Square Integrability and Uniqueness of the Solutions of the Kadomtsev–Petviashvili-I Equation

We prove that the solution of the Cauchy problem for the Kadomtsev–Petviashvili-I Equation obtained by the inverse spectral method belongs to the Sobolev space H^k(R²) for k 0, under the assumption that the initial datum is a small Schwartz function. This solution is shown to be the unique solution within a class of generalized solutions of the Kadomtsev–Petviashvili-I equation.     

Remarks on Undecidability,Incompleteness and the Integrability Problem

In their seminal paper Undecidability and incompleteness in classical mechanics (Int. J. Theor. Phys. 30:1041–1073, 1991), N.C.A. da Costa and F.A. Doria introduced a powerful method for studying the appearance of undecidability and incompleteness in mathematics and theoretical physics. In this work their results are applied to integrability theory. Specifically, it is pointed out that it is not possible to expect the existence of an algorithm able to decide whether a given partial differential equation is integrable or not.     

Integrability of the Bi-Yang–Baxter σ-Model

We construct a Lax pair with spectral parameter for a two-parameter doubly Poisson–Lie deformation of the principal chiral model.     

Geometric Integrability of the Camassa–Holm Equation

It is observed that the Camassa–Holm equation describes pseudo-spherical surfaces and that therefore, its integrability properties can be studied by geometrical means. An sl(2, R)-valued linear problem whose integrability condition is the Camassa–Holm equation is presented, a Miura transform and a modified Camassa–Holm equation are introduced, and conservation laws for the Camassa–Holm equation are then directly constructed. Finally, it is pointed out that this equation possesses a nonlocal symmetry, and its flow is explicitly computed.     

Study on the Level Monitoring System for the Ship-carriage-box

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Study of the Protection System for LHCD on the HL-2A Tokamak

LHCD experiment has been carried through in HL-1M tokamak since 1995, and the work is successful. This years the LHCD experiment would go ahead on the HL-2A tokamak that had been improved from HL-1M system.     

Study of reflection and transmission on the moving interface of medium

The laws of refection and transimission on a moving interface between two nonvacuum medium are studied and the new method, which can be used for handling reflection and transimission on the moving interfaces between the vacuum-nonvacuum media and between two nonvacuum medium is suggested. The formula of reflection and transmission coefficients that suitable for both cases are derived. The present paper not only enriches electrodynamical theory, but also laies the foundation of optical waveguide modulators and other similar device.     

Study of reflection and transmission on the moving interface of medium

The laws of refection and transimission on a moving interface between two nonvacuum medium are studied and the new method, which can be used for handling reflection and transimission on the moving interfaces between the vacuum-nonvacuum media and between two nonvacuum medium is suggested. The formula of reflection and transmission coefficients that suitable for both cases are derived. The present paper not only enriches electrodynamical theory, but also laies the foundation of optical waveguide modulators and other similar device.     

Study of the charge dependence of the pion–nucleon coupling constant on the basis of data on low-energy nucleon–nucleon interactions

The relation between quantities that characterize the pion–nucleon and nucleon–nucleon interactions is studied with allowance for the fact that, at low energies, nuclear forces in nucleon–nucleon systems are mediated predominantly by one-pion exchange. On the basis of the values currently recommended for the low-energy parameters of the proton–proton interaction, the charged pion–nucleon coupling constant is evaluated at g_π²±/4π = 14.55(13). This value is in perfect agreement with the experimental value of g_π²±/4π = 14.52(26) found by the Uppsala Neutron Research Group. At the same time, the value obtained for the charged pion–nucleon coupling constant differs sizably from the value of the pion–nucleon coupling constant for neutral pions, which is g_π² 0/4π = 13.55(13). This is indicative of a substantial charge dependence of the coupling constant.     

Cohomological uniqueness of the Cauchy problem solutions for the Einstein–Maxwell equation

In this paper we analyze the Cauchy problem for the Einstein–Maxwell equation in the case of non-characteristic initial hypersurface. To find the correct notions of characteristic and Cauchy data we introduce a complex, which we call the Einstein–Maxwell complex. Then the Cauchy problem acquires correctness in terms of an associated spectral sequence. We define a Cauchy data in such way that they allow us to reconstruct a cohomologously unique formal solution.     

