• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.647-653
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• 2012

In this paper, we consider fuzzy random sets as (measurable) mappings from a probability space into the set of fuzzy sets and prove a uniform strong law of large numbers for sequences of independent and identically distributed fuzzy random sets. Our results generalize those of Bass and Pyke(1984)and Jang and Kwon(1998).

• Communications for Statistical Applications and Methods
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• v.16 no.1
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• pp.157-162
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• 2009

The baker transformation is an ergodic transformation defined on the half open unit square. This paper considers the limiting behavior of the partial sum process of a martingale sequence constructed from the baker transformation. We get the uniform law of large numbers for the baker transformation.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1565-1571
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• 2017

The standard logistic map is an iterative function, which forms a discrete-time dynamic system. The chaotic logistic map is a kind of ergodic map defined over the unit interval. In this paper we study the limiting behaviors on the several processes induced by the chaotic logistic map. We derive the law of large numbers for the process induced by the chaotic logistic map. We also derive the uniform law of large numbers for this process. When deriving the uniform law of large numbers, we study the role of bracketing of the indexed class of functions associated with the process. Then we apply the idea of DeHardt (1971) associated with the bracketing method to the process induced by the logistic map. We finally illustrate an application to Monte Carlo integration.

• THE INTERNATIONAL COMMERCE & LAW REVIEW
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• v.16
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• pp.331-359
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• 2001

Uniform Electronic Transactions Act (1999) Drafted by the National Conference of Commissioners on Uniform State Laws. The Act allows the use of electronic records and electronic signatures in any transaction, except transactions subject to the Uniform Commercial Code. The fundamental purpose of this act is to remove perceived barriers to electronic commerce. The Act's a procedural statute. It does not mandate either electronic signatures or records, but provides a means to effectuate transactions when they are used. The primary objective is to establish the legal equivalence of electronic records and signatures with paper writings and manually-signed signatures. With regard to the general scope of the Act, the Act's coverage is inherently limited by the definition of "transaction." The Act does not apply to all writings and signatures, but only to electronic records and signatures relating to a transaction, defined as those interactions between people relating to business, commercial and governmental affairs. The exclusion of specific Articles of the Uniform Commercial Code reflects the recognition that, particularly in the case of Articles 5, 8 and revised Article 9, electronic transactions were addressed in the specific contexts of those revision processes. In the context of Articles 2 and 2A the UETA provides the vehicle for assuring that such transactions may be accomplished and effected via an electronic medium. At such time as Articles 2 and 2A are revised the extent of coverage in those Articles(Acts) may make application of this Act as a gap-filling law desirable. Similar considerations apply to the recently promulgated Uniform Computer Information Transactions Act (UCITA). Another fundamental premise of the Act is that it be minimalist and procedural. The general efficacy of existing law, in an electronic context, so long as biases and barriers to the medium are removed, confirms this approach. The Act defers to existing substantive law. Specific areas of deference to other law in this Act include: i) the meaning and effect of "sign" under existing law, ii) the method and manner of displaying, transmitting and formatting information in section 8, iii) rules of attribution in section 9, and iv) the law of mistake in section 10.

• Language and Information
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• v.14 no.1
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• pp.145-163
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• 2010

This paper aims to propose that Benford's Law, non-uniform distribution of the leading digits in lists of numbers from many real-life sources, also appears in linguistic texts. The first digits in the frequency lists of morphemes from Sejong Morphologically Analyzed Corpora represent non-uniform distribution following Benford's Law, but showing complexity of numerical sources from complex systems like earthquakes. Benford's Law in texts is a principle reflecting regular distribution of low-frequency linguistic types, called LNRE(large number of rare events), and governing texts, corpora, or sample texts relatively independent of text sizes and the number of types. Although texts share a similar distribution pattern by Benford's Law, we can investigate non-uniform distribution slightly varied from text to text that provides useful applications to evaluate randomness of texts distribution focused on low-frequency types.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.75-83
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• 2011

In this paper the Baum-Katz law of large numbers for negatively orthant dependent random variables is studied. The complete convergence of negatively orthant dependent random variables under some conditions of uniform integrablity is also obtained.

