Abstract:
The variety of definitions of Fourier transforms can create confusion for practical applications. This paper examines the choice of formulas for Fourier transforms and determines the appropriate choices for geoscience applications. One set of Discrete Fourier Transforms can be defined that approximate Fourier integrals and provide transforms between sampled continuous functions in both domains. For applications involving transforms between a continuous function and a discrete function a second set of Discrete Fourier Transforms is needed with different scaling factors. Two classes of application are presented: those where either form of transforms can be used and those where it is necessary to use a particular transform to obtain the correct results.

Abstract:
This paper presents the unsteady
magnetohydrodynamic (MHD) flow of a generalized Burgers’ fluid between two side
walls perpendicular to a plate. The flow is generated from rest at time ？induced by
stress applied on the bottom plate. The stress is assumed to be like sawtooth
pulses with quadratic edges. The solutions obtained by means of the Laplace,
and Fourier cosine and sine transforms are presented as a sum between the
corresponding Newtonian and non-Newtonian contributions. Graphs are sketched
for various parameters of interest.

Abstract:
The purpose of the present work is to study the order of magnitude of the Fourier transforms f ( ) for large of complex-valued functions f(z) sating certain Lipschitz conditions in the non-Euclidean hyperbolic plane H2.

Abstract:
The processes of tsunami evolution during its generation in search for possible amplification mechanisms resulting from unilateral spreading of the sea floor uplift is investigated. We study the nature of the tsunami build up and propagation during and after realistic curvilinear source models represented by a slowly uplift faulting and a spreading slip-fault model. The models are used to study the tsunami amplitude amplification as a function of the spreading velocity and rise time. Tsunami waveforms within the frame of the linearized shallow water theory for constant water depth are analyzed analytically by transform methods (Laplace in time and Fourier in space) for the movable source models. We analyzed the normalized peak amplitude as a function of the propagated uplift length, width and the average depth of the ocean along the propagation path.

Abstract:
Spherical Harmonic Transforms (SHTs) which are non-commutative Fourier transforms on the sphere are critical in global geopotential and related applications. Among the best known global strategies for discrete SHTs of band-limited spherical functions are Chebychev quadratures and least squares for equiangular grids. With proper numerical preconditioning, independent of latitude, reliable analysis and synthesis results for degrees and orders over 3800 in double precision arithmetic have been achieved and explicitly demonstrated using white noise simulations. The SHT synthesis and analysis can easily be modified for the ordinary Fourier transform of the data matrix and the mathematical situation is illustrated in a new functional diagram. Numerical analysis has shown very little differences in the numerical conditioning and computational efforts required when working with the two-dimensional (2D) Fourier transform of the data matrix. This can be interpreted as the spectral form of the discrete SHT which can be useful in multiresolution and other applications. Numerical results corresponding to the latest Earth Geopotential Model EGM 2008 of maximum degree and order 2190 are included with some discussion of the implications when working with such spectral sequences of fast decreasing magnitude.

Abstract:
A study is made of the Lamb plane problem in an infinite thermo-visco-elastic micropolar medium with the effect of gravity. The visco-elasticity is characterized by the rate dependent theory of micro-visco-elasticity generalizing the classical Kelvin-Voigt theory. The action of time harmonic loading is treated in detail. The solutions for the displacement fields, couple stresses and the temperature field are obtained in general and particular cases.

Abstract:
This paper seeks to review certain salient aspects of Quantum Mechanics in the light of the Classical theories.. There is also an effort to find an alliance between Quantum Mechanics and Relativity based on the Fourier Transforms. This leads to the theoretical prediction of the gravitons and the “Otherons”. The finiteness or barrier limitations of physical quantities has been discussed with the help of the Taylor series.

Abstract:
In this paper we have proved some operation transform formulae for fractional Hartley transform in section 2. Solution of Time Independent Schr dinger Equation for the Quantum Harmonic Oscillator was found using the above operation transform formulae in section 3.

Abstract:
This work studies the canonical representations (Berezin representations) for para-Hermitian symmetric spaces of rank one. These spaces are exhausted up to the covering by spaces G/H with G = SL(n,R),H = GL(n-1,R) . For Hermitian symmetric spaces G/K, canonical representations were introduced by Berezin and Vershik-Gelfand-Graev. They are unitary with respect to some invariant non-local inner product (the Berezin form). We consider canonical representations in a wider sense: we give up the condition of unitarity and let these representations act on spaces of distributions. For our spaces G/H, the canonical representations turn out to be tensor products of representations of maximal degenerate series and contragredient representations. We decompose the canonical representations into irreducible constituents and decompose boundary representations.

Abstract:
This work presents a theoretical study of contact problem. The Fourier integral transform method based on the surface elasticity theory is adopted to derive the fundamental solution for the contact problem with surface effects, in which both the surface tension and the surface elasticity are considered. As a special case, the deformation induced by a triangle distribution force is discussed in detail. The results are compared with those of the classical contact problem. At nano-scale, the contributions of the surface tension and the surface elasticity to the stress and displacement are not equal at the contact surface. The surface tension plays a major role to the normal stress, whereas the shear stress is mainly affected by the surface elasticity. In addition, the hardness of material depends strongly on the surface effects. This study is helpful to characterize and measure the mechanical properties of soft materials through nanoindentation.