A Bitangential Interpolation Problem on the Closed Unit Ball for Multipliers of the Arveson Space

We solve a bitangential interpolation problem for contractive multipliers on the Arveson space with an arbitrary interpolating set in the closed unit ball . The solvability criterion is established in terms of positive kernels. The set of all solutions is parametrized by a Redheffer transform. Submitted: February 2, 2002.     

Extending the Balas-Yu bounds on the number of maximal independent sets in graphs to hypergraphs and lattices

A result of Balas and Yu (1989) states that the number of maximal independent sets of a graph G is at most ^p+1, where is the number of pairs of vertices in G at distance 2, and p is the cardinality of a maximum induced matching in G. In this paper, we give an analogue of this result for hypergraphs and, more generally, for subsets of vectors in the product of n lattices =₁××_n, where the notion of an induced matching in G is replaced by a certain binary tree each internal node of which is mapped into . We show that our bounds may be nearly sharp for arbitrarily large hypergraphs and lattices. As an application, we prove that the number of maximal infeasible vectors x=₁××_n for a system of polymatroid inequalities does not exceed max{Q,^logt/c(2Q,)}, where is the number of minimal feasible vectors for the system, , , and c(,) is the unique positive root of the equation 2^c(^c/log–1)=1. This bound is nearly sharp for the Boolean case ={0,1}ⁿ, and it allows for the efficient generation of all minimal feasible sets to a given system of polymatroid inequalities with quasi-polynomially bounded right-hand sides . This research was supported by the National Science Foundation (Grant IIS-0118635), and by the Office of Naval Research (Grant N00014-92-J-1375). The second and third authors are also grateful for the partial support by DIMACS, the National Science Foundation's Center for Discrete Mathematics and Theoretical Computer Science.Mathematics Subject Classification (2000):20E28, 20G40, 20C20     

To the problem of the vector and axial-vector dominance of weak interactions

The problem of the vector and axial-vector dominance of weak interactions within the framework of the quark model of superconductivity type is discussed.     

Interpolation for multipliers on reproducing kernel Hilbert spaces

All solutions of a tangential interpolation problem for contractive multipliers between two reproducing kernel Hilbert spaces of analytic vector-valued functions are characterized in terms of certain positive kernels. In a special important case when the spaces consist of analytic functions on the unit ball of and the reproducing kernels are of the form and , the characterization leads to a parametrization of the set of all solutions in terms of a linear fractional transformation.

     

Padé approximation in time-domain boundary conditions of porous surfaces

Formulation and implementation of time-domain boundary conditions (TDBCs) at the surface of a reactive porous material are made challenging by the slow decay, complexity, or noncausal nature of many commonly used models of porous materials. In this paper, approaches are described that improve computational efficiency and enforce causality. One approach involves approximating the known TDBC for the modified Zwikker-Kosten impedance model as a summation of decaying exponential functions. A second approach, which can be applied to any impedance model, involves replacing the characteristic admittance with its Padé approximation. Then, approximating fractional derivatives with decaying exponentials, a causal and recursive TDBC is formulated.     

Some analytical aspects in field theories with dynamical mass generation

The consequence of dynamical mass generation on the singularity structure of propagators is discussed. First the phenomena of dynamical mass generation is discussed in the framework of Euclidean gap equations, then a possible Minkowski solution is looked for. The examples are reviewed and studied for several models: Yukawa, QED, QCD and Wess-Zumino. It is argued that the absence of propagator pole goes hand in hand with the nontrivial solution for mass function. The consequences are discussed.     

Galvanomagnetic study of the quantum-well valence band of germanium in the Ge<Subscript>1−x</Subscript>Si<Subscript>x</Subscript>/Ge/Ge<Subscript>1−x</Subscript>Si<Subscript>x</Subscript> potential well

The structure of the quantum-well valence band in a Ge(111) two-dimensional layer is calculated by the self-consistent method. It is shown that the effective mass characterizing the motion of holes along the germanium layer is almost one order of magnitude smaller than the mass for the motion of heavy holes along the [111] direction in a bulk material (this mass is responsible for the formation of quantum-well levels). This creates a unique situation in which a large number of subbands appear to be populated at moderate values of the layer thickness d _w and the hole concentration p _s . The depopulation of two or more upper subbands in a 38-nm-thick germanium layer at a hole concentration p _s = 5 × 10¹⁵ m^?2 is revealed from the results of measuring the magnetoresistance in a strong magnetic field aligned parallel to the germanium layers. The destruction of the quantum Hall state at a filling factor ν = 1 indicates that the two lower subbands merge together in a self-formed potential profile of the double quantum well. It is demonstrated that, in a quasi-two-dimensional hole gas, the latter effect should be sensitive to the layer strain.     

Factorization in the model of unstable particles with continuous masses

We study processes with unstable particles in intermediate time-like states. It is shown that the amplitudes squared of such processes factor exactly in the framework of the model of unstable particles with continuous masses. Decay widths and cross sections can then be represented in a universal factorized form for an arbitrary set of interacting particles. This exact factorization is caused by specific structure of propagators in the model. We formulate the factorization method and perform a phenomenological analysis of the factorization effects. The factorization method considerably simplifies calculations while leading to compact and reasonable results.     

Probing Structural Compositions of Porous Media with Two-dimensional Nuclear Magnetic Resonance

Combination of two-dimensional nuclear magnetic resonance (2-D NMR) correlation maps and a simple three-component model are proposed here to identify the structural composition of porous media. Homogeneous magnetic field and field with constant gradient of a novel Halbach sensor are employed for respective relaxation and diffusion measurements. NMR results are compared and confirmed with independent measurements on a scanning electron microscope and by energy dispersive spectrometer methods.     

Unusual Behavior of Nanocrystalline Strontium Oxide Toward Hydrogen Sulfide

The thermodynamically favored reaction of solid strontium oxide with gaseous hydrogen sulfide is kinetically enhanced to a large degree by the use of higher surface area nanocrystalline SrO in the form of brush-like collections of metal oxide fibers. An unusual feature is that the reaction SrO + H₂S SrS + H₂O proceeds stoichiometrically at room temperature, but at higher temperatures the reaction efficiency goes down, apparently due to rapid temperature induced crystal growth of the nanocrystalline SrO. The samples studied vary in crystallite size from 20 to 27nm, while average particle size (nanocrystal aggregates) varies in the following order; aerogel prepared SrO (100nm) 相似文献