Weak descartes systems in generalized spline spaces

A class of generalized spline spaces is introduced for which a basis of functions with local support is constructed by using a recursion relation. It is shown that this basis forms a weak Descartes system. Moreover, an interpolation property is given.     

On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form

We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12].     

Some new results in multiplicative and additive Ramsey theory

There are several notions of largeness that make sense in any semigroup, and others such as the various kinds of density that make sense in sufficiently well-behaved semigroups including and . It was recently shown that sets in which are multiplicatively large must contain arbitrarily large geoarithmetic progressions, that is, sets of the form , as well as sets of the form . Consequently, given a finite partition of , one cell must contain such configurations. In the partition case we show that we can get substantially stronger conclusions. We establish some combined additive and multiplicative Ramsey theoretic consequences of known algebraic results in the semigroups and , derive some new algebraic results, and derive consequences of them involving geoarithmetic progressions. For example, we show that given any finite partition of there must be, for each , sets of the form together with , the arithmetic progression , and the geometric progression in one cell of the partition. More generally, we show that, if is a commutative semigroup and a partition regular family of finite subsets of , then for any finite partition of and any , there exist and such that is contained in a cell of the partition. Also, we show that for certain partition regular families and of subsets of , given any finite partition of some cell contains structures of the form for some .

     

Description of Unstable Systems in Relativistic Quantum Mechanics in the Lax-Phillips Theory

We discuss some of the experimental motivation for the need for semigroup decay laws and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and, therefore, all physical properties of the resonant states can be computed. We show that the parametrized relativistic quantum theory is a natural setting for the realization of the Lax-Phillips theory.     

Scattering of waves by periodically moving bodies

We consider solutions of the scalar wave equation vanishing on the boundary of an obstacle which undergoes periodic motion. In analogy with the Lax-Phillips theory, we show that the scattering matrix, as a function of frequency, is holomorphic in a lower half-plane, and meromorphic in an upper half-plane, provided rays are not trapped. The poles of the scattering matrix correspond to certain outgoing eigenfunctions, and there is a near-field expansion of finite energy solutions in terms of these eigenfunctions.     

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.     

Spin correlation in t&tmacr; production from p&pmacr; collisions at radicals = 1.8 TeV

The D0 collaboration has performed a study of spin correlation in t&tmacr; production for the process t&tmacr;-->bW(+)&bmacr;W-, where the W bosons decay to enu or &mgr;nu. A sample of six events was collected during an exposure of the D0 detector to an integrated luminosity of approximately 125 pb(-1) of sqrt[s] = 1.8 TeV p&pmacr; collisions. The standard model (SM) predicts that the short lifetime of the top quark ensures the transmission of any spin information at production to the t&tmacr; decay products. The degree of spin correlation is characterized by a correlation coefficient kappa. We find that kappa>-0.25 at the 68% confidence level, in agreement with the SM prediction of kappa = 0.88.     

Optically active cyclic hexapeptides with covalently attached pyrene probes: selective alkaline earth metal ion recognition using excimer emission

[structure: see text] The synthesis of two optically active pyrene-modified cyclic hexapetides and their selectivity toward the complexation of alkaline earth metal ions are reported. Complexation was studied by optical and chiroptical methods. The cyclic peptides are forming 2:1 sandwich complexes with the metal ions.     

Tonks-Langmuir problem for a bi-Maxwellian plasma

An analytical solution of the Tonks-Langmuir (TL) problem with a bi-Maxwellian electron energy distribution function (EEDF) is obtained for a plasma slab. The solution shows that the ambipolar potential, the plasma density distribution, and the ion flux to the wall are mainly governed by the cold electrons, while the ionization rate and voltage drop across the wall sheath are governed by the hot electrons. The ionization rate by direct electron impact is found to be spatially rather uniform, contrary to the T-L solution where it is proportional to the plasma density distribution. The temperature of hot electrons defined by the ionization balance is found to be close to that of the T-L solution for a mono-Maxwellian EEDF, and is in reasonable agreement with experiments carried out in a low pressure capacitance RF discharge. The energy balance for cold electrons in this discharge shows that their heating by hot electrons via Coulomb interaction is equalized by the cold electrons' escape to the RF electrodes during collapse of the RF sheath