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Linear Mathematical Models in Chemical Engineering最新文献

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PDEs with Self-Adjoint Operators 具有自伴随算子的偏微分方程
Linear Mathematical Models in Chemical Engineering Pub Date : 2018-07-03 DOI: 10.1142/9789813270886_0010
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引用次数: 0
FRONT MATTER 前页
Linear Mathematical Models in Chemical Engineering Pub Date : 2018-07-03 DOI: 10.1142/9789813270886_fmatter
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引用次数: 0
Similarity Transformations 相似变换
Linear Mathematical Models in Chemical Engineering Pub Date : 2018-07-03 DOI: 10.1142/9789813270886_0012
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引用次数: 0
First Order PDEs 一阶偏微分方程
Linear Mathematical Models in Chemical Engineering Pub Date : 2018-07-03 DOI: 10.1142/9789813270886_0011
C. E. Gutiérrez
{"title":"First Order PDEs","authors":"C. E. Gutiérrez","doi":"10.1142/9789813270886_0011","DOIUrl":"https://doi.org/10.1142/9789813270886_0011","url":null,"abstract":"1. Systems of 1st order ordinary differential equations 2 1.1. Existence of solutions 2 1.2. Uniqueness 4 1.3. Differentiability of solutions with respect to a parameter 6 2. Quasi-linear pdes 10 2.1. Step 1 10 2.2. Step 2 11 2.3. Cauchy problem 11 3. Degenerate case 12 4. Examples 14 4.1. Example 1 14 4.2. Example 2 14 4.3. Example 3 14 4.4. A maximum principle for a first order pde 15 5. Fully nonlinear case 15 5.1. Cauchy problem 17 5.2. Uniqueness 21 5.3. Solution of the eikonal equation 22 5.4. Higher dimensional case 23 6. A transversality problem 24 7. The Legendre transform 25 References 27","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116926308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
BACK MATTER 回到问题
Linear Mathematical Models in Chemical Engineering Pub Date : 2018-07-03 DOI: 10.1142/9789813270886_bmatter
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引用次数: 0
Linear Difference Equations 线性差分方程
Linear Mathematical Models in Chemical Engineering Pub Date : 2018-07-03 DOI: 10.1142/9789813270886_0007
M. Tirelli
{"title":"Linear Difference Equations","authors":"M. Tirelli","doi":"10.1142/9789813270886_0007","DOIUrl":"https://doi.org/10.1142/9789813270886_0007","url":null,"abstract":"Dynamic economic models are a useful tool to study economic dynamics and get a better understanding of relevant phenomena such as growth and business cycle. Equilibrium conditions are normally identified by a system of difference equations and a set of boundary conditions (describing limit values of some variables). Thus, studying equilibrium properties requires studying the properties of a system of difference equations. In many interesting cases such difference equations are nonlinear; as you will see, even the textbook, deterministic, neoclassical, growth model is represented by a system of nonlinear equations. Although nonlinearities make the study of dynamic economic systems difficult, we can still hope to derive useful characterizations and results. This is achieved either locally, in a neighborhood of an equilibrium point, or globally for log-linearized systems. In both cases, non-linear systems are studied using the theory of linear difference equations. In these notes we shall summarize some useful results in this theory and apply them to deal with dynamic economic systems. In these class notes I present some useful material on how to solve linear difference equations and study solution stability. These notes are incomplete; many important questions are left unexplained; but students can find additional, sharp and clear material in Elaydi (2005) ”An Introduction to Difference Equations”, Springer-Verlag. A general, introductory, reference is Simon & Blume, ”Mathematics for Economists”, Norton. For issues on linear algebra, my favorite textbook is Serge Lang ”Linear Algebra”, Springer-Verlag.","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126741150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 24
Model Formulation 模型公式
Linear Mathematical Models in Chemical Engineering Pub Date : 2018-07-03 DOI: 10.1017/cbo9781107279124.004
A. Rasmuson, B. Andersson, L. Olsson, Ronnie Andersson
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引用次数: 10
Appendix 附录
Linear Mathematical Models in Chemical Engineering Pub Date : 2018-07-03 DOI: 10.1142/9789813270886_0014
{"title":"Appendix","authors":"","doi":"10.1142/9789813270886_0014","DOIUrl":"https://doi.org/10.1142/9789813270886_0014","url":null,"abstract":"","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122648839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Model Simplifications and Approximations 模型简化和近似
Linear Mathematical Models in Chemical Engineering Pub Date : 2018-07-03 DOI: 10.1142/9789813270886_0002
{"title":"Model Simplifications and Approximations","authors":"","doi":"10.1142/9789813270886_0002","DOIUrl":"https://doi.org/10.1142/9789813270886_0002","url":null,"abstract":"","PeriodicalId":233526,"journal":{"name":"Linear Mathematical Models in Chemical Engineering","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134374891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Examining a Model 检查模型
Linear Mathematical Models in Chemical Engineering Pub Date : 2018-07-03 DOI: 10.1142/9789813270886_0003
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引用次数: 10
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