• Title/Summary/Keyword: Reciprocal theorem

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Analysis of a Panel Contribution of a Vehicle Compartment Using the Acoustic Reciprocal Theorem (음향 상호성 이론을 이용한 승용차 차실 판넬의 기여도 해석)

  • Kim, M.G.;Park, T.W.;Lee, S.H.
    • Transactions of the Korean Society of Automotive Engineers
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    • v.2 no.2
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    • pp.59-72
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    • 1994
  • For a panel contribution of the passenger vehicle compartment, a model was created for acoustic analysis of the passenger vehicle compartment and through the acoustic normal modal analysis, frequencies and mode shapes of the resonance modes were calculated. Also, the contribution analysis of each panel was executed using acoustic reciprocal theorem, and through this analysis, normalized responses at the particular point indicate the relative contribution of each panel for generating noise and vibration

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3-Dimensional Elastic-Plastic Contact Analysis Considering Subsurface Plastic Strain in a Half-Space (반무한체 표면아래의 소성변형을 고려한 3차원 탄소성 접촉해석)

  • Cho, Yong-Joo;Moon, Kil-Hwan;Lee, Sang-Don
    • Tribology and Lubricants
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    • v.24 no.2
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    • pp.90-95
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    • 2008
  • An elastic-plastic contact analysis is developed using a semi-analytical method. The elastic contact is solved within a Hertz theorem. The reciprocal theorem with initial strains is then introduced, to express the surface geometry as a function of contact stress and plastic strains. The irreversible nature of plasticity leads to an incremental formulation of the elastic-plastic contact problem, and an algorithm to solve this problem is set up. Closed form expression, which give residual stresses and surface displacements from plastic strains, are obtained by integration of the reciprocal theorem. The distribution of contact stress, residual stress and plastic strain are obtained by the changed surface geometry.

The Optical Novelty Filter Using a Self-pumped Phase Conjugator and LCTV (자기펌핑 위상공액경과 액정TV를 이용한 Novelty 필터)

  • 문영훈;이권윤;백남식;박한규
    • Journal of the Korean Institute of Telematics and Electronics A
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    • v.29A no.4
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    • pp.14-21
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    • 1992
  • An optical novelty filter is implemented using photorefractive materal(BaTiO$_{3}$) as a recording materal and commercial liquid crystal TV as a spatial light polarization modulator. If a signal beam incident at the proper, the loop and the crossing angle inside th e crystal is formed to get maximum diffraction efficiency and BaTiO$_{3}$ as a self-pumped phase conjugation mirror show that phase conjugate reflectivity was 20 times as much as ordinary polarization if signal beam is extraordinary. In this paper, the stoke's theorem which is a reciprocal theorem for which is a reciprocal theorem for beam path is experimentally proved, and good output images were obtained with optical experiment of novelty filter which is formed by use of Michelson interferometer.

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ON THE STABILITY OF RECIPROCAL-NEGATIVE FERMAT'S EQUATION IN QUASI-β-NORMED SPACES

  • Kang, Dongseung;Kim, Hoewoon B.
    • The Pure and Applied Mathematics
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    • v.26 no.2
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    • pp.85-97
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    • 2019
  • In this paper we introduce the reciprocal-negative Fermat's equation induced by the famous equation in the Fermat's Last Theorem, establish the general solution in the simplest cases and the differential solution to the equation, and investigate, then, the generalized Hyers-Ulam stability in a $quasi-{\beta}-normed$ space with both the direct estimation method and the fixed point approach.

Ussing's flux ratio theorem for nonlinear diffusive transport with chemical interactions

  • Bracken, A.J.;McNabb, A.;Suzuki, M.
    • 제어로봇시스템학회:학술대회논문집
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    • 1994.10a
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    • pp.747-752
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    • 1994
  • Ussing's flux ratio theorem (1978) reflects a reciprocal relationship behavior between the unidirectional fluxes in asymmetric steady diffusion-convection in a membrane slab. This surprising result has led to many subsequent studies in a wide range of applications, in particular involving linear models of time dependent problems in biology and physiology. Ussing's theorem and its extensions are inherently linear in character. It is of considerable interest to ask to what extent these results apply, if at all, in situations involving, for example, nonlinear reaction. A physiologically interesting situation has been considered by Weisiger et at. (1989, 1991, 1992) and by McNabb et al. (1990, 1991) who studied the role of albumin in the transport of ligands across aqueous diffusion barriers in a liver membrane slab. The results are that there exist reciprocal relationships between unidirectional fluxes in the steady state, although albumin is chemically interacting in a nonlinear way of the diffusion processes. However, the results do not hold in general at early times. Since this type of study first started, it has been speculated about when and how the Ussing's flux ratio theorem fails in a general diffusion-convection-reaction system. In this paper we discuss the validity of Ussing-type theorems in time-dependent situations, and consider the limiting time behavior of a general nonlinear diffusion system with interaction.

