach space, with σ（T）={1}. In 1983, Esterle-Berkani＇ s conjecture was proposed for the decay of differences （I - T） T^n as follows： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.     

Harmonic Calculus on Fractals - A Measure Geometric Approach I

Differentiation of functions w.r.t. finite atomless measures with compact support on the real line is introduced. The related harmonic calculus is similar to that of the classical Lebesgue case. As an application we obtain the Weyl exponent for the spectral asymptotics of the Laplacians w.r.t. linear Cantor-type measures with arbitrary weights.     

Bargaining over the division of a shrinking pie: An axiomatic approach

The Bargaining Problem paradigm is extended to time-consuming conflict situations. Such a situation can be represented by a chain of bargaining domains, each representing the conflict at a different point in time. The solution function selects a point in the union of all these domains. We characterize a solution function which satisfies several requirements and explore its properties. One of the results is that an extension of the Adding requirement (Thomson-Myerson 1980) is enough, under some conditions, to yield a solution point, so there is no need to extend the stronger requirements of Independence of Irrelevant Alternatives (Nash 1950) or Monotonicity (Kalai-Smorodinsky 1975).     

A few points on omnidirectional band gaps in one-dimensional photonic crystals

The universal condition for the formation of omnidirectional band gaps (OBG) in photonic crystal (PC) was derived with consideration of permeability of the materials. And it was found that there are four kinds of PCs: one of them has no OBG, and one always possesses OBG. For the other two kinds of PCs, there are OBG for only TM or TE waves respectively. Moreover, in all PCs, the OBG can be broadened by decreasing the refractive index of the ambient medium or/and increasing the contrast between the wave impedances of the component materials of the PC. PACS 42.70.Qs; 71.20.Tx     

相位差与q变形广义相干叠加态的压缩特性

对于q变形的非简谐振子广义相干态的叠加态β〉+eiφβeiδ〉,其量子涨落的可能高阶压缩阶数可以表示为k≠2πn/δ,这里n是整数.当δ=π时,压缩阶数不能是偶数即只能是奇数,这正是q变形非简谐振子广义奇偶相干态的结果.由此表明参数相位差δ对决定q变形的非简谐振子广义相干态叠加态的高阶压缩阶数起决定性作用.     

Creation of a donor-acceptor pair for studying intraprotein electron transfer with the participation of amino-acid derivatives of fullerene C60

Efficient quenching of eosin phosphorescence by amino-acid derivatives of fullerene (AADFs) such as C₆₀-alanine and C₆₀-glycine in aqueous solutions indicates the possibility of transferring electrons from eosin to fullerene upon collisions or in the exciplex state. To investigate electron transfer in the protein structure, we studied the process of incorporation of C₆₀-alanine and C₆₀-glycine into the heme pocket of myoglobin by controlling Förster quenching. The dissociation constant for the protein-AADF complex was estimated.     

Integrability of a system of two nonlinear Schrödinger equations

P. P. Shirshov Institute of Oceanology, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 79, No. 2, pp. 180–184, May, 1989.