Study on the Cofluorescence Effect of Europium (III)–Yttrium (III)–Balofloxacin–Sodium Dodecyl Sulfate System and Its Analytical Application

A new fluorescence enhancement phenomenon in the europium(III)–balofloxacin–sodium dodecyl sulfate system was observed when yttrium(III) was added. Based on this, a sensitive cofluorescence assay for the estimation of balofloxacin was established. Under the optimized conditions, the enhanced fluorescence signal was linear over the concentration of balofloxacin ranging from 3.0 × 10^?9 to 7.0 × 10^?6 mol L^?1 with a correlation coefficient of 0.9993. The detection limit (3 σ) was determined as 8.3 × 10^?10 mol L^?1. The presented method was successfully applied to determination of balofloxacin in pharmaceutical preparations, human serum, and urine. The possible fluorescence enhancement mechanism was also discussed.     

Smooth and Peaked Solitary Wave Solutions of the Broer–Kaup System Using the Approach of Dynamical System

The bifurcations of traveling wave solutions of the Broer–Kaup system are investigated and all possible exact parametric representations of the smooth and peaked solitary waves are presented.     

Study of cohesive,electronic and magnetic properties of the Ni–In intermetallic system

Cohesive, electronic and magnetic properties of the intermetallic system Ni–In, specifically the stable phases Ni₃In-hP8, Ni₂In-hP6, NiIn-hP6 and Ni₂In₃-hP5, have been investigated. At present, these materials are of great interest in connection to the application of the In–Sn alloys as lead-free micro-soldering alloys, and considering Ni as the contact material. In spite of this, scarce literature regarding basic thermodynamic properties of the Ni–In intermetallic phases has been found. Full-Potential Linear Augmented Plane Wave method (FP-LAPW) within the framework of the Density Functional Theory (DFT) with exchange and correlation effects in the Generalized Gradient (GGA) and Local Density (LDA) approximations is used. All the calculations include spin polarization. Structural parameters, formation energies and cohesive properties of the different phases are studied through minimization of internal parameters. The electronic density of states (DOS) is analyzed for each optimized structure. We found that the NiIn-hP6 phase is the most stable one and only the Ni₃In-hP8 phase exhibits magnetic properties.     

Integrability of Liouville System on High Genus Riemann Surface.Ⅰ. Classical Case

By using the theory of uniformization of Riemann surfaces,we study properties of the Liouville equation and its general solution on a Riemann surface of genus g>1.After obtaining Hamiltonian formalism in terms of free fields and calculating classical exchange matrices,we prove the classical integrability of Liouville system on high genus Riemann surface.     

Integrability and Solutions of the(2+1)-dimensional Hunter–Saxton Equation

In this paper,the(2+1)-dimensional Hunter-Saxton equation is proposed and studied.It is shown that the(2+1)-dimensional Hunter–Saxton equation can be transformed to the Calogero–Bogoyavlenskii–Schiff equation by reciprocal transformations.Based on the Lax-pair of the Calogero–Bogoyavlenskii–Schiff equation,a non-isospectral Lax-pair of the(2+1)-dimensional Hunter–Saxton equation is derived.In addition,exact singular solutions with a finite number of corners are obtained.Furthermore,the(2+1)-dimensional μ-Hunter–Saxton equation is presented,and its exact peaked traveling wave solutions are derived.     

Study of the effect of adhesion and anharmonicity of atomic vibrations on the thermal conductance of “metal–dielectric” interfaces

Physics of the Solid State - The method for calculating the thermal conductance of “metal–dielectric” interfaces, which takes into account the adhesive interaction and...     

A New Approach to the Lenard–Magri Scheme of Integrability

We develop a new approach to the Lenard–Magri scheme of integrability of bi-Hamiltonian PDEs, when one of the Poisson structures is a strongly skew-adjoint differential operator.