Palestinian Conference on Modern Trends in Mathematics and Physics IIhttps://hdl.handle.net/20.500.11888/62622019-07-13T01:47:10Z2019-07-13T01:47:10ZComputing Slowly Advancing Features in Fast-Slow Systems without Scale Separation- A Young Measure ApproachEdriss Titihttps://hdl.handle.net/20.500.11888/95902017-05-03T09:37:03Z2010-08-02T00:00:00ZComputing Slowly Advancing Features in Fast-Slow Systems without Scale Separation- A Young Measure Approach; Computing Slowly Advancing Features in Fast-Slow Systems without Scale Separation- A Young Measure Approach
Edriss Titi
<p>In the first part of the talk, and in order to set the stage, we will offer a multi-scale and averaging strategy to compute the solution of a singularly perturbed system when the fast dynamics oscillates rapidly; namely, the fast dynamics forms cycle-like limits which advance along with the slow dynamics. We describe the limit as a Young measure with values being supported on the limit cycles, averaging with respect to which induces the equation for the slow dynamics. In particular, computing the tube of the limit cycles establishes a good approximation for arbitrarily small singular parameters. We will demonstrate this by exhibiting concrete numerical examples.<br />
In the second part of the talk we will examine singularly perturbed systems which may not possess a natural split into fast and slow state variables. Once again, our approach depicts the limit behavior as a Young measure with values being invariant measure of the fast contribution to the flow. These invariant measures are drifted by the slow contribution to the value. We keep track of this drift via slowly evolving observables. Averaging equations for the latter lead to computation of characteristic features of the motion and the location the invariant measures.<br />
To demonstrate our ideas computationally, we will present some numerical experiments involving a system derived from a spatial discretization of a Korteweg-de Vries-Burgers type equation, with fast dispersion and slow diffusion.<br />
This is a joint work with Z. Artstein, W. Gear, I. Kevrekidis, J. Linshiz and M. Slemrod</p>; <p>In the first part of the talk, and in order to set the stage, we will offer a multi-scale and averaging strategy to compute the solution of a singularly perturbed system when the fast dynamics oscillates rapidly; namely, the fast dynamics forms cycle-like limits which advance along with the slow dynamics. We describe the limit as a Young measure with values being supported on the limit cycles, averaging with respect to which induces the equation for the slow dynamics. In particular, computing the tube of the limit cycles establishes a good approximation for arbitrarily small singular parameters. We will demonstrate this by exhibiting concrete numerical examples.<br />
In the second part of the talk we will examine singularly perturbed systems which may not possess a natural split into fast and slow state variables. Once again, our approach depicts the limit behavior as a Young measure with values being invariant measure of the fast contribution to the flow. These invariant measures are drifted by the slow contribution to the value. We keep track of this drift via slowly evolving observables. Averaging equations for the latter lead to computation of characteristic features of the motion and the location the invariant measures.<br />
To demonstrate our ideas computationally, we will present some numerical experiments involving a system derived from a spatial discretization of a Korteweg-de Vries-Burgers type equation, with fast dispersion and slow diffusion.<br />
This is a joint work with Z. Artstein, W. Gear, I. Kevrekidis, J. Linshiz and M. Slemrod</p>
2010-08-02T00:00:00ZEmpirical Post Hoc Conditional Power FunctionMonjed H. SamuhFortunato Pesarinhttps://hdl.handle.net/20.500.11888/95872017-05-03T09:37:03Z2010-08-02T00:00:00ZEmpirical Post Hoc Conditional Power Function; Empirical Post Hoc Conditional Power Function
Monjed H. Samuh; Fortunato Pesarin
<p>Until very recently, many authors start using the so called post hoc power (also called a posteriori power, retrospective power, observed power or achieved power) in response to the demand of some scientific journals and editors especially when the outcome of the test is not significant or slightly significant. It is suggested as an estimator of the prospective power (also called a priori power or true power). This paper is raised at the time when misunderstandings and misconceptions abounded concerning retrospective power; it has been noticed that some authors disagree to calculate the post hoc power in the sense that it is unhelpful in the presence of the crude p-value and some others advocate the use of post hoc power in the sense that it has another interpretation than what we have from the crude p-value. This study tries to discover the nature of this concept, to summarize what is available in the literature and to dispel some confusion concerning this concept. Power function with new look within permutation approach (post hoc conditional power) is developed. Convergence of empirical post hoc conditional power to the empirical conditional power is investigated as well as the connection between them is studied. Real data application from the perspective of industry and simulation studies are considered.