Separation in distributive congruence lattices

We define separable sets in algebraic lattices. For a finitely generated congruence distributive variety V \mathcal{V} , we show a close connection between non-separable sets in congruence lattices of algebras in V \mathcal{V} and the structure of subdirectly irreducible algebras in V \mathcal{V} . We apply the general results to some lattice varieties.     

Fixed Point Theorems on Product Topological Spaces and Applications

A new collectively fixed point theorem for a family of set-valued mappings defined on product spaces of non-compact topological spaces without linear structure is proved and some special cases are also discussed. As applications, some non-empty intersection theorems of sets with convex sections and equilibrium existence theorem of abstract economies are obtained under much weaker assumptions. Our results includes a number of known results as many special cases.     

Rapid magnetization reversal in magnetic small particles induced by non-static bias field

Magnetization reversal processes by a switching field in single-domain nano-sized magnetic particles in the presence of a small transverse non-static bias field are studied. Applying an oscillating bias field instead of a static field, the reversal time becomes much shorter when the switching field is slightly stronger than the effective anisotropy field. A pulsed bias field of a suitably chosen duration in the nanosecond scale is found to induce a rapid switching, even when the switching field is smaller than the anisotropy field. The dependence of the reversal time on the frequency of an oscillating bias field and the duration of a pulsed bias field are studied. The present work thus complement the earlier studies on switching in the presence of a static bias field.     

Measurements of total and positronium-formation cross sections for the scattering of positrons by alkali atoms

We present a review of our recent measurements of total cross sections (Q _T's) for the scattering of positrons by Na, K, and Rb, and positronium-formation cross sections (Q _Ps's) for Na and K. For our total cross section measurements, a beam transmission technique has been used. For ourQ _Ps measurements, our approach involves setting upper and lower limits onQ _Ps using a combination of (1) measuring the transmission of the positron beam with the angular discrimination of the apparatus made as poor as possible, and (2) measuring the 511 keV annihilation gamma rays in coincidence produced by the decay of para-Ps formed in the scattering cell. Comparison with theoretical calculations shows that our measuredQ _T's andQ _Ps's for Na and K agree reasonably well with a close coupling approximation (CCA) calculation which takes into account the formation of Ps in then=1 andn=2 states. In the 3–10 eV energy range, this calculation predicts a peak in theQ _T's andQ _Ps's for K which also appears in our measurements. The absence of such a peak in our measuredQ _T's andQ _Ps's (preliminary) for Na in this energy range is also consistent with the same theory. Comparisons with five-state CCA calculations ofQ _T which do not take Ps-formation into account also show good agreement with our positron-Na, K, and RbQ _T measurements for energies above 20 eV, but show dramatic departures from our measurements below 10 eV for K and Rb.     

Global optimization by random perturbation of the gradient method with a fixed parameter

The paper deals with the global minimization of a differentiable cost function mapping a ball of a finite dimensional Euclidean space into an interval of real numbers. It is established that a suitable random perturbation of the gradient method with a fixed parameter generates a bounded minimizing sequence and leads to a global minimum: the perturbation avoids convergence to local minima. The stated results suggest an algorithm for the numerical approximation of global minima: experiments are performed for the problem of fitting a sum of exponentials to discrete data and to a nonlinear system involving about 5000 variables. The effect of the random perturbation is examined by comparison with the purely deterministic gradient method.     

Influence of intrachain hydrogen bonding on the cyclization of a polystyrene chain

Cyclization of a polystyrene chain (M_n = 10,600; M_w/M_n = 1.09) both ends labeled with 4-(1-pyrenyl)butanoamide groups was studied in cyclohexane between 25 and 95°C. The amide groups (peptide bonds) at both ends can form an intrachain hydrogen bond between the amide hydrogen at one chain end and the carbonyl oxygen at the other. The presence of two sets of conformers, random coils, and chains cyclized through hydrogen bonding, complicates the data analysis. The pyrene excimer kinetics of this polymer is well described by a model composed of two monomers (hydrogen bonded and nonbonded chains) and one excimer, in equilibrium. The cyclization rate constant for hydrogen-bonded chains is larger than the one for nonhydrogen-bonded chains. The pyrene excimer binding energy (ca. 1.6 kcal/mol) is lower than the published value for nonhydrogen-bonded chains (～ 9 kcal/mol), suggesting that intrachain hydrogen bonding hinders the stabilization of the excimer. © 1994 John Wiley & Sons, Inc.     

完全二部图Ka,b的迭线图L^m（Ka，b）的谱特征

本证明了当(a，b)不属于{(1，8)，(2，4)，(3，6)，(4，4)，(2s^2-s，2s^2 s))时，L^m(Ka,b)以谱为特征，其中a≤b，s≥2．