• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.585-596
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• 1998

Some new problems of the theory of the finite automata are considered. Applying the finite automata in various tasks of the formal languages theory is observed. Special proof of Kleene's theorem is obtained. This proof is used for the defining the star-height of the finite automaton. The proper-ties of the last object are considered. The star-height of the finite automaton is used for reformulating the star-height problem of regular expression for finite automata. The method of the reduction of the star-height problem to the task of making special finite automaton is obtained. This reformulating can help to solve the star-height problem by new way.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1521-1536
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• 2017

This paper introduces a representation style of variable binding using dependent types when formalizing meta-theoretic properties. The style we present is a variation of the Coquand-McKinna-Pollack's locally-named representation. The main characteristic is the use of dependent families in defining expressions such as terms and formulas. In this manner, we can handle many syntactic elements, among which wellformedness, provability, soundness, and completeness are critical, in a compact manner. Another point of our paper is to investigate the roles of free variables and constants. Our idea is that fresh constants can entirely play the role of free variables in formalizing meta-theories of first-order predicate logic. In order to show the feasibility of our idea, we formalized the soundness and completeness of LJT with respect to Kripke semantics using the proof assistant Coq, where LJT is the intuitionistic first-order predicate calculus. The proof assistant Coq supports all the functionalities we need: intentional type theory, dependent types, inductive families, and simultaneous substitution.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.59-76
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• 2011

Starting from a collection V as a model which satisfies the axioms of NBG, we call the elements of V as sets and the subcollections of V as classes. We reconstruct the G$\ddot{o}$del's proof of the consistency of GCH and AC with the axioms of Zermelo-Fraenkel set theory by using Mostowski-Shepherdson mapping theorem, reflection principles in Tarski-Vaught theorem and Montague-Levy theorem and the fact that NBG is a conservative extension of ZF.

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.165-172
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• 2008

We investigate the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition,${\Delta}^2u+c{\Delta}u=bu^{+}+s$, in ­${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show by degree theory that there exist at least three solutions of the problem.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.69-83
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• 2009

New Lefschetz fixed point theorems for compact absorbing contractive admissible maps between Frechet spaces are presented. Also we present new results for condensing maps with a compact attractor. The proof relies on fixed point theory in Banach spaces and viewing a Frechet space as the projective limit of a sequence of Banach spaces.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.6C
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• pp.259-266
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• 2011

Conducting statistical analysis of foundation resistance using sufficient number of well-performed load test results is prerequisite for the calibration of reliable resistance factors for foundation LRFD. In this study, a rational analysis method is proposed so that the proof pile load test results can be reflected in update of resistance statistical characteristics based on Bayesian theory. Then, resistance factors for driven steel pipe piles compatible with Korea foundation practices are updated by implementing this rational analysis method. To accomplish the resistance factor updates, (1) prior pile resistance distribution is constructed based on the results of pile load tests, which loads are imposed at least up to their ultimate limit loads. (2) likelihood function is obtained from the results of proof pile load tests, and (3) posterior pile resistance distribution is updated by combining these prior pile resistance distribution and likelihood function. The resistance factors are updated using the posterior pile resistance following the first-order reliability method (FORM). From the possible results of five consecutive proof pile load tests, the updated resistance factors vary within ranges of 0.27-0.96 and 0.19-0.68 for target reliability indices of 2.33 and 3.0, respectively. Consequently, it was found that the Bayesian theory-implemented method enables the updates of resistance factors in an efficient way when reliable resistance factors are not available due to the lack of well-performed pile load test results.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.565-570
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• 1994

In this article we prove a version of the Perron-Frobenius Theorem in linear algebra using the Brouwer's Fixed Point Theorem in topology. We will mostly concentrate on he qualitative aspect of the Perron-Frobenius Theorem rather than quantitative formulas, which would be enough for theoretical investigations in ergodic theory. By the nature of the method of the proof, we do not expect to obtain a numerical estimate. But we may regard it worthwhile to see why a certain type of result should be true from a topological and geometrical viewpoint. However, a geometric argument alone would give us a sharp numerical bounds on the size of the eigenvalue as shown in Section 2. Eigenvectors of a matrix A will be fixed points of a certain mapping defined in terms of A. We shall modify an existing proof of Frobenius Theorem and that will do the trick for Perron-Frobenius Theorem.

• The Korean Society of Law and Medicine
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• v.8 no.1
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• pp.179-211
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• 2007

To succeed the claim of medical malpractice litigation, the patient as a plaintiff should establish the medical fault of a physician as a defendant, and the causation between the fault and damages. Because of the extraordinary nature of medical province, however, this application of a legal principles is rigorous with the patient. In addition, given the causation between the validation of physician's fault and damage is not attested, patient is not awarded anything. In order to overcome a difficulty of patient's verification and ensure the right to fair process, it was demonstrated the lightening of burden of proof in medical malpractice litigation and the acceptance of the responsibility for an illegal act in a prescribed range in the absence of the causation between the physician's fault and damage. This paper deals with the judgement of causation and burden of proof in medical malpractice litigation, and the acceptance of responsibility in the absence of the causation between the physician's fault and damage. Also, this study recommends a tendency of our precedent through the comparative case method of ours and Japan.

• The Korean Society of Law and Medicine
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• v.11 no.1
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• pp.59-84
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• 2010

Medical practice is characterized by various physiological response and uncapacity of prediction, therefore when medical accident occur it's hard to prove medical professionals' mistake. Though medical accident by medical professionals' mistake will be compensated anyhow, about irresistible medical accidents, no one should be not bound to compensate, victims get into very difficult situation. So, the nation don't negligent irresistible medical accidents but compensate anyway. As in the past, to the legal principle's constitution of irresistible medical accidents, theory of liability without fault was adapted, and it was said this theory was illogical in theory of liability with fault. But the subject of compensation to irresistible medical accidents is nation, nation don't participate in medical treatment therefore there is no room to occur mistake. And it is not reasonable to regard medical agency as a truster of public service, to cast to it responsibility of medical accidents. The problem of compensation to irresistible medical accidents is understood under the theory of social compensation. Social compensation is consisted of compensation to sacrifice and contribution to nation and society and compensation to sacrifice revealed under danger, the compensation to irresistible medical accidents belongs to the latter. This is near to concept of relief, is applied to national compensation system supplementarily, and compensation have no option but to compensate minimum. And there are not relation between national compensation system of irresistible medical accidents and proof liability transposition and theory of liability with out fault, merely in side of sharing responsibility burden between medical treater and victim, it is reasonable to discuss transportation of proof liability and compulsive liability insurance together.

• Honam Mathematical Journal
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• v.19 no.1
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• pp.125-130
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• 1997

In this paper, we give a characterization of collectionwise normality using continuous functions. More precisely, we give a new and short proof of the Dowker's theorem using selection theory that a $T_1$ space X is collectionwise normal if every continuous mapping of every closed subset F of X into a Banach space can be continuously extended over X. This is also a generalization of Tietze's extension theorem.