Meshfree particle methods such as MPS method and SPH method have been much developed in recent years and established as a powerful tool in the fields of science and engineering, since they require no troublesome mesh generation and have flexible adaptation to changing shape of domains. On the other hand, there are few mathematical error analysis on their accuracy as discretization methods for partial differential equations. In this paper, we investigate a mathematical analysis of the truncation error for a discrete gradient operator of meshfree particle methods with weight functions, particularly MPS method.

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This paper presents a new modeling of occurrence intensities for several types of event with multivariate affine jump processes. We actually try the maximum likelihood estimation for a specific model that classifies enterprises into three categories with some historical record of downgrades and upgrades for the Japanese enterprises, so that we can examine whether some self-exciting effects and mutually exciting effects of downgrades or upgrades are observed among the three categories.

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We propose an extended AVL tree with 5-subtrees, for the purpose of increasing search efficiency. In this paper, we report the results of our numerical experiment and examine the efficiency of our extended tree. The data structure of this extended AVL tree contains 5 partially balanced subtrees that match prefixes character by character by implementing the radix search method. Within the results of our numerical experiment, it was revealed that our tree's data structure capability is 55%-70% faster than that of conventional AVL trees.

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