• Title/Summary/Keyword: Basic Theory

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Basic Results in the Theory of Hybrid Casual Nonlinear Differential Equations

  • DHAGE, BAPURAO CHANDRABHAN
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.1069-1088
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    • 2015
  • In this paper, some basic results concerning the existence, strict and nonstrict inequalities and existence of the maximal and minimal solutions are proved for a hybrid causal differential equation. Our results generalize some basic results of Leela and Laksh-mikantham [13] and Dhage and Lakshmikantham [10] respectively for the nonlinear first order classical and hybrid differential equations.

INTUITIONISTIC FUZZY NORMAL SUBGROUPS AND INTUITIONISTIC FUZZY COSETS

  • HUR, KUL;JANG, SU YEON;KANG, HEE WON
    • Honam Mathematical Journal
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    • v.26 no.4
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    • pp.559-587
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    • 2004
  • We study some properties of intuitionistic fuzzy normal subgroups of a group. In particular, we obtain two characterizations of intuitionistic fuzzy normal subgroups. Moreover, we introduce the concept of an intuitionistic fuzzy coset and obtain several results which are analogous of some basic theorems of group theory.

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Designing Instruction to Facilitate the Understanding of the Functional Concept: Based on the Situated Learning Theory (함수개념의 이해 촉진을 위한 수업 설계: 상황학습이론을 중심으로)

  • 최정임;허혜자
    • School Mathematics
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    • v.3 no.2
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    • pp.373-399
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    • 2001
  • The function is a basic and key concept to understand mathematical problems. However, many students have difficulties to expand the knowledge to other related concepts and to transfer the knowledge to real world problems. The reasons for the problem may be that the concept of function is taught by simplified and abstracted formula without fully understanding of the reasoning process. Also, the examples for the concepts are artificial and not related to students' experiences. Situated learning theory provides great implications to solve these problems. So, this study was designed to teach the concept of function more meaningful to students by appling situated learning theory. Thirty-eight middle school students were participated in this study. Students were provided the instruction designed according to the principles of situated learning theory. Then, they were asked to complete attitude survey questionnair and a performance assessment task. The result showed that the instruction based on situated learning theory was useful to Promote students' understanding and motivation for learning. More implications of the study was provided in the paper.

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Application of information theory to wireless cooperative communications (정보이론의 협력무선통신에의 응용)

  • Kim, Yoon-Hyun;Yang, Jae-Soo;Ha, Kwang-Jun;Kim, Jin-Young
    • 한국정보통신설비학회:학술대회논문집
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    • 2009.08a
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    • pp.337-343
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    • 2009
  • Information theory is one field of the applied mathematics quantitating the data in order to store data as many as in the medium or communicate through channel. it was released on the Shannon's paper, in 1948. With basis on this paper, It has been achieved dramatically development for communication, signal processing, and date procedure and transmission in the network In this paper, the basic concept of information theory is described through dealing with contents about meaning of information, entropy, and channel capacity. It is also handled how information theory is applied to the fields of sensor network, relay channel, MIMO system, and others.

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Thermoelastic damping in generalized simply supported piezo-thermo-elastic nanobeam

  • Kaur, Iqbal;Lata, Parveen;Singh, Kulvinder
    • Structural Engineering and Mechanics
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    • v.81 no.1
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    • pp.29-37
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    • 2022
  • The present paper deals with the application of one dimensional piezoelectric materials in particular piezo-thermoelastic nanobeam. The generalized piezo-thermo-elastic theory with two temperature and Euler Bernoulli theory with small scale effects using nonlocal Eringen's theory have been used to form the mathematical model. The ends of nanobeam are considered to be simply supported and at a constant temperature. The mathematical model so formed is solved to obtain the non-dimensional expressions for lateral deflection, electric potential, thermal moment, thermoelastic damping and frequency shift. Effect of frequency and nonlocal parameter on the lateral deflection, electric potential, thermal moment with generalized piezothermoelastic theory are represented graphically using the MATLAB software. Comparisons are made with the different theories of thermoelasticity.