Basic Needs and Much More With One Kilowatt Per Capita

Conventional thinkin g holds that increased energy consumption is a prerequisite for economic and social development. This belief, together With the prospect of dwindling global petroleum supplies and the high costs of expanding energy supply generally, lead many to believe that it is not feasible to improve living standards substantially in the developing countries. But by shifting to high-quality energy carriers and by exploiting cost-effective opportunities for more efficient energy use, it would be possible to satisfy basic human needs and to provide considerable further improvements in living standards without significantly increasing per-capita energy use above the present level.

Impedance tube technology for flow acoustics

Acoustic impedance of a termination, or of a passive subsystem, needs to be measured not only for acoustic lining materials but also in the exhaust systems of flow machinery, where mean flow introduces peculiar problems. Out of the various methods of measurement of acoustic impedance, the discrete frequency, steady state, impedance tube method [1] is most reliable, though time consuming, and requires no special instrumentation.

Development of special fastener elements

A special finite element (FASNEL) is developed for the analysis of a neat or misfit fastener in a two-dimensional metallic/composite (orthotropic) plate subjected to biaxial loading. The misfit fasteners could be of interference or clearance type. These fasteners, which are common in engineering structures, cause stress concentrations and are potential sources of failure. Such cases of stress concentration present considerable numerical problems for analysis with conventional finite elements. In FASNEL the shape functions for displacements are derived from series stress function solutions satisfying the governing difffferential equation of the plate and some of the boundary conditions on the hole boundary. The region of the plate outside FASNEL is filled with CST or quadrilateral elements. When a plate with a fastener is gradually loaded the fastener-plate interface exhibits a state of partial contact/separation above a certain load level. In misfit fastener, the extent of contact/separation changes with applied load, leading to a nonlinear moving boundary problem and this is handled by FASNEL using an inverse formulation. The analysis is developed at present for a filled hole in a finite elastic plate providing two axes of symmetry. Numerical studies are conducted on a smooth rigid fastener in a finite elastic plate subjected to uniaxial loading to demonstrate the capability of FASNEL.

A unified approach to the solution of plane problems of Magneto-elasticity with special reference to a hole in a thin infinite conducting plate

Under certain specific assumption it has been observed that the basic equations of magneto-elasticity in the case of plane deformation lead to a biharmonic equation, as in the case of the classical plane theory of elasticity. The method of solving boundary value problems has been properly modified and a unified approach in solving such problems has been suggested with special reference to problems relating thin infinite plates with a hole. Closed form expressions have been obtained for the stresses due to a uniform magnetic field present in the plane of deformation of a thin infinite conducting plate with a circular hole, the plate being deformed by a tension acting parallel to the direction of the magnetic field.

Thermodynamic implication of the special relativistic postulate

Abstract is not available.

Discontinuities in an arbitrarily moving gas in special relativity

Singular surface theory and ray theory are used to study the propagation of a weak discontinuity in an arbitrarily moving gas within the framework of special relativity. A differential equation is obtained describing the variation of the strength of the discontinuity along rays.

An Optimal Mechanism for Sponsored Search Auctions on the Web and Comparison With Other Mechanisms

In this paper, we first describe a framework to model the sponsored search auction on the web as a mechanism design problem. Using this framework, we describe two well-known mechanisms for sponsored search auction-Generalized Second Price (GSP) and Vickrey-Clarke-Groves (VCG). We then derive a new mechanism for sponsored search auction which we call optimal (OPT) mechanism. The OPT mechanism maximizes the search engine's expected revenue, while achieving Bayesian incentive compatibility and individual rationality of the advertisers. We then undertake a detailed comparative study of the mechanisms GSP, VCG, and OPT. We compute and compare the expected revenue earned by the search engine under the three mechanisms when the advertisers are symmetric and some special conditions are satisfied. We also compare the three mechanisms in terms of incentive compatibility, individual rationality, and computational complexity. Note to Practitioners-The advertiser-supported web site is one of the successful business models in the emerging web landscape. When an Internet user enters a keyword (i.e., a search phrase) into a search engine, the user gets back a page with results, containing the links most relevant to the query and also sponsored links, (also called paid advertisement links). When a sponsored link is clicked, the user is directed to the corresponding advertiser's web page. The advertiser pays the search engine in some appropriate manner for sending the user to its web page. Against every search performed by any user on any keyword, the search engine faces the problem of matching a set of advertisers to the sponsored slots. In addition, the search engine also needs to decide on a price to be charged to each advertiser. Due to increasing demands for Internet advertising space, most search engines currently use auction mechanisms for this purpose. These are called sponsored search auctions. A significant percentage of the revenue of Internet giants such as Google, Yahoo!, MSN, etc., comes from sponsored search auctions. In this paper, we study two auction mechanisms, GSP and VCG, which are quite popular in the sponsored auction context, and pursue the objective of designing a mechanism that is superior to these two mechanisms. In particular, we propose a new mechanism which we call the OPT mechanism. This mechanism maximizes the search engine's expected revenue subject to achieving Bayesian incentive compatibility and individual rationality. Bayesian incentive compatibility guarantees that it is optimal for each advertiser to bid his/her true value provided that all other agents also bid their respective true values. Individual rationality ensures that the agents participate voluntarily in the auction since they are assured of gaining a non-negative payoff by doing so.

On trade-off solution pairs in a special type of transportation problem

Abstract is not available.

Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

Beyond fractional derivatives: local approximation of other convolution integrals

Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs O(t(2)) computations owing to the repeated evaluation of integrals over intervals that grow like t. Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled in finite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives (Singh & Chatterjee 2006 Nonlinear Dyn. 45, 183-206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with O(t) computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e. g. in stability analyses.

Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.