Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

Use of Abel integral equations in water wave scattering by two surface-piercing barriers

In this paper the classical problem of water wave scattering by two partially immersed plane vertical barriers submerged in deep water up to the same depth is investigated. This problem has an exact but complicated solution and an approximate solution in the literature of linearised theory of water waves. Using the Havelock expansion for the water wave potential, the problem is reduced here to solving Abel integral equations having exact solutions. Utilising these solutions,two sets of expressions for the reflection and transmission coefficients are obtained in closed forms in terms of computable integrals in contrast to the results given in the literature which,involved six complicated integrals in terms of elliptic functions. The two different expressions for each coefficient produce almost the same numerical results although it has not been possible to prove their equivalence analytically. The reflection coefficient is depicted against the wave number in a number of figures which almost coincide with the figures available in the literature wherein the problem was solved approximately by employing complementary approximations. (C) 2009 Elsevier B.V. All rights reserved.

On some integral properties of hypergeometric functions

In this note certain integrals involving hypergeometric functions have been evaluated in convenient and elegant forms. © 1971 Indian Academy of Sciences.

A fourier-integral solution for the elastic quarter-plane

The problem of an elastic quarter-plane with arbitrary loadings on the boundaries has been solved using a Fourier-integral approach.

Approximation of solutions to fractional integral equation

In this paper we shall study a fractional integral equation in an arbitrary Banach space X. We used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem. We also prove the existence of global solution. The existence and convergence of the Faedo–Galerkin solution to the given problem is also proved in a separable Hilbert space with some additional assumptions on the operator A. Finally we give an example to illustrate the applications of the abstract results.

Sustainability and Mission Drift in Microfinance

Microfinance institutions (MFIs) are constrained by double bottom-lines: meeting social obligations (the first bottom-line) and obtaining financial self-sufficiency (the second bottom-line). The proponents of the first bottom-line, however, are increasingly concerned that there is a trade-off between these two bottom-lines—i.e., getting hold of financial self-sufficiency may lead MFIs to drift away from their original social mission of serving the very poor, commonly known as mission drift in microfinance which is still a controversial issue. This study aims at addressing the concerns for mission drift in microfinance in a performance analysis framework. Chapter 1 deals with theoretical background, motivation and objectives of the topic. Then the study explores the validity of three major and related present-day concerns. Chapter 2 explores the impact of profitability on outreach-quality in MFIs, commonly known as mission drift, using a unique panel database that contains 4-9 years’ observations from 253 MFIs in 69 countries. Chapter 3 introduces factor analysis, a multivariate tool, in the process of analysing mission drift in microfinance and the exercise in this chapter demonstrates how the statistical tool of factor analysis can be utilised to examine this conjecture. In order to explore why some microfinance institutions (MFIs) perform better than others, Chapter 4 looks at factors which have an impact on several performance indicators of MFIs—profitability or sustainability, repayment status and cost indicators—based on quality-data on 353 institutions in 77 countries. The study also demonstrates whether such mission drift can be avoided while having self-sustainability. In Chapter 5 we examine the impact of capital and financing structure on the performance of microfinance institutions where estimations with instruments have been performed using a panel dataset of 782 MFIs in 92 countries for the period 2000-2007. Finally, Chapter 6 concludes the study by summarising the results from the previous chapters and suggesting some directions for future studies.

Anti-windup Schemes for Proportional Integral and Proportional Resonant Controller

Problems like windup or rollover arise in a PI controller working under saturation. Hence anti-windup schemes are necessary to minimize performance degradation.Similar situation may occur in a Proportional Resonant(PR)controller in the presence of a sustained error input.Several methods can be employed based on existing knowledge on PI controller to counter this problem.In this paper few such schemes are proposed and implemented in FPGA and MATLAB and from the obtained results their possible use and limitations have been studied.

