Reductions in Organic Chemistry

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Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable.

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A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers.

In recent years there has been a surge of interest in self-similar solutions of the First and Second kind.


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They have been used in the context of a variety of problems, such as shock waves in gas dynamics, and filtration through elasto-plastic materials. Self-Similarity has simplified computations and the representation of the properties of phenomena under investigation. It handles experimental data, reduces what would be a random cloud of empirical points to lie on a single curve or surface, and constructs procedures that are self-similar.

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Variables can be specifically chosen for the calculations. Springer Professional.

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Principles of the Dimensional Analysis Abstract. Nearly all scientists at conjunction with simplifying a differential equation have probably used dimensional analysis. Dimensional analysis also called the factor-label method or the unit factor method is an approach to problem that uses the fact that one can multiply any number or expression without changing its value.

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A generalization of the Pi-theorem and dimensional analysis. This article introduces a generalization of dimensional analysis and its corollary, the Pi-theorem, to the class of problems in which some of the quantities that define the problem have fixed values in all the cases that are of interest. The procedure can reduce the number of dimensionless similarity variables beyond the prediction of Buckingham's theorem.

The generalized Pi-theorem tells when and how large a reduction is attainable.

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http://kick-cocoa.info/components/nelimydub/cyxij-carcasa-cellular.php Isoelectric Point. Citations Publications citing this paper. Development of a method for approximate solution of nonlinear ordinary differential equations using pendulum motion as an example Olexander Brunetkin , Maksym Maksymov , Oksana Maksymova , Anton Zosymchuk.


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