• 한국디지털정책학회:학술대회논문집
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• 2004.11a
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• pp.55-73
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• 2004

The Internet is a wonderland that can be enjoyed by the young, old, and those in-between. It is also a vast commercial market where many contracts are formed every second. The Internet and E-Commerce have created new situations that have generated sweeping proposals for fundamental changes in contract law. During the first half of the 20th Century. when many businesses expanded their geographic scope, there was a tremendous desire for uniform treatment of contracts for the sale of goods throughout the U.S.A. and the whole world. That same dynamic is now occurring in E-Commerce. There is a general recognition of the desirability of uniform contract law to govern E-commerce, but to date that does not exist, though there are extensive proposals for reform of contract law on the Internet. E-Commerce is currently plagued by some of the same problems that led to the passage of the UCC. In the absence of uniform legislation, state-by-state differences are inevitable with respect to E-Commerce. State-by-state differences in E-Commerce contract law is widely viewed as undesirable. To deal with this problem, a number of uniform bills have been proposed including UCITA, UETA, and revisions to Article 2 of the UCC (Subpart B). The thrust of these uniform acts is to create legal parity between paper records and electronic records. There is considerable resistance by consumer groups to this parity and progress towards Passage of UCITA, UETA, and revised Article 2 has been slow. The UCITA covers licenses of computer software but does not cover the sale oil goods on the Internet. The scope of the UCITA includes computer software. multimedia interactive products, computer data and databases, and Internet and online information, The UETA deals comprehensively with E-Commerce and contract law. The UCC covers the sale of goods, which does not necessarily involve E-Commerce. The basic principles of contract law are modified to deal with Internet transactions. Intent is inferred from the operations of electronic agents and "signatures" can occur with a response to an invitation to click to accept.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1819-1826
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• 2015

Following an idea of Ornstein and Sucheston, Foguel proved the so-called uniform "zero-two" law: let T : $L^1$(X, $\mathcal{F}$, ${\mu}$) ${\rightarrow}$ $L^1$(X, $\mathcal{F}$, ${\mu}$) be a positive contraction. If for some $m{\in}{\mathbb{N}}{\cup}\{0\}$ one has ${\parallel}T^{m+1}-T^m{\parallel}$ < 2, then $\lim_{n{\rightarrow}{\infty}}{\parallel}T^{m+1}-T^m{\parallel}=0$. There are many papers devoted to generalizations of this law. In the present paper we provide a multi-parametric generalization of the uniform zero-two law for $L^1$-contractions.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.935-946
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• 2019

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history. We consider Hawkes processes with uniform immigrants which is a special case of the Hawkes processes with renewal immigrants. We study the limit theorems for Hawkes processes with uniform immigrants. In particular, we obtain a law of large number, a central limit theorem, and a large deviation principle.

• THE INTERNATIONAL COMMERCE & LAW REVIEW
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• v.25
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• pp.41-71
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• 2005

"UNIDROIT Principles 2004" focused on an enlargement rather than a revision. An additional Section or Chapter so to speak, which are about, the Authority of a Agents, Third Party Rights, Set-off, Assignment of Rights, Transfer of Obligations and Assignment of Contracts, and Limitation Periods have been added, while the only change of substance made to the 1994 Edition, apart from two paragraphs in the Preamble, and three new provisions in Chapter 1 and 2 which are necessary to adapt the Principles to the needs of electronic contracting. The Principles which have the nature of the restatement of international uniform laws (for example CISG) are continuous exercise. Therefore we should note whether in the future our concerns would be on a additional topics on a improvement of the current text by monitoring the reception of the "UNIDROIT Principles 2004" in practice, and the application by contracting parties. The purposes of the Principles may be classified into three ; the rules of law governing the contract, means of interpreting and supplementing international uniform law or domestic law, or models for national and international legislator. Among them, the function of governing law may be applied by the express choice by the parties or by the implied choice like "general principles of law" or "les mercatoria", and it may be applied in the absence of any choice of law by the parties. Among there importance functions, this writer would like to emphasize the function to supplementing international uniform law instruments. The reason is that the CISG which has been established as an international uniform sales act and to which our country would be a contracting State from March, 2005, needs a lot of gap-filling. For this purpose it is advisable the parties to insert following provisions in their contract. "This contract shall be governed by the CISG, supplemented when necessary by the UNIDROIT Principles 2004" Thus success in practice of the UNIDROIT Principles over the last then years has surpassed the most optimistic expectations. It is hoped that the 2004 Edition of the UNIDROIT Principles will be just as favorably received by legislators, business persons, lawyers, arbitrators and judges and become even better known and more widely used throughout the World.