Greening India Mission

The Government of India has announced the Greening India Mission (GIM) under the National Climate Change Action Plan. The Mission aims to restore and afforest about 10 mha over the period 2010-2020 under different sub-missions covering moderately dense and open forests, scrub/grasslands, mangroves, wetlands, croplands and urban areas. Even though the main focus of the Mission is to address mitigation and adaptation aspects in the context of climate change, the adaptation component is inadequately addressed. There is a need for increased scientific input in the preparation of the Mission. The mitigation potential is estimated by simply multiplying global default biomass growth rate values and area. It is incomplete as it does not include all the carbon pools, phasing, differing growth rates, etc. The mitigation potential estimated using the Comprehensive Mitigation Analysis Process model for the GIM for the year 2020 has the potential to offset 6.4% of the projected national greenhouse gas emissions, compared to the GIM estimate of only 1.5%, excluding any emissions due to harvesting or disturbances. The selection of potential locations for different interventions and species choice under the GIM must be based on the use of modelling, remote sensing and field studies. The forest sector provides an opportunity to promote mitigation and adaptation synergy, which is not adequately addressed in the GIM. Since many of the interventions proposed are innovative and limited scientific knowledge exists, there is need for an unprecedented level of collaboration between the research institutions and the implementing agencies such as the Forest Departments, which is currently non-existent. The GIM could propel systematic research into forestry and climate change issues and thereby provide global leadership in this new and emerging science.

Studies of cryotreatment on the performance of integral diaphragm pressure transducers for space application

The integral diaphragm pressure transducers machined out of precipitation hardened martensite stainless steel (APX4) are widely used for propellant pressure measurements in space applications. These transducers are expected to exhibit dimensional stability and linearity for their entire useful life. These vital factors are very critical for the reliable performance and dependability of the pressure transducers. However, these transducers invariably develop internal stresses during various stages of machining. These stresses have an adverse effect on the performance of the transducers causing deviation from linearity. In order to eliminate these possibilities, it was planned to cryotreat the machined transducers to improve both the long-term linearity and dimensional stability. To study these effects, an experimental cryotreatment unit was designed and developed based on the concept of indirect cooling using the concept of cold nitrogen gas forced closed loop convection currents. The system has the capability of cryotreating large number of samples for varied rates of cooling, soaking and warm-up. After obtaining the initial levels of residual stress and retained austenite using X-ray diffraction techniques, the pressure transducers were cryotreated at 98 K for 36 h. Immediately after cryotreatment, the transducers were tempered at 510 degrees C for 3 h in vacuum furnace. Results after cryo treatment clearly indicated significant reduction in residual stress levels and conversion of retained austenite to martensite. These changes have brought in improvements in long term zero drift and dimensional stability. The cryotreated pressure transducers have been incorporated for actual space applications. (c) 2010 Published by Elsevier Ltd.

Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Path-integral derivation of the superconformal anomaly for the N=1 supersymmetric Yang-Mills theory

Fujikawa's method of evaluating the supercurrent and the superconformal current anomalies, using the heat-kernel regularization scheme, is extended to theories with gauge invariance, in particular, to the off-shell N=1 supersymmetric Yang-Mills (SSYM) theory. The Jacobians of supersymmetry and superconformal transformations are finite. Although the gauge-fixing term is not supersymmetric and the regularization scheme is not manifestly supersymmetric, we find that the regularized Jacobians are gauge invariant and finite and they can be expressed in such a way that there is no one-loop supercurrent anomaly for the N=1 SSYM theory. The superconformal anomaly is nonzero and the anomaly agrees with a similar result obtained using other methods.

Path-integral derivation of the superconformal anomaly for the Wess-Zumino model

Fujikawa's method of evaluating the anomalies is extended to the on-shell supersymmetric (SUSY) theories. The supercurrent and the superconformal current anomalies are evaluated for the Wess-Zumino model using the background-field formulation and heat-kernel regularization. We find that the regularized Jacobians for SUSY and superconformal transformations are finite. The results can be expressed in a form such that there is no supercurrent anomaly but a finite nonzero superconformal anomaly, in agreement with similar results obtained using other methods.

Nonnegative integral solution of linear equations

A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.