纽结理论在数论中的应用

基于纽结理论,利用Torus纽结 T(m, n)（m,n须为互素）及Jones多项式和Alexander多项式在二阶导数下的性质,证明了(m2-1)(n2-1),(m-1)(n-1)(2mn-m-n-1)可分别被24与12整除。     

For a fixed Turaev shadow Jones-Vassiliev invariants depend polynomially on the gleams

We use Turaev's technique of shadows and gleams to parametrize the set of all knots in S ³ with the same Hopf projection. We show that the Vassiliev invariants arising from the Jones polynomial J _t (K) are polynomials in the gleams, i.e., for , the n-th order Vassiliev invariant u _n , defined by , is a polynomial of degree 2n in the gleams. Received: April 30, 1996     

On the Nontriviality of the Polynomial Invariant of Two-Component Link

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A Simple Synthesis of a Model of the Tetracyclic Bisketal Lactone Mainframe of Saudin

The partial structure 2 of the bisketal‐type, tetracyclic saudin ( 1 ), an important natural product, was de novo synthesized. A key step was the Jones oxidation of the epoxide 3 , which gave rise to epoxide‐ring opening, followed by acetal hydrolysis, alcohol oxidation, and, finally, intramolecular acetal formation. The resulting key intermediate was finally oxidized to the target lactone 2 .     

Gravitational smoothing as a global optimization strategy

An optimization scheme for atomic cluster structures, based on exaggerating the importance of the gravitational force, is introduced. Results are presented for calculations on Lennard-Jones clusters of 13, 38, and 55 atoms, and the 13-atom Morse cluster.     

Thermophysical Properties of H<Subscript>2</Subscript>O–Ar Plasmas at Temperatures 400–50,000 K and Pressure 0.1 MPa

The article presents the calculation of thermophysical properties of the mixture water steam–argon which has been used to further enhance the characteristics of plasma torches stabilized by the water wortex. The calculations were performed at the temperatures 400–50,000 K and at 0.1 MPa. First, the composition and thermodynamic properties are determined by classical methods. Further the calculations of viscosity, electrical conductivity and thermal conductivity of the mixture are computed in the 4th approximation of the Chapman–Enskog method. The computation of collision integrals is described with special respect to the interactions of charged particles where the necessary calculations for the Coulomb potential screened at the Debye length were enlarged to cover the 4th approximation. Then the formulae describing the method based on the variational principle of solving the system of Boltzmann integrodifferential equations are shortly introduced and the transport coefficients are presented.     

Excess energy and equation of state of fluids with hard-core potential models from a second-order Monte Carlo perturbation theory

Monte Carlo simulations in the NVT ensemble of the reference hard-sphere fluid have been performed to obtain the “exact” first- and second-order terms in the inverse temperature expansion of the free energy of fluids with hard-core potentials. The results have been used to obtain parametrizations of the free energy of fluids with Sutherland potentials with variable range as well as for a fluid with a hard-core Lennard–Jones potential. The results for the excess energy and the equation of state are compared with simulation data available in the literature for these fluids.     

The Reduction of CS2N3 − Ion In Acidic Solution

Abstract

The electrochemical behaviour of 1, 2, 3, 4-thiatriazol-5-thiolate CS₂N₃ ^? ion in acidic solutions has been investigated. A cathodic wave has been detected, (E_1/2 =?1.05V versus S.C.E., M=1.0M (NaC10₄) and NaCS₂N₃ 1.00 × 10^?3M). The characteristics of this wave have been investigated by D.C., A.C. polarography and controlled potential electrolysis. A mechanism which involves the interaction of CS₂N₃ ^? with mercury and cyclic regeneration of mercury has been proposed. The reduction of CS₂N₃ ^? by amalgamated zinc has been also investigated and the results correlated with the pseudo-halide electrochemical reduction.     

Method to enhance the accuracy of the retardance measurement of quarter-wave plates

A novel method used for the enhancement of the accuracy of the retardance measurement of a quarter-wave plate employing two polaroids and a prism is reported under the condition of knowing the direction of the fast-axis of the plate. The theoretical analysis of the principle and the uncertainty formula are given. An application example is also demonstrated. The measured result of the example is verified with an experiment. The main advantages of this method include the accuracy enhancement, simple measuring setup and easy operation.     

Polymer complexes: supramolecular modeling for determination and identification of the bond lengths in novel polymer complexes from their infrared spectra

Synthesis and characterization of allyl propenyl‐2‐(4‐derivatives phenylazo)butan‐3‐one (HL_n) are described. The monomers obtained contain N?N and carbonyl functional groups in different positions with respect to the allyl group. This structural difference affects the stereochemical structure of the uranyl polymer complexes prepared by the direct reaction of uranyl acetate with the monomers. The polymer complexes are characterized by elemental analyses, ¹H and ¹³C NMR, electronic and vibrational spectroscopy and other theoretical methods. The bonding sites of the hydrazone are deduced from IR and NMR spectra and each of the ligands were found to bond to the UO₂²⁺ ion in a bidentate fashion. The monomers obtained contain N?N and carbonyl functional groups in different positions with respect to the allyl group. IR spectra show that the allyl azo homopolymer (HL_n) acts as a neutral bidentate ligand by coordinating via the two oxygen atom of the carbonyl group, thereby forming a six‐membered chelating ring. The υ₃ frequency of UO₂²⁺ has been shown to be a good molecular probe for studying the coordinating power of the ligands. The υ₃‐values of UO₂²⁺ from IR spectra have been used to calculate the force constant, F_UO (in 10^?8 N/Å) and the bond length R_UO (in Å) of the U? O bond. We adopted a strategy based upon both theoretical and experimental investigations. The theoretical aspects are described in terms of the well‐known theory of 5d–4f transitions. The necessary structural data (coordination geometries and electronic structures) are determined from a framework for the modeling of novel polymer complexes. The Wilson, G. F. matrix method, Badger's formula and the Jones and El‐Sonbati equations were used to determine the stretching and interaction force constants from which the U? O bond distances were calculated. The bond distances of these complexes were also investigated. The effect of Hamett's constant is also discussed. Copyright © 2006 John Wiley & Sons, Ltd.