• East Asian mathematical journal
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• v.29 no.1
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• pp.13-22
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• 2013

As a fuzzy counterpart of stochastic calculus, fuzzy calculus including Liu integral and Liu formula were introduced. In order to deal with the problems with several fuzzy dynamic factors, Liu process, Liu integral and Liu formula are extended to the case of multi-dimensional in this paper.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.507-527
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• 2021

In this paper, we study existence of extremal solutions for fuzzy differential equations driven by Liu process. To show extremal solutions, we define partial ordering relative to fuzzy process. This is an extension of the results of Kwun et al. [5] and Rodríguez-López [13] to fuzzy differential equations in credibility space.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.2
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• pp.145-153
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• 2014

With reasonable control selections on the space of functions, various application models can take the shape of a well-defined control system on mathematics. In the credibility space, controlability management of fuzzy differential equation is as much important issue as stability. This paper addresses exact controllability for fuzzy differential equations in the credibility space in the perspective of Liu process. This is an extension of the controllability results of Park et al. (Controllability for the semilinear fuzzy integro-differential equations with nonlocal conditions) to fuzzy differential equations driven by Liu process.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.235-249
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• 2012

In the paper by Liu and Lin (Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799), a new kind of precise asymptotics in the law of large numbers for the sequence of i.i.d. random variables, which includes complete convergence as a special case, was studied. This paper is devoted to the study of this new kind of precise asymptotics in the law of large numbers for moving average process under $\phi$-mixing assumption and some results of Liu and Lin [6] are extended to such moving average process.

• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.2-8
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• 2013

Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

• 한국정보디스플레이학회:학술대회논문집
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• 2006.08a
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• pp.1235-1238
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• 2006

One-Drop-Filling (ODF) process is an advanced vacuum filling process in LCoS manufacture line. The merits not only increase the throughput of liquid crystal filling process but also reduce the number of equipments. Studying application of ODF process in LCoS panel manufacturing is the purpose of is this article. The accuracy of liquid crystal drop size, the stability of seal dispensing and the nozzle size etc. In the tiny panel manufacture are more important than those factors in normal panel manufacture.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.7
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• pp.3720-3746
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• 2017

At present, numerous hospitals and medical institutes have implemented Telecare Medicine Information Systems (TMIS) with authentication protocols to enable secure, efficient electronic transactions for e-medicine. Numerous studies have investigated the use of authentication protocols to construct efficient, robust health care services, and recently, Liu et al. presented an authenticated key agreement mechanism for TMIS. They argued that their mechanism can prevent various types of attacks and preserve a secure environment. However, we discovered that Liu et al.'s mechanism presents some vulnerabilities. First, their mechanism uses an improper identification process for user biometrics; second, the mechanism is not guaranteed to protect against server spoofing attacks; third, there is no session key verification process in the authentication process. As such, we describe how the above-mentioned attacks operate and suggest an upgraded security mechanism for TMIS. We analyze the security and performance of our method to show that it improves security relative to comparable schemes and also operates in an efficient manner.

• Trans-
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• v.5
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• pp.65-82
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• 2018

What distinguishes Impression Liu Sanjie, directed by Zhang yimou from other stage performances lies in its use of space. Firstly, it breaks the regular way of performing in a limited theater space but instead, impression Liu sanjie bases the stage activities on the real nature scenery. Secondly, it promotes the local culture by combining the unique color effect of the particular nature scenery with its use of the scenery's natural space, with an aesthetic precision. In another word, Impression Liu Sanjie is not a simple performance set on the natural scenery but more of a promotion to the local culture, through the concept of "environment friend" between human and nature, which is brought by mixing the unique color of natural scenery and its natural space. This research analyzes the Impression Liu Sanjie's use of space basing on Proxemics by Edward T Hall. Impression Liu Sanjie adapts its character from a folk tale, employs the form of natural scenery performance, and at the same time to the largest extent throughout its creating process respects the local culture and its natural space. As a result, the performance presents the idea of "environmentally friendly".

• East Asian mathematical journal
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• v.17 no.2
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• pp.265-273
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• 2001

In this paper, we prove that under certain conditions the Ishikawa iterative method with errors converges strongly to the unique solution of the nonlinear strongly accretive operator equation Tx=f. Related results deal with the solution of the equation x+Tx=f. Our results extend and improve the corresponding results of Liu, Childume, Childume-Osilike, Tan-Xu, Deng, Deng-Ding and others.

• 한국전기화학회:학술대회논문집
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• 2004.06a
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• pp.219-224
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• 2004