• Bulletin of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.133-140
• /
• 2002

On compact complex hyperbolic manifolds of complex dimension two, we show that the dimension of the space of infinitesimal deformations of self-dual conformal structures is smaller than that of the deformation obstruction space and that every self-dual metric with covariantly constant Ricci tensor must be a standard one upto rescalings and diffeomorphisms.

• Journal of the Korean Mathematical Society
• /
• v.37 no.5
• /
• pp.687-705
• /
• 2000

The main purpose of this paper is to study differentiable one-parameter groups and cosine families of operators acting on white noise functions and their associated infinitesimal generators. In particular, we prove the heredity of differentiable one-parameter group and cosine family of operators under the second quantization of the Cuchy problems for the first and second or der differential equations.

• Journal of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.695-708
• /
• 2003

We study the existence of solutions for overdetermined PDE systems that admit prolongation to a complete system. We reduce the problem to a Pfaffian system on a submanifold of the jet space of unknown functions and then express the integrability conditions in terms of the coefficients of the original system. As possible applications we present some local problems in CR geometry: determining the CR embeddibility into spheres and the existence of infinitesimal CR automorphisms.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.541-545
• /
• 2007

In this paper, we study the infinitesimal transformation on the fibred Riemannian space. The conharmonic curvature tensor is invariant under the conharmonic transformation. We have proved that the conharmonically flat fibred Riemannian space with totally geodesic fibre is locally the Riemannian product of the base space and a fibre.

• Korean Journal of Mathematics
• /
• v.29 no.3
• /
• pp.547-554
• /
• 2021

The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.3
• /
• pp.365-374
• /
• 2020

Given a noncompact semisimple Lie group G and its maximal compact Lie subgroup K such that the right multiplication of each element in K gives an isometry on G, consider a principal bundle G → G/K, which is a Riemannian submersion. We study the infinitesimal holonomy isometries. Given a closed curve at eK in the base space G/K, consider the holonomy displacement of e by the horizontal lifting of the curve. We prove that the correspondence is continuous.

• Kyungpook Mathematical Journal
• /
• v.63 no.1
• /
• pp.97-104
• /
• 2023

In the present paper, we characterize, for a class of almost Kenmotsu manifolds, those that admit quasi Yamabe solitons. We show that if a (k, 𝜇)'-almost Kenmotsu manifold admits a quasi Yamabe soliton (g, V, 𝜆, 𝛼) where V is pointwise collinear with 𝜉, then (1) V is a constant multiple of 𝜉, (2) V is a strict infinitesimal contact transformation, and (3) (£_Vh')X = 0 holds for any vector field X. We present an illustrative example to support the result.

• Kyungpook Mathematical Journal
• /
• v.18 no.1
• /
• pp.109-117
• /
• 1978

• Journal of the Institute of Electronics and Information Engineers
• /
• v.49 no.9
• /
• pp.287-292
• /
• 2012

In this paper, design of a conductivity detector using a synchronous demodulation is presented to detect the electric conductivity of liquids with low noise. For the purpose, the detector is constructed by the combination of a carrier generator, conductivity detecting cell, and synchronous demodulator. The signal-to-noise ratio(SNR) of the detector is improved by adjusting the frequency bandwidth of the demodulator, whereby infinitesimal conductivity signals can easily be measured under various noise environments. As an application example, a conductivity detector, which is applied to the air monitoring in a fabrication process of semiconductor chips, is designed using the synchronous demodulation. The validity of the design technique is verified by experiments. Since experimental results are shown to approach the design performance of the detector, the synchronous demodulation proves to be useful to the design of a conductivity detector for measuring the infinitesimal electric conductivity of liquids.

• Transactions of the Korean Society of Machine Tool Engineers
• /
• v.12 no.2
• /
• pp.44-52
• /
• 2003

This research suggests a cutting force model for the ball end milling processes. This model includes the effect of tool run out and tool deflection. In the proposed model, the flutes of ball end mills are considered as series of infinitesimal elements and each cutting edge is assumed to be straight for the analysis of the oblique cutting process, in which the small cutting edge element has been analyzed as an orthogonal cutting process n the plane including the cutting velocity and the chip-flow vector. Therefor, the cutting forces can be calculated through the model using the orthogonal cutting data obtained from the orthogonal cutting test. In order to enhance the performance of the model, the flutes of ball end mill are defined to keep geometric consistency at the peak of the ball part and the junction with the end mill part. The divided infinitesimal cutting edges are regulated to be even lengths. Some experiments show the validity of the developed model in the various cutting coalitions.