On the Transform Method of Solution of an External Crack Problem

The breakdown of the usual method of Fourier transforms in the problem of an external line crack in a thin infinite elastic plate is discovered and the correct solution of this problem is derived using the concept of a generalised Fourier transform of a type discussed first by Golecki [1] in connection with Flamant's problem.

Isolation of hen's egg yolk very low density lipoproteins by DEAE-cellulose chromatography

A procedure has been developed for the isolation of very low density lipoproteins from hen's egg yolk plasma using DEAE-cellulose chromatography. This procedure is rapid and does not require ultracentrifugation and should, therefore, serve as a useful procedure for use in laboratories where this facility does not exist.

Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method

We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser–Parr–Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

On the bottleneck linear programming problem

In this paper, the results on primal methods for Bottleneck Linear Programming (BLP) problem are briefly surveyed, the primal method is presented and the degenerate case related to Bottleneck Transportation Problem (BTP) is explicitly considered. The algorithm is based on the idea of using auxiliary coefficients as is done by Garfinkel and Rao [6]. The modification presented for the BTP rectifies the defect in Hammer's method in the case of degenerate basic feasible solution. Illustrative numerical examples are also given.

Two-Impurity Kondo Problem

The two-impurity Kondo problem is studied by use of perturbative scaling techniques. The physics is determined by the interplay between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the two impurity spins and the Kondo effect. In particular, for a strong ferromagnetic RKKY interaction the susceptibility exhibits three structures as the temperature is lowered, corresponding to the ferromagnetic locking together of the two impurity spins followed by a two-stage freezing out of their local moments by the conduction electrons due to the Kondo effect.

A time minimising transportation problem with quality dependent time

The usual assumption made in time minimising transportation problem is that the time for transporting a positive amount in a route is independent of the actual amount transported in that route. In this paper we make a more general and natural assumption that the time depends on the actual amount transported. We assume that the time function for each route is an increasing piecewise constant function. Four algorithms - (1) a threshold algorithm, (2) an upper bounding technique, (3) a primal dual approach, and (4) a branch and bound algorithm - are presented to solve the given problem. A method is also given to compute the minimum bottle-neck shipment corresponding to the optimal time. A numerical example is solved illustrating the algorithms presented in this paper.

On the orthogonality of suboptimum estimate in the combined estimation and control problem

By deriving the equations for an error analysis of modeling inaccuracies for the combined estimation and control problem, it is shown that the optimum estimation error is orthogonal to the actual suboptimum estimate.

Some Generalisations of the Time Minimising Assignment Problem

The time minimising assignment problem is the problem of finding an assignment of n jobs to n facilities, one to each, which minimises the total time for completing all the jobs. The usual assumption made in these problems is that all the jobs are commenced simultaneously. In this paper two generalisations of this assumption are considered, and algorithms are presented to solve these general problems. Numerical examples are worked out illustrating the algorithms.

Radiation induced depinning of a charge density wave system

The frequency-dependent response of a pinned charge density wave is considered in terms of forced vibration of an oscillator held in an anharmonic well. It is shown that the effective pinning-frequency can be reduced by applying a d.c. field. If a strong a.c. field, superposed on a d.c. field is applied on such a system “jumps” can be observed in the frequency dependent response of the system. The conditions at which these “jumps” occur are investigated with reference to NbSe3. The possibility of observing such phenomena in other systems like superionic conductors, non-linear dielectrics like ferroelectrics is pointed out. The characteristics are expressed in terms of some “scaled variables” — in terms of which the characteristics show a universal behaviour

A probabilistic approach to the problem of electron localization in disordered systems and sharpness of the mobility edge

By applying the theory of the asymptotic distribution of extremes and a certain stability criterion to the question of the domain of convergence in the probability sense, of the renormalized perturbation expansion (RPE) for the site self-energy in a cellularly disordered system, an expression has been obtained in closed form for the probability of nonconvergence of the RPE on the real-energy axis. Hence, the intrinsic mobility mu (E) as a function of the carrier energy E is deduced to be given by mu (E)= mu 0exp(-exp( mod E mod -Ec) Delta ), where Ec is a nominal 'mobility edge' and Delta is the width of the random site-energy distribution. Thus mobility falls off sharply but continuously for mod E mod >Ec, in contradistinction with the notion of an abrupt 'mobility edge' proposed by Cohen et al. and Mott. Also, the calculated electrical conductivity shows a temperature dependence in qualitative agreement with experiments on disordered semiconductors.

An inhomogeneity problem in couple stress theory

Using Hilbert theory and Mindlin's couple stress theory, the problem of two-dimensional circular inhomogeneity (when the inserted material is of different size than the size of the cavity and having different elastic constants) is studiedin this paper. Stress could be bounded at infinity. The formulation is valid also for regions other then the circular ones when the matrix is finite has also been tackled. Numerical results are in conformity with the fact that the effect of couple stresses is negligible when the ratio of the smallest dimension of the body to the cahracteristic length is large.

On the orthogonality of suboptimum estimate in the combined estimation and control problem

By deriving the equations for an error analysis of modeling inaccuracies for the combined estimation and control problem, it is shown that the optimum estimation error is orthogonal to the actual suboptimum estimate.

A problem in micropolar elasticity

In this paper a three-dimensional analysis for statics and dynamics of a class of simply supported rectangular plates made up of micropolar elastic material is presented. The solution is in the form of series, in which each term is explicitly determined. For free vibrations, the frequencies are obtained by the solution of a closed form characteristic equation.

On the orthogonality of suboptimum estimate in the combined estimation and control problem

By deriving the equations for an error analysis of modeling inaccuracies for the combined estimation and control problem, it is shown that the optimum estimation error is orthogonal to the actual suboptimum estimate.