• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.173-187
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• 2021

In this paper, we deal with the notion of a v-semi-slant submersion from an almost Hermitian manifold onto a Riemannian manifold. We investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. Given such a map with totally umbilical fibers, we have a condition for the fibers of the map to be minimal. We also obtain an inequality of a proper v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and a v-semi-slant angle. Moreover, we give some examples of such maps and some open problems.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.1-16
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• 2022

In this paper, we define and study warped product skew semi-invariant submanifolds of a locally golden Riemannian manifold. We investigate a necessary and sufficient condition for a skew semi-invariant submanifold of a locally golden Riemannian manifold to be a locally warped product. An equality between warping function and the squared normed second fundamental form of such submanifolds is established. We also construct an example of warped product skew semi-invariant submanifolds.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.411-423
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• 2003

Some B.-Y. Chen inequalities for different kind of submanifolds of generalized complex space forms are established.

• Transactions of Materials Processing
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• v.25 no.3
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• pp.182-188
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• 2016

Flexibly-reconfigurable roll forming (FRRF) is a novel sheet metal forming technology conducive to producing multi-curvature surfaces by controlling the strain distribution along longitudinal direction. In FRRF, a sheet metal is shaped into the desired curvature by using reconfigurable rollers and gaps between the rollers. As FRRF technology and equipment are under development, a simulation model corresponding to the physical FRRF would aid in investigating how the shape of a sheet varies with input parameters. To facilitate the investigation, the current study exploits regression analysis to construct a predictive model for the longitudinal curvature of the sheet. Variables considered as input parameters are sheet compression ratio, radius of curvature in the transverse direction, and initial blank width. Samples were generated by a three-level, three-factor full factorial design, and both convex and saddle curvatures are represented by a quadratic regression model with two-factor interactions. The fitted quadratic equations were verified numerically with R-squared values and root mean square errors.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1095-1103
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• 2016

B. Y. Chen introduced a series of curvature invariants, known as Chen invariants, and proved sharp estimates for these intrinsic invariants in terms of the main extrinsic invariant, the squared mean curvature, for submanifolds in Riemannian space forms. Special classes of submanifolds in Sasakian manifolds play an important role in contact geometry. F. Defever, I. Mihai and L. Verstraelen [8] established Chen first inequality for C-totally real submanifolds in Sasakian space forms. Also, the differential geometry of slant submanifolds has shown an increasing development since B. Y. Chen defined slant submanifolds in complex manifolds as a generalization of both holomorphic and totally real submanifolds. The slant submanifolds of an almost contact metric manifolds were defined and studied by A. Lotta, J. L. Cabrerizo et al. A Chen first inequality for slant submanifolds in Sasakian space forms was established by A. Carriazo [4]. In this article, we improve this Chen first inequality for special contact slant submanifolds in Sasakian space forms.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.395-403
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• 2002

In the third phase of the response surface methods, the first-order model is assumed and the curvature of the response surface is checked with a fractional factorial design augmented by centre runs. We further assume that a true model is a quadratic polynomial. To choose an optimal design, Box and Draper(1959) suggested the use of an average mean squared error (AMSE), an average of MSE of y(x) over the region of interest R. The AMSE can be partitioned into the average prediction variance (APV) and average squared bias (ASB). Since AMSE is a function of design moments, region moments and a standardized vector of parameters, it is not possible to select the design that minimizes AMSE. As a practical alternative, Box and Draper(1959) proposed minimum bias design which minimize ASB and showed that factorial design points are shrunk toward the origin for a minimum bias design. In this paper we propose a robust AMSE design which maximizes the minimum efficiency of the design with respect to a standardized vector of parameters.