We devise fast and provably accurate algorithms to transform between an N × N × N Cartesian voxel representation of a three-dimensional function and its expansion into the ball harmonics, that is, the eigenb...
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We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network *** numerical method is based on a nonlinear finite difference scheme on a uniform Cartesian grid in...
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We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network *** numerical method is based on a nonlinear finite difference scheme on a uniform Cartesian grid in a two-dimensional(2D)*** focus is on the impact of different discretization methods and choices of regularization parameters on the symmetry of the numerical *** particular,we show that using the symmetric alternating direction implicit(ADI)method for time discretization helps preserve the symmetry of the solution,compared to the(non-symmetric)ADI ***,we study the effect of the regularization by the isotropic background perme-ability r＞0,showing that the increased condition number of the elliptic problem due to decreasing value of r leads to loss of *** show that in this case,neither the use of the symmetric ADI method preserves the symmetry of the ***,we perform the numerical error analysis of our method making use of the Wasserstein distance.
In response to the demand for rapid geometric modeling in Monte Carlo radiation transportation calculations for large-scale and complex geometric scenes,functional improvements,and algorithm optimizations were perform...
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In response to the demand for rapid geometric modeling in Monte Carlo radiation transportation calculations for large-scale and complex geometric scenes,functional improvements,and algorithm optimizations were performed using CAD-to-Monte Carlo geometry conversion(CMGC)*** representation(BRep)to constructive solid geometry(CSG)conversion and visual CSG modeling were combined to address the problem of non-convertible geometries such as spline *** splitting surface assessment method in BRep-to-CSG conversion was optimized to reduce the number of Boolean operations using an Open ***,in turn,reduced the probability of CMGC conversion *** auxiliary surface generation algorithm was optimized to prevent the generation of redundant auxiliary surfaces that cause an excessive decomposition of CAD geometry *** optimizations enhanced the usability and stability of the CMGC model *** was applied successfully to the JMCT transportation calculations for the conceptual designs of five China Fusion Engineering Test Reactor(CFETR)*** rapid replacement of different blanket schemes was achieved based on the baseline CFETR *** geometric solid number of blankets ranged from hundreds to tens of *** correctness of the converted CFETR models using CMGC was verified through comparisons with the MCNP calculation *** CMGC supported radiation field evaluations for a large urban scene and detailed ship *** enabled the rapid conversion of CAD models with thousands of geometric solids into Monte Carlo CSG *** analysis of the JMCT transportation simulation results further demonstrated the accuracy and effectiveness of the CMGC.
We consider an antiferromagnet in one space dimension with easy-axis anisotropy in a perpendicular magnetic field. We study propagating domain wall solutions that can have a velocity up to a maximum vc. The width of t...
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This paper deals with a new epidemiological model of SIRS with stochastic perturbations. The primary objective is to establish the existence of a unique non-negative nonlocal solution. Using the basic reproduction num...
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Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka–Volterra model which defined the interaction bet...
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Let R be a unitary operator whose spectrum is the circle. We show that the set of unitaries U which essentially commute with R (i.e., [U, R] ≡ UR − RU is compact) is path-connected. Moreover, we also calculate the se...
The paper presents a survey of the results obtained by the members of the department of Mathematical Statistics in the field of analytic and asymptotic properties of mixture probability models. Much attention is paid ...
The paper presents a survey of the results obtained by the members of the department of Mathematical Statistics in the field of analytic and asymptotic properties of mixture probability models. Much attention is paid to the representation of some widely applied absolutely continuous probability distributions (gamma, Weibull, Student, Snedecor–Fisher, Mittag-Leffler, Burr, etc.) as mixtures of distributions possessing maximum differential entropy (normal and exponential). Some useful discrete distributions that are representable as mixed Poisson distributions are discussed as well. Examples are presented of limit theorems for statistics constructed from samples with random sizes in which the distributions mentioned above are limit laws. Also, the estimates of convergence rate in these theorems are presented. Some problems related to the application of methods of intellectual analysis of big arrays of dynamically accumulated data based on mixture probability models are discussed.
This paper proposes a numerical scheme for the (2 + 1)-dimensional nonlinear Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation (ZK-BBME). The ZK-BBME represents a long-wave model with large wavelength that explains...
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Support Vector Machine (SVM) has received much attention in machine learning due to its profound theoretical research and practical application results. Support Vector Regression (SVR) has become a powerful tool for s...
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