1 
Quantifying Uncertainty in a Mathematical Model of the Transmission of Chikungunya in the CaribbeanJanuary 2019 (has links)
archives@tulane.edu / 1 / Erin Stafford

2 
Islam in Ijẹbu OdeAbdul, Musa Ọladipupọ Ajilogba January 1968 (has links)
Note: / This work has been undertaken beacuse os the fascinating mixedreligious social set up it offers in the town, the model it is likely to serve to the Nigerian community in this aspect of coexistence of religions. Even though all the three strong religious beliefes existing in the country  traditional, Muslim and Christian  have strong footing and long standing in this town, yet religion has been reduced to a secondary position on the social activities of the people; so much so that there is hardly any family which is exclusively Muslim or Christian or traditional. [...]

3 
An ODE Model of Biochemotherapy Treatment for CancerMoore, James 01 May 2007 (has links)
Cancer is one of the most prevalent and deadly diseases in the United States today. There are many approaches to treating cancer, but here we focus on biochemotherapy which is a combination of chemotherapy and immunotherapy. The intent of immunotherapy is to boost the body’s natural resistance to cancer which is often repressed by the regulatory branch of the immune system. Here we show that this repression may be overcome by chemotherapy followed closely by immunotherapy. However, giving immunotherapy at the wrong time can may actually promote tumor growth.

4 
Dynamic modeling issues for power system applicationsSong, Xuefeng 17 February 2005 (has links)
Power system dynamics are commonly modeled by parameter dependent nonlinear differentialalgebraic equations (DAE) x p y x f ) and 0 = p y x g ) . Due to
(,, (,, the algebraic constraints, we cannot directly perform integration based on the DAE. Traditionally, we use implicit function theorem to solve for fast variables y to get a reduced model in terms of slow dynamics locally around x or we compute y numerically at each x . However, it is well known that solving nonlinear algebraic equations analytically is quite difficult and numerical solution methods also face many uncertainties since nonlinear algebraic equations may have many solutions, especially around bifurcation points. In this thesis, we apply the singular perturbation method to model power system dynamics in a singularly perturbed ODE (ordinarydifferential equation) form, which makes it easier to observe time responses and trace bifurcations without reduction process. The requirements of introducing the fast dynamics are investigated and the complexities in the procedures are explored. Finally, we propose PTE (Perturb and Taylors expansion) technique to carry out our goal to convert a DAE to an explicit state space form of ODE. A simplified unreduced Jacobian matrix is also introduced. A dynamic voltage stability case shows that the proposed method works well without complicating the applications.

5 
Asymptotics of higherorder Painlevé equationsMorrison, Tegan Ann January 2009 (has links)
Doctor of Philosophy (PhD) / We undertake an asymptotic study of a second Painlevé hierarchy based on the JimboMiwa Lax pair in the limit as the independent variable approaches infinity. The hierarchy is defined by an infinite sequence of nonlinear ordinary differential equations, indexed by order, with the classical second Painlevé equation as the first member. We investigate general and special asymptotic behaviours admitted by each equation in the hierarchy. We show that the general asymptotic behaviour is described by two related hyperelliptic functions, where the genus of the functions increases with each member of the hierarchy, and we prove that there exist special families of solutions which are represented by algebraic formal power series. For specific values of the constants which appear in the higherorder second Painlevé equations, exact solutions are also constructed. Particular attention is given to the fourthorder analogue of the classical second Painlevé equation. In this case, the general asymptotic behaviour is given to leadingorder by two related genus2 hyperelliptic functions. These functions are characterised by four complex parameters which depend on the independent variable through the perturbation terms of the leadingorder equations, and we investigate how these parameters change with respect to this variable. We also show that the fourthorder equation admits two classes of algebraic formal power series and that there exist families of true solutions with these behaviours in specified sectors of the complex plane, as well as unique solutions in extended sectors. To complement our asymptotic study of higherorder Painlevé equations, we consider a new setting in which classical Painlevé equations arise. We study reactiondiffusion equations with quadratic and cubic source terms, with a spatiotemporal dependence included in those terms, and show that solutions of these equations are given by first and second Painlevé transcendents.

6 
Obervational analysis of the inhomogeneous universeHumphreys, Neil Paul January 1997 (has links)
No description available.

7 
Asymptotics of higherorder Painlevé equationsMorrison, Tegan Ann January 2009 (has links)
Doctor of Philosophy (PhD) / We undertake an asymptotic study of a second Painlevé hierarchy based on the JimboMiwa Lax pair in the limit as the independent variable approaches infinity. The hierarchy is defined by an infinite sequence of nonlinear ordinary differential equations, indexed by order, with the classical second Painlevé equation as the first member. We investigate general and special asymptotic behaviours admitted by each equation in the hierarchy. We show that the general asymptotic behaviour is described by two related hyperelliptic functions, where the genus of the functions increases with each member of the hierarchy, and we prove that there exist special families of solutions which are represented by algebraic formal power series. For specific values of the constants which appear in the higherorder second Painlevé equations, exact solutions are also constructed. Particular attention is given to the fourthorder analogue of the classical second Painlevé equation. In this case, the general asymptotic behaviour is given to leadingorder by two related genus2 hyperelliptic functions. These functions are characterised by four complex parameters which depend on the independent variable through the perturbation terms of the leadingorder equations, and we investigate how these parameters change with respect to this variable. We also show that the fourthorder equation admits two classes of algebraic formal power series and that there exist families of true solutions with these behaviours in specified sectors of the complex plane, as well as unique solutions in extended sectors. To complement our asymptotic study of higherorder Painlevé equations, we consider a new setting in which classical Painlevé equations arise. We study reactiondiffusion equations with quadratic and cubic source terms, with a spatiotemporal dependence included in those terms, and show that solutions of these equations are given by first and second Painlevé transcendents.

