Schrödinger Operator Perturbed by Operators Related to Null Sets

We discuss the Schrödinger operator with positive singular perturbations given by operators which act in the space constructed by a positive measure supported by a null set. We construct examples when perturbations are given by the one-dimensional Laplacian on a segment.     

A comparative study of indoor radon level measurements in the dwellings of Punjab and Himachal Pradesh, India

The LR-115 type-II plastic track detector has been used for measuring the indoor radon levels in the dwellings of some villages of Punjab and Himachal Pradesh. In Punjab, the villages surveyed are Rampura Phul, Lehra Mahabat and Pitho (villages in Bathinda district), and Amritsar city. The average indoor radon levels in these areas are found to vary from 64 to 152 Bq/m³, which are quite within the safe limits recommended by International Commission on Radiological Protection (Ann. ICRP 23(2)). The indoor radon levels have also been measured in the dwellings of Hamirpur district of Himachal Pradesh. The villages surveyed in this area are Nukhel, Badarn, Galore-Khas, Har-Upper, Tikker Brahamana and Awah-Lower where radon concentration has been found to vary from 261 to 724 Bq/m³. These values are higher than the recommended limit.     

Stable Determination of Convex Bo dies from Intersection Bo dies

In this paper, by means of the dual Brunn-Minkowski theories and methods as well as the integral transform, we have established a stability version of nonsymmetric convex bodies from intersection bodies. In addition, a stability results of symmetric convex bodies from Lp-counterparts is established.     

Time-harmonic BEM for 2-D piezoelectricity applied to eigenvalue problems

We will derive the fundamental generalized displacement solution, using the Radon transform, and present the direct formulation of the time-harmonic boundary element method (BEM) for the two-dimensional general piezoelectric solids. The fundamental solution consists of the static singular and the dynamics regular parts; the former, evaluated analytically, is the fundamental solution for the static problem and the latter is given by a line integral along the unit circle. The static BEM is a component of the time-harmonic BEM, which is formulated following the physical interpretation of Somigliana’s identity in terms of the fundamental generalized line force and dislocation solutions obtained through the Stroh–Lekhnitskii (SL) formalism. The time-harmonic BEM is obtained by adding the boundary integrals for the dynamic regular part which, from the original double integral representation over the boundary element and the unit circle, are reduced to simple line integrals along the unit circle.The BEM will be applied to the determination of the eigen frequencies of piezoelectric resonators. The eigenvalue problem deals with full non-symmetric complex-valued matrices whose components depend non-linearly on the frequency. A comparative study will be made of non-linear eigenvalue solvers: QZ algorithm and the implicitly restarted Arnoldi method (IRAM). The FEM results whose accuracy is well established serve as the basis of the comparison. It is found that the IRAM is faster and has more control over the solution procedure than the QZ algorithm. The use of the time-harmonic fundamental solution provides a clean boundary only formulation of the BEM and, when applied to the eigenvalue problems with IRAM, provides eigen frequencies accurate enough to be used for industrial applications. It supersedes the dual reciprocity BEM and challenges to replace the FEM designed for the eigenvalue problems for piezoelectricity.     

用于光声层析成像的虚拟阵列探测及逆拉东变换

提出用固定孔径的换能器虚拟阵列探测器进行数据采集,该换能器只需对样品进行180扫描。实验中,使用调Q Nd: YAG激光器作为光源,激光器输出激光波长为532 nm,重复频率为10 Hz,脉宽为7 ns;使用非聚焦换能器进行光声信号探测,其接收面直径为6 mm,中心频率为2.25 MHz,接收到光声信号用逆拉东变换进行图像重建。以小白鼠的离体爪子作为成像对象,换能器由旋转电机控制并以2作为旋转步长进行180旋转扫描获取实验数据,运用逆拉东变换进行了图像重建。所重建的图像比较清晰地反映了爪子内部的骨骼分布。由此表明,逆拉东变换可以用于光声成像,并且实现了有限角度的光声成像。     

Radon变换在二维条码图像识别中的应用

分忻了DataMatrix（简称DM）二维条码的符号结构特点，根据Radon变换的基本思想方法，提出一种对识别无间断的连续线段很有效的算法和一种对识别“铁路线”很有效的算法，运用这两途中算法，在二维条码图像最小模块仅为2.7像素的情况下，在图像轻微弯曲的情况下，可以对二维条码图像中的黑边和铁路线快速准确地定位，该算法可以应用于QR Code、DataMatrix、Code93和龙贝码等二维条码的图像识别。     

Correlation between radon exhalation and radium content in granite samples used as construction material in Saudi Arabia

Measurements of radon exhalation for a total of 205 selected samples of construction materials used in Saudi Arabia were carried out using an active radon gas analyzer with an emanation container. It was found that granite samples were the main source of radon exhalation. The radon exhalation rates per unit area from these granite samples varied from below the minimum detection limit up to with an average of 1.5 . The radium contents of 27 granite samples were measured using an HPGe-based γ spectroscopy setup. The ²²⁶Ra content of the granites varied from below the minimum detection limit up to , with an average of . The linear correlation coefficient between exhaled radon and radium content was found to be 0.90.     

A novel approach for testing passive radon monitors with an exposure standard based on alpha track detector

Best practices concerning qualification tests of radon passive detectors recommend the application of radon standard atmospheres at controlled conditions. A measurement technique has been developed, based on the application of the new on/off alpha track passive radon detector developed at ENEA. The capability of switch and pumping functions of this device has removed the time lag due to the radon transfer inside its sensitive volume and the post-exposure due to the residual radon decay. A special exposure facility has been developed based on a set of the above passive detectors connected with flange adapters to a radon chamber wall. This apparatus can be used substantially as a radon exposure standard (RES). Results of standardization tests at the ENEA Radon Facilities are given. The paper also addresses requirements for simple and small exposure facilities that permit accurate timed exposures and can be used for testing passive devices.     

Radon变换CHD反演方法的稳定化数值方法

本文利用Ｔｉｋｈｏｎｏｖ正则化方法、线性插值给出了Ｒａｄｏｎ变换ＣＨＤ反演方法的稳定化数值方法。克服了Ｒａｄｏｎ变换ＣＨＤ反演方法的不稳定性，且便于计算机实现。