Current Issue : January - March Volume : 2020 Issue Number : 1 Articles : 5 Articles
In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A\nnumerical scheme for the equation has been derived to obtain 2- Alpha in time and fourth-order in space.We improve the results by\nconstructing a compact scheme of second-order in time while keeping fourth-order in space. ...................
We describe two new derivations of the chi-square distribution. The first derivation\nuses the induction method, which requires only a single integral to\ncalculate. The second derivation uses the Laplace transform and requires\nminimum assumptions. The new derivations are compared with the established\nderivations, such as by convolution, moment generating function, and\nBayesian inference. The chi-square testing has seen many applications to\nphysics and other fields. We describe a unique version of the chi-square test\nwhere both the variance and location are tested, which is then applied to environmental\ndata. The chi-square test is used to make a judgment whether a\nlaboratory method is capable of detection of gross alpha and beta radioactivity\nin drinking water for regulatory monitoring to protect health of population.\nA case of a failure of the chi-square test and its amelioration are described.\nThe chi-square test is compared to and supplemented by the t -test....
The Davey-Stewartson Equation (DSE) is an equation system that reflects the evolution in finite depth of soft nonlinear packets\nof water waves that move in one direction but in which the wavesâ?? amplitude is modulated in spatial directions. This paper\nuses the Generalized Elliptic Equation Rational Expansion (GEERE) technique to extract fresh exact solutions for the DSE. As\na consequence, solutions with parameters of trigonometric, hyperbolic, and rational function are achieved. To display the physical\ncharacteristics of this model, the solutions obtained are graphically displayed. Modulation instability assessment of the outcomes\nacquired is also discussed and it demonstrates that all the solutions built are accurate and stable....
We study graph weights which naturally occur in Mayerâ??s theory and\nRee-Hooverâ??s theory for the virial expansion in the context of an imperfect\ngas. We pay particular attention to the Mayer weight and Ree-Hoover weight\nof a 2-connected graph in the case of the hard-core continuum gas in one dimension.\nThese weights are calculated from signed volumes of convex polytopes\nassociated with the graph. In the present paper, we use the method of\ngraph homomorphisms, to develop other explicit formulas of Mayer weights\nand Ree-Hoover weights for infinite families of 2-connected graphs....
This paper is concerned about testing whether a cross-covariance matrix deviates\nfrom a pre-assigned one or not. For this purpose, a new test statistic is\nconstructed based on the Frobenius norm of the difference between the\nsample cross-covariance matrix and the pre-assigned matrix. The test is implemented\nby applying the parametric bootstrap scheme. We conduct a simulation\nstudy to examine the performance of the test and compare it with\nother competitive tests. As multiple simulation examples show, our empirical\npowers are clearly superior to others in detecting any deviation of the\ncross-covariance from the pre-assigned matrix. In addition, the proposed\ntest is insensitive to non-cross-covariance elements in the covariance matrix.\nAs an illustration, we also investigate its performance in testing pairwise\ntime-reversibility....
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