Superfield form of discrete gauge states in ĉ = 1 2d supergravity

A general formula for the discrete states (NeveuSchwarz sector) in N = 1 2D super-Liouville theory is written down in the world-sheet supersymmetric form. We then derive a set of gauge states at the discrete momenta. These discrete gauge states are shown to carry the ω_∞ charges and serve as the symmetry parameters in the old covariant quantization of the theory.     

Property changes of electroplated Cu/Co alloys and multilayers by organic additives

We investigated the change of magnetic properties of the electroplated Cu/Co alloys and multilayers caused by organic additives and high temperature annealing. When plated with a pure Cu/Co electrolyte, the alloy contained ∼25% of Cu and ∼75% of Co. The alloy was made of hcp-Co, fcc-Co and Cu(1 1 1) and was super-paramagnetic at room temperature. As we add a few organic additives in the plating electrolyte, the hcp-Co of the films disappeared. The organic additives contained in the electrolytes changed paramagnetic Cu/Co multilayers to ferromagnets. High-temperature thermal annealing increased coercivity due to the growth of the Co grains.     

Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz distributions

We reformulate and prove the Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz tempered distributions and Fourier hyperfunctions.     

A Multisensor Deconvolution Problem

Meisters and Peterson gave an equivalent condition under which the multisensor deconvolution problem has a solution when there are two convolvers, each the characteristic function of an interval. In this article we find additional conditions under which the deconvolution problem for multiple characteristic functions is solvable. We extend the result to the space of Gevrey distributions and prove that every linear operator S, fromthe space of Gevrey functions with compact support onto itself, which commutes with translations can be represented as convolution with a unique Gevrey distribution T of compact support. Finally, we find explicit formula for deconvolvers when the convolvers satisfy weaker conditions than the equivalence conditions using nonperiodic sampling method.     

An expedient synthesis of an isofervenulin analogue

An efficient approach has been developed for the synthesis of an isofervenulin analogue 1 employing a one‐pot condensation‐substitution reaction of a chlorocarboethoxytriazine (electrophile) with a urea (nucleophile). The resulting cyclization reaction resulted in the synthesis of a pyrimido‐heterocycle in good yield in either acidic or basic media. The former was assisted by utilizing trimethylsilyl chloride.     

Phase formation and control of morphology in sputtered Cu-In alloy layers

The dependence of structural properties and surface morphology of Cu-In alloy layers on the composition and sputtering deposition sequence were investigated by X-ray diffraction, scanning electron microscopy and energy-dispersive X-ray spectroscopy. The properties of the co-sputtered alloy layers changed abruptly around the composition boundary when the Cu/In ratio reached 1/2. This can be explained by the effective heat of formation (EHF) model, which has been used to predict the sequence of phase formation for metal diffusion couples. The use of a co-sputtered alloy layer with a high In concentration was not suitable for fabricating solar cells, because the film had a very rough morphology due to large In islands formed on the CuIn₂ phase. However, it was possible to minimize this phase by In sputtering followed by co-sputtering with a Cu/In ratio of 1 (Cu-In/In/Glass). This permitted the fabrication of a homogeneous Cu-In alloy layer, which was not possible through the simple co-sputtering.     

Laplacians and the Cheeger Inequality for Directed Graphs

We consider Laplacians for directed graphs and examine their eigenvalues. We introduce a notion of a circulation in a directed graph and its connection with the Rayleigh quotient. We then define a Cheeger constant and establish the Cheeger inequality for directed graphs. These relations can be used to deal with various problems that often arise in the study of non-reversible Markov chains including bounding the rate of convergence and deriving comparison theorems.Received September 8, 2004     

Quantum Dynamics of Systems Connected by a Canonical Transformation

Quantum Hamiltonian systems corresponding to classical systems related by a general canonical transformation are considered. The differential equation to find the unitary operator, which corresponds to the canonical transformation and connects quantum states of the original and transformed systems, is obtained. The propagator associated with their wave functions is found by the unitary operator. Quantum systems related by a linear canonical point transformation are analyzed. The results are tested by finding the wave functions of the under-, critical-, and over-damped harmonic oscillator from the wave functions of the harmonic oscillator, free-particle system, and negative harmonic potential system, using the unitary operator to connect them, respectively.