α-FUZZY PAIRWISE RETRACT OF L-VALUED PAIRWISE STRATIFICATION SPACES

The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L = [0,1] was introduced by Martin (1980). Liu and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces.     

A RIEMANN-HILBERT PROBLEM IN A RIEMANN SURFACE

One of the inspirations behind Peter Lax’s interest in dispersive integrable systems, as the small dispersion parameter goes to zero, comes from systems of ODEs discretizing 1-dimensional compressible gas dynamics [17]. For example, an understanding of the asymptotic behavior of the Toda lattice in different regimes has been able to shed light on some of von Neumann’s conjectures concerning the validity of the approximation of PDEs by dispersive systems of ODEs. Back in the 1990s several authors have worked on the long time asymptotics of the Toda lattice [2, 7, 8, 19]. Initially the method used was the method of Lax and Levermore [16], reducing the asymptotic problem to the solution of a minimization problem with constraints (an "equilibrium measure" problem). Later, it was found that the asymptotic method of Deift and Zhou (analysis of the associated Riemann-Hilbert factorization problem in the complex plane) could apply to previously intractable problems and also produce more detailed information. Recently, together with Gerald Teschl, we have revisited the Toda lattice; instead of solutions in a constant or steplike constant background that were considered in the 1990s we have been able to study solutions in a periodic background. Two features are worth noting here. First, the associated Riemann-Hilbert factorization problem naturally lies in a hyperelliptic Riemann surface. We thus generalize the Deift-Zhou "nonlinear stationary phase method" to surfaces of nonzero genus. Second, we illustrate the important fact that very often even when applying the powerful Riemann-Hilbert method, a Lax-Levermore problem is still underlying and understanding it is crucial in the analysis and the proofs of the Deift-Zhou method!     

Balanced and Unbalanced Components of Moist Atmospheric Flows with Phase Changes

Atmospheric variables(temperature, velocity, etc.) are often decomposed into balanced and unbalanced components that represent low-frequency and high-frequency waves, respectively. Such decompositions can be defined, for instance, in terms of eigenmodes of a linear operator. Traditionally these decompositions ignore phase changes of water since phase changes create a piecewise-linear operator that differs in different phases(cloudy versus non-cloudy). Here we investigate the following question: How can a balanced–unbalanced decomposition be performed in the presence of phase changes? A method is described here motivated by the case of small Froude and Rossby numbers,in which case the asymptotic limit yields precipitating quasi-geostrophic equations with phase changes. Facilitated by its zero-frequency eigenvalue, the balanced component can be found by potential vorticity(PV) inversion, by solving an elliptic partial differential equation(PDE), which includes Heaviside discontinuities due to phase changes. The method is also compared with two simpler methods: one which neglects phase changes, and one which simply treats the raw pressure data as a streamfunction. Tests are shown for both synthetic, idealized data and data from Weather Research and Forecasting(WRF) model simulations. In comparisons, the phase-change method and no-phase-change method produce substantial differences within cloudy regions, of approximately 5K in potential temperature, due to the presence of clouds and phase changes in the data. A theoretical justification is also derived in the form of a elliptic PDE for the differences in the two streamfunctions.     

CALCULATION OF α_3 COEFFICIENT OF SCALAR FIELD BY POINT SEPARATION METHOD

The α_3 coefficient of scalar field in arbitrary Riemann space-time background is calculated by point separation method in this article. The primary expression of α_3 involves 25 invariants. Using the identities derived in the appendix, we can reduce α_3 from 25 invariants to 17 invariants which agree with Gilkey's formula for α_s coefficient of the scalar field derived by geometric methods and reasons. Recently we derived two important invariant identilies, using these identities we can reduce α_3 from 17 invariants to 15 invariants which would much simplify the calculation of the energymomentum tensor of vacuum polarization.     

