Shape-preserving bivariate polynomial approximation inC([−1,1]×[−1,1])

In this paper we construct bivariate polynomials attached to a bivariate function, that approximate with Jackson-type rate involving a bivariate Ditzian-Totik ω2-modulus of smoothness and preserve some natural kinds of bivariate monotonicity and convexity of function.The result extends that in univariate case-of D. Leviatan in [5-6], improves that in bivariate case of the author in [3] and in some special cases, that in bivariate case of G. Anastassiou in [1].     

Hydrodynamics of binary fluid phase segregation

Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field u when the system is segregated into two phases (at low temperatures) with a sharp interface between them. u satisfies the incompressible Navier-Stokes equations together with a jump boundary condition for the pressure across the interface which, in turn, moves with a velocity given by the normal component of u. Numerical simulations of the Vlasov-Boltzmann equations for shear flows parallel and perpendicular to the interface in a phase segregated mixture support this analysis. We expect similar behavior in real fluid mixtures.     

Quasi-solitonic behavior of self-written waveguides created by photopolymerization

We investigated the condition of unique self-written channel and multichannel propagation inside bulk photopolymerizable materials. Light was introduced in the medium by a single-mode optical fiber. At a very low beam power of 5 muW , a unique uniform-channel waveguide without any broadening was obtained by polymerization. When the input power is increased to 100 muW , the guide becomes chaotic and multichannel. We connected two fibers separated by a 1-cm distance. The results open the door to studies of the optical and electro-optical properties of photopolymerized guides doped by nonlinear optical chromophores and to possible applications in integrated optical devices.     

Fluctuation forces in a three-layer medium with rough boundaries. III. Aspects of perturbation theory in the Casimir range

The problem of calculating the Casimir force that acts in a system of two metallic plates with rough boundaries separated by an insulating layer is considered. An algorithm for constructing a perturbation series in the small function of the roughness profile is developed.Scientific Council on the Problem Complex Kibernetika, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 3, pp. 474–482, June, 1992.     

Activation and transfer of oxygen-X : A new autoxidative rearrangement of tetrahydropteridines

The structure 2a proposed by Viscontini and Okada for the autoxidation product of 5-methyl-6,7-diphenyl-5,6,7,8-tetrahydropterin 1 was found to be incorrect. Alternative structures 3a, 3b were deduced from spectroscopic data. X-ray analysis of the acetyl derivative 8 proved the oxidation product to be 2-amino-8-methyl-4,9-dioxo-cis-6,7-diphenyl-6,7,8,9-tetrahydro-4H-pyrazino(1,2-a)-s-triazine 3a. The mechanism of the rearrangement may involve an intermediate 4a-peroxy-pterin. A similar rearrangement on peroxide-level was observed for the corresponding lumazine 14.     

Perturbations of subalgebras of type II1 factors

In this paper we consider two von Neumann subalgebras and of a type II₁ factor . For a map φ on , we define

     

Hyperplane arrangement cohomology and monomials in the exterior algebra

We show that if is the complement of a complex hyperplane arrangement, then the homology of has linear free resolution as a module over the exterior algebra on the first cohomology of . We study invariants of that can be deduced from this resolution. A key ingredient is a result of Aramova, Avramov, and Herzog (2000) on resolutions of monomial ideals in the exterior algebra. We give a new conceptual proof of this result.

     

On Norden Metrics which Are Locally Conformal to Anti-Kählerian Metrics

We build examples of Norden metrics on × S ¹, where R ^{2 n} _n is either a pseudosphere or a pseudohyperbolic space. These turn out to be locally conformal to flat anti-Kählerian metrics, strongly non anti-Kählerian, and with a parallel Lee form. Conversely, any connected complete anti-Hermitian manifold possessing these properties is shown to be locally analytically homothetic to × S ¹.     

The Order of Best Approximation in Some Classes of Functions

Starting from the equivalence between the Ditzian–Totik modulus and , where , in this article large classes of functions are introduced for which the modulus can be easily calculated. As a consequence, very good estimates for the bestapproximation are obtained. The attempts to estimate or calculate themodulus can be a very intricateproblem.     

Cross section for b-Jet production in &pmacr;p collisions at radicals = 1.8 TeV

Bottom-quark production in &pmacr;p collisions at sqrt[s] = 1.8 TeV is studied with 5 pb(-1) of data collected in 1995 by the D0 detector at the Fermilab Tevatron Collider. The differential production cross section for b jets in the central rapidity region ( | y(b)|<1) as a function of jet transverse energy is extracted from a muon-tagged jet sample. Within experimental and theoretical uncertainties, D0 results are found to be higher than, but compatible with, next-to-leading-order QCD predictions.