• Kyungpook Mathematical Journal
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• 제49권3호
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• pp.473-481
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• 2009

In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n(${\geq}$ 5), k be positive integers, and let $S_1$ = {z : $z^n$ = 1}, $S_2$ = {$a_1$, $a_2$, ${\cdots}$, $a_m$}, where $a_1$, $a_2$, ${\cdots}$, $a_m$ are distinct nonzero constants. If two non-constant entire functions f and g satisfy $E_f(S_1,2)$ = $E_g(S_1,2)$ and $E_{f^{(k)}}(S_2,{\infty})$ = $E_{g^{(k)}}(S_2,{\infty})$, then one of the following cases must occur: (1) f = tg, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = t{$a_1$, $a_2$, ${\cdots}$, $a_m$}, where t is a constant satisfying $t^n$ = 1; (2) f(z) = $de^{cz}$, g(z) = $\frac{t}{d}e^{-cz}$, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = $(-1)^kc^{2k}t\{\frac{1}{a_1},{\cdots},\frac{1}{a_m}\}$, where t, c, d are nonzero constants and $t^n$ = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).

• 한국지하수토양환경학회지:지하수토양환경
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• 제15권6호
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• pp.46-52
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• 2010

Derivative analysis, based on the derivative of the drawdown as a function of time (i.e., rate of drawdown change), was applied to the evaluation of hydraulic parameters of the aquifer as an aid of the aquifer test interpretation based on the Theis solutions. Pumping tests were conducted at a coastal fractured aquifer in Muan county, Korea, of which the drawdown data, measured at the two observation wells, were used for derivative analysis. Wellbore storage and transition period were hard to identify at conventional log-log and semi long plots, but was easily recognized by distinctive curves of positive unit slope, hump and negative unit slope in the derivative plot. For the observation well of OW-2 at which wellbore storage and transition lasted over an hour, conventional aquifer analysis would suffer from the uniqueness problems and in further result in erroneous hydraulic parameters. Derivative analysis was found to be effective for distinguishing the drawdown data directly reflecting the aquifer property from those reflecting non aquifer effects such as wellbore storage and transition, which offers a unified methodology to yield correct hydraulic parameters from aquifer test data.

• Kyungpook Mathematical Journal
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• 제61권4호
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• pp.745-763
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• 2021

For a value s ∈ ℂ∪ {∞}, two meromorphic functions f and g are said to share the value s, CM, (or IM), provided that f(z)-s and g(z)-s have the same set of zeros, counting multiplicities, (respectively, ignoring multiplicities). We say that a meromorphic function f shares s ∈ Ŝ partially with a meromorphic function g if E(s, f) ⊆ E(s, g). It is easy to see that "partially shared values CM" are more general than "shared values CM". With the help of partially shared values, in this paper, we prove some uniqueness results between a non-constant meromorphic function and its generalized differences or shifts. We exhibit some examples to show that the result of Charak et al. [8] is not true for k = 2 or k = 3. We find some gaps in proof of the result of Lin et al. [24]. We not only correct these resuts, but also generalize them in a more convenient way. We give a number of examples to validate certain claims of the main results of this paper and also to show that some of conditions are sharp. Finally, we pose some open questions for further investigation.

• 농촌계획
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• 제28권3호
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• pp.25-33
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• 2022

Due to the standardized urban development since the industrial era, many urban spaces have experienced non-placeness. Recently, although interest in urban landscape, history, and cultural elements has been increasing, landscape management and control measures are being implemented mainly in large cities due to the low status of rural areas in the country. From this point of view, this study tried to lay the foundation for basic research in related fields by classifying the characteristics and types of streetscapes located near large cities, and to suggest directions that should be considered when managing streetscapes in the future. As a result of the analysis of landscape adjectives, the village felt secluded due to the low density compared to the city street overall, but it did not have a unique image of the region. Three factors were derived through factor analysis, and preference was affected in the order of aesthetic, regularity, and uniqueness. In addition, the research site was classified into three types through cluster analysis, and it was confirmed that the differences by type were due to aesthetics and naturalness. On the other hand, the uniqueness is generally low in all regions, so it seems that fundamental countermeasures are needed.

