• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• 대한수학회논문집
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• 제38권4호
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• pp.1001-1017
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• 2023

Let R be a commutative graded ring with nonzero identity and n a positive integer. Our principal aim in this paper is to introduce and study the notions of graded n-irreducible and strongly graded n-irreducible ideals which are generalizations of n-irreducible and strongly n-irreducible ideals to the context of graded rings, respectively. A proper graded ideal I of R is called graded n-irreducible (respectively, strongly graded n-irreducible) if for each graded ideals I₁, . . . , I_n+1 of R, I = I₁ ∩ · · · ∩ I_n+1 (respectively, I₁ ∩ · · · ∩ I_n+1 ⊆ I ) implies that there are n of the I_i 's whose intersection is I (respectively, whose intersection is in I). In order to give a graded study to this notions, we give the graded version of several other results, some of them are well known. Finally, as a special result, we give an example of a graded n-irreducible ideal which is not an n-irreducible ideal and an example of a graded ideal which is graded n-irreducible, but not graded (n - 1)-irreducible.

• Bulletin of the Korean Chemical Society
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• 제32권5호
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• pp.1625-1629
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• 2011

Kinetic studies of the reactions of O,O-diphenyl Z-S-aryl phosphorothioates with X-benzylamines have been carried out in dimethyl sulfoxide at 55.0 $^{\circ}C$. The Hammett (log $k_2$ vs ${\sigma}_X$) and Bronsted [log $k_2$ vs $pK_a(X)$] plots for substituent X variations in the nucleophiles are biphasic concave downwards with a maximum point at X = H, and the unusual positive ${\rho}_X$ and negative ${\beta}_X$ values are obtained for the strongly basic benzylamines. The sign of the cross-interaction constant (${\rho}_{XZ}$) is negative for both the strongly and weakly basic nucleophiles. Greater magnitude of ${\rho}_{XZ}$ value is observed with the weakly basic nucleophiles (${\rho}_{XZ}$ = -2.35) compared to with the strongly basic nucleophiles (${\rho}_{XZ}$ = -0.03). The deuterium kinetic isotope effects ($k_H/k_D$) involving deuterated benzylamines [$XC_6H_4CH_2ND_2$] are primary normal ($k_H/k_D$ > 1). The proposed mechanism is a concerted $S_N2$ involving a frontside nucleophilic attack with a hydrogen bonded, four-center-type transition state for both the strongly and weakly basic nucleophiles. The unusual positive ${\rho}_X$ and negative ${\beta}_X$ values with the strongly basic benzylamines are rationalized by through-space interaction between the ${\pi}$-clouds of the electron-rich phenyl ring of benzylamine and the phenyl ring of the leaving group thiophenoxide.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

• 한국항공우주학회지
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• 제34권1호
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• pp.24-31
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• 2006

본 연구에서는 완전 내재적 기법을 이용한 2계 자유도 모델에 대한 플러터 해석을 수행하였다. 유동해석을 위하여 2차원 Navier-Stokes 지배방정식을 ε-SST 난류모델과 DP-SGS 병렬화 기법을 이용해 구성하였다. 구조해석을 위하여 피치 와 플런지의 2계 자유도를 갖는 모델을 구성하였으며 시간영역에서의 해석을 위하여 유동해석과 마찬가지로 이중 시간 전진 기법을 이용하였다. 가상 시간 전진에서 유체-구조 결합을 통해서 강성결합을 구현하였으며 이를 천음속 플러터 예측에 적용하였다. 플러터 해석의 전형적인 응답인 감쇠응답, 중립응답, 발산응답 및 limit cycle oscillation (LCO) 등을 계산하였으며, 더불어 플러터 속도 경계곡선을 작성하였다. 천음속 플러터 해석은 난류모델 뿐만 아니라 유체-구조 결합 방법에 따라 다른 특성을 보임을 확인하였다.

• 호남수학학술지
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• 제38권2호
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• pp.259-267
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• 2016

A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. Recently, the authors introduced the classes of QTAG-modules namely as socle-regular and strongly socle-regular QTAG-modules which properly contain the classes of transitive and fully transitive QTAG-modules respectively. Here we define strongly and quasi transitivities and study the inter relations between various type of transitivities.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권4호
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• pp.239-247
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. Moreover we show that I has at least 2m critical points when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities with $(P.S.)^*_c$ condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.

• 대한조선학회논문집
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• 제49권2호
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• pp.196-202
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• 2012

In this study, numerical analysis of viscous flows is carried out based on the unstructured grid. There exist some difficulties in expressing and computing numerical derivatives on the unstructured grid due to lack of the structured characteristics. The general computer algorithms are developed to perform numerical derivatives easily and extended to be applicable to various geometries composed of hybrid meshes. And the optimal method of strongly implicit procedure is newly contrived to accelerate the rate of convergence in solving the pressure Poisson equation. To verify numerical schemes, the driven cavity problems of 2 and 3 dimension are simulated. The numerical results are compared with others and our numerical schemes are shown to be valid.

• East Asian mathematical journal
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• 제28권5호
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• pp.597-604
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• 2012

Let C be a nonempty closed convex subset of real Hilbert space H and F = $\{S(t):t{\geq}0\}$ a nonexpansive self-mapping semigroup of C, and $f:C{\rightarrow}C$ is a fixed contractive mapping. Consider the process {$x_n$} : $$\{{x_{n+1}={\beta}_nx_n+(1-{\beta}_n)z_n\\z_n={\alpha}_nf(x_n)+(1-{\alpha}_n)S(t_n)P_C(x_n-r_nAx_n)$$. It is shown that {$x_n$} converges strongly to a common element of the set of fixed points of nonexpansive semigroups and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.

• Korean Journal of Mathematics
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• 제28권3호
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• pp.623-638
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• 2020

In this article, we initially present the concept of the fuzzy generalized m-bi-ideals in semigroups, then making use of their important types like prime, semiprime and strongly fuzzy generalized m-bi-ideals, we give the important characterizations of the semigroups. We also characterize the m-regular and m-intraregular semigroups using the properties of the irreducible and strongly irreducible fuzyy generalized m-bi-ideals.