Uniform Asymptotic Expansion of the Voltage Potential in the Presence of Thin Inhomogeneities with Arbitrary Conductivity

Asymptotic expansions of the voltage potential in terms of the "radius" of a diametrically small(or several diametrically small) material inhomogeneity(ies) are by now quite well-known. Such asymptotic expansions for diametrically small inhomogeneities are uniform with respect to the conductivity of the inhomogeneities.In contrast, thin inhomogeneities, whose limit set is a smooth, codimension 1 manifold,σ, are examples of inhomogeneities for which the convergence to the background potential,or the standard expansion cannot be valid uniformly with respect to the conductivity, a, of the inhomogeneity. Indeed, by taking a close to 0 or to infinity, one obtains either a nearly homogeneous Neumann condition or nearly constant Dirichlet condition at the boundary of the inhomogeneity, and this difference in boundary condition is retained in the limit.The purpose of this paper is to find a "simple" replacement for the background potential, with the following properties:(1) This replacement may be(simply) calculated from the limiting domain Ω\σ, the boundary data on the boundary of Ω, and the right-hand side.(2) This replacement depends on the thickness of the inhomogeneity and the conductivity,a, through its boundary conditions on σ.(3) The difference between this replacement and the true voltage potential converges to 0 uniformly in a, as the inhomogeneity thickness tends to 0.     

Synthesis and characterization of C3N4 hard films

C3N4 films have been synthesized on both Si and Pt substrates by microwave plasma chemical vapor deposition (MPCVD) method. X-ray spectra were calculated for single phase α-C3N4 and β-C3N4 respectively. The experimental X-ray spectra of films deposited on both Si and Pt substrates showed all the strong peaks of α-C3N4 and β-C3N4, so the films are mixtures of α-C3N4 and β-C3N4. The N/C atomic ratio is in the range of 1.0-2.0. X-ray photoelectron spectroscopy (XPS) analysis indicated that the binding energy of C 1s and N 1s are 286.2 eV and 399.5 eV respectively, corresponding to polarized C-N bond. Fourier transform infrared absorption (FT-IR) and Raman spectra support the existence of C-N covalent bond in the films. Nano-indentation hardness tests showed that the bulk modulus of a film deposited on Pt is up to 349 GPa.     

The structure and magnetic properties of Fe- N thin films

200 nm Fe-N thin films deposited on glass substrates by RF sputtering were vacuum annealed at 250-350℃ under 12000 A/m magnetic field. Heat treatment was effective in improving the soft magnetic properties of the Fe-N film. When the nitrogen content was in the range of 5-7 at. %,the thin films consisted of α′ + α" after heat treatment and had excellent soft magnetic properties of 4πMs = 2.4 T, Hc ＜ 80 A/m, μr = 1500 under 2-10 MHz. The properties of the films meet the needs of a write head material used in the dual element GMR/inductive heads. The fromation mechanism and lattice constants of the α′ phase in Fe-N thin film are different from Jack's results obtained from γ→α′transformation in bulk samples. The linear relationship between a, c and Ca'N for thin film was obtained asc = 2. 866+ 1.559Ca'N,a = 2.866 + 0.181Ca'N.``     

A MATHEMATICAL MODEL OF THE OVERVOLTAGE CAUSED BY THE SATURATED CHARACTERISTIC OF POTENTIAL TRANSFORMERS IN ISOLATED NEUTRAL SYSTEMS AND THE UNIQUENESS OF ITS PERIODIC SOLUTION

Safe operation of power systems is disturbed by the ferroresonance overvoltage that is caused by the saturation magnetization of electromagnetic type potential transformers and a great deal of attention has been paid to this study in many countries. However, so far, most of the mathematical models describing such overvoltage have been derived from single-phase circuit, which is a simplification of three-phase circuit under some assamed conditions. since the special features of three-phase nonlinear circuit were drawn off, the conclusions derived from the simplified mathematical model are difficult to understand and can not be accepted.In this paper we give a mathematical model that is established according to a three-phase circuit with a three-phase potential transformer made up by three simple-phase potential transformers. So the resonance phenomena of a three-phasenonlinear circuit can be directly studied quantitatively and qualitatively. After that, we give a unique theorem of periodic solution and its appli cations.     

