Heat problems for a starlike shaped plate

The Fourier solution of the heat problem for a circular plate is generalized to a starlike shaped plate. We show that the classical solution can be used even in this more general case, provided that a suitable change of variables in the polar co-ordinate system is performed.     

SQUID-based measuring systems

A program has been developed and initiated at the Indira Gandhi Centre for Atomic Research (IGCAR) for the utilization of SQUID sensors in various application areas. DC SQUID sensors based on Nb-AlO _x -Nb Josephson junctions have been designed and developed inhouse along with associated flux-locked loop (FLL) electronics. A compact low field SQUID magnetometer insertible in a liquid helium storage dewar has also been developed inhouse and is in use. Efforts to build a high field SQUID magnetometer, SQUID-DAC system, are in progress. A planar gradiometric DC SQUID sensor for non-destructive evaluation (NDE) application to be used in relatively unshielded environment has been designed and developed. An easily portable NDE cryostat with a small lift-off distance, to be used in external locations has been designed and tested. The magnetic field produced by a given two-dimensional current density distribution is inverted using the Fourier transform technique.     

Nanoelectromechanical systems

Nanoelectromechanical systems (NEMS) are nano-to-micrometer scale mechanical resonators coupled to electronic devices of similar dimensions. NEMS show promise for fast, ultrasensitive force microscopy and for deepening our understanding of how classical dynamics arises by approximation to quantum dynamics. This article begins with a survey of NEMS and then describes certain aspects of their classical dynamics. In particular, we show that for weak coupling the action of the electronic device on the mechanical resonator can be effectively that of a thermal bath, this despite the device being a driven, far-from-equilibrium system.     

Principal Eigenvalues for Isaacs Operators with Neumann Boundary Conditions

In this paper we show the existence of two principal eigenvalues associated to general non-convex fully nonlinear elliptic operators with Neumann boundary conditions in a bounded C ² domain. We study these objects and we establish some of their basic properties. Finally, Lipschitz regularity, uniqueness and existence results for the solution of the Neumann problem are given.      

Methodological analysis of supply chains management applications

Formal modelling may be used to express management operational plans to achieve the desired normative objectives of firms. The plans so formulated should be demonstrably optimal with regard to certain specific objectives assumed by top management and ought to provide accurate results, when enacted, with a given tolerance at a prespecified probability.     

Anatomy of a polarization switch of a vertical-cavity semiconductor laser

Using a streak camera we have measured the three Stokes polarization parameters during a polarization switch of a vertical-cavity semiconductor laser. The switch occurs along a corkscrew path on the Poincare sphere and takes on average a few nanoseconds; this value agrees with a theoretical treatment based upon the Fokker-Planck equation.     

Formal methods in pattern recognition: A review

There is lot of excitement with Pattern Recognition methods with high precision, since this problem area is a well-established field of Operations Research (O.R.). Recent work of some researchers has shown that O.R. methods in general and Optimisation methods in particular, can be applied to give some very good results. Thus this research area has been won back from the Artificial Intelligence community and is quickly becoming once more a fast growing field in O.R. The aim of this review is to examine the early success of classification methods and Pattern Recognition methods, consider their downfall and examine the new techniques that have been applied to make it like a resurgent Phoenix. It will be shown that optimisation methods, if carried out properly, through a formal analysis of their structure and their requirements can achieve correct classification with probability one. Many researchers make it more difficult for themselves by not considering the formalisation of the task concerned and so adapt heuristics to the problem. Computational methods taken from the Irvine Repository database on recognition instances will be placed in evidence. The outline of the paper is as follows. After the introduction a historical sketch of the field will be presented. Then in Section 3, the need for formal methods will be argued and various results on formal requirements as convergence etc. will be derived. Many of these formal requirements are of course related to the best-unbiased estimate (b.u.e) requirements in Statistics. In Section 4 some popular algorithms for Pattern Recognition will be presented and their degree of satisfaction of the formal requirements stressed, allowing in Section 5 to present many applications, so that conclusions can be reached in Section 6. It will be found that the satisfaction of the formal requirements is a necessary and sufficient condition to reach recognition with probability one.