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Full-Text Articles in Physical Sciences and Mathematics
Characterization Of Eigenfunctions Of The Laplace-Beltrami Operator Through Radial Averages On Rank One Symmetric Spaces., Muna Naik Dr.
Characterization Of Eigenfunctions Of The Laplace-Beltrami Operator Through Radial Averages On Rank One Symmetric Spaces., Muna Naik Dr.
Doctoral Theses
Let X be a rank one Riemannian symmetric space of noncompact type and ∆ be the Laplace–Beltrami operator of X. The space X can be identified with the quotient space G/K where G is a connected noncompact semisimple Lie group of real rank one with finite centre and K is a maximal compact subgroup of G. Thus G acts naturally on X by left translations. Through this identification, a function or measure on X is radial (i.e. depends only on the distance from eK), when it is invariant under the left-action of K. We consider right-convolution operators Θ on functions …
Wavelet Analysis On Local Fields Of Positive Characteristic., Quiser Jahan Dr.
Wavelet Analysis On Local Fields Of Positive Characteristic., Quiser Jahan Dr.
Doctoral Theses
In this chapter, we will give a brief history of wavelet analysis on R. We will also list some bask results on local felds which will be used in subvequent chapters.1.1 Wavelets on RWe fiest start with a brief history of wavelets und some basic defnitions and results conceming the orthonormal wavekts on R.1.1.1 A brief historyIn the last few decades vaveler theory has growa extensively and has drawn great atlention sot only in mathematies bu also in engineering, pitysics, computer science and many other fields. In signal and image processing, wavelets play a very important role.In 1910, A. Haar …
Isomorphism Of Schwartz Spaces Under Fourier Transform., Joydip Jana Dr.
Isomorphism Of Schwartz Spaces Under Fourier Transform., Joydip Jana Dr.
Doctoral Theses
Classical Fourier analysis derives much of its power from the fact that there are three function spaces whose images under the Fourier transform can be exactly determined. They are the Schwartz space, the L2 space and the space of all C ∞ functions of compact support. The determination of the image is obtained from the definition in the case of Schwartz space, through the Plancherel theorem for the L 2space and through the Paley-Wiener theorem for the other space.In harmonic analysis of semisimple Lie groups, function spaces on various restricted set-ups are of interest. Among the multitude of these spaces …
Uncertainty Principles On Nilpotent Lie Groups., Sanjay Parui Dr.
Uncertainty Principles On Nilpotent Lie Groups., Sanjay Parui Dr.
Doctoral Theses
No abstract provided.
Cryptographic And Combinatorial Properties Of Boolean Functions And S-Boxes., Kishan Chand Gupta Dr.
Cryptographic And Combinatorial Properties Of Boolean Functions And S-Boxes., Kishan Chand Gupta Dr.
Doctoral Theses
In this thesis we study combinatorial aspects of Boolean functions and S-boxes with impor- tant cryptographic properties and construct new functions possesing such properties. These have possible applications in the design of private key (symmetric key) cryptosystems.Symmetric key cryptosystems are broadly divided into two classes.1. Stream Ciphers,2. Block Ciphers.Some recent proposals of stream ciphers are SNOW [37], SCREAM [52], TURING (98], MUGI (117), HBB (102], RABBIT (9), HELIX (38] and some proposals of block ciphers are DES, AES, RC6 [97), MARS (12], SERPENT (6], TWOFISH (104].In stream cipher cryptography a pseudorandom sequence of bits of length cqual to the message …
On Logistic And Some New Discrimination Rules:Charecterizations,Inference And Application., Supratik Roy Dr.
On Logistic And Some New Discrimination Rules:Charecterizations,Inference And Application., Supratik Roy Dr.
Doctoral Theses
Introduction and Summary Consider the problem of classification of an observation into one of two specified populations. Fisher's classification rale, just as several other rules commonly used in practice, depends only on the ratio of the individual densities fi(x), i = 1,2. This led Cox (1966),/27) to model the "posterior odds" by a simple function. Specifically,Cox's logistic discrimination (LGD) rule is then based on the statistic a + 'ßx. This has the advantage that individual densities f.(x) need not be known and we only need to estimate the parameters a and B.Another advantage, which is claimed , is that the …
Wiener Tauberian Theorems On Semisimple Lie Group., Rudra Pada Sarkar Dr.
Wiener Tauberian Theorems On Semisimple Lie Group., Rudra Pada Sarkar Dr.
Doctoral Theses
In their celebrated study of Harmonic analysis on semi-simple Lie groups Ehrenpreis and Mautner [E-M] noticed that the analogue of the claasical Wiener Tauberian theorem resting on the unitary dual does not hold for semisimple Lle groups. A simple proof of this fact due to M. Duflo appears in (H). Ehrenpreis and Mautner went on in (E-M] to formulate the problem on the commutative Banach algebra of the SO2(R)-biinvariant functions in L1(SL2(R))1, and obtained two different versions of the theorem involving, this time, the dual of the Banach algebra which includes, beside the unitary dual of G, a part of …
Pompeiu Problem And Analogues Of The Weiner-Tauberian Theorem For Certain Homogeneous Spaces., Rama Rawat Dr.
Pompeiu Problem And Analogues Of The Weiner-Tauberian Theorem For Certain Homogeneous Spaces., Rama Rawat Dr.
Doctoral Theses
Let G be a connected locally compact unimodular group acting transitively on a locally compact space X. For a function f on X and g € G, define of by 9f(x) = fA 9.a), a € X. One of the recurring themes in analysis is the question of when a function f in a given function space F(X) will have property that Span{gf : g € G} is dense in F(X). If X = R and G = R, the celebrated Wiener-Tauberian theorem answers this question completely for the space L1(R): The span of the translates of fE L1(R) is …
Fourier Transforms Of Very Rapidly Decreasing Functions On Certain Lie Groups., M. Sundari Dr.
Fourier Transforms Of Very Rapidly Decreasing Functions On Certain Lie Groups., M. Sundari Dr.
Doctoral Theses
Recall that for a function f ϵ L1(Rn ), its Fourier transform fÌ‚ is definedby: fÌ‚ (ƹ) = ʃ Rnf(x)ei(ƹ,x)dx ( 0.1.1)where (.,.) denotes the standard inner product on Rn and dr the Lebesgue measure on Rn. A celebrated theorem of L. Schwartz asserts that a function f on Rn is rapidly decreasing (or in the Schwartz class ) if and only if its Fourier transform is rapidly decreasing . In sharp contrast to Schwartz s theorem, is a result due to Hardy ([18) which says that ʃ and fÌ‚ cannot both be very rapidly decreasing . More precisely, if …
Studies On Design, Routing And Fault Tolerance Of Interconnection Network., Krishnendu Mukhopadhyay Dr.
Studies On Design, Routing And Fault Tolerance Of Interconnection Network., Krishnendu Mukhopadhyay Dr.
Doctoral Theses
A recent trend in computing is to distribute the computations among a set of processing elements. There are two basic appronches to this - one is to build a loosely-coupled system and the other is to form a tightly-coupled system [PS85].In a loosely-coupled system, the processors do not share common memory or a common clock; but sharing of important resources like data files, softwares, special hardware components etc., is possible without duplicating the resources themselves. The processing nodes may even be geographicully separated from each other and are connected through databuses, telephone/radio links, satellite, etc. Such loosely- coupled systems are …