• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.869-877
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• 2011

In this paper, we propose an efficient two-flow zero-knowledge blind identification protocol on the elliptic curve cryptographic (ECC) system. A. Saxena et al. first proposed a two-flow blind identification protocol in 2005. But it has a weakness of the active-intruder attack and uses the pairing operation that causes slow implementation in smart cards. But our protocol is secure under such attacks because of using the hash function. In particular, it is fast because we don't use the pairing operation and consists of only two message flows. It does not rely on any underlying signature or encryption scheme. Our protocol is secure assuming the hardness of the Discrete-Logarithm Problem in bilinear groups.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1465-1472
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• 2009

In This paper we shall study the existence of solutions of nonlinear two point boundary value problems for nonlinear 2nth-order differential equation $y^{(2n)}=f(t,y,y',{\cdots},y^{(2n-1)})$ with the boundary conditions $g_0(y(a),y'(a),{\cdots},y^{2n-3}(a))=0,g_1(y^{(2n-2)}(a),y^{(2n-1)}(a))=0$, $h_o(y(c),y'(c))=0,h_i(y^{(i)}(c),y^{(i+1)}(c))=0(i=2,3,{\cdots},2n-2)$.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.981-1000
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• 2009

This paper considers asset liability management problems when their deterministic equivalent formulations are general nonlinear optimization problems. The presented approach uses a nonmonotone trust region strategy for solving a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penalty-barrier function that involves both primal and dual variables. Each subproblem is solved approximately. The algorithm does not restrict a monotonic decrease of the objective function value at each iteration. If a trial step is not accepted, the algorithm performs a non monotone line search to find a new acceptable point instead of resolving the subproblem. We prove that the algorithm globally converges to a point satisfying the second-order necessary optimality conditions.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1073-1086
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• 2009

This paper considers the problems of martingale measures and risk-minimizing hedging strategies in the market with restricted information. By constructing a general restricted information market model, the explicit relation of arbitrage and the minimal martingale measure between two different information markets are discussed. Also a link among all equivalent martingale measures under restricted information market is given. As an example of restricted information markets, this paper constitutes a jump-diffusion process model and presents a risk minimizing problem under different information. Through $It\hat{o}$ formula and projection results in Schweizer[13], the explicit optimal strategy for different market information are given.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.349-369
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• 2017

In last 30 years, mathematical tangle theory is applied to molecular biology, especially to DNA topology. The recent issues and research results of this topic are reviewed in this paper. We introduce a tangle which models an enzyme-DNA complex. The studies of 2-string tangle equations related to Topoisomerase II action and site-specific recombination is discussed. And 3-string tangle analysis of Mu-DNA complex, n-string tangle analysis ($n{\geq}4$) of DNA-enzyme synaptic complexes are also discussed.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.277-290
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• 2020

We propose and analyze a chord summation algorithm, which combines the ideas of Viète and Archimedes to calculate the value of π. The error of the algorithm decreases exponentially per iteration and becomes pinched at a critical iteration, depending on the accuracy of the first input value, ${\sqrt{2}}$. The critical iteration is also analyzed.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.499-512
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• 2011

The purpose of this paper is twofold. The first is to establish a uniqueness theorem for entire function sharing two polynomials with its ${\kappa}$-th derivative, by using the theory of normal families. Meanwhile, the theorem generalizes some related results of Rubel and Yang and of Li and Yi. Several examples are provided to show the conditions are necessary. The second is to generalize the Br$\"{u}$-ck conjecture with the idea of sharing polynomial.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.267-288
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• 2014

We propose and analyze two-scale product approximation for semilinear heat equations in the mixed finite element method. In order to efficiently resolve nonlinear algebraic equations resulting from the mixed method for semilinear parabolic problems, we treat the nonlinear terms using some interpolation operator and exploit a two-scale grid algorithm. With this scheme, the nonlinear problem is reduced to a linear problem on a fine scale mesh without losing overall accuracy of the final system. We derive optimal order $L^{\infty}((0, T];L^2({\Omega}))$-error estimates for the relevant variables. Numerical results are presented to support the theory developed in this paper.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.251-266
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• 2014

In this paper, we use Newton's method to approximate a locally unique solution of an equation in Banach spaces and introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton's method than before [1]-[13], in some interesting cases, provided that the Fr$\acute{e}$chet-derivative of the operator involved is p-H$\ddot{o}$lder continuous (p${\in}$(0, 1]). Numerical examples involving two boundary value problems are also provided.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.791-815
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• 2014

We show amongst other that if $f,g:[a,b]{\rightarrow}\mathbb{C}$ are two functions of bounded variation and such that the Riemann-Stieltjes integral $\int_a^bf(t)dg(t)$ exists, then for any continuous functions $h:[a,b]{\rightarrow}\mathbb{C}$, the Riemann-Stieltjes integral $\int_{a}^{b}h(t)d(f(t)g(t))$ exists and $${\int}_a^bh(t)d(f(t)g(t))={\int}_a^bh(t)f(t)d(g(t))+{\int}_a^bh(t)g(t)d(f(t))$$. Using this identity we then provide sharp upper bounds for the quantity $$\|\int_a^bh(t)d(f(t)g(t))\|$$ and apply them for trapezoid and Ostrowski type inequalities. Some applications for continuous functions of selfadjoint operators on complex Hilbert spaces are given as well.