A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.

Analysis of grid connected induction generators driven by hydro/wind turbines under realistic system constraints

Results of an investigation dealing with the behaviour of grid-connected induction generators (GCIGs) driven by typical prime movers such as mini-hydro/wind turbines are presented. Certain practical operational problems of such systems are identified. Analytical techniques are developed to study the behavior of such systems. The system consists of the induction generator (IG) feeding a 11 kV grid through a step-up transformer and a transmission line. Terminal capacitors to compensate for the lagging VAr are included in the study. Computer simulation was carried out to predict the system performance at the given input power from the turbine. Effects of variations in grid voltage, frequency, input power, and terminal capacitance on the machine and system performance are studied. An analysis of self-excitation conditions on disconnection of supply was carried out. The behavior of a 220 kW hydel system and 55/11 kW and 22 kW wind driven system corresponding to actual field conditions is discussed

Analogues of the Wiener-Tauberian and Schwartz theorems for radial functions on symmetric spaces

We prove a Wiener Tauberian theorem for the L-1 spherical functions on a semisimple Lie group of arbitrary real rank. We also establish a Schwartz-type theorem for complex groups. As a corollary we obtain a Wiener Tauberian type result for compactly supported distributions.

Toeplitz Operators with Special Symbols on Segal-Bargmann Spaces

We study the boundedness of Toeplitz operators on Segal-Bargmann spaces in various contexts. Using Gutzmer's formula as the main tool we identify symbols for which the Toeplitz operators correspond to Fourier multipliers on the underlying groups. The spaces considered include Fock spaces, Hermite and twisted Bergman spaces and Segal-Bargmann spaces associated to Riemannian symmetric spaces of compact type.

Cascades of Selective Pulses on Connected Single-Quantum Transitions Leading to the Selective Excitation of Multiple-Quantum Coherences

A symmetric cascade of selective pulses applied on connected transitions leads to the excitation of a selected multiple-quantum coherence by a well-defined angle. This cascade selectively operates on the subspace of the multiple-quantum coherence and acts as a generator of rotation selectively on the multiple-quantum subspace. Single-transition operator algebra has been used to explain these experiments. Experiments have been performed on two- and three-spin systems. It is shown that such experiments can be utilized to measure the relaxation times of selected multiple-quantum coherences or of a specifically prepared initial longitudinal state of the spin system.

On the explicit determination of the polar decomposition in n-dimensional vector spaces

A method for the explicit determination of the polar decomposition (and the related problem of finding tensor square roots) when the underlying vector space dimension n is arbitrary (but finite), is proposed. The method uses the spectral resolution, and avoids the determination of eigenvectors when the tensor is invertible. For any given dimension n, an appropriately constructed van der Monde matrix is shown to play a key role in the construction of each of the component matrices (and their inverses) in the polar decomposition.

Present status of Gottigere Tank : Indicator of Decision maker’s apathy

Gottigere lake with a water spread area of about 14.98 ha is located in the Bellandur Lake catchment of the South Pennar River basin. In recent years, this lake catchment has been subjected to environmental stress mainly due to the rampant unplanned developmental activities in the catchment. The functional ability of the ecosystem is impaired due to structural changes in the ecosystem. This is evident from poor water quality, breeding of disease vectors, contamination of groundwater in the catchment, frequent flooding in the catchment due to topography alteration, decline in groundwater table, erosion in lake bed, etc. The development plans of the region (current as well as the proposed) ignore the integrated planning approaches considering all components of the ecosystem. Serious threats to the sustainability of the region due to lack of holistic approaches in aquatic resources management are land use changes (removal of vegetation cover, etc.), point and non-point sources of pollution impairing water quality, dumping of solid waste (building waste, etc.). Conservation of lake ecosystem is possible only when the physical and chemical integrity of its catchment is maintained. Alteration in the catchment either due to land use changes (leading to paved surface area from vegetation cover), alteration in topography, construction of roads in the immediate vicinity are detrimental to water yield in the catchment and hence, the sustenance of the lake. Open spaces in the form of lakes and parks aid as kidney and lung in an urban ecosystem, which maintain the health of the people residing in the locality. Identification of core buffer zones and conservation of buffer zones (500 to 1000 m from shore) is to be taken up on priority for conservation and sustainable management of Bangalore lakes. Bangalore is located over a ridge delineating four watersheds, viz. Hebbal, Koramangala, Challaghatta and Vrishabhavathi. Lakes and tanks are an integral part of natural drainage and help in retaining water during rainfall, which otherwise get drained off as flash floods. Each lake harvests rainwater from its catchment and surplus flows downstream spilling into the next lake in the chain. The topography of Bangalore has uniquely supported the creation of a large number of lakes. These lakes form chains, being a series of impoundments across streams. This emphasises the interconnectivity among Bangalore lakes, which has to be retained to prevent Bangalore from flooding or from water scarcity. The main source of replenishment of groundwater is the rainfall. The slope of the terrain allows most of the rainwater to flow as run-off. With the steep gradients available in the major valleys of Bangalore, the rainwater will flow out of the city within four to five hours. Only a small fraction of the rainwater infiltrates into the soil. The infiltration of water into the subsoil has declined with more and more buildings and paved road being constructed in the city. Thus the natural drainage of Bangalore is governed by flows from the central ridge to all lower contours and is connected with various tanks and ponds. There are no major rivers flowing in Bangalore and there is an urgent need to sustain these vital ecosystems through proper conservation and management measures. The proposed peripheral ring road connecting Hosur Road (NH 7) and Mysore Road (SH 17) at Gottigere lake falls within the buffer zone of the lake. This would alter the catchment integrity and hence water yield affecting flora, fauna and local people, and ultimately lead to the disappearance of Gottigere lake. Developmental activities in lake catchments, which has altered lake’s ecological integrity is in violation of the Indian Fisheries Act – 1857, the Indian Forest Act – 1927, Wildlife (Protection) Act – 1972, Water (Prevention and Control of Pollution) Act – 1974, Water (Prevention and Control of Pollution) Act – 1977, Forest (Conservation Act) – 1980, Environmental (Protection) Act – 1986, Wildlife (Protection) Amendment Act – 1991 and National Conservation Strategy and Policy Statement on Environment and Development – 1992. Considering 65% decline of waterbodies in Bangalore (during last three decades), decision makers should immediately take preventive measures to ensure that lake ecosystems are not affected. This report discusses the impacts due to the proposed infrastructure developmental activities in the vicinity of Gottigere tank.

