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.
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. KCI Citation Count: 0
화학반응식 균형과 안정성을 위한 새로운 유사 역행렬법 Risteski, Ice B
Journal of the Korean Chemical Society,
2008, Letnik:
52, Številka:
3
Journal Article
Recenzirano
Odprti dostop
this work is given a new pseudoniverse matrix method for balancing chemical equations. Here offered method is founded on virtue of the solution of a Diophantine matrix equation by using of a ...Moore-Penrose pseudoinverse matrix. The method has been tested on several typical chemical equations and found to be very successful for the all equations in our extensive balancing research. This method, which works successfully without any limitations, also has the capability to determine the feasibility of a new chemical reaction, and if it is feasible, then it will balance the equation. Chemical equations treated here possess atoms with fractional oxidation numbers. Also, in the present work are introduced necessary and sufficient criteria for stability of chemical equations over stability of their extended matrices. 이 논문에 화학반응식 균형을 맞추기 위한 새로운 유사 역행렬법이 기술되었다. 여기에 제공된 방법은 Moore-Penrose 유사 역행렬을 사용한 Diophantin 행렬식의 해에 기초를 둔다. 방법은 전형적인 여러 화학반응식에 시험적용되었고 폭넓은 균형연구에서 모든 반응식에 매우 성공적이었다. 이 방법은 아무 제한없이 성공적으로 적용되고, 또한 새로운 화학반응식의 타당성에 대한 검증력도 있고, 만일 새식이 타당하다면 화학식 균형을 이룰 것이다. 여기서 다루어진 화학반응식들은 소수산화수를 지닌 원자를 포함하고 있다. 또한, 화학반응식의 확장된 행렬의 안정성에 대한 화학반응식의 안정성의 필요충분조건을 이 연구에 소개하였다.
The subject of complex vector functional equations is a new area in the theory of functional equations. This monograph provides a systematic overview of the authors' recently obtained results ...concerning both linear and nonlinear complex vector functional equations, in all aspects of their utilization. It is intended for mathematicians, physicists and engineers who use functional equations in their investigations.
The theoretical basis for a new computational method is given for the topology of the meniscus trajectories during continuous steel casting. The method is based on the solution of the meniscus ...equation in 913. Here the topology is treated only in the sense of the categorization of trajectories in an orientation space. This suggests a new type of efficient self-adaptive scheme suitable for the solution of the shape of the meniscus. In the present work a new approach is used to overcome previously unknown pathological, non-physical predictions in various constitutive models derived using closure approximations. The generalized meniscus equation as well as its stability is solved. Here it is shown, for the first time, that the cyclic change of the shape of the meniscus depends on the coordinates, while up to now the cyclic change of the meniscus was presented only as a function of the time over the expression of the mould velocity.
In this present work it is given an opinion for a new approach to guitar teaching philosophy in a sufficiently sophisticated way, which surpasses up to now all known looks. With a goal to shed light ...on this important topic, this work will introduce a new guitar teaching philosophy on the virtue of musical-aesthetical knowledge of classical guitar music. With the intention to better understand this approach, emphasis is made throughout the prismof the guitar experience and from the viewpoint of new needs of classical guitar study.
We give a new matrix method for solving both homogeneous and nonhomogeneous linear complex vector functional equations with constant complex coefficients.
이 논문에 화학반응식 균형을 맞추기 위한 새로운 유사 역행렬법이 기술되었다. 여기에 제공된 방법은 Moore-Penrose 유사 역행렬을 사용한 Diophantin 행렬식의 해에 기초를 둔다. 방법은 전형적인 여러 화학반응식에 시험적용되었고 폭넓은 균형연구에서 모든 반응식에 매우 성공적이었다. 이 방법은 아무 제한없이 성공적으로 적용되고, 또한 새로운 ...화학반응식의 타당성에 대한 검증력도 있고, 만일 새식이 타당하다면 화학식 균형을 이룰 것이다. 여기서 다루어진 화학반응식들은 소수산화수를 지닌 원자를 포함하고 있다. 또한, 화학반응식의 확장된 행렬의 안정성에 대한 화학반응식의 안정성의 필요충분조건을 이 연구에 소개하였다. this work is given a new pseudoniverse matrix method for balancing chemical equations. Here offered method is founded on virtue of the solution of a Diophantine matrix equation by using of a Moore-Penrose pseudoinverse matrix. The method has been tested on several typical chemical equations and found to be very successful for the all equations in our extensive balancing research. This method, which works successfully without any limitations, also has the capability to determine the feasibility of a new chemical reaction, and if it is feasible, then it will balance the equation. Chemical equations treated here possess atoms with fractional oxidation numbers. Also, in the present work are introduced necessary and sufficient criteria for stability of chemical equations over stability of their extended matrices. KCI Citation Count: 1
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