8 
Uzvišenost ideje – komparativna analiza engleske klasicističke i romantičarske ode / The Sublimity of an idea – the comparativeanalysis of the English classicistic and romanticodeBogdanović Mirko 09 February 2015 (has links)
<p>Oda kao umjetnička forma, lijepo i uzvišeno, razum i mašta, dinamički i<br />matematički uzvišeno, uzvišenost forme i uzvišenost ideje, subjektivizacija uzvišenosti, neki<br />su od ključnih pojmova kojima se bavi ovo istraživanje. Međutim, u širem kontekstu, ono<br />obuhvata i pojmove individualnog i opšteg, vječnog i prolaznog, konačnog i beskonačnog,<br />ljudskog i mitskog, ljudskog i božanskog, čovjeka i prirode. Sva ta pitanja, naime, prožimaju<br />se u uzvišenim okvirima ode, koja je svojim postojanjem obilježavala najsvjetlije tačke<br />pojedinih epoha i upisivala ih u veličanstvenu hroniku ljudske istorije. Ovaj rad predstavlja<br />osvrt na tu zlatnu hroniku u kojoj će, nadamo se, i naša epoha upisati nekoliko stihova.</p> / <p>Ode as an artistic form, beautiful and sublime, reason and imagination,<br />dynamically and mathematically sublime, the sublimity of a form and the sublimity of an<br />idea, subjectivity of the sublime, are some of the key terms of this study. However, in<br />somewhat wider context, it also includes the individual and the universal, eternal and<br />temporal, finite and infinite, human and mythical, human and divine, man and nauture. All<br />these questions are intertwined in the sublime frame of an ode, which, by its own existence,<br />has marked the brightest spots of each epoch and written them in the magnificent chronicle of<br />human history. This work represents the retrospect of that golden chronicle in which our own<br />epoch will hopefully write a few lines.</p>

9 
An Ordinary Differential Equation Based Model For Clustering And Vector QuantizationCheng, Jie 01 January 2009 (has links)
This research focuses on the development of a novel adaptive dynamical system approach to vector quantization or clustering based on only ordinary differential equations (ODEs) with potential for a realtime implementation. The ODEbased approach has an advantage in making it possible realtime implementation of the system with either electronic or photonic analog devices. This dynamical system consists of a set of energy functions which create valleys for representing clusters. Each valley represents a cluster of similar input patterns. The proposed system includes a dynamic parameter, called vigilance parameter. This parameter approximately reflects the radius of the generated valleys. Through several examples of different pattern clusters, it is shown that the model can successfully quantize/cluster these types of input patterns. Also, a hardware implementation by photonic and/or electronic analog devices is given In addition, we analyze and study stability of our dynamical system. By discovering the equilibrium points for certain input patterns and analyzing their stability, we have shown the quantizing behavior of the system with respect to its parameters. We also extend our model to include competition mechanism and vigilance dynamics. The competition mechanism causes only one label to be assigned to a group of patterns. The vigilance dynamics adjust vigilance parameter so that the cluster size or the quantizing resolution can be adaptive to the density and distribution of the input patterns. This reduces the burden of retuning the vigilance parameter for a given input pattern set and also better represents the input pattern space. The vigilance parameter approximately reflects the radius of the generated valley for each cluster. Making this parameter dynamic allows the bigger cluster to have a bigger radius and as a result a better cluster. Furthermore, an alternative dynamical system to our proposed system is also introduced. This system utilizes sigmoid and competitive functions. Although the results of this system are encouraging, the use of sigmoid function makes analyze and study stability of the system extremely difficult.

10 
Painleve Analysis, Lie Symmetries and Integrability of Nonlinear Ordinary Differential EquationsLu, Yixia January 2005 (has links)
The Painleve analysis plays an important role in investigating local structure of the solutions of differential equations, while Lie symmetries provide powerful tools in global solvability of equations. In this research, the method of Painleve analysis is applied to discrete nonlinear Schrodinger equations and to a family of second order nonlinear ordinary differential equations. Lie symmetries are studied together with the Painleve property for second order nonlinear ordinary differential equations.In the study of the local singularity of discrete nonlinear Schrodinger equations, the Painleve method shows the existence of solution blow up at finite time. It also determines the rate of blowup. For second order nonlinear ordinary differential equations, the Painleve test is introduced and demonstrated in detail using several examples. These examples are used throughout the research. The Painleve property is shown to be significant for the integrability of a differential equation.After introducing oneparameter groups, a family of differential equations is determined for discussing solvability and for drawing more meaningful conclusions. This is the most general family of differential equations invariant under a given oneparameter group. The first part of this research is the classification of the integrals in the general solutions of differential equations obtained by quadratures. The second part is the application of Riemann surfaces and algebraic curves in the projective complex space to the integrands. The theories of Riemann surfaces and algebraic curves lead us to an effective way to understand the nature of the integral defined on a curve. Our theoretical work then concentrates on the blowingup of algebraic curves at singular points. The calculation of the genus, which essentially determines the shape of a curve, becomes possible after a sequence of blowingups.The research shows that when combining both the Painleve property and Lie symmetries possessed by the differential equations studied in the thesis, the general solutions can be represented by either elementary functions or elliptic integrals.

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