• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.605-616
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• 2003

In this paper, some rank equalities related to generalized inverses $A^{(2)}_{T,S}$ of a matrix are presented. As applications, a variety of rank equalities related to the M-P inverse, the Drazin inverse, the group inverse, the weighted M-P inverse, the Bott-Duffin inverse and the generalized Bott-Duffin inverse are established.

• East Asian mathematical journal
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• v.28 no.2
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• pp.197-213
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• 2012

In this paper we study Soltan & Meidman's method that is able to be used in mathematical discovery. We analyze Soltan & Meidman's book "Tozdestva i Neravenstva v Treugolike" that is published in Moldova Republic. In this work we formulate Soltan & Meidman's method related with discovery of triangle's various equalities, and use the method to discovery mathematical equalities. As a result we suggest some new mathematical equalities related with triangle's sides and its proof.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.151.1-151
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• 2001

This paper establishes some integral equalities formulated by zeros located in the convergence region of Laplace transformable function. Using the definition of Laplace transform, it is shown that time-domain integral equalities have to be satisfied by the function, and those can be applied to understanding of the fundamental limitations of the control system represented by the transfer function, which has been Laplace transform. In the unity-feedback control scheme, another integral equality is also derived on the output response of the system with open-loop poles and zeros located in the convergence region.

• International Journal of Control, Automation, and Systems
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• v.1 no.1
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• pp.76-82
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• 2003

This paper establishes some integral equalities formulated by zeros located in the convergence region of a Laplace transformable function. Using the definition of the Laplace transform, it shows that Laplace transformable functions have to satisfy the integral equalities in the time-domain, which can be applied to the understanding of the fundamental limitations on the control system represented by the transfer function. In the unity-feedback control scheme, another integral equality is derived on the output response of the system with open-loop poles located in the convergence region of the output function. From these integral equalities, two sufficient conditions related to undershoot and overshoot phenomena in the step response, respectively, are investigated.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.915-922
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• 2013

In this paper, we investigate some properties of 2-norm midpoints and 2-normed equalities in 2-normed spaces.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.583-599
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• 2016

In this paper, aspects of equalities with monomial left-hand side presented in Korean elementary school mathematics textbooks are analyzed focusing on the component of expressions. According to this analysis, the textbooks deal with equalities with monomial left-hand side as though the students already know them, rather than to introduce and deal with them systematically. In this paper, the following four suggestions based on this analysis are proposed as conclusions. First, A-type equalities (with one kinds of calculation symbols and two or more numbers, variables, denominative numbers in the right-hans side) and B-type equalities (with two or more kinds of calculation symbols and two or more numbers, variables, denominative numbers in the right-hans side) may need to be introduced by the explicit description. Second, it is necessary to establish clearly the order of dealing with numeric expressions, expressions with ${\Box}$(blank) expression, expressions with words, expressions with ${\Box}$(variable), expressions with variables. Third, it needs to be noted that equalities with monomial left-hand side cab be used with a variety of meanings. Fourth, it is necessary to widen the range of the number constituting equalities with monomial left-hand side to the natural number 0 and as well as fractions, decimals.

• Communications of Mathematical Education
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• v.22 no.1
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• pp.53-63
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• 2008

In this paper we study a new proof method of equalities and inequalities using moment of inertia. We analyze proof method using moment of inertia, and describe how to prove equalities and inequalities using moment of inertia.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.1059-1078
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• 2009

In this paper we study metric equalities related with distance between excenter and other points of triangle. Especially we find metric equalities between excenter and incenter, circumcenter, center of mass, orthocenter, vertex, prove these formulas, and transform these formulas into new formula containing another elements of triangle. We in detail describe proof process of these equalities, indicate references of some formulas that don't exist within secondary school curriculum.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.887-898
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• 2011

In this paper, we first discuss the convergence of the continued fractions of generalized Rogers-Ramanujan type in the modified sense. Then we prove several equalities concerning these continued fractions. The proofs of our main results are mainly based on the Bauer-Muir transformation.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.193-209
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• 2021

In this research, we offer two new quantum integral equalities for recently defined qε2-integral and derivative, the derived equalities then used to prove quantum integral inequalities of Simpson's and Newton's type for preinvex functions. We also considered the special cases of established results and offer several new and existing results inside the literature of Simpson's and Newton's type inequalities.