• Title/Summary/Keyword: Sum relation

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Teaching and Learning Models for Mathematics using Mathematica (I)

  • Kim, Hyang-Sook
    • Research in Mathematical Education
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    • v.7 no.2
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    • pp.101-117
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    • 2003
  • In this paper, we give examples of models we have created for use in university mathematics courses. We explain the concept of linear transformation, investigate the roles of each component of 2 ${\times}$ 2 and 3 ${\times}$ 3 transformation matrices, consider the relation between sound and trigonometry, visualize the Riemann sum, the volume of surfaces of revolution and the area of unit circle. This paper illustrates how one can use Mathematica to visualize abstract mathematical concepts, thus enabling students to understand mathematics problems effectively in class. Development of these kinds of teaching and learning models can stimulate the students' curiosity about mathematics and increase their interest.

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Licensing Contract between International Joint Venture Partners and Compensation Structure (국제합작투자에서 합작파트너 간 내부기술계약과 기술대가 지급방식 선택에 관한 연구)

  • Lee, Eung-Sok
    • Journal of Technology Innovation
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    • v.15 no.1
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    • pp.175-201
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    • 2007
  • Licensing contracts between partners in International Joint Ventures(IJV) have not only aspects of relation contract, which is interdependent and long-term cooperative relationships in interpartner but also aspects of discrete contract which is exposed to opportunistic risk caused by IJV partners who maximize individual profit instead of joint payoff maximization. In this circumstance, appropriate compensation structures such as lump-sum and royalty can reduce conflicts and spur interpartner cooperation. In addition, compensation structures that stipulate each party's rights, duties, and responsibilities under various sets of environmental conditions have strong implications for transaction cost minimization and joint payoff maximization. On the other hands, compensation structures such as lump-sum and royalty in IJV licensing contract have benefits and costs depending on IJV partners uncertainty, partner dependency, and environment uncertainty. Therefore, the purpose of this paper is to empirically show how partner uncertainty, partner dependence and environment uncertainty influence compensation structure chosen by licensor in IJV.

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IDENTITIES OF SYMMETRY FOR THE HIGHER ORDER q-BERNOULLI POLYNOMIALS

  • Son, Jin-Woo
    • Journal of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.1045-1073
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    • 2014
  • The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss's multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iterated Volkenborn integral, we derive serval identities of symmetry related to the q-extension power sums and the higher order q-Bernoulli polynomials. Many previous results are special cases of the results presented in this paper, including Tuenter's classical results on the symmetry relation between the power sum polynomials and the Bernoulli numbers in [A symmetry of power sum polynomials and Bernoulli numbers, Amer. Math. Monthly 108 (2001), no. 3, 258-261] and D. S. Kim's eight basic identities of symmetry in three variables related to the q-analogue power sums and the q-Bernoulli polynomials in [Identities of symmetry for q-Bernoulli polynomials, Comput. Math. Appl. 60 (2010), no. 8, 2350-2359].

Color Image Segmentation by statistical approach (확률적 방법을 통한 컬러 영상 분할)

  • Gang Seon-Do;Yu Heon-U;Jang Dong-Sik
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2006.05a
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    • pp.1677-1683
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    • 2006
  • Color image segmentation is useful for fast retrieval in large image database. For that purpose, new image segmentation technique based on the probability of pixel distribution in the image is proposed. Color image is first divided into R, G, and B channel images. Then, pixel distribution from each of channel image is extracted to select to which it is similar among the well known probabilistic distribution function-Weibull, Exponential, Beta, Gamma, Normal, and Uniform. We use sum of least square error to measure of the quality how well an image is fitted to distribution. That P.d.f has minimum score in relation to sum of square error is chosen. Next, each image is quantized into 4 gray levels by applying thresholds to the c.d.f of the selected distribution of each channel. Finally, three quantized images are combined into one color image to obtain final segmentation result. To show the validity of the proposed method, experiments on some images are performed.

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Microbiogenic Sediments In The Nagdong Estuary, Korea

  • Kim, Won Hyung;Park, Yong-Ahn
    • 한국해양학회지
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    • v.15 no.1
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    • pp.34-48
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    • 1980
  • The ostracode foraminifera microbiogenic sediments of the Nagdon Estuary, which is a deltaic, have been analysed. Twenty four species representing seventeen genera of ostracodes and some species representing twenty three genera of foraminifera are identified and counted. From these data their geographical distribution patterns aree obtained and biotopes are determined in relation to the sediment distribution and hydrological parameters. There are several tendencies in the distribution of ostracodes and foraminifera. Both ostracode and foraminiferall population increased seaward. The ratio of foraminiferal population to the sum of the ostracode and the foraminiferal population, as well as the ratio of calcareous foraminifera to the sum of calcareous and agglutinated foraminiferal population, also increased seaward. The biotopes can be divided into two. Biotope I is the innershore environment and Biotope II offshore environment.

