序二

幻方是我国古代的伟大发明之一,是我们先祖高智慧的结晶,是数学的源头,是一门有趣而又深奥的学问.幻方以对称、整齐、均衡、和谐等多种美的特性,使众多学者迷恋.可是,现在中小学生却很少知道幻方,虽然小学一年级数学教科书已有三阶幻方的习题,但以后各年级数学教科书中却无幻方的影子,这实在是十分遗憾的事情.幻方的历史是那样的古老,内容是那样的丰富,思想蕴意又是那样的深奥,应用又是如此的广泛,它对提高学生的学习兴趣,开发青少年的智力,是有极大好处的.我真希望青少年朋友都来研究它,尤其希望中、小学教师能将幻方引入课堂.我热切希望把幻方放到小学、中学的数学教科书中去.

Quantum Effect in Mesoscopic Open Electron Resonator

The open electron resonator is a mesoscopic device that has attracted considerable attention due to its remarkable behavior： conductance oscillations. In this paper, using an improved quantum theory to mesoscopic circuits developed recently by Li and Chen, the mesoscopic electron resonator is quantized based on the fundamental fact that the electric charge takes discrete value. With presentation transformation and unitary transformation, the SchrSdinger equation becomes an standard Mathieu equation. Then, the detailed energy spectrum and wave functions in the system axe obtained, which will be helpful to the observation of other characters of electron resonator. The average of currents and square of the current are calculated, the results show the existence of the current fluctuation, which causes the noise in the circuits, the influence of inductance to the noise is discussed. With the results achieved, the stability characters of mesoscopic electron resonator are studied firstly, these works would be benefit to the design and control of integrate circuit.

A NEW SINGULARITY EXTRACTION TECHNIQUE FOR TDEFIE

A new singularity extraction technique is presented to calculate accurately the singular integrals in Time Domain Electric Field Integral Equation (TDEFIE).In singularity extraction pro- cedure,through the aid of the first order Taylor series of time base function including time-retardation,the singularity of the integrand can be removed.The surface current density and backscattered far-field response of a conducting cube illuminated by a Gaussian plane wave is com- puted using the presented technique.Comparisons are made with the results obtained by the Inverse Discrete Fourier Transform (IDFT) of the frequency domain and the results obtained by using Ve- chinski's time averaging technique,which demonstrate that the presented method with this new time domain singularity extraction technique to solve TDEFIE is very accurate and stable.

Supersymmetric Sawada-Kotera-Ramani Equation: Bilinear Approach

In this paper, using the Hirota＇s bilineax method, we consider the N = 1 supersymmetric Sawada-Kotera- Ramani equation and obtain the Bazcklund transformation of it. Its one- and two-supersoliton solutions axe obtained and N-supersoliton solutions for N ≥ 3 are given under the condition kiξj = kjξi.

Soliton, Positon and Negaton Solutions of Extended KdV Equation

Darboux transformation （DT） provides us with a comprehensive approach to construct the exact and explicit solutions to the negative extended KdV （eKdV） equation, by which some new solutions such as singular soliton, negaton, and positon solutions are computed for the eKdV equation. We rediscover the soliton solution with finiteamplitude in [A.V. Slyunyaev and E.N. Pelinovskii, J. Exp. Theor. Phys. 89 （1999） 173] and discuss the difference between this soliton and the singular soliton. We clarify the relationship between the exact solutions of the eKdV equation and the spectral parameter. Moreover, the interactions of singular two solitons, positon and negaton, positon and soliton, and two positons are studied in detail.

Adsorption Kinetics of Pb^(2+) and Cu^(2+) on Variable Charge Soils and Minerals: Ⅱ. Equations for Describing Experimental Data

Different mathematical methods, including linearization, differential, integration and nonlinear least squares approximation (Newton-Marquardt method), were used to fit different kinetic equations, such as zero-order, first-order (i. e, membrane diffusion), second-order, parabolic-diffusion, Elovich, two-constant equations, to the experimental data of Pb2+ and Cu2+ adsorption on variable charge soils and kaolinite. Assuming each M2+ occupied two adsorption sites, two more equations, the so-called surface second-order equation and third-order equation were derived and compared with the above equations according to the fitting results, which showed that the second-order equation and surface second-order equation, being one equation in different expressions under some conditions, were better than the other equations in describing the Pb2+ and Cu2+ adsorption kinetics, and the latter was the best.

Supersymmetric Quantum Mechanics and SUSY Dependent SU(2) Symmetry for a Spin-1/2 Charged Particle in a Magnetic Field

We find that in a supersymmetric quantum mechanics （SUSY QM） system, in addition to supersymmetric algebra, an associated SU（2） algebra can be obtained by using semiunitary （SUT） operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z-axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SUτ（2） SUσ（2） symmetry in the context of the relativistic Pauli Hamilt onian squared. We show that there exists also an SU（2） symmetry associated with the supersvmmetrv of the Dirac particle.

DFT-Study on Antioxydant of 3-Alkyl-4-P henylacetylam i no-1H-1,2,4-Triazol-5-O nes and Its Derivatives

In this article, we have performed B3LYP/6-31＋G（d） calculations of geometrical and reaction enthalpies of antioxidant mechanisms for ADPHT 1-4 （3-alkyl-4-phenylacetylamino-lH-1,2,4-triazol-5-ones） and its derivatives： HAT （hydrogen atom transfer）, SET-PT （single electron transfer-proton transfer） and SPLET （sequential proton-loss electron transfer） were investigated in gas and solution-phases. Solvent contribution to enthalpies was computed employing integral equation formalism IEF-PCM （integral equation formalism method） method. It turned out that the lowest BDEs （bond dissociation energies） is obtained for C-H bonds due to captodative effect in various media. Results indicate that HAT mechanism represents the most anticipated process in gas-phase from thermodynamic point of view. But, the SPLET represents the thermodynamically preferred reaction pathway in solvents （2-propanol, acetonitrile, DMF （N,N-dimethylformamide） and water）. The authors showed that bond dissociation energies, IP （ionization potential） and PA （proton affinity） are sufficient to evaluate the thermodynamically preferred mechanism.