• Communications of the Korean Mathematical Society
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• v.35 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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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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• v.10 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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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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• v.27 no.3
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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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• v.59 no.1
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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.

• The Pure and Applied Mathematics
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• v.28 no.2
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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.

• The Journal of the Korea Contents Association
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• v.18 no.5
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• pp.292-302
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• 2018

This article examines how India's major colonial cities-Madras, Calcutta, Bombay (today, Chennai, Kolkata, Mumbai) and New Delhi- are described in India's history textbooks and analyzed them from the perspective of Indians. It is explained the major colonial cities as the process of making the cities and their political, social, economic and cultural changes, the separation between British and Indian, urban planning, colonial architectures built by British colonial power in Indian history textbooks. The viewpoint of its descriptions is featured by the coexistence of 'deprivation, exclusion, discrimination, resistance, challenge' and 'grant of opportunity, acceptation, absorption'. That is, this characteristic maintains a mutual confrontational and inseparable relation. And in a multi-layer, it enables to consider the inherent characteristics of a colonial city reflecting the British ruling ideology and the society within which the rulers and proprietors are forming without simplifying the cultural characteristics. It is clear that there was a resistance against the unreasonable discrimination and exclusion that had been suffered by the British colonial government as well.

• Kyungpook Mathematical Journal
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• v.45 no.1
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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.

• Journal of the Korean Operations Research and Management Science Society
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• v.7 no.1
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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.