• Title, Summary, Keyword: curvature function

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GRADIENT YAMABE SOLITONS WITH CONFORMAL VECTOR FIELD

  • Fasihi-Ramandi, Ghodratallah;Ghahremani-Gol, Hajar
    • Communications of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.165-171
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    • 2021
  • The purpose of this paper is to investigate the geometry of complete gradient Yamabe soliton (Mn, g, f, λ) with constant scalar curvature admitting a non-homothetic conformal vector field V leaving the potential vector field invariant. We show that in such manifolds the potential function f is constant and the scalar curvature of g is determined by its soliton scalar. Considering the locally conformally flat case and conformal vector field V, without constant scalar curvature assumption, we show that g has constant curvature and determines the potential function f explicitly.

FOURIER TRANSFORM AND Lp-MIXED PROJECTION BODIES

  • Liu, Lijuan;Wang, Wei;He, Binwu
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.5
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    • pp.1011-1023
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    • 2010
  • In this paper we define the $L_p$-mixed curvature function of a convex body. We develop a formula connection the support function of $L_p$-mixed projection body with Fourier transform of the $L_p$-mixed curvature function. Using this formula we solve an analog of the Shephard projection problem for $L_p$-mixed projection bodies.

A NOTE ON SURFACES IN THE NORMAL BUNDLE OF A CURVE

  • Lee, Doohann;Yi, HeungSu
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.2
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    • pp.211-218
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    • 2014
  • In 3-dimensional Euclidean space, the geometric figures of a regular curve are completely determined by the curvature function and the torsion function of the curve, and surfaces are the fundamental curved spaces for pioneering study in modern geometry as well as in classical differential geometry. In this paper, we define parametrizations for surface by using parametric functions whose images are in the normal plane of each point on a given curve, and then obtain some results relating the Gaussian curvature of the surface with curvature and torsion of the given curve. In particular, we find some conditions for the surface to have either nonpositive Gaussian curvature or nonnegative Gaussian curvature.

NEW RELATIONSHIPS INVOLVING THE MEAN CURVATURE OF SLANT SUBMANIFOLDS IN S-SPACE-FORMS

  • Fernandez, Luis M.;Hans-Uber, Maria Belen
    • Journal of the Korean Mathematical Society
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    • v.44 no.3
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    • pp.647-659
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    • 2007
  • Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.

A Note on Test for Model Adequacy in Nonlinear Regression

  • Kahng, Myung-Wook
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.3
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    • pp.689-694
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    • 2004
  • We investigate the test for model adequacy in nonlinear regression. We can expect the usual likelihood ratio statistic to be unaffected by any parametric- effect curvature; only the effect of intrinsic curvature needs to be considered. Multiplicative correction factor is derived for the limiting distribution of test statistic, which is a function of the intrinsic curvature arrays.

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SHAPE OPERATOR AH FOR SLANT SUBMANIFOLDS IN GENERALIZED COMPLEX SPACE FORMS

  • KIM, DONG-SOO;KIM, YOUNG-HO;LEE, CHUL-WOO
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.189-201
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    • 2005
  • In this article, we establish relations between the sectional curvature function K and the shape operator, and also relationship between the k-Ricci curvature and the shape operator for slant submanifolds in generalized complex space forms with arbitrary codimension.

Sensitivity analysis of variable curvature friction pendulum isolator under near-fault ground motions

  • Shahbazi, Parisa;Taghikhany, Touraj
    • Smart Structures and Systems
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    • v.20 no.1
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    • pp.23-33
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    • 2017
  • Variable Curvature Friction Pendulum (VCFP) bearing is one of the alternatives to control excessive induced responses of isolated structures subjected to near-fault ground motions. The curvature of sliding surface in this isolator is varying with displacement and its function is non-spherical. Selecting the most appropriate function for the sliding surface depends on the design objectives and ground motion characteristics. To date, few polynomial functions have been experimentally tested for VCFP however it needs comprehensive parametric study to find out which one provides the most effective behavior. Herein, seismic performance of the isolated structure mounted on VCFP is investigated with two different polynomial functions of the sliding surface (Order 4 and 6). By variation of the constants in these functions through changing design parameters, 120 cases of isolators are evaluated and the most proper function is explored to minimize floor acceleration and/or isolator displacement under different hazard levels. Beside representing the desire sliding surface with adaptive behavior, it was shown that the polynomial function with order 6 has least possible floor acceleration under seven near-field ground motions in different levels.