• 대한수학회지
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• 제58권6호
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• pp.1461-1484
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• 2021

We deal with the following elliptic equations: $\{-div({\varphi}^{\prime}(\left|{\nabla}z\right|^2){\nabla}z)+V(x)\left|z\right|^{{\alpha}-2}z={\lambda}{\rho}(x)\left|z\right|^{r-2}z+h(x,z),\\z(x){\rightarrow}0,\;as\;\left|x\right|{\rightarrow}{\infty},$ in ℝ^N , where N ≥ 2, 1 < p < q < N, 1 < α ≤ p^*q'/p', α < q, 1 < r < min{p, α}, φ(t) behaves like t^q/2 for small t and t^p/2 for large t, and p' and q' the conjugate exponents of p and q, respectively. Here, V : ℝ^N → (0, ∞) is a potential function and h : ℝ^N × ℝ → ℝ is a Carathéodory function. The present paper is devoted to the existence of at least two distinct nontrivial solutions to quasilinear elliptic problems of Schrödinger type, which provides a concave-convex nature to the problem. The primary tools are the well-known mountain pass theorem and a variant of Ekeland's variational principle.

• 전기학회논문지
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• 제58권8호
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• pp.1485-1495
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• 2009

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the ${\lambda}-P$ function method is used to calculate ED for the fitness function of GA. The ${\lambda}-P$ function method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with two kinds of ED problems, namely ED with multiple fuel units (EDMF) and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all the ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.

• 대한수학회논문집
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• 제37권2호
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• pp.445-454
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• 2022

Using the concept of the strong differential subordination introduced in [2], we find conditions on the functions θ, 𝜑, G, F such that the first order strong subordination θ(p(z)) + $\frac{G(\xi)}{\xi}$zp'(z)𝜑(p(z)) ≺≺ θ(q(z)) + F(z)q'(z)𝜑(q(z), implies p(z) ≺ q(z), where p(z), q(z) are analytic functions in the open unit disk 𝔻 with p(0) = q(0). Corollaries and examples of the main results are also considered, some of which extend and improve the results obtained in [1].

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.81-93
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• 2023

By utilizing a certain Libera integral operator considered on analytic multivalent functions in the unit disk U. Using the hypergeometric function and the Libera integral operator, we included a new convolution operator that expands on some previously specified operators in U, which broadens the scope of certain previously specified operators. We introduced and investigated the properties of new subclasses of functions f (z) ∈ A_p using this operator.

• 한국인터넷방송통신학회논문지
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• 제15권6호
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• pp.257-266
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• 2015

비 볼록 발전비용함수에 대한 최적화 문제는 다항시간으로 해를 구하는 알고리즘이 알려져 있지 않아 전기분야에서는 부득이 2차 함수만을 사용하고 있다. 본 논문은 비 볼록 발전비용함수의 경제급전 최적화 문제에 대한 밸브지점 최적화 알고리즘을 제안하였다. 제안된 알고리즘은 초기 치로 최대 발전량 $P_i{\leftarrow}P_i^{max}$로 설정하고, 평균 발전단가가 $_{max}\bar{c}_i$인 발전기 i의 발전량을 밸브지점 $P_{ik}$로 감소시키는 방법을 적용하였다. 제안된 알고리즘을 13과 40-발전기 데이터에 적용한 결과 기존의 휴리스틱 알고리즘보다 좋은 성능을 보였다. 따라서 비 볼록 발전비용함수의 경제급전문제 최적 해는 각 발전기의 밸브지점 발전량으로 수렴함을 보였다.

• Korean Journal of Mathematics
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• 제29권2호
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• pp.395-407
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• 2021

By considering a certain univalent function that maps the unit disk 𝕌 onto a strip domain, we introduce new subclasses of analytic and p-valent functions and determine the coefficient bounds for functions belonging to these new classes. Relevant connections of some of the results obtained with those in earlier works are also provided.

• 대한수학회지
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• 제37권2호
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• pp.253-267
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• 2000

• 호남수학학술지
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• 제35권1호
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• pp.37-49
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• 2013

Consider a non-degenerate open convex cone C with vertex the origin in the $n$2-dimensional Euclidean space $E^n$. We study volume properties of strictly convex hypersurfaces in the cone C. As a result, for example, if the volume of the region of an elliptic cone C cut off by the tangent hyperplane P of M at $p$ is independent of the point $p{\in}M$, then it is shown that the hypersurface M is part of an elliptic hyperboloid.

• 대한전자공학회논문지
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• 제22권2호
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• pp.82-89
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• 1985

MCO 문제의 해석을 하기 위한 weight P-norm방법을 연구하여 새로운 non-inferior해를 구하였다. Weight 최소화방법을 MOSFET NAND 게이트에 적용하여 최적 non-inferior해를 구하였다. 또한 본 논문에서 응용한 최소화방법은 목적함수가 non-convex일때도 적용된다. 본 논문의 최소화 방법의 결과를 Lightner의 결과와 비교하여 효율성을 입증하였다.

• International Journal of Control, Automation, and Systems
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• 제6권4호
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• pp.468-476
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• 2008

This paper presents a novel approach to economic dispatch (ED) with nonconvex fuel cost function as combinatorial optimization problems (COP) while most of the conventional researches have been developed as function optimization problems (FOP). One nonconvex fuel cost function can be divided into several convex fuel cost functions, and each convex function can be regarded as a generation type (G-type). In that case, ED with nonconvex fuel cost function can be considered as COP finding the best case among all feasible combinations of G-types. In this paper, a genetic algorithm is applied to solve the COP, and the $\lambda$-P table method is used to calculate ED for the fitness function of GA. The $\lambda$-P table method is reviewed briefly and the GA procedure for COP is explained in detail. This paper deals with three kinds of ED problems, namely ED considering valve-point effects (EDVP), ED with multiple fuel units (EDMF), and ED with prohibited operating zones (EDPOZ). The proposed method is tested for all three ED problems, and the test results show an improvement in solution cost compared to the results obtained from conventional algorithms.