Products of compact spaces and the axiom of choice II

This is a continuation of [2]. We study the Tychonoff Compactness Theorem for various definitions of compactness and for various types of spaces (first and second countable spaces, Hausdorff spaces, and subspaces of ?^K). We also study well ordered Tychonoff products and the effect that the multiple choice axiom has on such products.     

Determination of the nature and concentration of solutes using the swelling granule method

A procedure and instrument for the determination of dissolved electrolytes and nonelectrolytes in solutions are described. The analysis was performed by measuring the size of a polymer granule placed in the test solution. It was found that various polymers can be used for the determination of the nature or concentration of a solute. This allows one to perform the analysis in various solvents. The use of small granules allows one to decrease the sample volume to tenths fractions of a microliter.     

Induction of formation of presynaptic terminals in neuroblastoma cells by synapsin IIb

The synapsins are a family of closely related phosphoproteins (termed synapsins Ia, Ib, IIa and IIb) associated with synaptic vesicles and implicated in the short-term regulation of neurotransmitter release from nerve endings. During development, expression of the synapsins correlates temporally with synapse formation, but there has been no direct evidence that they are involved in synaptogenesis. Here we report that overexpression of synapsin IIb in the neuroblastoma x glioma hybrid clonal cell line NG108-15 leads, during cell differentiation, to marked increases in the number of neuritic varicosities and in the numbers of small clear vesicles and large dense core vesicles per varicosity, as well as to the appearance of synapse-like cell-cell contacts. Thus, synapsin IIb may be involved in the regulation of synapse formation and, as a result, in long-term neuronal signalling.     

The microscopic investigation of structures of moving flux lines by neutron and muon techniques

We have used a variety of microscopic techniques to reveal the structure and motion of flux line arrangements, when the flux lines in low T _c type II superconductors are caused to move by a transport current. Using small-angle neutron scattering by the flux line lattice (FLL), we are able to demonstrate directly the alignment by motion of the nearest-neighbor FLL direction. This tends to be parallel to the direction of flux line motion, as had been suspected from two-dimensional simulations. We also see the destruction of the ordered FLL by plastic flow and the bending of flux lines. Another technique that our collaboration has employed is the direct measurement of flux line motion, using the ultra-high-resolution spectroscopy of the neutron spin-echo technique to observe the energy change of neutrons diffracted by moving flux lines. The muon spin rotation (μSR) technique gives the distribution of values of magnetic field within the FLL. We have recently succeeded in performing μSR measurements while the FLL is moving. Such measurements give complementary information about the local speed and orientation of the FLL motion. We conclude by discussing the possible application of this technique to thin film superconductors.     

Performance analysis of test scheduling schemes for a multi-access communications network

In this paper, we investigate the performance of two implementable test scheduling schemes for a multi-access communication channel whose components are subject to failure or malfunction. We relate the reliability of the system design, as reflected by system failure rate parameters, and the frequency at which the system (or nodal subsystem) is tested for failure detection, to the underlying key message delay and throughput performance. We derive queue-size distribution results for a discreteGeom ^(X)/D/1 system, representing the operation of the multi-access channel, or of a network node operating as a communications or queueing processor, which is maintained by a periodic or near periodic test scheduling scheme. Explicit formulas are presented for the system behavior as exhibited by the generating functions of the system queue-size distributions. The mean message delay is then calculated. The mean delay (or mean system size/workload performance index) can then be optimized by selecting the proper scheme parameters, under specified system (and component) failure conditions, noting that performing a test at too high a rate leads to inefficient system bandwidth utilization, while if tests are not carried out often enough, excessive message (or task) retransmissions and delays ensue.     

Resonance analysis of the finite-damping nonlinear vibration system under random disturbances

In this paper we propose a new technique for obtaining an approximate probability density for the resonance and off-resonance response of the finite-damping nonlinear vibration system under both random disturbances and deterministic excitation.     

