Dissociative excitation cross sections of the lead atom in collisions between electrons and PbI2 molecules

Dissociative excitation of the lead atom in e-PbI₂ collisions has been studied experimentally. 27 excitation cross sections were measured for an energy of the exciting electrons equal to 100 eV. Nine optical excitation functions were recorded with variation of the electron energy in the range 0–100 eV. The most probable reaction channels for low electron energies are discussed, as well as the ratio of the dissociative excitation cross sections for the lead atom in e-PbI₂ and e-PbCl₂ collisions. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 6, pp. 701–706, November–December, 2006.     

Spectral line suppression and sideband narrowing via quantum interference

We reveal that for a realistic system, interference effects are obtained such as the suppression of central line and inner sidebands and the narrowing of the outer fluorescence sidebands. For this purpose, we consider a spontaneous decay from an excited state to a metastable state when the excited and metastable states are resonantly coupled to an auxiliary metastable state by a laser field and a microwave field, respectively. The fluorescence spectrum evolves from a five-peaked structure into a doublet of ultrasharp lines as the ratio of the laser field Rabi frequency to the microwave Rabi frequency is decreased. The physical origin is presented in terms of dressed states.     

Clifford Analysis Techniques for Spherical PDE

For a ? R\alpha \in \mathbf{R}, the class of a-\alpha -order spherical harmonic functions in an open set W í\Omega \subseteq S^n-1\mathbf{S}^{n-1}, H^a(W)H^{\alpha }(\Omega ) is defined as the C²-C^{2}-solutions of D_au=0\Delta _{\alpha }u=0; where D_a=D_s+a(n+a-2)\Delta _{\alpha }=\Delta _{s}+\alpha (n+\alpha -2) is the spherical Laplace--Beltrami operator of order a\alpha and D_s\Delta _{s} is the radially independent part of the Laplace operator. We obtain a Green's integral formula for the functions in H^a(W)H^{\alpha }(\Omega ) with kernel expressed as a Gegenbauer function. As generalizations, higher order spherical iterated Dirac operators are defined in a polynomial form. Integral representations of the null solutions to these operators and an intertwining formula relating these operators on the sphere and their analogues in Euclidean space are presented.     

Toward Fuzzy Optimization without Mathematical Ambiguity

Fuzzy programming has been discussed widely in literature and applied in such various disciplines as operations research, economic management, business administration, and engineering. The main purpose of this paper is to present a brief review on fuzzy programming models, and classify them into three broad classes: expected value model, chance-constrained programming and dependent-chance programming. In order to solve general fuzzy programming models, a hybrid intelligent algorithm is also documented. Finally, some related topics are discussed.     

信用担保风险的模糊综合评审研究

信用担保机构是连接银行和企业的桥梁，对于改善企业融资环境和拓展银行业务具有重要意义，信用担保风险的评审是担保机构能否生存及有效运行的关键。信用风险的评审机制主观性强，对担保项目进行客观，公正的评审比较困难。本采用模糊数学中的综合判别方法，全面考虑风险评审所涵盖的各种风险指标及其重要度，建立了定性分析与定量分析方法相结合的信用担保风险综合评审模型，为担保机构提供了一种相对科学、客观的评审方法。     

Linear nonstationary optical dimensional resonances in atomic nanostructures

The existence of linear nonstationary optical resonances in a diatomic nanostructural object with a dipole-dipole atomic interaction has been proved. A new solution to the joint system of modified Bloch optical equations and nonlocal field equations is obtained for time intervals much shorter than the times of phase and energy relaxation. Formulas for effective polarizabilities of the object’s atoms, which have a set of dimensional resonances, are derived. The frequencies of these resonances significantly differ from the eigenfrequencies of the object’s atoms, and their properties depend on the interatomic distance, light-pulse duration, initial atomic inversions, and the orientation of the object’s axis relative to the direction of incidence of the external light wave.     

Infinite paths in planar graphs III, 1‐way infinite paths

An infinite graph is 2‐indivisible if the deletion of any finite set of vertices from the graph results in exactly one infinite component. Let G be a 4‐connected, 2‐indivisible, infinite, plane graph. It is known that G contains a spanning 1‐way infinite path. In this paper, we prove a stronger result by showing that, for any vertex x and any edge e on a facial cycle of G, there is a spanning 1‐way infinite path in G from x and through e. Results will be used in two forthcoming papers to establish a conjecture of Nash‐Williams. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Balancing a Rotor with Two Coupled Perfectly Rigid Bodies

The steady motions of a vertical rotor balanced by two coupled perfectly rigid bodies (PRBs) are analyzed for stability. The rotor executes plane-parallel motions. The PRBs can rotate together about the rotor axis and about its transverse axes through equal angles but in opposite directions. It is established that when the mass of the PRBs is much less than that of the rotor and the rotor spins with a superresonant speed, only the basic steady motions, which are those of the best-balanced rotor, are asymptotically stable.     

Forward-angle yields of 2≤Z≤11 isotopes in the reaction of 18O(35A MeV) with 9Be

A systematic investigation of the forward-angle inclusive yields of 2≤Z≤11 isotopes produced in collisions of ¹⁸O projectile nuclei with a ⁹Be target in the Fermi energy region (35A MeV) is performed. The measurements were based on the use of the COMBAS double achromatic kinematical separator in the spectrometry mode at the Flerov Laboratory of Nuclear Reactions at the Joint Institute for Nuclear Research, FLNR (JINR, Dubna). The velocity, isotopic, and element distributions are presented. There is no unique mechanism that would explain the total set of results obtained in this experiment. A dominant role of low-energy reaction mechanisms is observed. The intensity of secondary beams of halolike nuclei ¹¹Li, ¹²Be, and ¹⁴Be is determined.     

Quantum discreteness effects and flicker fluctuations in tunneling conductivity

An analysis of events in the tunneling junction shows that the interaction of one-electron processes in a many-electron system may be a source of scale-invariant low-frequency fluctuations of conductivity (the interaction consists in that the quantum probability of an electron transition depends on fast random changes in the environment in the course of the transition, including the changes caused by analogous transitions). The theory relates flicker fluctuations in the tunneling conductivity to the discrete character of the spectrum of electron states and explains the nonlinearity of the noise-current characteristic observed in nanocomposites.