Solutions of nonlinear evolution inclusions

In this paper, the solution of the nonlinear evolution inclusion problem of the form u^′(t)+B(t,u(t))∋f(t) is studied. In this problem, the operators are of type (M) or type (S₊), which are different from those of pseudo-monotone operators that had been studied by many authors. At the same time, we study the perturbation problem. In fact, many kinds of evolution equations can be generalized by this problem. The former results are improved and generalized by our conclusions, and we will give more applications.     

Global well-posedness and decay estimates of strong solutions to a two-phase model with magnetic field

In this paper, we consider the Cauchy problem for a two-phase model with magnetic field in three dimensions. The global existence and uniqueness of strong solution as well as the time decay estimates in $H^2({\mathbb{R}}^3)$ are obtained by introducing a new linearized system with respect to $(n^{\gamma }?{\stackrel{?}{n}}^{\gamma },n?\stackrel{?}{n},P?\stackrel{?}{P},u,H)$ for constants $\stackrel{?}{n}\ge 0$ and $\stackrel{?}{P}>0$, and doing some new a priori estimates in Sobolev Spaces to get the uniform upper bound of $(n?\stackrel{?}{n},n^{\gamma }?{\stackrel{?}{n}}^{\gamma })$ in $H^2({\mathbb{R}}^3)$ norm.     

Lorentz transforms of the invariant Dirac algebra

The Dirac equation, as a 4×4-hyperbolic system on ³, possesses an invariant algebra of global pseudodifferential operators-in the sense that conjugation with the Dirac time propagator leaves the algebra invariatn (cf. [CX]. Chapter 10). In this paper we examine the relation between the two invariant algebras att=0 and att'=0 when (t,x) and (t',x') are coordinates of Minkowsky space related by a (proper) Lorentz transform. For vanishing electromagnetic potentials these algebras are transforms of each other by the implied change of dependent and independent variables. In the general case such a space-time transform will make the potentials time dependent, hence also the algebra dependent on the initial plane.     

Invariance Principles in Metric Diophantine Approximation

In [7], LeVeque proved a central limit theorem for the number of solutions p,q of

Explicit congruences for the partition function modulo every prime

Let p(n) denote the number of unrestricted partitions of the positive integer n, and let m be a prime $\geq 13$. We prove, for k = 1, explicit congruences of the form where $r_{m,k}, \delta_{m,k}$ are integers depending on m and k and $\phi_{m,k}(z)$ are explicitly computable level one holomorphic modular forms of small weight. We also give theoretical and numerical support that the congruences also hold for k > 1. Our main idea is a level reduction result for the modular forms which originated from Atkin-Lehner. From our result, we deduce periodicity properties for the partition function with short periods which improve upon recent results of K. Ono. Received: 24 January 2002     

Generalized measures in gauge theory

LetP M be a principalG-bundle. We construct well-defined analogs of Lebesgue measure on the spaceA of connections onP and Haar measure on the groupG of gauge transformations. More precisely, we define algebras of cylinder functions on the spacesA,G, andA/G, and define generalized measures on these spaces as continuous linear functionals on the corresponding algebras. Borrowing some ideas from lattice gauge theory, we characterize generalized measures onA,G, andA/G in terms of graphs embedded inM. We use this characterization to construct generalized measures onA andG whenG is compact. The uniform generalized measure onA is invariant under the group of automorphisms ofP. It projects down to the generalized measure onA/G considered by Ashtekar and Lewandowski in the caseG = SU(n). The generalized Haar measure onG is right- and left-invariant as well as Aut(P)-invariant. We show that averaging any generalized measure onA against generalized Haar measure gives aG-invariant generalized measure onA.     

Matrix IR spectra and quantum chemical studies of the reaction between difluorostannylene and hept-1-yne. The first direct observation of a carbene analog π-complex with alkne

IR studies of SnF₂ and hept-1-yne codeposited in an argon matrix at 12 K has revealed new bands at 540, 565, 1011, 2088 and 3256 cm^–1, assigned to the formation of a complex between SnF₂ and the alkyne. Quantum chemical AM1 and PM3 calculations confirm this assignment to the -complex of SnF₂ and the triple bond of hept-1-yne, and show that the complex forms without an activation barrier. The energy of the formation of the complex according to AM1 and PM3 calculations is 7.4 and 9.1 kcal/mol, respectively. The calculations indicate that the product of the cycloaddition of SnF₂ to a triple bond, stannyrene, is significantly less stable than the -complex.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 54–56, January, 1994.