</p>; <p>Until very recently, many authors start using the so called post hoc power (also called a posteriori power, retrospective power, observed power or achieved power) in response to the demand of some scientific journals and editors especially when the outcome of the test is not significant or slightly significant. It is suggested as an estimator of the prospective power (also called a priori power or true power). This paper is raised at the time when misunderstandings and misconceptions abounded concerning retrospective power; it has been noticed that some authors disagree to calculate the post hoc power in the sense that it is unhelpful in the presence of the crude p-value and some others advocate the use of post hoc power in the sense that it has another interpretation than what we have from the crude p-value. This study tries to discover the nature of this concept, to summarize what is available in the literature and to dispel some confusion concerning this concept. Power function with new look within permutation approach (post hoc conditional power) is developed. Convergence of empirical post hoc conditional power to the empirical conditional power is investigated as well as the connection between them is studied. Real data application from the perspective of industry and simulation studies are considered.</p>
2010-08-02T00:00:00ZOn Á-Rings: A Generalization Of Integral DomainsAyman Badawihttps://hdl.handle.net/20.500.11888/95892017-05-03T09:37:03Z2010-08-02T00:00:00ZOn Á-Rings: A Generalization Of Integral Domains; On Á-Rings: A Generalization Of Integral Domains
Ayman Badawi
<p>Let R be a commutative ring with 1 6= 0 and Nil(R) be its set of nilpotent elements. Recall that a prime ideal of R is called a divided prime if P ½ (x) for every x 2 RnP. The class of rings: H = fR j R is a commutative ring and Nil(R) is a divided prime ideal of Rg has been studied extensively by the speaker(i.e. Badawi). Observe that if R is an integral domain, then R 2 H. Hence H is a much larger class than the class of integral domains. If R 2 H, then R is called a Á-ring.<br />
I wrote the ¯rst paper on Á-rings in 1999 :"Á-pseudo-valuation rings," appeared in Advances in Commutative Ring Theory, 101-110, Lecture Notes Pure Appl. Math. 205, Marcel Dekker, New York/Basel, 1999.</p>; <p>Let R be a commutative ring with 1 6= 0 and Nil(R) be its set of nilpotent elements. Recall that a prime ideal of R is called a divided prime if P ½ (x) for every x 2 RnP. The class of rings: H = fR j R is a commutative ring and Nil(R) is a divided prime ideal of Rg has been studied extensively by the speaker(i.e. Badawi). Observe that if R is an integral domain, then R 2 H. Hence H is a much larger class than the class of integral domains. If R 2 H, then R is called a Á-ring.<br />
I wrote the ¯rst paper on Á-rings in 1999 :"Á-pseudo-valuation rings," appeared in Advances in Commutative Ring Theory, 101-110, Lecture Notes Pure Appl. Math. 205, Marcel Dekker, New York/Basel, 1999.</p>
2010-08-02T00:00:00ZThe Spectrum of the Coloration Matrix for the Complete Partite GraphSubhi Ruziehhttps://hdl.handle.net/20.500.11888/95882017-05-03T09:37:03Z2010-08-02T00:00:00ZThe Spectrum of the Coloration Matrix for the Complete Partite Graph; The Spectrum of the Coloration Matrix for the Complete Partite Graph
Subhi Ruzieh
<p>This paper talks about eigenvalues of graphs and finding them through making use of the coloration partition. We first define the concept of coloration. We then apply it to compute eigenvalues of some graphs. The concentration will be on graphs having a nontrivial coloration like the complete bipartite graphs K(m, n) and the complete 3 - partite graphs K(m, n, p). The idea can be carried through to the complete n-partite graphs, but the computations then will become more difficult to be concluded.</p>; <p>This paper talks about eigenvalues of graphs and finding them through making use of the coloration partition. We first define the concept of coloration. We then apply it to compute eigenvalues of some graphs. The concentration will be on graphs having a nontrivial coloration like the complete bipartite graphs K(m, n) and the complete 3 - partite graphs K(m, n, p). The idea can be carried through to the complete n-partite graphs, but the computations then will become more difficult to be concluded.</p>
2010-08-02T00:00:00Z