A note on a class of singular integro-differential equations

A simplified analysis is employed to handle a class of singular integro-differential equations for their solutions

Reduced Order Suboptimal Control Design for a Class of Nonlinear Distributed Parameter Systems Using POD and /spl thetas/-D Techniques

A new computational tool is presented in this paper for suboptimal control design of a class of nonlinear distributed parameter systems. First proper orthogonal decomposition based problem-oriented basis functions are designed, which are then used in a Galerkin projection to come up with a low-order lumped parameter approximation. Next, a suboptimal controller is designed using the emerging /spl thetas/-D technique for lumped parameter systems. This time domain sub-optimal control solution is then mapped back to the distributed domain using the same basis functions, which essentially leads to a closed form solution for the controller in a state feedback form. Numerical results for a real-life nonlinear temperature control problem indicate that the proposed method holds promise as a good suboptimal control design technique for distributed parameter systems.

An optimal dynamic inversion approach for controlling a class of one-dimensional nonlinear distributed parameter systems

Combining the principles of dynamic inversion and optimization theory, a new approach is presented for stable control of a class of one-dimensional nonlinear distributed parameter systems, assuming the availability a continuous actuator in the spatial domain. Unlike the existing approximate-then-design and design-then-approximate techniques, here there is no need of any approximation either of the system dynamics or of the resulting controller. Rather, the control synthesis approach is fairly straight-forward and simple. The controller formulation has more elegance because we can prove the convergence of the controller to its steady state value. To demonstrate the potential of the proposed technique, a real-life temperature control problem for a heat transfer application is solved. It has been demonstrated that a desired temperature profile can be achieved starting from any arbitrary initial temperature profile.

A New Class of Exactly Solvable Interacting Fermion Models in One Dimension

We investigate a model containing two species of one-dimensional fermions interacting via a gauge field determined by the positions of all particles of the opposite species. The model can be salved exactly via a simple unitary transformation. Nevertheless, correlation functions exhibit nontrivial interaction-dependent exponents. A similar model defined on a lattice is introduced and solved. Various generalizations, e.g., to the case of internal symmetries of the fermions, are discussed. The present treatment also clarifies certain aspects of Luttinger's original solution of the "Luttinger model."

Petri net-based modeling of a class of complex digital systems

We present through the use of Petri Nets, modeling techniques for digital systems realizable using FPGAs. These Petri Net models are used for logic validation at the logic design phase. The technique is illustrated by modeling practical circuits. Further, the utility of the technique with respect to timing analysis of the modeled digital systems is considered. Copyright (C) 1997 Elsevier Science Ltd

Residence time distribution for a class of Gaussian Markov processes

We study the distribution of residence time or equivalently that of "mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter alpha. The persistence exponent for these processes is simply given by theta=alpha but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as theta increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha. For some special values of alpha, we obtain closed form expressions of the distribution function. [S1063-651X(99)03306-1].

The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena

Two mixed boundary value problems associated with two-dimensional Laplace equation, arising in the study of scattering of surface waves in deep water (or interface waves in two superposed fluids) in the linearised set up, by discontinuities in the surface (or interface) boundary conditions, are handled for solution by the aid of the Weiner-Hopf technique applied to a slightly more general differential equation to be solved under general boundary conditions and passing on to the limit in a manner so as to finally give rise to the solutions of the original problems. The first problem involves one discontinuity while the second problem involves two discontinuities. The reflection coefficient is obtained in closed form for the first problem and approximately for the second. The behaviour of the reflection coefficient for both the problems involving deep water against the incident wave number is depicted in a number of figures. It is observed that while the reflection coefficient for the first problem steadily increases with the wave number, that for the second problem exhibits oscillatory behaviour and vanishes at some discrete values of the wave number. Thus, there exist incident wave numbers for which total transmission takes place for the second problem. (C) 1999 Elsevier Science B.V. All rights reserved.

