• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1992.04a
• /
• pp.279-284
• /
• 1992

This paper presents the theoretical development and qualitiative evaluation of a new concept in the mathematical modeling of dynamicstructures. We use both test data and analytical approximations to identify the parameters of an incomplete model. The model has the capability of prodicting the response of the points of interest on the structure over the frequency range of interest and can be used to predict the changes in natural frequencies and normal modes due to structural changes. The theory was tested by running simulated tests on a relatively simple structure, identifying the parameters of the incomplete model, and using this model to predict the effects on frequency and mode shapes of several mass and stiffness changes. The conditions of the test were varied by selecting different numbers of points of meansurement, varying the frequency range, and by including assumed measurement error. It is recommended that the theroetical development be continued and that applications to more complex structures be carried out in order todevelop a better understanding of the limitations and capabilites of the method. A successful, more definitive evaluation could lead to immediate practical applications.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1177-1194
• /
• 2009

In this paper we establish the general solution of the functional equation f(2x+y)+f(x-2y)=2f(x+y)+2f(x-y)+f(-x)+f(-y) and investigate the Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1293-1305
• /
• 2009

Molodtsov [D. Molodtsov, Soft set theory First results, Comput. Math. Appl. 37 (1999) 19-31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of BCC-algebras. The notion of (trivial, whole) soft BCC-algebras and soft BCC-subalgebras are introduced, and several examples are provided. Relations between a fuzzy subalgebra and a soft BCC-algebra are given, and the characterization of soft BCC-algebras is established.

• Korean Journal of Mathematics
• /
• v.19 no.4
• /
• pp.343-349
• /
• 2011

Let D be an integral domain, $D^w$ be the $w$-integral closure of D, X be an indeterminate over D, and $N_v=\{f{\in}D[X]{\mid}c(f)_v=D\}$. In this paper, we introduce the concept of $t$-locally APVD. We show that D is a $t$-locally APVD and a UMT-domain if and only if D is a $t$-locally APVD and $D^w$ is a $PvMD$, if and only if D[X] is a $t$-locally APVD, if and only if $D[X]_{N_v}$ is a locally APVD.

• Korean Journal of Mathematics
• /
• v.21 no.4
• /
• pp.421-428
• /
• 2013

We observe the basic structure of the products of coefficients of nilpotent (left) polynomials in skew polynomial rings. This study consists of a process to extend a well-known result for semi-Armendariz rings. We introduce the concept of ${\alpha}$-skew n-semi-Armendariz ring, where ${\alpha}$ is a ring endomorphism. We prove that a ring R is ${\alpha}$-rigid if and only if the n by n upper triangular matrix ring over R is $\bar{\alpha}$-skew n-semi-Armendariz. This result are applicable to several known results.

• Korean Journal of Mathematics
• /
• v.21 no.4
• /
• pp.401-419
• /
• 2013

Let $n{\geq}0$ be an arbitrary integer. We define the class of almost n-simply presented abelian p-groups. It naturally strengthens all the notions of almost simply presented groups introduced by Hill and Ullery in Czechoslovak Math. J. (1996), n-simply presented p-groups defined by the present author and Keef in Houston J. Math. (2012), and almost ${\omega}_1-p^{{\omega}+n}$-projective groups developed by the same author in an upcoming publication [3]. Some comprehensive characterizations of the new concept are established such as Nunke-esque results as well as results on direct summands and ${\omega}_1$-bijections.

• Kyungpook Mathematical Journal
• /
• v.54 no.4
• /
• pp.629-638
• /
• 2014

The concept of prime and weakly prime ideal in semigroups has been introduced by G. Szasz [4]. In this paper, we define the involution in po-${\Gamma}$-semigroups, then we extend some results on prime, semiprime and weakly prime ideals to the involution po-${\Gamma}$-semigroup S. Also, we characterize intra-regular involution po-${\Gamma}$-semigroups. We establish that in the involution po-${\Gamma}$-semigroup S such that the involution preserves the order, an ideal of S is prime if and only if it is both weakly prime and semiprime and if S is commutative, then the prime and weakly prime ideals of S coincide. Finally, we prove that if S is a po-${\Gamma}$-semigroup with order preserving involution, then the ideals of S are prime if and only if S is intra-regular.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.7 no.1
• /
• pp.34-40
• /
• 2007

Balasubramaniam and Muralisankar (2004) proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equations with nonlocal initial condition. Park et al. (2006) found the sufficient condition of this system. Recently, Kwun et al. (2006) proved the existence and uniqueness of solutions for the semilinear fuzzy integrodifferential equations with nonlocal initial conditions and forcing term with memory in $E_N$. In this paper, we study the controllability for this system by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_N$.

• Journal for History of Mathematics
• /
• v.17 no.3
• /
• pp.1-12
• /
• 2004

In the Analysis, there have been many cases of confusion on topological structure and uniform structure because they were dealt in metric spaces. The concept of metric spaces is generalized into that of topological spaces but its uniform aspect was much later generalized into the uniform structure by A. Weil. We first investigate Weil's life and his mathematical achievement and then study the history of the uniform structure and its development.

• Journal for History of Mathematics
• /
• v.17 no.3
• /
• pp.23-32
• /
• 2004

In this paper, Ive investigated algebraic concepts which are contained in Euclid's Elements. In the Books II, V, and VII∼X of Elements, there are concepts of quadratic equation, ratio, irrational numbers, and so on. We also analyzed them for mathematical meaning with modem symbols and terms. From this, we can find the essence of the genesis of algebra, and the implications for students' mathematization through the experience of the situation where mathematics was made at first.