Current Issue : April - June Volume : 2019 Issue Number : 2 Articles : 6 Articles
In this paper, we focus on the perturbed risk model with dependent relation\nand consider the relevance from two aspects. For one side, we use copula\nfunction to model the structure of the claim size and interclaim time, and on\nthe other side, we establish the change of premium rat depending on the\nrandom thresholds. At last, we obtain the Integro-differential equations and\nits Laplace transforms of the Gerber-Shiu functions for the new risk model....
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This paper is devoted to the study of lump solutions to the (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation.\nFirst we use a direct method to construct a class of exact solutions which contain six arbitrary real constants. Then we use these\nsolutions to generate lump solutions with four real parameters.We also determine the amplitude and velocity of these lumps....
In this paper, we highlight the complimentary nature of the results of Anco & Bluman and Ibragimov in the construction of\nconservation laws that whilst the former establishes the role of multipliers, the latter presents a formal procedure to determine\nthe flows. Secondly, we show that there is an underlying relationship between the symmetries and conservation laws in a general\nsetting, extending the results of Kara &Mahomed;. The results take apparently differently forms for point symmetry generators and\nhigher-order symmetries. Similarities exist, to some extent, with a previously established result relating symmetries andmultipliers\nof a differential equation. A number of examples are presented....
In this article, we discuss the long-time dynamical behavior of the stochastic\nnon-autonomous nonclassical diffusion equations with linear memory and\nadditive white noise in the weak topological space........
In the paper, the authors express the Fussâ??Catalan numbers as several forms in terms of the\nCatalanâ??Qi function, find some analytic properties, including the monotonicity, logarithmic convexity,\ncomplete monotonicity, and minimality, of the Fussâ??Catalan numbers, and derive a double inequality\nfor bounding the Fussâ??Catalan numbers....
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