• Title/Summary/Keyword: Tian

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OSCILATION AND STABILITY OF NONLINEAR NEUTRAL IMPULSIVE DELAY DIFFERENTIAL EQUATIONS

  • Duan, Yongrui;Tian, Peng;Zhang, Shunian
    • Journal of applied mathematics & informatics
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    • v.11 no.1_2
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    • pp.243-253
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    • 2003
  • In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equations are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.

Meshfree/GFEM in hardware-efficiency prospective

  • Tian, Rong
    • Interaction and multiscale mechanics
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    • v.6 no.2
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    • pp.197-210
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    • 2013
  • A fundamental trend of processor architecture evolving towards exaflops is fast increasing floating point performance (so-called "free" flops) accompanied by much slowly increasing memory and network bandwidth. In order to fully enjoy the "free" flops, a numerical algorithm of PDEs should request more flops per byte or increase arithmetic intensity. A meshfree/GFEM approximation can be the class of the algorithm. It is shown in a GFEM without extra dof that the kind of approximation takes advantages of the high performance of manycore GPUs by a high accuracy of approximation; the "expensive" method is found to be reversely hardware-efficient on the emerging architecture of manycore.

Stress analyses of solids with rectangular holes by 3-D special hybrid stress elements

  • Tian, Z.S.;Liu, J.S.;Fang, B.
    • Structural Engineering and Mechanics
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    • v.3 no.2
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    • pp.193-199
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    • 1995
  • Two kinds of special 3-dimensional 12-node finite elements-each one contains a traction-free planar surface-have been developed based on Hellinger-Reissner principle by assumed stress hybrid method. Example solutions have demonstrated the advantage of using these special elements for analyzing plates and solids with rectangular holes.

ON THE HYBRID MEAN VALUE OF GENERALIZED DEDEKIND SUMS, GENERALIZED HARDY SUMS AND KLOOSTERMAN SUMS

  • Qing Tian;Yan Wang
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.3
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    • pp.611-622
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    • 2023
  • The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that q is a prime.

Study on the Concept of Space and Modeled Space of the Jiu-Gong (공간의 개념과 구궁의 공간모델화에 대한 연구)

  • Kim Yang Chan;Kang Jung Soo
    • Journal of Physiology & Pathology in Korean Medicine
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    • v.16 no.5
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    • pp.851-856
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    • 2002
  • All creatures are living in the space and time. As the space and time are prior to experience, they are preconditions for an incident to happen and preconditions for each other to coexist as well. Therefore, time can be recognized through the change of space and the space can be understood by the passage of time. In western philosophy, the space was understood as an object, place, interval, mind and etc. In oriental philosophy, even though one space is just a part of bigger space, the space may represent the universal space, and the various spaces are no more than a space. The space itself doesn't have any color, form, beginning and end, or liu-he(六合). However, it is the biggest concept that we can find everywhere. In order to understand the space, we need to find our position by expressing subjective positions like above and below, left and right, before and after, and objective positions like high and low, east and west, south and north. In oriental philosophy, the sun is the standard point in finding position; its front side is south, the backside is north, the left side is east, the right side is west, the upper side is south and the lower side north. Based on the finding position which is stated above and by taking each characteristics of he-luo-xi-wen(河洛羲文) and interrelations among them, the space can be modeled. Followings are the results obtained from this study: Tian doesn't fill in west and north. Di doesn't fill in east and south. Tian-dao(天道) turns to left, and Di-dao(地道) turns to right. There is no direct way to get to Dui-chong-fang without passing by Zhong-gong(中宮). The solid figure of eighty-one Bian-ju(變局) and sixty-four Gua-tu(卦圖).