• Honam Mathematical Journal
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• v.27 no.4
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• pp.641-647
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• 2005

This note is a verification on the relations between multiplicative and almost multiplicative linear maps; and the continuity of almost multiplicative linear maps.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.849-866
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• 2024

In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.641-649
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• 2016

A linear functional T on a $Fr{\acute{e}}echet$ algebra (A, (pn)) is called almost multiplicative with respect to the sequence ($p_n$), if there exists ${\varepsilon}{\geq}0$ such that ${\mid}Tab-TaTb{\mid}{\leq}{\varepsilon}p_n(a)p_n(b)$ for all $n{\in}\mathbb{N}$ and for every $a,b{\in}A$. We show that an almost multiplicative linear functional on a $Fr{\acute{e}}echet$ algebra is either multiplicative or it is continuous, and hence every almost multiplicative linear functional on a functionally continuous $Fr{\acute{e}}echet$ algebra is continuous.

• Education of Primary School Mathematics
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• v.8 no.1
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• pp.33-50
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• 2004

This study is intended to investigate the effect on the development of multiplicative thinking and multiplicative ability by teaching repeated addition, rate, comparison, area-array, and combination problems. Two research questions are established: first, is there any difference of multiplicative thinking between the experimental group(the modeling of problem situation learning group) and the control group(the traditional learning group)\ulcorner Second, is there any difference of multiplicative ability between the experimental group and the control group\ulcorner The treatment process for the experimental group is based on modeling problem situations for nine lesson periods. In order to answer the research questions the chi-square analysis was used for the first research question and the t-test was used for the second one. The findings are summarized as follows: there is no significant difference of multiplicative thinking be1ween the experimental and the control group but there is significant difference of multiplicative ability.

• Communications of Mathematical Education
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• v.20 no.3 s.27
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• pp.443-467
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• 2006

The purpose of this study was to study the 2nd grade elementary students' common thinking and differences of additive and multiplicative thinking. For meaningful discussion of the above, we have established the following research questions. 1. What are the properties of the multiplicative thinking of 2nd grade elementary students? - What are the common properties of the multiplicative thinking of 2nd grade elementary students? - What are the properties of the various multiplicative thinking levels? 2. How is multiplicative thinking presented in Korean math textbooks? The conclusions of this study were followings: First, the 2nd grade elementary students in the multiplicative thinking learnt used by translating multiplication into specific situations. And they often used different models of multiplication. Second, additive thinking developed into the multiplicative thinking. After being helped by their teachers, students who thought additively were then able to think multiplicatively. Whereas after being helped by their teachers, students who were already competent at multiplicative thinking gained a deeper understanding. Third, they learned the commutative property of multiplication after their understanding of the 'repeated addition approach' and the multiplicative approach was sufficiently reinforced. Last, students should be taught using different models based on the repeated addition approach.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.1-7
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• 2022

A mapping T : R → R (not necessarily additive) is called multiplicative left 𝛼-centralizer if T(xy) = T(x)𝛼(y) for all x, y ∈ R. A mapping F : R → R (not necessarily additive) is called multiplicative (generalized)(𝛼, 𝛽)-derivation if there exists a map (neither necessarily additive nor derivation) f : R → R such that F(xy) = F(x)𝛼(y) + 𝛽(x)f(y) for all x, y ∈ R, where 𝛼 and 𝛽 are automorphisms on R. The main purpose of this paper is to study some algebraic identities with multiplicative (generalized) (𝛼, 𝛽)-derivations and multiplicative left 𝛼-centralizer on the left ideal of a prime ring R.

• ETRI Journal
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• v.18 no.3
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• pp.147-160
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• 1996

We investigate noise-induced phase transitions in globally coupled active rotators with multiplicative and additive noises. In the system there are four phases, stationary one-cluster, stationary two-cluster, moving one-cluster, and moving two-cluster phases. It is shown that multiplicative noise induces a bifurcation from one-cluster phase to two-cluster phase. Pinning force also induces a bifurcation from moving phase to stationary phase suppressing the multiplicative noise effect. Additive noise reduces both effects of multiplicative noise and pinning force urging the system to the stationary one-cluster phase. The frustrated effects of pinning force and additive and multiplicative noises lead to a reentrant transition at intermediate additive noise intensity. Nature of the transition is also discussed.

• Water for future
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• v.22 no.3
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• pp.331-339
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• 1989

The monthly flows with periodicity and trend were forecasted by multiplicative ARIMA model and then the applicability of the model was tested based on 23 years of the historical monthly flow data at Jindong river stage gauging station in the Nakdong River Basin. The parameter estimation was made with 21 years of data and the remaining two years of monthly data were used to compare the forecasted flows by ARIMA (2,0,0)$\times$$(0,1,1)_{12}$ with the observed. The results of forecast showed a good agreement with the observed, implying the applicability of multiplicative ARIMA model for forecasting monthly river flows at the Jindong site.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.1-5
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• 2004

A multiplicative plane partition is a two-dimensional array of positive integers larger than 1 that are nonincreasing both from left to right and top to bottom and whose multiple is a given number n. For a natural number n, let $f_2(n)$ be the number of multiplicative plane partitions of n. In this paper, we prove $f_2(n)\;{\leq}\;n^2$ and a table of them up to $10^5$ is provided.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.201-210
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• 2012

A modified multiplicative update algorithms is presented for computing the nearest correlation matrix. The convergence property is analyzed in details and a sufficient condition is given to guarantee that the proposed approach will not breakdown. A number of numerical experiments show that the modified multiplicative updating algorithm is efficient, and comparable with the existing algorithms.