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Pedagogical implication of Euclid's proof about Pythagorean theorem (피타고라스 정리에 대한 Euclid의 증명이 갖는 교육적 함의)

  • 박문환;홍진곤
    • School Mathematics
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    • v.4 no.3
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    • pp.347-360
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    • 2002
  • This study analyzed the mathematical and didactical contexts of the Euclid's proof about Pythagorean theorem and compared with the teaching methods about Pythagorean theorem in school mathematics. Euclid's proof about Pythagorean theorem which does not use the algebraic methods provide students with the spatial intuition and the geometric thinking in school mathematics. Furthermore, it relates to various mathematical concepts including the cosine rule, the rotation, and the transfor-mation which preserve the area, and so forth. Visual demonstrations can help students analyze and explain mathematical relationship. Compared with Euclid's proof, Algebraic proof about Pythagorean theorem is very simple and it supplies the typical example which can give the relationship between algebraic and geometric representation. However since it does not include various spatial contexts, it forbid many students to understand Pythagorean theorem intuitively. Since both approaches have positive and negative aspects, reciprocal complementary role is required in pedagogical aspects.

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UNIMODULAR ROOTS OF RECIPROCAL LITTLEWOOD POLYNOMIALS

  • Drungilas, Paulius
    • Journal of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.835-840
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    • 2008
  • The main result of this paper shows that every reciprocal Littlewood polynomial, one with {-1, 1} coefficients, of odd degree at least 7 has at least five unimodular roots, and every reciprocal Little-wood polynomial of even degree at least 14 has at least four unimodular roots, thus improving the result of Mukunda. We also give a sketch of alternative proof of the well-known theorem characterizing Pisot numbers whose minimal polynomials are in $$A_N=\{[{X^d+ \sum\limits^{d-1}_{k=0} a_k\;X^k{\in} \mathbb{Z}[X]\;:\;a_k={\pm}N,\;0{\leqslant}k{\leqslant}d-1}\}$$ for positive integer $N{\geqslant}2$.

A COMPACTNESS RESULT FOR A SET OF SUBSET-SUM-DISTINCT SEQUENCES

  • Bae, Jae-Gug
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.515-525
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    • 1998
  • In this paper we obtain a "compactness" result that asserts the existence, in certain sets of sequences, of a sequence which has a maximal reciprocal sum. We derive this result from a much more general theorem which will be proved by introducing a metric into the set of sequences and using a topological argument.

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A BEM implementation for 2D problems in plane orthotropic elasticity

  • Kadioglu, N.;Ataoglu, S.
    • Structural Engineering and Mechanics
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    • v.26 no.5
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    • pp.591-615
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    • 2007
  • An improvement is introduced to solve the plane problems of linear elasticity by reciprocal theorem for orthotropic materials. This method gives an integral equation with complex kernels which will be solved numerically. An artificial boundary is defined to eliminate the singularities and also an algorithm is introduced to calculate multi-valued complex functions which belonged to the kernels of the integral equation. The chosen sample problem is a plate, having a circular or elliptical hole, stretched by the forces parallel to one of the principal directions of the material. Results are compatible with the solutions given by Lekhnitskii for an infinite plane. Five different orthotropic materials are considered. Stress distributions have been calculated inside and on the boundary. There is no boundary layer effect. For comparison, some sample problems are also solved by finite element method and to check the accuracy of the presented method, two sample problems are also solved for infinite plate.

ON THE STABILITY OF THE GENERALIZED G-TYPE FUNCTIONAL EQUATIONS

  • KIM, GWANG-HUI
    • Communications of the Korean Mathematical Society
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    • v.20 no.1
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    • pp.93-106
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    • 2005
  • In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $f({{\varphi}(x)) = {\Gamma}(x)f(x)$. As a consequence in the cases ${\varphi}(x) := x+p:= x+1$, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.