• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.295-310
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• 2014

This paper provides a study of lightlike submanifolds of a generalized Robertson-Walker (GRW) space-time. In particular, we investigate lightlike submanifolds with curvature invariance, parallel second fundamental forms, totally umbilical second fundamental forms, null sectional curvatures and null Ricci curvatures, respectively.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.863-874
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• 2012

We provide a study of lightlike hypersurfaces of a generalized Robertson-Walker (GRW) space-time. In particular, we investigate lightlike hypersurfaces with curvature invariance, parallel second fundamental forms, totally umbilical second fundamental forms, null sectional curvatures and null Ricci curvatures, respectively.

• Kyungpook Mathematical Journal
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• v.24 no.1
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• pp.25-37
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• 1984

• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.49-86
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• 2013

This article is a continuation of the paper [21]. In this paper we deal with Maass-Jacobi forms on the Siegel-Jacobi space $\mathbb{H}{\times}\mathbb{C}^m$, where H denotes the Poincar$\acute{e}$ upper half plane and $m$ is any positive integer.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.595-606
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• 2022

In this paper, we have studied f-biharmonic submanifolds in locally conformal almost cosymplectic space forms and have derived condition on second fundamental form for f-biharmonic submanifolds. Also, we have discussed its integral submanifolds in locally conformal almost cosymplectic space forms.

• Korean Journal of Clinical Pharmacy
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• v.16 no.1
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• pp.40-45
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• 2006

In clinical trials, it is important to have well designed case report forms (CRF) in order to obtain good quality of data. If CRF design at the first stage of your study goes wrong, after all efforts have been made, you may find practical difficulties in data analysis at the final stage of your study because of incomplete or wrong information. In this paper, the following rules fundamental to CRF design are introduced: rules in general, rules of format or style, categorized responses, forms with multiple records per subject, and international studies. Investigators are well aware of research goals, however sometimes they do not know how to express it on CRF. If they understand the rules fundamental to CRF design, time for CRF development will be saved and CRF completeness will be enhanced.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.425-444
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• 2013

We construct some hyperbolic hyperelliptic space forms whose fundamental groups are generated by only two or three isometries. Each occurring group is obtained from a supergroup, which is an extended Coxeter group generated by plane re ections and half-turns. Then we describe covering properties and determine the isometry groups of the constructed manifolds. Furthermore, we give an explicit construction of space form of the second smallest volume nonorientable hyperbolic 3-manifold with one cusp.

• Earthquakes and Structures
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• v.10 no.1
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• pp.25-51
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• 2016

In this study, graph product rules are applied to the dynamic analysis of regular skeletal structures. Graph product rules have recently been utilized in structural mechanics as a powerful tool for eigensolution of symmetric and regular skeletal structures. A structure is called regular if its model is a graph product. In the first part of this paper, the formulation of time history dynamic analysis of regular structures under seismic excitation is derived using graph product rules. This formulation can generally be utilized for efficient linear elastic dynamic analysis using vibration modes. The second part comprises of random vibration analysis of regular skeletal structures via canonical forms and closed-form eigensolution of matrices containing special patterns for symmetric structures. In this part, the formulations are developed for dynamic analysis of structures subjected to random seismic excitation in frequency domain. In all the proposed methods, eigensolution of the problems is achieved with less computational effort due to incorporating graph product rules and canonical forms for symmetric and cyclically symmetric structures.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.167-182
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• 2018

In this paper, we prove the optimal inequalities for the generalized normalized ${\delta}$-Casorati curvature and the normalized scalar curvature for different submanifolds in generalized (${\kappa},{\mu}$)-space forms. The proof is based on an optimization procedure involving a quadratic polynomial in the components of the second fundamental form. We also characterize the submanifolds on which equalities hold.

• Kyungpook Mathematical Journal
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• v.24 no.2
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• pp.115-125
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• 1984