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Handbook of Mellin Transforms
The Mellin transformation is widely used in various problems of pure and applied mathematics, in particular, in the theory of differential and integral equations and the theory of Dirichlet series. It is found in extensive applications in mathematical physics, number theory, mathematical statistics, theory of asymptotic expansions, and especially, in the theory of special functions and integral transformations. It is essentially used in algorithms of integration in computer algebra systems. Since the majority of integrals encountered in applications can be reduced to the form of the corresponding Mellin transforms with specific parameters, this handbook can also be used for definite and inde...
The Mellin Transformation and Fuchsian Type Partial Differential Equations
This volume provides a systematic introduction to the theory of the multidimensional Mellin transformation in a distributional setting. In contrast to the classical texts on the Mellin and Laplace transformations, this work concentrates on the local properties of the Mellin transformations, ie on those properties of the Mellin transforms of distributions u which are preserved under multiplication of u by cut-off functions (of various types). The main part of the book is devoted to the local study of regularity of solutions to linear Fuchsian partial differential operators on a corner, which demonstrates the appearance of non-discrete asymptotic expansions (at the vertex) and of resurgence effects in the spirit of J. Ecalle.
Tables of Mellin Transforms
This book contains tables of integrals of the Mellin transform type z-l J (a) 1> (z) q,(x)x dx o t Since the substitution x = e- transforms (a) into (b) 1> (z) the Mellin transform is sometimes referred to as the two sided Laplace transform. The use of the Mellin transform in various problems in mathematical analysis is well established. Parti cularly widespread and effective is its application to problems arising in analytic number theory. This is partially due to the fact that if ¢(z) corresponding to a given q,(x) by (a) is known, then ¢(z) belonging to xaq,(x) or more general to P xaq,(x ) (p real) is likewise known. (See particularly the rules in sections 1. 1 and 2. 1 of this book. )...
Mellin-Transform Method for Integral Evaluation
This book introduces the Mellin-transform method for the exact calculation of one-dimensional definite integrals, and illustrates the application if this method to electromagnetics problems. Once the basics have been mastered, one quickly realizes that the method is extremely powerful, often yielding closed-form expressions very difficult to come up with other methods or to deduce from the usual tables of integrals. Yet, as opposed to other methods, the present method is very straightforward to apply; it usually requires laborious calculations, but little ingenuity. Two functions, the generalized hypergeometric function and the Meijer G-function, are very much related to the Mellin-transform...
Mellin-transform Method for Integral Evaluation
Introduces the Mellin-transform method for the exact calculation of one-dimensional definite integrals, and illustrates the application of this method to electromagnetics problems. The Mellin-transform method is discussed first. Then the method is applied in three examples to obtain results, which, at least in the antenna/electromagnetics literature, are believed to be new.
Newfoundland Modern
The architecture of Newfoundland typically evokes images of spare but colourful houses and outbuildings by the sea.Newfoundland Modernreveals another dimension that challenges this impression. In over 220 drawings and photographs, Robert Mellin presents the development of architecture in the decades immediately following Newfoundland's 1949 union with Canada. Newfoundland's wholehearted embrace of modern architecture in this era affected planning as well as the design of cultural facilities, commercial and public buildings, housing, recreation, educational facilities, and places of worship, and Premier Joseph Smallwood often relied on modern architecture to demonstrate the progress made by h...
Tilting
There is an almost elemental appeal in the rural fishing villages of Nova Scotia, Maine, and Newfoundland. Their intimate connection to nature, to the land, water, and (often harsh) weather; their reliance on ingenuity, on-hand materials, and craftsmanship; and their values of thrift and endurance serve as inspiration and as touchstones for those of us caught up in the hubbub of modern life. Tilting, Newfoundland is a celebration of all these virtues and an eclectic documentation of the buildings, landscape, and lifestyle of this remote community on a small island far off the Canadian coast. Through photographs, firsthand historical anecdotes, and delicate pencil drawings, author Robert Mell...
The Mellin Transformation and Fuchsian Type Partial Differential Equations
'Et moi, .. Of si j'avail su comment en revenir. je One selVice mathematics has rendered the n'y semis point alll!.' human race. It has put common sense back Jules Verne when: it belongs, on the topmon shelf next to the dusty canister labelled 'discarded nonsense'. The series is divergent; therefore we may be Eric T. Bell able to do something with iL O. Heaviside Mathematics is a tool for thought A highly necessary tool in a world where both feedback and nonlineari ties abound, Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sci ences, Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics .. , '; 'One service logic has rendered computer science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Transforms and Applications Handbook
Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properti...
South China Sea
THUNDER ON THE RIM On the South China Sea an oil rig erupts in flames—as AK-47 tracer rounds stitch the night and men die in pools of blood. The SOSUS underwater network catapults news of the attack to Washington—while ChiCom troops mass on the Vietnamese border. Ten divisions of Chinese shock troops blast their way south, overrunning the U.S.-U.N-led Emergency Response Force. But the West's best warriors fight back. U.S. Special Forces, British SAS, and the legendary Gurkhas, their Kukri knives drawn, go toe-to-toe with the invaders. Tomcats and F-18s pulverize the jungle. And the Military Sealift Command hurls Aegis cruisers and Wasp-Iwo Jima, and Spruance-class attack ships—spearheaded by Sea Wolf subs--into the South China Sea. From Japan to Malaysia, the Pacific Rim is ablaze—in a hell called . . . WORLD WAR III - SOUTH CHINA SEA "Superior to the Tom Clancy genre, with characters that came alive . . .and the military aspect far more realistic."—The Spectator