A facile entry into a new class of spiroheterocycles: synthesis of dispiro[oxindolechromanone/flavanone/tetralone]pyrroloisoquinoline ring systems

A series of novel dispiroheterocyclic systems have been synthesized by the cycloaddition of a new azomethine ylide generated by the decarboxylative route from tetrahydroisoquinoline-3-carboxylic acid and isatin with various dipolarophiles containing exocyclic double bond such as 3-arylidene-4-chromanone, 3-arylidene-4-flavanone and 2-arylidenetetrahydro-1-naphthalenone in moderate to good yield. The regio and stereochemistry of the title compounds was established by single crystal X-ray structure and spectroscopic techniques. (C) 2002 Elsevier Science Ltd. All rights reserved.

A new class of three dimensional D-pi-A trigonal cryptand derivatives for second-order nonlinear optics

Synthesis, crystal structures, linear and nonlinear optical properties of tris D-pi-A cryptand derivatives with C-3 symmetry are reported. Three fold symmetry inherent in the cryptand molecules has been utilized for designing these molecules. Molecular nonlinearities have been measured by hyper-Rayleigh scattering (HRS) experiments. Among the compounds studied, L-1 adopts non-centrosymmetric crystal structure. Compounds L-1, L-2, L-3 and L-4 show a measurable SHG powder signal. These molecules are more isotropic and have significantly higher melting points than the classical p-nitroaniline based dipolar NLO compounds, making them useful for further device applications. Besides, different acceptor groups can be attached to the cryptand molecules to modulate their NLO properties.

A new class of magnetic materials: Sr2FeMoO6 and related compounds

Ordered double perovskite oxides of the general formula A2BB′O6 have been known for several decades to have interesting electronic and magnetic properties. However, a recent report of a spectacular negative magnetoresistance effect in a specific member of this family, namely Sr2FeMoO6, has brought this class of compounds under intense scrutiny. It is now believed that the origin of the magnetism in this class of compounds is based on a novel kinetically-driven mechanism. This new mechanism is also likely to be responsible for the unusually high temperature ferromagnetism in several other systems, such as dilute magnetic semiconductors, as well as in various half-metallic ferromagnetic systems, such as Heussler alloys.

An adaptive cascade compensator for a wide class of stable minimum or nonminimum phase plants through time moment estimation

Model Reference Adaptive Control (MRAC) of a wide repertoire of stable Linear Time Invariant (LTI) systems is addressed here. Even an upper bound on the order of the finite-dimensional system is unavailable. Further, the unknown plant is permitted to have both minimum phase and nonminimum phase zeros. Model following with reference to a completely specified reference model excited by a class of piecewise continuous bounded signals is the goal. The problem is approached by taking recourse to the time moments representation of an LTI system. The treatment here is confined to Single-Input Single-Output (SISO) systems. The adaptive controller is built upon an on-line scheme for time moment estimation of a system given no more than its input and output. As a first step, a cascade compensator is devised. The primary contribution lies in developing a unified framework to eventually address with more finesse the problem of adaptive control of a large family of plants allowed to be minimum or nonminimum phase. Thus, the scheme presented in this paper is confined to lay the basis for more refined compensators-cascade, feedback and both-initially for SISO systems and progressively for Multi-Input Multi-Output (MIMO) systems. Simulations are presented.

Perfluoroalkyl bile esters: a new class of efficient gelators of organic and aqueous-organic media

A new class of fluorinated gelators derived from bile acids is reported. Perfluoroalkyl chains were attached to the bile acids through two different ester linkages and were synthesized following simple transformations. The gelation property of these derivatives is a function of the bile acid moiety, the spacer and the fluoroalkyl chain length. By varying these parameters, gels were obtained in aromatic hydrocarbons, DMSO and DMSO/DMF-H(2)O mixtures of different proportions. Several derivatives of deoxycholic and lithocholic acids were found to be efficient organogelators, while the reported bile-acid based organogelators are mostly derived from the cholic acid moiety. The efficient gelators among these compounds formed gels well below 1.0% (w/v) and hence they can be termed as supergelators. The mechanical properties of these gels could be modulated by changing either the bile acid moiety or by varying the length of the fluoroalkyl segment. The presence of CO(2)-philic perfluoroalkyl groups is also expected to enhance their solubility in supercritical CO(2) and hence these compounds are promising candidates for making aerogels.