• 대한수학회논문집
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• 제35권2호
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• pp.625-637
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• 2020

The object of the present paper is to characterize 3-dimensional trans-Sasakian manifolds of type (α, β) admitting ∗-Ricci solitons and ∗-gradient Ricci solitons. Under certain restrictions on the smooth functions α and β, we have proved that a trans-Sasakian 3-manifold of type (α, β) admitting a ∗-Ricci soliton reduces to a β-Kenmotsu manifold and admitting a ∗-gradient Ricci soliton is either flat or ∗-Einstein or it becomes a β-Kenmotsu manifold. Also an illustrative example is presented to verify our results.

• 대한수학회지
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• 제55권2호
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• pp.391-413
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• 2018

In this paper we introduce a new tensor named semi-projective curvature tensor which generalizes the projective curvature tensor. First we deduce some basic geometric properties of semi-projective curvature tensor. Then we study pseudo semi-projective symmetric manifolds $(PSPS)_n$ which recover some known results of Chaki [5]. We provide several interesting results. Among others we prove that in a $(PSPS)_n$ if the associated vector field ${\rho}$ is a unit parallel vector field, then either the manifold reduces to a pseudosymmetric manifold or pseudo projective symmetric manifold. Moreover we deal with semi-projectively flat perfect fluid and dust fluid spacetimes respectively. As a consequence we obtain some important theorems. Next we consider the decomposability of $(PSPS)_n$. Finally, we construct a non-trivial Lorentzian metric of $(PSPS)_4$.

• JSTS:Journal of Semiconductor Technology and Science
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• 제10권2호
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• pp.100-106
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• 2010

The impact of surface quantization on device parameters of a Si metal oxide semiconductor (MOS) capacitor has been analyzed in the present work. Variation of conduction band bending, position of discrete energy states, variation of surface potential, and the variation of inversion carrier concentration at charge centroid have been analyzed for different gate voltages, substrate doping concentrations and oxide thicknesses. Oxide thickness calculated from the experimental C-V data of a MOS capacitor is different from the actual oxide thickness, since such data include the effect of surface quantization. A correction factor has been developed considering the effect of charge centroid in presence of surface quantization at strong inversion and it has been observed that the correction due to surface quantization is crucial for highly doped substrate with thinner gate oxide.

• 대한수학회논문집
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• 제34권4호
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• pp.1289-1301
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• 2019

In the present paper, we prove that if there exists a second order parallel tensor on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution and $h^{\prime}{\neq}0$, then either the manifold is isometric to $H^{n+1}(-4){\times}{\mathbb{R}}^n$, or, the second order parallel tensor is a constant multiple of the associated metric tensor of $M^{2n+1}$ under certain restriction on k, ${\mu}$. Besides this, we study Ricci soliton on an almost Kenmotsu manifold with generalized $(k,{\mu})^{\prime}$-nullity distribution. Finally, we characterize such a manifold admitting generalized Ricci soliton.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.691-705
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• 2019

In the present paper is to classify Beta-almost (${\beta}$-almost) Ricci solitons and ${\beta}$-almost gradient Ricci solitons on almost $CoK{\ddot{a}}hler$ manifolds with ${\xi}$ belongs to ($k,{\mu}$)-nullity distribution. In this paper, we prove that such manifolds with V is contact vector field and $Q{\phi}={\phi}Q$ is ${\eta}$-Einstein and it is steady when the potential vector field is pointwise collinear to the reeb vectoer field. Moreover, we prove that a ($k,{\mu}$)-almost $CoK{\ddot{a}}hler$ manifolds admitting ${\beta}$-almost gradient Ricci solitons is isometric to a sphere.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.163-174
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• 2019

The object of this paper is to classify paracontact metric ($k,{\mu}$)-spaces satisfying certain curvature conditions. We show that a paracontact metric ($k,{\mu}$)-space is Ricci semisymmetric if and only if the metric is Einstein, provided k < -1. Also we prove that a paracontact metric ($k,{\mu}$)-space is ${\phi}$-Ricci symmetric if and only if the metric is Einstein, provided $k{\neq}0$, -1. Moreover, we show that in a paracontact metric ($k,{\mu}$)-space with k < -1, a second order symmetric parallel tensor is a constant multiple of the associated metric tensor. Several consequences of these results are discussed.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권2호
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• pp.143-153
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• 2021

In this paper, we study some curvature properties of Sasakian 3-manifolds associated to Ƶ-tensor. It is proved that if a Sasakian 3-manifold (M, g) satisfies one of the conditions (1) the Ƶ-tensor is of Codazzi type, (2) M is Ƶ-semisymmetric, (3) M satisfies Q(Ƶ, R) = 0, (4) M is projectively Ƶ-semisymmetric, (5) M is Ƶ-recurrent, then (M, g) is of constant curvature 1. Several consequences are drawn from these results.

• 한국콘텐츠학회논문지
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• 제18권5호
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• pp.292-302
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• 2018

이 글은 인도의 대표적인 식민도시인 뉴델리, 마드라스, 캘커타, 봄베이(현재의 첸나이, 콜카타, 뭄바이)가 교과서에 어떻게 서술되고 있는지 살펴보고 이를 바탕으로 인도인의 관점에서 본 식민도시에 관해 분석하고자 한다. 인도 교과서에서 식민도시들은 도시가 만들어지는 과정과 그에 따른 정치 사회 경제 문화적 변화, 영국인과 인도인 간의 분리, 도시 계획, 식민지배 기간 동안 축조된 건축물들에 대해 서술하고 있으며, 이에 관한 서술관점은 '박탈, 배척, 차별, 저항, 도전'과 '기회의 부여, 수용, 흡수'의 관점이 혼재되어 있다는 점이 특징이다. 즉 식민도시를 둘러싼 서술관점은 대립적이면서도 상호 불가분의 관계를 견지하고 있는데, 영국의 통치 이데올로기가 반영된 식민도시가 가질 수밖에 없는 태생적 특징, 그 안에서 지배자와 피지배자가 만들어가는 사회, 문화적 특징을 단순화시키지 않고 다층적 고찰이 가능하도록 하고 있다. 그러면서도 피지배자로 겪었던 불합리한 차별과 배제에 대한 저항이 있었던 점은 분명히 하고 있다.

• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.21-31
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• 2005

We introduce the notions of nilpotent element, quasi-regular element in a semiring which is a distributive lattice of rings. The concept of Jacobson radical is introduced for this kind of semirings.

• 한국경영과학회지
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• 제7권1호
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• pp.45-50
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• 1982

The present paper provides a method for solving a complementary programming problem with quadratic objective function subject to linear constraints. The procedure developed is based on the simplex method for quadratic programming problem. An example is added to illustrate the procedure.