• 제목/요약/키워드: Complex Abstract

검색결과 142건 처리시간 0.032초

A New Topology of Solutions of Chemical Equations

  • Risteski, Ice B.
    • 대한화학회지
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    • 제57권2호
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    • pp.176-203
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    • 2013

  • In this work is induced a new topology of solutions of chemical equations by virtue of point-set topology in an abstract stoichiometrical space. Subgenerators of this topology are the coefficients of chemical reaction. Complex chemical reactions, as those of direct reduction of hematite with a carbon, often exhibit distinct properties which can be interpreted as higher level mathematical structures. Here we used a mathematical model that exploits the stoichiometric structure, which can be seen as a topology too, to derive an algebraic picture of chemical equations. This abstract expression suggests exploring the chemical meaning of topological concept. Topological models at different levels of realism can be used to generate a large number of reaction modifications, with a particular aim to determine their general properties. The more abstract the theory is, the stronger the cognitive power is.

  • https://doi.org/10.5012/jkcs.2013.57.2.176 인용 PDF KSCI KPUBS HTML

$L_1$ analytic fourier-feynman transform on the fresnel class of abstract wiener space

  • Ahn, Jae-Moon
    • 대한수학회보
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    • 제35권1호
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    • pp.99-117
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    • 1998

  • Let $(B, H, p_1)$ be an abstract Wiener space and $F(B)$ the Fresnel class on $(B, H, p_1)$ which consists of functionals F of the form : $$ F(x) = \int_{H} exp{i(h,x)^\sim} df(h), x \in B, $$ where $(\cdot, \cdot)^\sim$ is a stochastic inner product between H and B, and f is in $M(H)$, the space of complex Borel measures on H. We introduce an $L_1$ analytic Fourier-Feynman transforms for functionls in $F(B)$. Furthermore, we introduce a convolution on $F(B)$, and then verify the existence of the $L_1$ analytic Fourier-Feynman transform for the convolution product of two functionals in $F(B)$, and we establish the relationships between the $L_1$ analytic Fourier-Feynman tranform of the convolution product for two functionals in $F(B)$ and the $L_1$ analytic Fourier-Feynman transforms for each functional. Finally, we show that most results in [7] follows from our results in Section 3.

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