Index transforms with Weber-type kernels

New index transforms with Weber-type kernels, consisting of products of Bessel functions of the first and second kind, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on the wedge for a fourth-order partial differential equation.     

Asymptotically Constant Solutions of Functional Difference Systems

We consider the functional difference system ( A ) j x i ( n )= f i ( n ; X ), 1 h i h k , where X =( x 1 ,…, x k ) and f 1 (·; X ),…, f k (·; X ) are real-valued functionals of X , which may depend quite arbitrarily on values of X ( l ) for multiple values of l ] Z . We give sufficient conditions for ( A ) to have solutions that approach specified constant vectors as n M X . Some of the results guarantee only that the solutions are defined for n sufficiently large, while others are global. The proof of the main theorem is based on the Schauder-Tychonoff theorem. Applications to specific quasi-linear systems are included.     

Estimating Precision in Functional Images

Abstract

Functional imaging of biologic parameters like in vivo tissue metabolism is made possible by Positron Emission Tomography (PET). Many techniques have been suggested for extracting such images from dynamic time-course sequences of reconstructed PET scans. Quantitating the precision of these estimates is important for drawing inferences on the biologic parameters. Analytic variance formulas are not immediate owing to the nonlinear methods used in extraction. The usual resampling approach is infeasible because each image reconstruction in PET is a computationally demanding solution to a high-dimensional linear inverse problem. We suggest an alternative simulation approach that approximates the distribution of reconstructed PET scans and performs a parametric bootstrap in the imaging domain. Results on a simplified model chosen to match the characteristics of PET reconstruction are very encouraging. Mixture analysis is used to estimate functional images; however, the suggested approach is general enough to extend to other techniques or imaging methods.     

Anomalous change of groundwater radon concentration monitored at Nakaizu well in 2011

An anomalous increase in radon concentration was measured at the Nakaizu observatory on the Izu Peninsula prior to the 2011 Tohoku earthquake using a custom-made radon counter. Since the increase was more than three times the standard deviation of radon concentration variations over 35 years of recorded data, it is considered likely that it is a precursor to the earthquake. Following the earthquake, the radon concentration decreased exponentially to the background level. The anomalous increase is explained using a modified volatilization model containing three important aquifer parameters: the groundwater saturation ratio, the fracture surface area per unit volume, and the porosity. The modified model can also explain the radon concentration behavior prior to the 1978 Izu-Oshima-Kinkai earthquake.     

Study of indoor radon and thoron progeny levels in surrounding areas of Nalbari, Assam, India

With the growing understanding of the role of radon and its daughter products as major sources of radiation exposure, the importance of large number of estimation of radon concentration in various parts of the country is realized. Inhalation of radon, thoron and their decay products is the major source of the total radioactive dose received by the human population from natural radiation. The indoor radon and thoron progeny levels in Nalbari area of Assam are studied by using the LR-115 (type II) Solid State Nuclear Track Detector in Plastic Twin Chamber dosimeter. Radon and thoron progeny levels in different types of dwellings for one full calendar year are presented in this paper. For Assam Type (A.T.) houses, indoor radon progeny concentrations vary from 0.17 to 0.64 mWL with an annual geometric mean of 0.27 mWL and that for Reinforced Cement Concrete (R.C.C.) houses vary from 0.22 mWL to 0.60 mWL with the annual geometric mean of 0.37 mWL. The thoron progeny levels in A.T. houses also vary from 0.01 to of 0.05 mWL with an annual geometric mean of 0.02 mWL and that for R.C.C. houses vary from 0.02 to 0.08 mWL with the annual geometric mean of 0.04 mWL.      

Infinitely many singular interactions on noncompact manifolds

We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional non-compact manifold. To facilitate the reading of the paper, we first present the arguments in the setting of Cartan–Hadamard manifolds and then subsequently discuss the general case. For this purpose, we employ the heat kernel techniques as well as some comparison theorems of Riemannian geometry, thus generalizing the arguments in the flat case following the approach presented in Albeverio et al. (2004).     

D-admissible hybrid control of a class of singular systems

This paper mainly studies the problem of designing a hybrid state feedback D-admissible controller for a class of linear and nonlinear singular systems. Based on the relationship between singular discrete systems and singular delta operator systems, several necessary and sufficient conditions for a linear singular delta operator system to be D-admissible (i.e. regular, causal and all finite poles lie in a prescribed circular region) with different representations are derived. Then, the existence conditions and explicit expressions of a desirable D-admissible controller are given by means of matrix inequalities and strict linear matrix inequalities, respectively. We further extend the obtained results to singular delta operator systems with Lipschitz nonlinear perturbations, and the design methods of hybrid controller are presented for the nonlinear case as well. Finally, numerical examples as well as simulations are provided to illustrate the effectiveness of the theoretical outcomes obtained in the paper.     

Interpolating solutions of the Poisson equation in the disk based on Radon projections

We consider an algebraic method for reconstruction of a function satisfying the Poisson equation with a polynomial right-hand side in the unit disk. The given data, besides the right-hand side, is assumed to be in the form of a finite number of values of Radon projections of the unknown function. We first homogenize the problem by finding a polynomial which satisfies the given Poisson equation. This leads to an interpolation problem for a harmonic function, which we solve in the space of harmonic polynomials using a previously established method. For the special case where the Radon projections are taken along chords that form a regular convex polygon, we extend the error estimates from the harmonic case to this Poisson problem. Finally we give some numerical examples.     

General expression of the calibration curve for the CR-39 radon track detectors

The CR-39 detectors are widely used as passive radon dosimeters, as well as in physics laboratories or for industrial applications. For what concerns radon monitoring, the calibration curve which is usually adopted corresponds to a linear relation between the actual etched track density and the track density counted by an automatic acquisition system. This linear calibration provides very accurate radon exposure assessments in a restricted range of etched track density, however it neglects the effect of the tracks overlapping that becomes as relevant as the track density increases. In the present work the mathematical expression of the area covered by a set of uniformly distributed tracks is deduced. This result allows then to infer the probability that the system acquires the right track density, providing a general calibration curve for a solid state radon track detector. The process of track production and reading routine is also simulated adopting a Monte Carlo approach, showing that the obtained results are in agreement with the function proposed as calibration curve. Moreover, a linear dependence between the track average area and the rate parameter of the calibration curve has been observed. Finally a semi-empirical correlation based on the previous results is proposed.     

Optical asymmetric watermarking using modified wavelet fusion and diffractive imaging

In most of the existing image encryption algorithms the generated keys are in the form of a noise like distribution with a uniform distributed histogram. However, the noise like distribution is an apparent sign indicating the presence of the keys. If the keys are to be transferred through some communication channels, then this may lead to a security problem. This is because; the noise like features may easily catch people׳s attention and bring more attacks. To address this problem it is required to transfer the keys to some other meaningful images to disguise the attackers. The watermarking schemes are complementary to image encryption schemes. In most of the iterative encryption schemes, support constraints play an important role of the keys in order to decrypt the meaningful data. In this article, we have transferred the support constraints which are generated by axial translation of CCD camera using amplitude-, and phase- truncation approach, into different meaningful images. This has been done by developing modified fusion technique in wavelet transform domain. The second issue is, in case, the meaningful images are caught by the attacker then how to solve the copyright protection. To resolve this issue, watermark detection plays a crucial role. For this purpose, it is necessary to recover the original image using the retrieved watermarks/support constraints. To address this issue, four asymmetric keys have been generated corresponding to each watermarked image to retrieve the watermarks. For decryption, an iterative phase retrieval algorithm is applied to extract the plain-texts from corresponding retrieved watermarks.