• Journal of Applied and Pure Mathematics
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• 제4권5_6호
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• pp.287-297
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• 2022

In this paper, we consider a risk-minimization hedging problem for a special European contingent claims. The existence and uniqueness of strategy are given constructively. Firstly, a non-standard European contingent is demonstrated as stochastic payment streams. Then the existence of the risk minimization strategy and also the uniqueness are proved under two kinds market information by using Galtchouk-Kunita-Watanabe decomposition and constructing a 0-achieving strategy risk-minimizing strategies in full information. And further, we have proven risk-minimizing strategies exists and is unique under restrict information by constructing a weakly mean-selffinancing strategy.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.259-273
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• 2024

In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.

• 충청수학회지
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• 제29권2호
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• pp.337-346
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• 2016

Within white noise approach, we study the existence and uniqueness of the solution of an initial value problem for generalized white noise functionals, and then as a corollary we discuss the linear stochastic differential equation associated with a convolution of white noise functionals.

• 대한수학회보
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• 제37권2호
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• pp.303-316
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• 2000

The Cauchy problem for degenerate parabolic equations with absorption is studied. We prove the existence of a fundamental solution. Also a Harnack type inequality is established and the existence and uniqueness of initial trace for nonnegative solutions is shown.

• 호남수학학술지
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• 제37권1호
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• pp.99-112
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• 2015

In this paper we consider the periodic Cauchy problem for the generalized two-component Hunter-Saxton system with analytic initial data and we prove a Cauchy-Kowalevski type theorem for the generalized two-component Hunter-Saxton system, that establishes the existence and uniqueness of real analytic solutions.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.411-427
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• 2015

In this article, we main study the uniqueness problem of meromorphic function which difference polynomials sharing common values. We consider the entire function $(f^n(f^m-1)\prod_{j=1}^{s}f(z+c_j)^{{\mu}j})^{(k)}$ and the meromorphic function $f^n(f^m-1)\prod_{j=1}^{s}f(z+c_j)^{{\mu}j}$ to get the main results which extend Theorem 1.1 in paper[5] and theorem 1.4 in paper[6].

• Kyungpook Mathematical Journal
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• 제58권3호
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• pp.519-531
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• 2018

In this paper, we investigate the uniqueness problem of entire functions sharing two polynomials with their k-th derivatives. We look into the conjecture given by $L{\ddot{u}}$, Li and Yang [Bull. Korean Math. Soc., 51(2014), 1281-1289] for the case $F=f^nP(f)$, where f is a transcendental entire function and $P(z)=a_mz^m+a_{m-1}z^{m-1}+{\ldots}+a_1z+a_0({\not{\equiv}}0)$, m is a nonnegative integer, $a_m,a_{m-1},{\ldots},a_1,a_0$ are complex constants and obtain a result which improves and generalizes many previous results. We also provide some examples to show that the conditions taken in our result are best possible.

• Communications for Statistical Applications and Methods
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• 제17권6호
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• pp.791-801
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• 2010

마이크로데이터 제공시 발생될 수 있는 노출(disclosure)과 노출위험을 나타내는데 사용되는 측도인 유일성(uniqueness) 그리고 모집단 유일성의 개수를 추정하기 위한 초모집단 모형으로 Multinomial-Dirichlet 모형, Takemura의 Poisson-Gamma 모형, Modified Multinomial-Dirichlet 모형, Bethlehem의 Poisson-Gamma 모형을 다룬다. 이 4개의 모형에 대해 마이크로데이터 제공에 따른 임계모집단 크기(critical population size)를 결정한다.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.889-906
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• 2020

In this article, we consider the uniqueness problem of the shift polynomials $f^n(z)(f^m(z)-1){\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$ and $f^n(z)(f(z)-1)^m{\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$, where f(z) is a transcendental entire function of finite order, cj (j = 1, 2, …, s) are distinct finite complex numbers and n(≥ 1), m(≥ 1), s and µj (j = 1, 2, …, s) are integers. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo [Commun. Math. Stat. 3 (2015), 227-238].

• 대한수학회논문집
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• 제36권3호
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• pp.515-526
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• 2021

The paper has been devoted to study the uniqueness problem of meromorphic function and its linear differential polynomial sharing two values. We have pointed out gaps in one of the theorem due to [1]. We have further extended the corrected form of Chen-Li-Li's result which in turn extend the an earlier result of [8] in a large extent. In fact, we have subtly use the notion of weighted sharing of values in this particular section of literature which was unexplored till now. A handful number of examples have been provided by us pertinent to different discussions. Specially we have given an example to show that one condition in a theorem can not be dropped.