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Uniqueness Implies Existence and Uniqueness Conditions for Boundary Value Problems for 4 th Order Differential Equations Nasiba Albatni University of Dayton
| Content Provider | Semantic Scholar |
|---|---|
| Author | Veliz-Cuba, Alan |
| Copyright Year | 2016 |
| Abstract | In studies in disconjugacy, it has been established for many years that under suitable hypotheses, the uniqueness of solutions of $n-$point conjugate boundary value problems on an interval (a, b) implies the existence of solutions for any conjugate point boundary value problem on (a, b) for an nth order differential equation. In this talk, we consider a fourth order ordinary differential equation and we consider a family of boundary value problems different than and related to the conjugate boundary value problems. In particular, we shall assume the uniqueness of solutions of 4 − point right focal type boundary value problems and show the existence of solutions of a broad family of two, three and four point boundary value problems. The primary tool is an unpublished precompactness condition for families of solutions of ordinary differential equations. The precompactness condition is due to Jackson and Schrader. Boolean modeling of gene networks Alan Veliz-Cuba University of Dayton Abstract: Due to the lack of kinetic information of biochemical interactions, it is difficult to study and analyze continuous models of gene networks. The nonlinearity of these interactions makes the problem even less tracktable. The Boolean framework (where gene activity is assumed to be either 0=OFF or 1=ON) provides a complementary approach that focuses on qualitative analysis. In this talk, I will show how the Boolean framework is used in modeling biological systems, and how tools from graph theory and combinatorics are well-suited for the analysis of these Boolean models. Due to the lack of kinetic information of biochemical interactions, it is difficult to study and analyze continuous models of gene networks. The nonlinearity of these interactions makes the problem even less tracktable. The Boolean framework (where gene activity is assumed to be either 0=OFF or 1=ON) provides a complementary approach that focuses on qualitative analysis. In this talk, I will show how the Boolean framework is used in modeling biological systems, and how tools from graph theory and combinatorics are well-suited for the analysis of these Boolean models. This talk will have the format of a tutorial/lecture. Dynamics of Conjunctive Boolean Networks |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://ecommons.udayton.edu/cgi/viewcontent.cgi?article=1025&context=mth_coll |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
