Principles of Mathematical Modeling

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The book reflects the interests and experiences of the authors, but it explores mathematical modeling across a wide range of applications, from mechanics to social science.

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A general approach is adopted, where ideas and examples are favored over rigorous mathematical procedures. This insightful book will be of interest to specialists, teachers, and students across a wide range of disciplines..

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Mathematical models of instruments-fundamental principles

Manufacturer warranty may not apply Learn more about Amazon Global Store. About the Author Professor Alexander A. The system includes two genes, a1 and a2, coding for individual mRNAs, m1 and m2, wherefrom proteins b1 and b2 are translated. Monomer of protein b1 forms dimer d1.

Principles of Mathematical Modelling | Ideas, Methods, Examples | Taylor & Francis Group

Protein b2 is a specific factor responsible for degrading mRNA m1; protein b1 inhibits the transcription of gene a2 and simultaneously activates transcription of its own gene a1; while dimer d1 of protein b1 inhibits transcription from its own gene a1. In norm, gene a1 is inactive.


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Its primary activation depends on the outside signal Os. Gene a2 in norm synthesizes mRNA with a certain nonzero activity. Both mRNA and proteins have limited life spans. Let us enumerate all the elementary processes specified for this network:.

The description complies with the following scheme. Certain processes may be described in combination. In our example, these are elementary processes 2 and 3, describing mRNA translation; processes 10 and 11; and processes 12 and For example, process 1 describes constitutive transcription of gene a2, a pair of processes 2 and 3 describes translation of mRNAs synthesized from genes a1 and a2, etc.

This number describes completely the formalism accepted for description of the process.

For example, formal block 4 generalized Michaelis- Menten scheme 1 is used for describing processes 1- 5 and 9; block 1 bimolecular reaction , for processes 6- 7; or block 2 irreversible monomolecular reaction , for processes For the sake of definiteness, we will call these named variable as products. Within each list, products are separated with commas.

Description

The order of products conforms strictly to the order of formal variables in the corresponding blocks listed in Fig. The first information block detailed below is located before a colon : , having a meaning of separation.


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The second information block located after the colon contains the data on constants in a form of list of actual parameter names and their values separated with commas. Principles of Mathematical Modeling e-bok av Clive Dym. Ladda ned. Spara som favorit.

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