Sliding mode control-based algorithms for consensus in connected swarms

In this article, finite-time consensus algorithms for a swarm of self-propelling agents based on sliding mode control and graph algebraic theories are presented. Algorithms are developed for swarms that can be described by balanced graphs and that are comprised of agents with dynamics of the same order. Agents with first and higher order dynamics are considered. For consensus, the agents' inputs are chosen to enforce sliding mode on surfaces dependent on the graph Laplacian matrix. The algorithms allow for the tuning of the time taken by the swarm to reach a consensus as well as the consensus value. As an example, the case when a swarm of first-order agents is in cyclic pursuit is considered.

Operational experience on a grid connected 100 kWe biomass gasification power plant in Karnataka, India

The paper reports the operational experience from a 100 kWe gasification power plant connected to the grid in Karnataka. Biomass Energy for Rural India (BERI) is a program that implemented gasification based power generation with an installed capacity of 0.88 MWe distributed over three locations to meet the electrical energy needs in the district of Tumkur. The operation of one 100 kWe power plant was found unsatisfactory and not meeting the designed performance. The Indian Institute of Science, Bangalore, the technology developer, took the initiative to ensure the system operation, capacity building and prove the designed performance. The power plant connected to the grid consists of the IISc gasification system which includes reactor, cooling, cleaning system, fuel drier and water treatment system to meet the producer gas quality for an engine. The producer gas is used as a fuel in Cummins India Limited, GTA 855 G model, turbo charged engine and the power output is connected to the grid. The system has operated for over 1000 continuous hours, with only about 70 h of grid outages. The total biomass consumption for 1035 h of operation was 111 t at an average of 107 kg/h. Total energy generated was 80.6 MWh reducing over loot of CO(2) emissions. The overall specific fuel consumption was about 1.36 kg/kWh, amounting to an overall efficiency from biomass to electricity of about 18%. The present operations indicate that a maintenance schedule for the plant can be at the end of 1000 h. The results for another 1000 h of operation by the local team are also presented. (C) 2011 International Energy Initiative. Published by Elsevier Inc. All rights reserved.

An eight-connected metal organic framework based on Cu(5) clusters: Synthesis, structure, magnetic and catalytic properties

A reaction of copper acetate, 5-nitroisophthalic acid in a water-methanol mixture under solvothermal condition results in a new metal-organic framework compound, [Cu(5)(mu(3)-OH)(2)(H(2)O)(6){(NO(2))-C(6)H(3)-(COO)(2)}(4)]center dot 5H(2)O, (1). The compound contains Cu5 pentameric cluster units connected by 5-nitro isophthalate (NIPA) moieties forming a CdCl(2)-like layer, which are further connected by another NIPA moiety forming the three-dimensional structure. The water molecules in (1) can be reversibly adsorbed. The removal of water accompanies a change in the colour as well as a structural re-organization. Magnetic studies suggest strong antiferromagnetie correlations between the Cu5 cluster units. The compound (1) exhibits heterogeneous Lewis acid catalysis for the cyanosilylation of imines with more than 95 % selectivity. Compound (1) has been characterized by IR, UV-vis, TGA, powder XRD studies.

Study of symmetrical and related components through the theory of linear vector spaces

The paper proposes a study of symmetrical and related components, based on the theory of linear vector spaces. Using the concept of equivalence, the transformation matrixes of Clarke, Kimbark, Concordia, Boyajian and Koga are shown to be column equivalent to Fortescue's symmetrical-component transformation matrix. With a constraint on power, criteria are presented for the choice of bases for voltage and current vector spaces. In particular, it is shown that, for power invariance, either the same orthonormal (self-reciprocal) basis must be chosen for both voltage and current vector spaces, or the basis of one must be chosen to be reciprocal to that of the other. The original �¿, ��, 0 components of Clarke are modified to achieve power invariance. For machine analysis, it is shown that invariant transformations lead to reciprocal mutual inductances between the equivalent circuits. The relative merits of the various components are discussed.

On an Integrated Transfer Matrix method for multiply connected mufflers

The commercial automotive mufflers are generally of a complicated shape with multiply connected parts and complex acoustic elements. The analysis of such complex mufflers has always been a great challenge. In this paper, an Integrated Transfer Matrix method has been developed to analyze complex mufflers. Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The paper presents a generalized one-dimensional (1-D) approach, using the transfer matrices of simple acoustic elements, which are available from the literature. The present approach is robust and flexible owing to its capability to construct an overall matrix of the muffler with the transfer matrices of individual acoustic elements and boundary conditions, which can then be used to evaluate the transmission loss, insertion loss, etc. Results from the present approach have been validated through comparisons with the available experimental and three-dimensional finite element method (FEM) based results. The results show good agreement with both measurements and FEM analysis up to the cut-off frequency. (C) 2011 Elsevier Ltd. All rights reserved.