• 대한수학회보
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• 제34권1호
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• pp.9-17
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• 1997

Define $\bar{g}{\upsilon, \omega) = -\upsilon_1\omega_1 + \cdots + \upsilon_n\omega_n$ for $\upsilon, \omega in R^n$. $R^n$ together with this metric is called the Lorentzian n-space, denoted by $L^n$, and $R^n$ together with the Euclidean metric is called the Euclidean n-space, denoted by $E^n$. A Lorentzian surface in $L^n$ means an orientable connected 2-dimensional Lorentzian submanifold of $L^n$ equipped with the induced Lorentzian metrix g from $\bar{g}$.

• 대한수학회지
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• 제45권1호
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• pp.41-61
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• 2008

We study Lorentzian surfaces with the constant Gaussian curvatures or the constant mean curvatures in the 3-dimensional Lorentzian space and their transformations. Such surfaces are associated to the Lorentzian Grassmannian systems and some transformations on such surfaces are given by dressing actions on those systems.

• 호남수학학술지
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• 제31권2호
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• pp.177-183
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• 2009

In this article, we study ruled surfaces in a Lorentzian space-time, which have finite type immersion. We give a condition for bi-finite type surfaces to be of finite type.

• 대한수학회지
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• 제43권6호
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• pp.1339-1355
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• 2006

This paper develops in detail the differential geometry of ruled surfaces from two perspectives, and presents the underlying relations which unite them. Both scalar and dual curvature functions which define the shape of a ruled surface are derived. Explicit formulas are presented for the computation of these functions in both formulations of the differential geometry of ruled surfaces. Also presented is a detailed analysis of the ruled surface which characterizes the shape of a general ruled surface in the same way that osculating circle characterizes locally the shape of a non-null Lorentzian curve.

• Progress in Superconductivity
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• 제9권2호
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• pp.146-151
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• 2008

Measurements of surface resistance ($R_s$) of high temperature superconductor (HTS) films with accuracy are essential for microwave applications of HTS materials. In using the dielectric resonator method, uncertainties in the unloaded quality factor of the resonator cause significant errors in the measured $R_s$ of HTS films. We compare the Rs values of $YBa_2Cu_3O_{7-{\delta}}$ films calculated from the $Q_0$ as determined from the Lorentzian fit with that from the $Q_0$ as determined from the S-parameter circle-fit at temperatures between 15 K and 77 K. The two sets of values appeared to differ by 5%, 7%, 6%, and 11% at temperatures of 15, 60, 70, and 77 K, respectively, from each other, implying that careful error analysis needs to be performed in obtaining the $R_s$ of HTS films by using the Lorentzian-fit method, with the ones determined from the S-parameter circle-fit used as the reference.

• Progress in Superconductivity
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• 제8권2호
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• pp.143-151
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• 2007

Accurate measurements of the microwave surface resistance (Rs) of high temperature superconductor (HTS) films are important with regard to applications of HTS materials for wireless communications. As the surface resistance values of HTS films are usually extracted from the measured unloaded quality factor ($Q_0$) of resonators made of HTS films, it is essential to measure the resonator $Q_0$ with accuracy. The $TE_{011}\;mode\;Q_0$ of sapphire resonators with the endplates made of $YBa_2Cu_3O_{7-{\delta}}$(YBCO) film on $LaAlO_3$ is measured by using the S-parameter circle-fit method at a frequency of about 19.6 GHz and temperatures of 30 K to 90 K, which is compared with the measured values by using the Lorentzian-fit method. Good agreements are found between the two sets of $Q_0$ values measured by using the two different methods whether the resonator is used in a weak-coupling scheme or a strong-coupling scheme, showing reliability of both methods fur measuring the resonator $Q_0$ accurately. The $Q_0$ of sapphire resonators with a gap between the top plate and the rest of the resonator is also discussed.

• 대한수학회보
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• 제50권2호
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• pp.441-444
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• 2013

It is shown that any two-dimensional globally hyperbolic spacetime with noncompact Cauchy surfaces has no null cut points.

• 대한수학회보
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• 제60권5호
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• pp.1265-1280
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• 2023

The aim of this paper is to investigate Betchov-Da Rios equation by using null Cartan, pseudo null and partially null curve in Minkowski spacetime. Time derivative formulas of frame of s parameter null Cartan, pseudo null and partially null curve are examined, respectively. By using the obtained derivative formulas, new results are given about the solution of Betchov-Da Rios equation. The differential geometric properties of these solutions are obtained with respect to Lorentzian causal character of s parameter curve. For a solution of Betchov-Da Rios equation, it is seen that null Cartan s parameter curves are space curves in three-dimensional Minkowski space. Then all points of the soliton surface are flat points of the surface for null Cartan and partially null curve. Thus, it is seen from the results obtained that there is no surface corresponding to the solution of Betchov-Da Rios equation by using the pseudo null s parameter curve.

• Carbon letters
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• 제8권4호
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• pp.292-298
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• 2007

In order to investigate functional groups on the surface of Multi-walled Carbon Nanotubes (MWCNTs) induced by oxyfluorination, XPS (X-ray photoelectron spectroscopy) analysis was carried out. All core level spectra of MWCNTs were deconvoluted to several Pseudo-Voigt functions (sum of Gaussian-Lorentzian functions). Both O1s and F1s binding energy of oxyfluorinated MWCNTs shifted high value as increment of fluorine mixing ratio. The carbon-fluorine covalent bonding concentration increased as increment of fluorine mixing ratio. The shape and intensity of OF10-MWCNTs are similar with those of as-received MWCNTs. However, the intensity and binding energies of main peak position of OF20-MWCNTs and OF30-MWCNTs were dramatically increased by oxyfluorination.

• 호남수학학술지
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• 제44권2호
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• pp.259-270
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• 2022

This paper is devoted to the geometry of vector fields and timelike flows in terms of anholonomic coordinates in three dimensional Lorentzian space. We discuss eight parameters which are related by three partial differential equations. Then, it is seen that the curl of tangent vector field does not include any component in the direction of principal normal vector field. This implies the existence of a surface which contains both s - lines and b - lines. Moreover, we examine a normal congruence of timelike surfaces containing the s - lines and b - lines. Considering the compatibility conditions, we obtain the Gauss-Mainardi-Codazzi equations for this normal congruence of timelike surfaces in the case of the abnormality of normal vector field is zero. Intrinsic geometric properties of these normal congruence of timelike surfaces are obtained. We have dealt with important results on these geometric properties.