Local Monte Carlo estimation methods in the solution of global illumination equation

In this article, we consider local estimations of the Monte Carlo method for solving the equation of the global illumination. The local estimations allow directly calculating the luminance at a predetermined point, in a given direction for an arbitrary bidirectional reflectance distribution function (BRDF). Thus, there is no need to construct the map of the illumination. Thereby it is much more effective than direct modeling or the method of finite element. The use in lighting calculations of the object described by the spherical harmonics is also discussed in the article

Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains

Liquid low-level radioactive wastes treatment by using hydrophobized track-etched membranes

In this paper, we present the results of liquid low-level radioactive wastes (LLLRW) treatment by direct contact membrane distillation (DCMD) using polyethylene terephthalate (PET) track-etched membranes (TeMs). PET TeMs were modified by styrene and triethoxyvinylsilane (TEVS) using UV-induced grafting. Modification led to increase in the contact angle to 99° of PET TeMs (pore size from 150 to 300 nm). Hydrophobic PET TeMs were investigated by X-ray photoelectron spectroscopy (XPS), Fourier-transform infrared spectroscopy (FTIR), goniometric analysis, gas permeability test, liquid entry presser (LEP) analysis and scanning electron microscope (SEM). Prepared membranes were tested in treatment of LLLRW by DCMD. The influence of pore size on water flux and rejection degree was studied. Rejection degree was evaluated by conductometry and atomic emission methods. Decontamination factors (evaluated by gamma-ray spectroscopy) for 60Co, 137Cs, and 241Am were found to be 85, 1900 and 5 respectively. In most cases degree of rejection of Cs, Mo, Sr, Sb, Al, Ca, Fe, K, Mg and Na ions were more than 90% and close to 100%. The use of TeMs with a narrow pores size distribution and without tortuous channels allowed us to achieve better purification from radioactive wastes in comparison with hollow-fiber membranes. © 2019 Elsevier LtdMinistry of Education and Science of the Republic of Kazakhstan: AP05132110This study was funded by the Ministry of Education and Science of the Republic of Kazakhstan (grant No AP05132110 “Preparation of track-etched membranes with specified properties for membrane distillation and forward osmosis”)

Local Monte Carlo estimation methods in the solution of global illumination equation

In this article, we consider local estimations of the Monte Carlo method for solving the equation of the global illumination. The local estimations allow directly calculating the luminance at a predetermined point, in a given direction for an arbitrary bidirectional reflectance distribution function (BRDF). Thus, there is no need to construct the map of the illumination. Thereby it is much more effective than direct modeling or the method of finite element. The use in lighting calculations of the object described by the spherical harmonics is also discussed in the article

Reconstruction of the scattering function of overspread radar targets

This study addresses the problem of stochastic radar target measurement. The authors develop an algorithm that allows for the reconstruction of the scattering function of a wide-sense stationarity with uncorrelated scattering radar target from the autocorrelation of the response of the target to a deterministic sounding signal. Although conventional methods are applicable only when the scattering function is supported on a `rectangle' with area <;1, the authors' method can handle area 1 support sets of `arbitrary' geometry. Based on the suggested theoretical recovery procedure, the authors propose an unbiased scattering function estimator

Relation of instant radiosity method with local estimations of Monte Carlo method

This article discusses mathematical foundations of local estimations of the Monte Carlo method. The basic algorithm of visualization of the 3D scenes based on local estimations, which are an analog of the famous algorithm Instant Radiosity, is considered. An algorithm for radiance object view-independent calculation based on local estimations of Monte Carlo method is shown Additionally, questions of representation of radiance object as spherical harmonics expansion in each computational point are analyzed. The assumption of possible direct calculation of radiance object coefficients of expansion in spherical harmonics by Monte Carlo method is brought in, and problems are identified