一类非最小相位随机系统的离散自适应滑动模态控制

This paper presents the discrete adaptive sliding mode control of input-output non-minimum phase system in the presence of the stochastic disturbance. The non-minimum phase system can be transformed into a minimum phase system by a operator. According to the minimum phase system, the controller and the adaptive algorithm we designed ensures the stability of system and holds that the mean-square deviation from the sliding surface is minimized.     

ASYMPTOTIC BEHAVIOR OF THE TE AND TM APPROXIMATIONS TO SECOND HARMONIC GENERATION

We consider a Second Harmonic Generation （SHG） problem of an optical signal wave with an optical pump in a medium represented by a smooth bounded domain Ω→∩ IR^d which is assumed to contain a heterogeneous material： a compactly imbedded subdomain B^r →∩∩ in the shape of a small ball contains a nonlinear material, while Ω／ B^r is filled with a linear material. We begin by proving existence and uniqueness of the solution to the TE approximation of SHG for arbitrary bounded susceptibilities, thus improving the result obtained by Bao and Dobson （ Eur. J. Appl. Math. 6 （1995）, 573-590） under small enough susceptibilities assuption. We then establish an existence and uniqueness result of a solution to the TM approximation problem. In both parts we study the asymptotic behavior of the system as the size of the nonlinear material vanishes： error estimates and asymptotic expansion of the solution are derived for both TE and TM approximations.     

Modeling dendritic solidification of Al–3%Cu using cellular automaton and phase-field methods

We compared a cellular automaton (CA)–finite element (FE) model and a phase-field (PF)–FE model to simulate equiaxed dendritic growth during the solidification of cubic crystals. The equations of mass and heat transports were solved in the CA–FE model to calculate the temperature field, solute concentration, and the dendritic growth morphology. In the PF–FE model, a PF variable was used to identify solid and liquid phases and another PF variable was considered to determine the evolution of solute concentration. Application to Al–3.0 wt.% Cu alloy illustrates the capability of both CA–FE and PF–FE models in modeling multiple arbitrarily-oriented dendrites in growth of cubic crystals. Simulation results from both models showed quantitatively good agreement with the analytical model developed by Lipton–Glicksman–Kurz (LGK) in the tip growth velocity and the tip equilibrium liquid concentration at a given melt undercooling. The dendrite morphology and computational time obtained from the CA–FE model are compared to those of the PF–FE model and the distinct advantages of both methods are discussed.     

Averaging the resolvent with a space-correlated random potential

The problem of the quasi-particle spectrum in a binary disordered alloy with a space-correlated random potential is considered. The extended space formalism is used to represent the average resolvent. To calculate the mass operator, some self-consistent approximation procedures are suggested that coincide with the well-known self-consistent approximations for α=0 (where α is the short-range order parameter). The elaborated theory ensures the correct passage to the Green's function of a perfect crystal in the limits α→1 and α→−1 for any concentration and 50% concentration, respectively. The approximations possess the correct analytic properties for all values of the parameter α. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 114, No. 2, pp. 296–313, February, 1998.     

Decay study of20Na and its beta-delayed16O recoiling

The decay of²⁰Na of astrophysical reactions has been studied deeply via²⁰Ne(p, n)²⁰Na reaction. A new β-delayed α decay with α energy of 5 896 ± 6 keV and relative intensity of 0.002 4 ± 0. 000 3 was discovered. At the same time the¹⁶O recoiling in β⁺-delayed α decay of²⁰Na was observed in experiment for the first time. From these, it is inferred that a β-delayed low energy α decay of²⁰Na with energy of ∼780 keV and relative intensity of ∼1.4 was mixed in¹⁶O recoiling. In¹⁶O recoiling and the low energy α decay, the energy loss for low energy charged particles through matter was discussed in detail. At last, two methods for discriminating the β-delayed low energy α decay of²⁰Na were proposed. Project supported by the Chinese Academy of Sciences and the National Natural Science Foundation of China.     

