Regularities and their relations to error bounds

In this paper, we mainly study various notions of regularity for a finite collection {C₁,,C_m} of closed convex subsets of a Banach space X and their relations with other fundamental concepts. We show that a proper lower semicontinuous function f on X has a Lipschitz error bound (resp., -error bound) if and only if the pair {epi(f),X×{0}} of sets in the product space X× is linearly regular (resp., regular). Similar results for multifunctions are also established. Next, we prove that {C₁,,C_m} is linearly regular if and only if it has the strong CHIP and the collection {N_C1(z),,N_Cm(z)} of normal cones at z has property (G) for each zC:=_i=1^mC_i. Provided that C₁ is a closed convex cone and that C₂=Y is a closed vector subspace of X, we show that {C₁,Y} is linearly regular if and only if there exists >0 such that each positive (relative to the order induced by C₁) linear functional on Y of norm one can be extended to a positive linear functional on X with norm bounded by . Similar characterization is given in terms of normal cones.Mathematics Subject Classifications: 90C25, 90C31, 49J52, 46A40This research was supported by an Earmarked grant from the Research Grant Council of Hong Kong     

Sensitive wavelength-modulated photoacoustic spectroscopy with a pulsed optical parametric oscillator

With a laser-excited acoustic wave as the carrier wave and by modulation of the light wavelength of a multikilohertz-repetition-rate optical parametric oscillator at a lower frequency than the acoustic frequency, we demonstrate a wavelength-amplitude double-modulation technique and achieve an enhancement factor of 35 in sensitivity in photoacoustic trace gas detection with the technique.     

A factorization theorem for comaps of geometric lattices

A function γ: K → L between two geometric lattices K and L is a normalized comap if it preserves the relations: x covers or equals y, meets of modular pairs, and the minimum. The theorem, a normalized comap can be factored into an injection followed by a retraction onto a modular flat, is proved.     

Heat Flow for the Minimal Surface with Plateau Boundary Condition

The heat flow for the minimal surface under Plateau boundary condition is defined to be a parabolic variational inequality,and then the existence,uniqueness,regularity,continuous dependence on the initial data and the asymptotics are studied.It is applied as a deformation of the level sets in the critical point theory.     

A dual method for discrete Chebychev curve fitting

This paper presents a special purpose dual algorithm for obtaining a Chebychev approximation to an overdetermined system of linear equations. The method is founded on the principles of linear programming and is designed to take advantage of the problem's special structure. It is shown that, while maintaining a reduced basis, certain iterations of the standard dual algorithm may be combined into one. Two computer code implementations of the method are discussed and a computational comparison with another algorithm for Chebychev approximation is given.     

The surface alloying behavior of martensitic stainless steel cut with wire electrical discharge machine

The surface alloying behavior of tempered martensitic stainless steel multi-cut with wire electrical discharge machine (WEDM) is studied in this paper. Before machined with WEDM, the steel specimens were quenched at 1050 °C and then tempered at 200 °C, 400 °C, and 600 °C, respectively. The microstructure and surface morphology of the multi-cut surfaces were examined with scanning and transmission electron microscopes integrated with an energy-dispersive X-ray spectrometer for chemical composition analysis. Experimental results show that the cut surfaces of the steel specimens were alloyed with wire-electrode material in various extent. Especially the cut surface was much more alloyed when the steel was cut with the first rough cutting pass by using negatively biased potential and final fine cutting using positively biased potential. Alloying degree of cut surfaces can be distinguished with their anodic polarization curves in 0.5 M HClO₄ + 0.2 wt% NaCl at 27 °C. Higher passive current density induces deeper alloyed surface. On the severely alloyed surface, a secondary anodic peak in the potential of 120 mV (versus Ag/AgCl_sat.) of its anodic polarization curve was observed. The presence of the secondary anodic peak was attributed to dissolution of copper, which was the major element of wire-electrode material from the alloyed surface.     

Temperature programmed desorption study of acetylene on a clean,H-covered,and O-covered Pt(111) surface

The reactions of acetylene on a clean, a H-covered and an O-covered Pt(111) surface were studied by temperature programmed desorption for various coverages of acetylene, and acetylene to H or O ratios. The desorption products were quantitatively determined. On a clean surface, acetylene decomposes to hydrogen and surface carbon. A small amount of self-hydrogenation to ethylene also occurs during decomposition. On a H-covered surface, hydrogenation to CH₄, C₂H₆, and ethylene, and decomposition to hydrogen and surface carbon occur simultaneously. The reactions on these two surfaces can be explained by the presence of two sites. One site is a bare surface Pt atom on which decomposition is the primary reaction pathway. The other site is a Pt atom with adsorbed H on which hydrogenation is the primary reaction pathway. On the O-covered surface, the decomposition reaction takes place together with an oxidation reaction which yields CO, CO₂, and water. The oxidation reaction probably proceeds via an intermediate that has a stoichiometry of CH. Results on the O-covered surface are consistent with the model that oxygen absorbs in islands, and the oxidation reaction takes place at the perimeter of the islands. These results are compared with those of ethylene reaction on the same Pt surfaces.     

The radon transforms of a combinatorial geometry,I

Over a field of characteristic zero, the rank of the point-copoint incidence matrix of a combinatorial geometry of rank ? 2 equals the number of points. The proof uses a finite analogue of the Radon transform.     

Infrared hall effect in high- T(c) superconductors: evidence for non-fermi-liquid hall scattering

Infrared ( 20-120 and 900-1100 cm(-1)) Faraday rotation and circular dichroism are measured in high- T(c) superconductors using sensitive polarization modulation techniques. Optimally doped YBa2Cu3O7 thin films are studied at temperatures in the range ( 15相似文献   

Analytic solutions of a two-dimensional rectangular heat equation

Analytical solutions of a two-dimensional heat equation are obtained by the method of separation of variables. In the analysis presented here, the partial differential equation is directly transformed into a set of ordinary differential equations. The closed-form transient temperature distributions and heat transfer rates are generalized to a linear combination of the products of Fourier-Bessel series of the exponential type.