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ON WEIGHTED BROWDER SPECTRUM

  • Dharmarha, Preeti;Kumari, Sarita
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.1
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    • pp.1-13
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    • 2022
  • The main aim of the article is to introduce new generalizations of Fredholm and Browder classes of spectra when the underlying Hilbert space is not necessarily separable and study their properties. To achieve the goal the notions of 𝛼-Browder operators, 𝛼-B-Fredholm operators, 𝛼-B-Browder operators and 𝛼-Drazin invertibility have been introduced. The relation of these classes of operators with their corresponding weighted spectra has been investigated. An equivalence of 𝛼-Drazin invertible operators with 𝛼-Browder operators and 𝛼-B-Browder operators has also been established. The weighted Browder spectrum of the sum of two bounded linear operators has been characterised in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces.

A study on The elderly과s decision-making and life-adjustment in the family Its Relatied Variables (노인의 가정내 의사결정과 생활적응 관련변인)

  • 지금수;김현지
    • Journal of Family Resource Management and Policy Review
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    • v.3 no.2
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    • pp.61-76
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    • 1999
  • The purpose of this study is to investigate the degree of influence on the elderly’s life adjustment and decision making in the family. For these research tasks the data were collected through interview. the respondents were 296 of man and woman elderly who lived in JeonJu. It was analyzed by various statistical methods such as Frequency, Percentile, ANOVA, correlate, t-test, Multiple Regression Analysis. The finding of this study are as follows; 1) Decision-making of the elderly in family had significant differences I the area of sex, the sum of monthly personal expenses, satisfaction level of personal expenses, subjective economic level and self-esteem in the order named. 2) Elderly life-adjustment had significant differences in the area of the residential district, the present job, the situation of a apouse, religion, education, the sum of the monthly personal expenses, health, satisfaction level of personal expenses, subjective economics level and self-esteem. 3) When we observe relationship with the elderly decision-making in family and life-adjustment, relation decision-making in family and life-adjustment appeared positively. 4) Decision-making of the elderly in family had the significant differences according to the variables such as sex, the sum of monthly personal expenses, and self-esteem in the order named, and the most influential factor among them was sex. 5) Elderly life-adjustment had the significant differences according to the variables such as self-esteem, decision-making, religion, health, the sum of the monthly personal expenses, the residential district in the order named. The most influential factor was self-esteem and the explanary of those variables for the elderly life-adjustment was 55.1%.

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SYMMETRY PROPERTIES FOR A UNIFIED CLASS OF POLYNOMIALS ATTACHED TO χ

  • Gaboury, S.;Tremblay, R.;Fugere, J.
    • Journal of applied mathematics & informatics
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    • v.31 no.1_2
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    • pp.119-130
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    • 2013
  • In this paper, we obtain some generalized symmetry identities involving a unified class of polynomials related to the generalized Bernoulli, Euler and Genocchi polynomials of higher-order attached to a Dirichlet character. In particular, we prove a relation between a generalized X version of the power sum polynomials and this unified class of polynomials.

Transitivity and cognitive interpretations (전이성과 인지적 이해)

  • Huh, Jong-Hoi
    • English Language & Literature Teaching
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    • v.11 no.1
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    • pp.245-260
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    • 2005
  • Various kinds of cognitive aspects must be inclusively considered for understanding to transitivity. Basically, transitivity is not a notion of pure lexical items, pure syntactic dimensions and only semantic interpretation. That is, transitivity is affected by the extralinguistic phenomena which contain speakers psychological and cognitive interpretations. It is based on human cognitive abilities to interpret the exact meaning of language expressions. To sum up, transitivity has a relation with the observer's (speaker's) cognitive interpretation within the entire contexts.

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Implementation of Pronoun Readings in English: A Categorial Grammar Approach.

  • Lee, Yong-Hun
    • Korean Journal of English Language and Linguistics
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    • v.1 no.4
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    • pp.609-627
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    • 2001
  • Pronouns are frequently used in English, and their resolution is important to capture meaning of sentences. This paper provides a computational implementation for pronoun readings in English, based on Chierchia's (1988) Binding Theory in Categorial Grammar. A CCG-like system is newly devised for implementing his ideas, where syntactic phenomena are represented by the functor-argument relations of categories. This relation triggers resolution algorithms, and reflexives and pronominals are resolved succinctly. In sum, this paper gives an efficient resolution algorithm for English pronouns within Categorial Grammar.

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