• 기술혁신학회지
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• 제18권1호
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• pp.73-97
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• 2015

중소기업 활성화를 위한 정부 R&D지원이 다양하게 이루어지고 있으나 이와 관련한 기존 대부분의 연구는 정부 R&D지원 중 재무적인 부분에 초점이 맞추어져 있었다. 그러나 최근 들어 정부의 재정적 한계로 인해 정부의 비재무적인 R&D지원책에 대한 관심이 높아지고 있다. 본 연구에서는 중소기업을 대상으로 정부 R&D지원을 재무적, 비재무적 전략으로 유형화하고, 유형별 기술혁신 성과를 분석하였다. 동시에 R&D의 성과가 기업의 특성별로 다양할 수 있는 만큼 성과변수를 기술개발 가능성, 기술혁신성, 기술독창성으로 구분하여 지원방식과 성과의 특성 간 관계성에 대해 접근하고자 하였다. 분석 결과, 정부 R&D지원은 중소기업의 기술적 성과에 긍정적인 영향을 미치는 것으로 나타났다. 하지만 재무적 지원의 강도는 기술독창성에는 영향을 미치지 않는 것으로 나타나 정부 R&D지원의 규모효과에는 한계가 예상된다.

• 한국지구물리탐사학회:학술대회논문집
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• 한국지구물리탐사학회 2003년도 Proceedings of the international symposium on the fusion technology
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• pp.340-343
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• 2003

This study presents a practical procedure for the Bayesian inversion of geophysical data by Markov chain Monte Carlo (MCMC) sampling and geostatistics. We have applied geostatistical techniques for the acquisition of prior model information, and then the MCMC method was adopted to infer the characteristics of the marginal distributions of model parameters. For the Bayesian inversion of dipole-dipole array resistivity data, we have used the indicator kriging and simulation techniques to generate cumulative density functions from Schlumberger array resistivity data and well logging data, and obtained prior information by cokriging and simulations from covariogram models. The indicator approach makes it possible to incorporate non-parametric information into the probabilistic density function. We have also adopted the MCMC approach, based on Gibbs sampling, to examine the characteristics of a posteriori probability density function and the marginal distribution of each parameter. This approach provides an effective way to treat Bayesian inversion of geophysical data and reduce the non-uniqueness by incorporating various prior information.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.427-435
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• 2007

The existence theorem and continuous dependence property in $"L^2"$ sense for solutions of backward stochastic differential equation (shortly BSDE) with Lipschitz coefficients were respectively established by Pardoux-Peng and Peng in [1,2], Mao and Cao generalized the Pardoux-Peng's existence and uniqueness theorem to BSDE with non-Lipschitz coefficients in [3,4]. The present paper generalizes the Peng's continuous dependence property in $"L^2"$ sense to BSDE with Mao and Cao's conditions. Furthermore, this paper investigates the continuous dependence property in "almost surely" sense for BSDE with Mao and Cao's conditions, based on the comparison with the classical mathematical expectation.

• 대한수학회논문집
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• 제36권1호
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• pp.51-62
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• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.

• 대한수학회보
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• 제61권3호
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• pp.637-669
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• 2024

The goal of this paper is to study decay properties of weak solutions to Cauchy problem of the non-stationary fractional Navier-Stokes equations. By using the Fourier splitting method, we give the time L²-decay rate of weak solutions, which reveals that L²-decay is generally determined by its linear generalized Stokes flow. In second part, we establish various decay results and the uniqueness of the two dimensional fractional Navier-Stokes flows. In the end of this article, as an appendix, the existence of global weak solutions is given by making use of Galerkin' method, weak and strong compact convergence theorems.

• ETRI Journal
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• 제36권1호
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• pp.31-41
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• 2014

The heterogeneous network (HetNet) has been discussed in detail in the Long-Term Evolution (LTE) and LTE Advanced standards. However, the standardization of High-Speed Packet Access HetNet (HSPA HetNet) launched by 3GPP is pushing at full steam. Interference coordination (IC), which is responsible for dealing with the interference in the system, remains a subject worthy of investigation in regard to HSPA HetNet. In this paper, considering the network framework of HSPA HetNet, we propose a quasi-distributed IC (QDIC) scheme to lower the interference level in the co-channel HSPA HetNet. Our QDIC scheme is constructed as slightly different energy-efficient non-cooperative games in the downlink (DL) and uplink (UL) scenarios, respectively. The existence and uniqueness of the equilibrium for these games are first revealed. Then, we derive the closed-form best responses of these games. A feasible implementation is finally developed to achieve our QDIC scheme in the practical DL and UL. Simulation results show the notable benefits of our scheme, which can indeed control the interference level and enhance the system performance.