Primariness of spaces of continuous functions on ordinals

Necessary and sufficient conditions on an ordinal α are given, such thatC(α) is primary, and that the general linear group ofC(α) is contractible. In particularC(α) possesses both of these properties if α is countable. This is a part of the first author's Ph. D. dissertation, prepared at The Ohio State University under the supervision of Professor W. B. Johnson. The first author was supported by a University Fellowship of The Ohio State University. This author's research was partially supported by NSF Grant MPS-74-2449.     

Prevalence of Multifractal Functions in S<Superscript>v</Superscript> Spaces

Spaces called S^v were introduced by Jaffard [16] as spaces of functions characterized by the number ≃ 2^ν(α)j of their wavelet coefficients having a size ≳ 2^−αj at scale j . They are Polish vector spaces for a natural distance. In those spaces we show that multifractal functions are prevalent (an infinite-dimensional “almost-every”). Their spectrum of singularities can be computed from ν, which justifies a new multifractal formalism, not limited to concave spectra.     

On the embedding problem with noncommutative kernel of order p4. VI

In the case of number fields the embedding problem of a p-extension with non-Abelian kernel of order p⁴ is studied. The two kernels of order 3⁴ with generators α, γ and relations α⁹ = 1, [α,α]³=1,[α,αγγ]==1,[αγγ]=α³,γ³=1 or γ³=α³ and the kernel of order 2⁴ with generators α, β, γ and relations α⁴=1 β²,[αγ]=1, [α,γ]=1,[βγ]=α² are considered. For kernels of odd order the embedding problem is always solvable. For the kernel of order 16 the solvability conditions are reduced to those for the associated problems at the Archimedean points, and to the compatibility condition. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 74–82.     

Efficient solution approaches for a discrete multi-facility competitive interaction model

In this paper, we present efficient solution approaches for discrete multi-facility competitive interaction model. Applying the concept of “Tangent Line Approximation” presented by the authors in their previous work, we develop efficient computational approaches—both exact and approximate (with controllable error bound α). Computational experiments show that the approximate approach (with small α) performs extremely well solving large scale problems while the exact approach performs very well for small to medium-sized problems.     

Electron scattering at the domain wall

We study the transmission and reflection coefficients for the Hamiltonian of a spin-polarized electron passing through the domain wall in a ferromagnetic quantum wire. We prove that total reflection occurs for energies λ ∈ (−α, α) (−α is the boundary of the essential spectrum) for both sufficiently small and sufficiently large λ, which agrees with the ballistic magnetoresistance effect in ferromagnetic nanocontacts. For energies λ > α, almost total reflection becomes almost total transmission, and both effects occur without a spin flip.     

Solidification characteristics of Pd40Ni40P20 alloy under microgravity condition

The microstructure and solute distribution of Pd₄₀Ni₄₀P₂₀ alloy solidified both on board a Chinese retrievable satellite (μg) and on the earth (1g) were studied. It was found that the dendritic primary phase formed under microgravity condition was finer and shorter. In the central area of the sample some asteroidal patterns of the primary phase were present in the microstructure. The primary spacing of the dendrites at the cooling rate of 0. 056 K/s was smaller than that measured in the ground-based experiments at the same cooling rate, but almost the same as that cooled at 0.67 K/s on the ground. With these experimental results, mass transport coefficients both in space and on the earth were evaluated.     

Approximation d’un nombre réel par des unités algébriques

 In this paper, we prove that for any real number ξ, which is not an algebraic number of degree , there exist infinitely many real algebraic units α of degree n + 1 such that . We also show how the flexibility of H. Davenport and W. M. Schmidt’s method allows to replace, with the same exponent of approximation, units of degree over Z (i.e. elements α with both α and integral over Z) by units of degree over a finite intersection .

(Received 14 March 2000; in revised form 16 November 2000)