A limit-point criterion for a class of Sturm-Liouville operators defined in spaces

Using a recent result of Chernyavskaya and Shuster we show that the maximal operator determined by on , -\infty$">, where and the mean value of computed over all subintervals of of a fixed length is bounded away from zero, shares several standard ``limit-point at " properties of the case. We also show that there is a unique solution of that is in all , .

     

Flow equivalence and stochastic equivalence in G-networks

G-networks are novel product form queuing networks that, in addition to ordinary customers, contain unusual entities such as negative customers which eliminate normal customers, and triggers that move other customers from some queue to another. Recently we introduced one more special type of customer, a reset, which may be sent out by any server at the end of a service epoch, and that will reset the queue to which it arrives into its steady state when that queue is empty. A reset which arrives to a non-empty queue has no effect at all. The sample paths of a system with resets is significantly different from that of a system without resets, because the arrival of a reset to an empty queue will provoke a finite positive jump in queue length which may be arbitrarily large, while without resets positive jumps are only of size + 1 and they occur only when a positive customer arrives to a queue. In this paper we review this novel model, and then discuss its traffic equations. We introduce the concept of stationary equivalence for queueing models, and of flow equivalence for distinct queueing models. We show that the flow equivalence of two G-networks implies that they are also stationary equivalent. We then show that the stationary probability distribution of a G-network with resets is identical to that of a G-network without resets whose transition probabilities for positive (ordinary) customers has been increased in a specific manner. Our results show that a G-network with resets has the same form of traffic equations and the same joint stationary probability distribution of queue length as that of a G-network without resets.     

An intersection multiplicity in terms of -modules

The main aim of this paper is to discuss the relation between Serre's intersection multiplicity and the Euler form. The Euler form is defined to be an alternating sum of the length of -modules and is used by Mori and Smith to develop intersection theory over noncommutative rings. We show that they differ by a sign and that this relation is closely related to Serre's vanishing theorem.

     

Origin of the Nucleon Electromagnetic Form Factors Dipole Formula

Starting with the vector-meson-dominance parametrization of the electric and magnetic nucleon form factors, which are saturated just by the ground state vector-mesons , and , then aplying the strict Okubo-Zweig-Iizuka rule and the asymptotic behaviour of form factors as predicted by quark model of hadrons, the famous one-parameter dipole formula is derived. By its comparison with space-like data up to t=-5 GeV² the optimal value of the parameter under consideration is determined. Finaly, charge and magnetization distributions in proton and neutron are predicted.     

Microwave spectroscopic and ab initio studies of pyrolysis products of 2-nitrosopropene (syn form) and its pyrolysis mechanism

The pyrolysis products of CH₂=C(CH₃)---NO (syn form) have been determined by microwave spectroscopy. The pyrolysis products of CH₂=C(CH₃)---NO (syn form) and its ¹⁵N isotopic species were found to be CH₂=O, CH₃CN, and CH₃C¹⁵N. The produce of formaldehyde and methyl cyanide suggests that the C=C and N=O double bonds of CH₂=C(CH₃)---N=O (syn form) were broken. To explain the generation of the two molecules, a four-membered ring molecule (9) as an intermediate, is proposed. The four-membered ring molecule as an intermediate is also supported by ab initio MO calculation. Applying the pyrolysis mechanism obtained for 2-nitrosopropene (syn form) to that of 1,1,2-trichloronitrosoethane, one of its complicated pyrolysis mechanisms was explained. The rotational constants and geometrical parameters of two intermediates, 9 and CH₂=CCl---NO (13), were obtained by ab initio MO calculation (MP2/6-31G**) to predict their microwave spectra.     

Classical and Nonclassical Dynamic Problems of Sandwich Shells with a Transversely Soft Core

Based on the hypothesis of similarity of transverse displacements in thin-walled sandwich shells with a transversely soft core under dynamic and static loads, refined geometrically nonlinear dynamic equations of motion are constructed in the case of large variations in the parameters of the stress-strain state (SSS) in the tangential directions. For shells structurally symmetric across the thickness and loaded with initial static loads, linearized dynamic equations are derived, which, upon introducing the synphasic and antiphasic functions of displacements and forces, can be used to describe the synphasic and antiphasic buckling forms in the transverse and tangential directions. For nonshallow cylindrical and shallow spherical shells, the nonclassical problems on all possible vibration forms realized at zero indices of variability of the SSS parameters in the tangential directions are formulated and solved. For shallow shells of symmetric structure, the resolving equations are obtained by introducing, instead of tangential displacements and transverse tangential stresses in the core, the corresponding potential and vortex functions.     

Generalized Feynman–Kac Semigroups,Associated Quadratic Forms and Asymptotic Properties

In this paper, we study the Feynman–Kac semigroup T _t f(x)=E _x[f(X _t)exp(N _t)],where X _t is a symmetric Levy process and N _t is a continuous additive functional of zero energy which is not necessarily of bounded variation. We identify the corresponding quadratic form and obtain large time asymptotics of the semigroup. The Dirichlet form theory plays an important role in the whole paper.     

一类网络成本分配函数的规范性质

该文以数学方法论证了一类网络成本分配函数的性质,证明了成本分配函数具有规范形式的充要条件是它满足无记名性,可加性和等价性。并进一步论证了若成本分配函数还具有对成员数的单调递减性,它必是下游均等分配函数。     

矩阵的初等标准形与线性方程组

指出矩阵的初等标准形理论是线性方程组问题的理论基础     

Precise Measurement of Muon Capture on the Proton

The aim of the μCap experiment is a 1% measurement of the singlet capture rate Λ _S for the basic electro-weak reaction μ + p → n + ν_μ. This observable is sensitive to the weak form-factors of the nucleon, in particular to the induced pseudoscalar coupling constant g _P . It will provide a rigorous test of theoretical predictions based on the Standard Model and effective theories of QCD. The present method is based on high precision lifetime measurements of μ⁻ in hydrogen gas and the comparison with the free μ⁺ lifetime. The μ⁻ experiment will be performed in ultra-clean, deuterium-depleted H₂ gas at 10 bar. Low density compared to liquid H₂ is chosen to avoid uncertainties due to ppμ formation. A time projection chamber acts as a pure hydrogen active target. It defines the muon stop position in 3D and detects rare background reactions. Decay electrons are tracked in cylindrical wire-chambers and a scintillator array covering 75% of 4π. This revised version was published online in August 2006 with corrections to the Cover Date.