任意三角形单元上的三次Lagrange型插值逼近

本文推广了文［２］中的结果，对于任意三角形单元的三次Ｌａｇｒａｎｇｅ型插值多项式给出了原函数ｕ与被插函数Ｕ之间的误差估计     

S-wave baryons in an equally mixed scalar-vector square root potential model of independent quarks

A relativistic model of independent quarks based on Dirac equation with an equally mixed scalar-vector square root confining potential is used to compute the quark core contributions to the static properties like magnetic moments, charge radii and axial vector coupling constant ratios of the baryon octet. The results obtained with appropriate corrections due to centre-of-mass motion agree fairly well with experimental values. The model is also extended to the study of magnetic moments of the quark core of baryons in the charmed andb-flavoured sectors and the overall predictions so obtained compare well with other model predictions.     

Coherent potential approximation for a disordered diatomic linear chain having diagonal and off-diagonal randomness

A coherent potential approximation (cpa) for a mixed diatomic linear chain including both mass and force constant changes has been developed. In this case an impurity atom substituted at a particular site in one of the sublattices couples with two nearest neighbour atoms in the other sublattices. The diatomic linear chain is therefore considered as a tetratomic linear chain, the size of the unit cell being twice the original. Thecpa density of states and the dielectric susceptibility have been calculated. The numerical values of the later have been calculated in theata (averaget-matrix approximation) limit. Comparison of these results with the experimental and other computer calculations show a qualitative agreement.     

Symmetrization of matrix technique in a finite element context

A finite element Galerkin-based formulation of the mass conservation and momentum equations can require, if convective type terms are retained in the coefficient matrix, a non-symmetric solver. The resulting increase in core storage for efficient utilization of CPU time can be considerable. The current paper advocates a simple symmetrization of matrix technique, at element level which results in a considerable reduction in core requirement. The increase in CPU time required when solving linear systems of equations is considerable. However, for nonlinear systems the penalty can be negligible.     

Extensions of Lemke's algorithm for the linear complementarity problem

Lemke's algorithm for the linear complementarity problem fails when a desired pivot is not blocked. A projective transformation overcomes this difficulty. The transformation is performed computationally by adjoining a new row to a schema of the problem and pivoting on the element in this row and the unit constant column. Two new algorithms result; some conditions for their success are discussed.This research was partially supported by National Science Foundation, Grant GK-42092.     

Solution of nonlinear optimal control problems in Hilbert spaces by means of linear programming techniques

Optimal control problems in Hilbert spaces are considered in a measure-theoretical framework. Instead of minimizing a functional defined on a class of admissible trajectory-control pairs, we minimize one defined on a set of measures; this set is defined by the boundary conditions and the differential equation of the problem. The new problem is an infinite-dimensionallinear programming problem; it is shown that it is possible to approximate its solution by that of a finite-dimensional linear program of sufficiently high dimensions, while this solution itself can be approximated by a trajectory-control pair. This pair may not be strictly admissible; if the dimensionality of the finite-dimensional linear program and the accuracy of the computations are high enough, the conditions of admissibility can be said to be satisfied up to any given accuracy. The value given by this pair to the functional measuring the performance criterion can be about equal to theglobal infimum associated with the classical problem, or it may be less than this number. It appears that this method may become a useful technique for the computation of optimal controls, provided the approximations involved are acceptable.     

Linear response and relaxation in quantum lattice systems

For spin-lattice systems, the Kubo formula, expressing the relaxation function in terms of the linear response function, is found to be exact in the thermodynamic limit. In addition, analyticity properties are obtained.     

Work function of metals: Relation between theory and experiment

Theoretical approaches to calculation of work function within jellium model and the problem of extension of this model to include the lattice corrections to the work function are briefly discussed. Lattice corrections to the work function obtained from the experiment are estimated and compared with those calculated theoretically.

It is found that the mean value of the experimental lattice correction <δψ_hkl>_hkl compared to the mean work function is negligible. It is stated that the mean work function can be treated as a material constant characterizing a given metal, such as, e.g., binding energy.An expression for the dependence of jellium work function on r_s, valid in a metallic range of r_s, is given. A comparison between then theoretical and experimental results is presented and the role of correlation energy is examined. It is shown that more accurate approximations of the correlation energy than that given by Wigner's formula lead to a better agreement with experiment. A simple model is presented for explanation of work function changes on single crystal planes. Some recent results concerning the thermal dependence of work function are given. The dependence of the work function on the degree of coverage is discussed both for alkali and non-alkali atoms adsorption. Theoretical models are briefly reviewed and comparison between theory and experiment is made. A simple model is presented for explanation of the work function variation on rough planes in metallic non-alkali atoms chemisorption.     

Mossbauer study of ferrite systems Co x Mn1−x Fe2O4 and Ni x Mn1−x Fe2O4

Mössbauer spectra of Co _x Mn_1?x Fe₂O₄ and Ni _x Mn_1?x Fe₂O₄ ferrites withx values ranging from 0·1 to 0·8 in steps of 0·1 have been recorded at room temperature. All spectra exhibit well-defined Zeeman hyperfine patterns. It has been observed that hyperfine field at Fe³⁺ nucleus increases more rapidly by nickel substitution than by cobalt substitution. This has been explained in terms of exchange interactions and cation distribution in the spinels. Hyperfine fields, isomer shifts and quadrupole splittings have been determined.     

A procedure for one-parametric linear programming

A procedure is proposed for the parametric linear programming problem where all the coefficients are linear or polynomial functions of a scalar parameter. The solution vector and the optimum value are determined explicitly as rational functions of the parameter. In addition to standard linear programming technique, only the determination of eigenvalues is required. The procedure is compared to those by Dinkelbach and Zsigmond, and a numerical example is given.