• Journal for History of Mathematics
• /
• v.21 no.1
• /
• pp.79-96
• /
• 2008

In early 21st century, universities in Korea has been asked the new roles according to the changes of educational and social environment. With Korea's NURI and Brain Korea 21 project support, some chosen research oriented universities now should produce "teacher of teachers". We look 100 years back America's mathematics and see many resemblances between the status of US mathematics at that time and the current status of Korean mathematics, and find some answer for that. E. H. Moore had produced many good research mathematicians through his laboratory teaching techniques. R. L. Moore was his third PhD students. He developed his Texas/Moore method. In this article, we analyze what R. L. Moore had done through his American School of Topology and Moore method. We consider the meaning that early University of Texas case gives us in PBL(Problem Based Learning) process.

• Journal of the Korean Mathematical Society
• /
• v.50 no.6
• /
• pp.1349-1367
• /
• 2013

The weighted Moore-Penrose inverse will be introduced and studied in the context of Banach algebras. In addition, weighted EP Banach algebra elements will be characterized. The Banach space operator case will be also considered.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.1
• /
• pp.137-150
• /
• 2016

We introduce a new approach that allows us to solve, algorithmically, the contractive completion problem. In this article, we provide concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size $4{\times}4$ using a Moore-Penrose inverse of a matrix.

• Journal for History of Mathematics
• /
• v.20 no.3
• /
• pp.127-146
• /
• 2007

From 1876 to 1883, British mathematician James Joseph Sylvester worked as the founding head of Mathematics Department at the Johns Hopkins University which has been known as America's first school of mathematical research. Sylvester established the American Journal of Mathematics, the first sustained mathematics research journal in the United States. It is natural that we think this is the most exciting and important period in American mathematics. But we found out that the International Congress of Mathematicians held at the World's Columbian Exposition in Chicago, August 21-26, 1893 was the real turning point in American's dedication to mathematical research. The University of Chicago was founded in 1890 by the American Baptist Education Society and John D. Rockefeller. The founding head of mathematics department Eliakim Hastings Moore was the one who produced many excellent American mathematics Ph.D's in early stage. Many of Moore's students contributed to build up real American mathematics research power in early 20 century The University also has a well-deserved reputation as the "teacher of teachers". Beginning with Sylvester, we analyze what E.H. Moore had done as a teacher and a head of the new department that produced many mathematical talents such as L.E. Dickson(1896), H. Slaught(1898), O. Veblen(1903), R.L. Moore(1905), G.D. Birkhoff(1907), T.H. Hilderbrants(1910), E.W. Chittenden(1912) who made the history of American mathematics. In this article, we study how Moore's vision, new system and new way of teaching influenced American mathematical society at early stage of the top class mathematical research. and the meaning that early University of Chicago case gave.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1051-1063
• /
• 2018

The real moment-angle complex (or, more generally, real polyhedral product) and its real toric space have recently attracted much attention in toric topology. The aim of this paper is to give two interesting remarks regarding real polyhedral products and real toric spaces. That is, we first show that Moore's conjecture holds to be true for certain real polyhedral products. In general, real polyhedral products show some drastic difference between the rational and torsion homotopy groups. Our result shows that at least in terms of the homotopy exponent at a prime this is not the case for real polyhedral products associated to a simplicial complex whose minimal missing faces are all k-simplices with $k{\geq}2$. Moreover, we also show a structural theorem for a finite group G acting simplicially on the real toric space. In other words, we show that G always contains an element of order 2, and so the order of G should be even.

• Ocean Systems Engineering
• /
• v.13 no.2
• /
• pp.123-146
• /
• 2023

In this paper, Moore-Gibson-Thompson theory of thermoelasticity is considered to investigate the fundamental solution and vibration of plane wave in an isotropic photothermoelastic solid. The governing equations are made dimensionless for further investigation. The dimensionless equations are expressed in terms of elementary functions by assuming time harmonic variation of the field variables (displacement, temperature distribution and carrier density distribution). Fundamental solutions are constructed for the system of equations for steady oscillation. Also some preliminary properties of the solution are explored. In the second part, the vibration of plane waves are examined by expressing the governing equation for two dimensional case. It is found that for the non-trivial solution of the equation yield that there exist three longitudinal waves which advance with the distinct speed, and one transverse wave which is free from thermal and carrier density response. The impact of various models (i)Moore-Gibson-Thomson thermoelastic (MGTE)(2019), (ii) Lord and Shulman's (LS)(1967) , (iii) Green and Naghdi type-II(GN-II)(1993) and (iv) Green and Naghdi type-III(GN-III)(1992) on the attributes of waves i.e., phase velocity, attenuation coefficient, specific loss and penetration depth are elaborated by plotting various figures of physical quantities. Various particular cases of interest are also deduced from the present investigations. The results obtained can be used to delineate various semiconductor elements during the coupled thermal, plasma and elastic wave and also find the application in the material and engineering sciences.

• The Bulletin of The Korean Astronomical Society
• /
• v.39 no.2
• /
• pp.82-82
• /
• 2014

One of the subjects in clouds' structure and development is small scale structure of interstellar cloud. The possibility of AU scale structure (Marscher et al. 1993; Moore & Marscher 1995; Roy et al. 2012) is discussed, and this small scale structure is considered as the result of hydrogen volume density (Moore & Marscher 1995), or small-scale chemical and other inhomogeneities (Liszt & Lucas 2000). In order to study this subject with emission line, extremely high resolution is mandatory by VLBI system. However, the alternative method could be observing the absorption line of interstellar cloud on the continuum object. In this case, the resolution would be restricted to the size of the continuum object, if the size of the object is smaller than the resolution of a used telescope. We observed the previous researchers' three objects (BLLAC, NRAO150, B0528+138), whose spectrums are changed from 1993 to 1998 (Liszt & Lucas 2000), with KVN. Through KVN observation, we found the changes of optical depth spectrum compared with the previous spectrums. We will discuss the optical depth spectrum variation by time variation and the meaning of it.

• Archives of Craniofacial Surgery
• /
• v.21 no.2
• /
• pp.106-108
• /
• 2020

Premature fusion of one or other of the minor sutures can subtly influence the shape of the human skull. Although infrequently reported or not clinically recognized, it can such contribute to a variety of craniofacial dysmorphisms. We herein report a case of late presenting, isolated bilateral synostosis of the squamosal suture dysmorphologies whose presentation mimics aspects of sagittal synostosis.

• Bulletin of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.171-174
• /
• 1988

Let M be an n-dimensional compact connected and oriented Riemannian manifold isometrically immersed in an (n+2)-dimensional Euclidean space $R^{n+2}$. Moore [5] proved that if M is of positive curvature, then M is a homotopy sphere. This result is generalized by Baldin and Mercuri [2], Baik and Shin [1] to the case of non-negative curvature, which is stated as follows: If M of non-negative curvature, then M is either a homotopy sphere or diffeomorphic to a product of two spheres. In particular, if there is a point at which the curvature operator is positive, then M is homeomorphic to a sphere.e.

• Journal of the Korean Mathematical Society
• /
• v.48 no.1
• /
• pp.33-48
• /
• 2011

The notion of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,s)}$ of type s, whose nonzero elements are generalized Fibonacci numbers, is introduced in the paper [23]. Regular case s = 0 is investigated in [23]. In the present article we consider singular case s = -1. Pseudoinverse of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,-1)}$ is derived. Correlations between the matrix $\mathcal{F}_n^{(a,b,-1)}$ and the Pascal matrices are considered. Some combinatorial identities involving generalized Fibonacci numbers are derived. A class of test matrices for computing the Moore-Penrose inverse is presented in the last section.