Duhamel solutions of non-homogeneous -analogue wave equations

-analogue non-homogeneous wave equations are solved by a Duhamel solution strategy using constructions with -analogue Fourier multipliers to compensate for the dependence of the analogue differential Leibnitz rule on the parity of the functions involved.

     

A Cosserat shell model for interphases in elastic media

This study is concerned with the modeling of interphases in elastic media in general, and in composite materials in particular. The aim is to replace a boundary value problem consisting of a three-phase configuration, say that of fiber-interphase-matrix, by a simpler problem which involves the fiber and matrix only, plus certain matching conditions which simulate the interphase. The simplest of such known representations replaces a thin interphase by a “perfect contact interface” (a single surface) across which the displacements and tractions are assumed to be continuous. Another classical model replaces a thin and soft interphase by a “spring-type interface”, across which the tractions are continuous, but the displacement field undergoes a discontinuity. In the present paper, a Cosserat shell model of the interphase is derived which successfully models the original interphase in a unified manner, for the full range of its material parameters relative to those of the neighboring media. The model is derived in the setting of three-dimensional linear elasticity with small deformations and displacements. Comparisons with an existing exact solution of a coated fiber in an infinite matrix show that it performs extremely well even for moderately thick interphases.     

Simulation of immiscible multiphase flow in porous media: A focus on the capillary fringe of oil-contaminated aquifers

This paper deals with the analysis of some aspects of the vertical and lateral migration of oil spills in the unsaturated and the capillary zone of a phreatic aquifer. Our motivation stems from the fact that such contamination represents a severe danger for ground-water resources all over the world and from the present acute problem of jet-fuel contamination in some location of Israel. In the present study, we shall focus our efforts on the analysis of the upper layers of the aquifer which are often subjected to the most significant oil contamination. Neglecting coupled processes effects such as dilution, adsorption and volatilization, also adopting Richard's assumption, a three-phase flow model is introduced with capillary heads of the water and the oil as variables. The resulting model which is coupled and strongly non-linear is solved using a vertical two-dimensional Finite-Element procedure together with a quasi-Newton optimization algorithm. Applying that scheme, various scenarios of oil migration in the unsaturated and the capillary zone were simulated. Some migration characteristics prediced by the numerical simulations are discussed. In particular, the dynamics of the water and oil phases during the migration process is discussed.     

Complexes of gold(I), silver(I), and copper(I) with pentaaryl[60]fullerides

Gold(I), silver(I), and copper(I) phosphine complexes of 6,9,12,15,18-pentaaryl[60]fullerides 1a and 1b, namely, [(4-MeC(6)H(4))(5)C(60)]Au(PPh(3)) (2a), [(4-t-BuC(6)H(4))(5)C(60)]Au(PPh(3)) (2b), [(4-MeC(6)H(4))(5)C(60)]Ag(PCy(3)) (3a), [(4-t-BuC(6)H(4))(5)C(60)]Ag(PPh(3)) (3b), [(4-t-BuC(6)H(4))(5)C(60)]Ag(PCy(3)) (3c), [(4-MeC(6)H(4))(5)C(60)]Cu(PPh(3)) (4a), and [(4-t-BuC(6)H(4))(5)C(60)]Cu(PPh(3)) (4b), have been synthesized and characterized spectroscopically. All complexes except for 3c were also characterized by single-crystal X-ray diffraction. Several coordination modes between the cyclopentadienyl ring embedded in the fullerene and the metal centers are observed, ranging from η(1) with a slight distortion toward η(3) in the case of gold(I), to η(2)/η(3) for silver(I), and η(5) for copper(I). Silver complexes 3a and 3b are rare examples of crystallographically characterized Ag(I) cyclopentadienyls whose preparation was possible thanks to the steric shielding provided by fullerides 1a and 1b, which stabilizes these complexes. Silver complexes 3a and 3b both display unexpected coordination of the cyclopentadienyl portion of the fulleride anion with Ag(I). DFT calculations on the model systems (H(5)C(60))M(PH(3)) and CpMPH(3) (M = Au, Ag, or Cu) were carried out to probe the geometries and electronic structures of these metal complexes.