Strong Nearness Frames Having Enough Cauchy Filters

We prove results establishing sufficient conditions for the sum of two nearness frames to have enough Cauchy filters. From these results and the fact that, in the category of strong nearness frames having enough Cauchy filters and uniform frame maps, complete spatial frames form a coreflective subcategory, follow a variety of results where the open-sets contravariant functor from topological spaces to frames transforms products into sums and inverse limits into direct limits.     

Scaling of Prosocial Behavior in Cities

Previous research has examined how various behaviors scale in cities in relation to their population sizes. Behavior related to innovation and productivity has been found to increase per capita as the size of the city increases, a phenomenon known as superlinear scaling. Criminal behavior has also been found to scale superlinearly. Here we examine a variety of prosocial behaviors (e.g., voting and organ donation), which also would be presumed to be categorized into a single class of scaling with population. We find that, unlike productivity and innovation, prosocial behaviors do not scale in a unified manner. We argue how this might be due to the nature of interactions that are distinct for different prosocial behaviors.     

On the spectrum of the Laplacian

In this article we prove a generalization of Weyl’s criterion for the essential spectrum of a self-adjoint operator on a Hilbert space. We then apply this criterion to the Laplacian on functions over open manifolds and get new results for its essential spectrum.     

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.     

Thermal,chemical, and mineralogical characterization of ceramic tobacco pipes from Cyprus

This study is focused on simultaneous thermoanalytical investigations by TG/DTG-DTA technique applied for characterization of samples collected from archaeological site of Nicosia, Cyprus, dating to seventeenth century and gave new information on the firing technology. The ceramic samples derived from Ottomanic tobacco pipes were characterized by the related techniques such as X-ray powder diffraction for the mineralogical composition, and inductively coupled plasma-atomic emission spectrometry and micro-X-ray fluorescence spectroscopic analysis for the chemical content. It was found that they consisted mainly of quartz, calcite, feldspars, and micas. For the majority of the investigated ceramic samples, the thermal behavior investigation collaborates with their mineralogical findings, and resulted to the firing temperature at ~700 °C, due to the existence of calcite. Only in two samples with very high content in quartz, absence of calcite, low amounts of adsorbed water and of total mass loss, and absence of micas, the firing process resulted up to 1000 °C.     

The Yang-Mills Heat Semigroup on Three-Manifolds with Boundary

Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space H ₁. Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Marini boundary conditions. The last is a nonlinear boundary condition, specified by setting the normal component of the curvature to zero on the boundary. The Yang-Mills heat equation is a weakly parabolic nonlinear equation. We use gauge symmetry breaking to convert it to a parabolic equation and then gauge transform the solution of the parabolic equation back to a solution of the original equation. Apriori estimates are developed by first establishing a gauge invariant version of the Gaffney-Friedrichs inequality. A gauge invariant regularization procedure for solutions is also established. Uniqueness holds upon imposition of boundary conditions on only two of the three components of the connection form because of weak parabolicity. This work is motivated by possible applications to quantum field theory.     

Dissymetry of critical exponants in YBCO

We report on measurements of the specific heat of μg-size YBCO single crystals very close to the superconducting transition in zero field. Detailed data points are obtained down to reduced temperatures of 10^?5. Analysis of the derivative of the specific heat yields the critical exponents in an unambiguous way. α+ is positive ～0.5; α- is negative ～ ?0.3. The value of α+ is consistent with gaussian fluctuations above Tc, however the value of α- is inconsistent with either gaussian fluctuations or the 3DXY model.     

Conformation of alkanes in the gas phase and pure liquids

Monte Carlo (MC) statistical mechanics simulations have been carried out for the homologous alkane series of n-butane through n-dodecane in the gas phase and for the pure liquids at 298 K and 1 atm using the OPLS-AA force field. The study addresses potential cumulative deviations of computed properties and potential conformational differences between the gas phase and pure liquids, for example, from self-solvation in the gas phase. The average errors in comparison with experimental data for the computed densities and heats of vaporization are modest at 0.7% and 6.9%, respectively. Also, the invariant gas and liquid-phase results for average end-to-end distances and percentages of trans conformations for each nonterminal C-C bond assert that the conformer populations are not altered upon transfer from the gas phase to the pure liquid for the n-alkanes in this size range. Average end-to-end distances were also computed from the results of conformational searches and corroborated the MC findings. Quantitatively, the OPLS-AA result for the trans population of the C3-C4 bond in n-undecane is in close agreement with the findings from (13)C NMR experiments. Finally, previous work on determining the shortest n-alkane that does not have an all-trans global energy minimum has been extended. The smallest n-alkane with a hairpin geometry that is lower in energy than the all-trans conformer occurs for C(22)H(46) with OPLS-AA, though with a correction for GG sequences, the true turning point is likely in the C(16)-C(18) range.     

Resolutions of monomial almost complete intersections and generalizations

Let S=K[x₁,…,x_n] be a polynomial ring over a field kand let / be a monomial ideal of S. The main result of this paper is an explicit minimal resolution of kover R= S/Iwhen / is a monomial almost complete intersection ideal of S. We also compute an upper bound on the multigraded resolution of k over a generalization of monomial almost complete intersection ring.