Monte Carlo calculations of the energy deposited in biological samples and shielding materials

The energy deposited by gamma radiation from the Cs-137 isotope into body tissues (bone and muscle), tissue-like medium (water), and radiation shielding materials (concrete, lead, and water), which is of interest for radiation dosimetry, was obtained using a simple Monte Carlo algorithm. The algorithm also provides a realistic picture of the distribution of backscattered photons from the target and the distribution of photons scattered forward after several scatterings in the scatterer, which is useful in studying radiation shielding. The presented method in this work constitutes an attempt to evaluate the amount of energy absorbed by body tissues and shielding materials.     

Research on the passive nuclear level gauge

ABSTRACT

Using the ‘quadruple combination detection’ automatic calibration method to solve the traditional passive nuclear ash hopper material level meter calibration problem. The method adopts the ‘contour multistage measurement’ mode, fitted the ratio of absorbed dose rate detected by adjacent cascade probe with corresponding actual material level after measurement, then use the fitting parameters to calibrate automatically which do not need ash hopper stop working, And this can effectively save the calibration time and cost. The method can effectively eliminate the material level measuring error brought by the changes of radioactive activity in the coal ash, which improve the measuring precision and material level positioning accuracy. There are many factors affecting the radioactive activity of coal ash which vary in Different feeding period, or after refueling. And this may cause measurement error and misinformation. Using quadruple combination detection and contour multistage measurement mode, when the radioactive activity in the coal ash changes, the passive nuclear meter level gauge can be revised according to the calibration curve or calibrated automatically. Which eliminated the effects brought by the changing of coal ash radioactive activity, saved onerous repeatedly calibration procedure, also improve the accuracy of the calibration, avoid misjudgment, and can improve the accuracy of measurement.     

The arithmetic fourier transform and the visual pathway

The Arithmetic Fourier Transform is an algorithm for the computation of Fourier coefficients. In this paper it is extended to the computation of double Fourier coefficients by a repeated sum. We discuss the relevance of the repeated sum algorithm to signal processing by neurons in the visual pathway.     

An improved time domain linear sampling method for Robin and Neumann obstacles

We consider inverse obstacle scattering problems for the wave equation with Robin or Neumann boundary conditions. The problem of reconstructing the geometry of such obstacles from measurements of scattered waves in the time domain is tackled using a time domain linear sampling method. This imaging technique yields a picture of the scatterer by solving a linear operator equation involving the measured data for many right-hand sides given by singular solutions to the wave equation. We analyse this algorithm for causal and smooth impulse shapes, we discuss the effect of different choices of the singular solutions used in the algorithm, and finally we propose a fast FFT-based implementation.     

The Two-Dimensional,Linear Orthotropic Plate

We First define a continuous extension of the Laquerre polynomials and give some properties of this continuous extension. Then we define a continuous Laguerre transform for square integrable functions, give some properties of this transform and give a sampling theorem that is similar to the well known Shannon-Whittaker Sampling Theorem for Fourier transform. The inverse of this transform is also given.     

Local sampling set conditions in weighted shift-invariant signal spaces

How to represent a continuous signal in terms of a discrete sequence is a fundamental problem in sampling theory. Most of the known results concern global sampling in shift-invariant signal spaces. But in fact, the local reconstruction from local samples is one of the most desirable properties for many applications in signal processing, e.g. for implementing real-time reconstruction numerically. However, the local reconstruction problem has not been given much attention. In this article, we find conditions on a finite sampling set X such that at least in principle a continuous signal on a finite interval is uniquely and stably determined by their sampling value on the finite sampling set X in shift-invariant signal spaces.     

Approximation by Nonlinear Multivariate Sampling Kantorovich Type Operators and Applications to Image Processing

In this article, we study a nonlinear version of the sampling Kantorovich type operators in a multivariate setting and we show applications to image processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces L ^?(? ⁿ ) that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in L ^p (? ⁿ )-spaces, L ^αlog ^β L(? ⁿ )-spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and image processing applications are included.     

Parameterizing the global attractor of the navier-stokes equations by nodal values

In this paper we give an affirmative answer to the conjecture of Foias and Tern am that the elements of the global attractor of the two dimensional Navier Stokes equations are uniquely determined by their nodal values at a finite number of points in the underlying physical domain. This is kind of a sampling theorem for the elements of the the global attractor of the Navier Stokes equations.     

Conditioning in Markov Chain Monte Carlo

Abstract

The so-called “Rao-Blackwellized” estimators proposed by Gelfand and Smith do not always reduce variance in Markov chain Monte Carlo when the dependence in the Markov chain is taken into account. An illustrative example is given, and a theorem characterizing the necessary and sufficient condition for such an estimator to always reduce variance is proved.