Function with its Fourier transform supported on annulus and eigenfunction of Laplacian

We explore the possibilities of reaching the characterization of eigenfunction of Laplacian as a degenerate case of the inverse Paley-Wiener theorem (characterizing functions whose Fourier transform is supported on a compact annulus) for the Riemannian symmetric spaces of noncompact type. Most distinguished prototypes of these spaces are the hyperbolic spaces. The statement and the proof of the main result work mutatis-mutandis for a number of spaces including Euclidean spaces and Damek-Ricci spaces.Comment: 24 page

Effect of meditation on scaling behavior and complexity of human heart rate variability

The heart beat data recorded from samples before and during meditation are analyzed using two different scaling analysis methods. These analyses revealed that mediation severely affects the long range correlation of heart beat of a normal heart. Moreover, it is found that meditation induces periodic behavior in the heart beat. The complexity of the heart rate variability is quantified using multiscale entropy analysis and recurrence analysis. The complexity of the heart beat during mediation is found to be more.Comment: 7 Figure

Neutrino Radar

We point out that with improving our present knowledge of experimental neutrino physics it will be possible to locate nuclear powered vehicles like submarines, aircraft carriers and UFOs and detect nuclear testing. Since neutrinos cannot be shielded, it will not be possible to escape these detection. In these detectors it will also be possible to perform neutrino oscillation experiments during any nuclear testing.Comment: 8 pages late

Effect of heavy ion irradiation on microstructure and electron density distribution of zirconium alloy characterised by X-ray diffraction technique

Different techniques of the X-ray Diffraction Line Profile Analysis (XRDLPA) have been used to assess the microstructure of the irradiated Zr-1.0%Nb-1.0%Sn-0.1%Fe alloy. The domain size, microstrain, density of dislocation and the stacking fault probabilities of the irradiated alloy have been estimated as a function of dose by the Williamson-Hall Technique, Modified Rietveld Analysis and the Double Voigt Method. A clear signature in the increase in the density of dislocation with the dose of irradiated was revealed. The analysis also estimated the average density of dislocation in the major slip planes after irradiation. For the first time, we have established the changes in the electron density distribution due to irradiation by X-ray diffraction technique. We could estimate the average displacement of the atoms and the lattice strain caused due to irradiation from the changes in the electron density distribution as observed in the contour plots

Pure and Hybrid Evolutionary Computing in Global Optimization of Chemical Structures: from Atoms and Molecules to Clusters and Crystals

The growth of evolutionary computing (EC) methods in the exploration of complex potential energy landscapes of atomic and molecular clusters, as well as crystals over the last decade or so is reviewed. The trend of growth indicates that pure as well as hybrid evolutionary computing techniques in conjunction of DFT has been emerging as a powerful tool, although work on molecular clusters has been rather limited so far. Some attempts to solve the atomic/molecular Schrodinger Equation (SE) directly by genetic algorithms (GA) are available in literature. At the Born-Oppenheimer level of approximation GA-density methods appear to be a viable tool which could be more extensively explored in the coming years, specially in the context of designing molecules and materials with targeted properties

On the Schwartz space isomorphism theorem for rank one symmetric space

In this paper we give a simpler proof of the $L^p$-Schwartz space isomorphism $(0< p\leq 2)$ under the Fourier transform for the class of functions of left $\delta$-type on a Riemannian symmetric space of rank one. Our treatment rests on Anker's \cite{A} proof of the corresponding result in the case of left $K$-invariant functions on $X$. Thus we give a proof which relies only on the Paley--Wiener theorem.Comment: 16 page

Beurling's Theorem and characterization of heat kernel for Riemannian Symmetric spaces of noncompact type

We prove Beurling's theorem for rank 1 Riemmanian symmetric spaces and relate it to the characterization of the heat kernel of the symmetric space

Asymptotic mean value property for eigenfunctions of the Laplace-Beltrami operator on Damek-Ricci spaces

Let $S$ be a Damek-Ricci space equipped with the Laplace-Beltrami operator $\Delta$. In this paper we characterize all eigenfunctions of $\Delta$ through sphere, ball and shell averages as the radius (of sphere, ball or shell) tends to infinity

Beurling's Theorem and Lp−LqL^p-L^q Morgan's Theorem for Step Two Nilpotent Lie Groups

We prove Beurling's theorem and $L^p-L^q$ Morgan's theorem for step two nilpotent Lie groupsComment: 20 page

Beurling's Theorem for SL(2,R)SL(2,\R)

We prove Beurling's theorem for the full group $SL(2,\R)$. This is the {\em master theorem} in the quantitative uncertainty principle as all the other theorems of this genre follow from it