Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -     

Applications of electronic speckle interferometry (ESI) techniques for spacecraft structural components

Laser-based electronic speckle interferometry (ESI) techniques, viz., electronic speckle pattern interferometry (ESPI) and electronic speckle shearographic interferometry (ESSI) are used for testing of spacecraft structural components. The combined ESPI and ESSI system developed in house was successfully used for the non-destructive evaluation (NDE) of honeycomb sandwich panels and propellant tanks of Indian Space Research Organization (ISRO). Debonds between face sheet and the honeycomb core were identified using (i) thermal and (ii) dual vacuum stressing methods. On-line NDE of the propellant tanks under internal pressure loading for identification of the minute cracks and thickness reduction areas were successfully implemented by ESI.     

Development of measuring magnetic Compton profiles by grazing incidence geometry

A novel technique of measuring a magnetic Compton profile using the grazing angle geometry against a sample surface (Grazing Incidence Magnetic Compton Profile) has been successively developed. Measurements of a magnetic moment and a magnetic Compton profile are possible for a Fe 200 nm film on a thick glass substrate. The estimated thinnest limit for measurements is 100 nm for a Fe film.     

Polarization Sensitive Spectral Interferometric Optical Coherence Tomography for Biological Samples

A spectral interferometric optical coherence tomography (OCT) system which has polarization sensitivity is developed. This system reduces the mechanical scanning dimension by employing the principle of spectral interferometry, and measures a two dimensional cross-sectional image of biological tissue with one dimensional mechanical scanning. Sixteen OCT images with different polarization conditions are measured, and two dimensional distributions of each element of the Müller matrix of a sample to be measured are calculated.     

图的度序列不等式

用代数的方法证明了有关图度序列的几个不等式，并且得到了其相应的极图。     

The Convergence of (r|~)_s(b_0h_n-h_1b_(n-1))

This paper computes the Thorn map onγ2 and proves that it is represented by 2b2,0h1,2 in the ASS. The authors also compute the higher May differential of 62,0, from which it is proved thatγs(b0hn-h1bn-1) for 2≤s < p - 1 are permanent cycles in the ASS.     

THE LARGE TIME BEHAVIOR OF SPECTRAL APPROXIMATION FOR A CLASS OF PSEUDOPARABOLIC VISCOUS DIFFUSION EQUATION

The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estiation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d(AN,A)→0 are proved.     

Spectral distributions in nuclei: General principles and applications

The subject of spectral distribution methods where one derives and applies the locally smoothed forms of observables in nuclei is briefly reviewed. It is well understood that the local forms (with respect to energy) of the level density function, expectation values and strength densities are Gaussian, linear (or ratio of Gaussians) and a bivariate Gaussian respectively. To accomodate symmetries in the above forms, one has to deal with multivariate distributions in general; for example the angular-momentum (J) decomposition leads to a bivariate Gaussian form for the level density. These results extend to indefinitely large spaces by method of partitioning and they generate convolution forms. The origin of these remarkable spectral properties is discussed and shell model examples are given to substantiate their applicability to nuclear systems. Spectral distribution theory is a practical, usable theory because the smoothed forms are defined in terms of traces of low particle-rank operators, and the trace information propagates. Finally we discuss the application of the spectral methods for a wide range of nuclear problems; these include binding energies, orbit occupancies, electromagnetic andβ-decay sum rule quantities, analysis of operators, symmetry breaking, numerical level densities, and determination of bounds on time-reversal non-invariant part of nucleon-nucleon interaction.