Abstract:
Phenytoin (PHT) has been the most widely used medication to treat both partial and generalized seizures. However, over the past twenty years, a variety of new compounds have been released with comparable efficacy, fewer adverse effects, and more predictable pharmacokinetic properties. We surveyed neurologists and epileptologists to determine current practice patterns relating to the use of PHT using an online survey instrument. A total of 200 responses were obtained though response rates for each survey question varied. Of the respondents, 78.1% were epilepsy specialists; 60% were adult practitioners; and the remainder saw either, only children or both adults and children. For new onset partial seizures only 10 respondents said PHT would be their first or second choice, while 45% reported that they would not consider PHT. This study shows that in the era of newer medications, the role of PHT has been placed in the category of a reserve medication in intractable epilepsy. 1. Introduction Phenytoin (PHT) was first synthesized in 1908 at the University of Kiel in Germany. Anticonvulsant properties of this compound were first described by Merritt and Putnam in 1938, and PHT was brought to market by Parke Davis later that year [1–3]. Since its introduction as an anticonvulsant, PHT, marketed under the trade-name Dilantin, has been the predominant medication for the treatment of epilepsy for over 7 decades. The introduction of an IV formulation and later an IV pro-drug formulation (fosphenytoin) led to this medication being used as the first choice in the treatment of status epilepticus and acute repetitive seizures. However, with the introduction of numerous newer antiepileptic medications, with fewer adverse effects, better pharmacokinetic profiles, better patient tolerability, and proven efficacy, the role of phenytoin as a treatment of choice in epilepsy has become uncertain. The aim of the current study was to determine practice patterns among neurologists and epileptologists with regard to the use of PHT in the treatment of epilepsy. We also sought to understand the reasons why physicians prescribed (or did not prescribe) this important medication. We therefore surveyed neurologists and epileptologists to ascertain current practice regarding the use of PHT in treating persons with epilepsy. 2. Methods An online survey with eleven questions was created using the website http://www.surveymonkey.com/. A list of questions in the survey (and individual response rates for each question) is found in Table 1. Questions were designed to capture demographic and

Abstract:
A systematic algorithm for building integrating factors of the form mu(x,y') or mu(y,y') for non-linear second order ODEs is presented. When such an integrating factor exists, the algorithm determines it without solving any differential equations. Examples of ODEs not having point symmetries are shown to be solvable using this algorithm. The scheme was implemented in Maple, in the framework of the ODEtools package and its ODE-solver. A comparison between this implementation and other computer algebra ODE-solvers in tackling non-linear examples from Kamke's book is shown.

Abstract:
In the vector space of algebraic curvature operators we study the reaction ODE $$\frac{dR}{dt} = R^2+R^{#}= Q(R)$$ which is associated to the evolution equation of the Riemann curvature oper- ator along the Ricci flow. More precisely, we analyze the stability of a special class of zeros of this ODE up to suitable normalization. In particular, we show that the ODE is unstable near the curvature operators of the Riemannian product spaces $M \times \mathbb{R}^k, \ k \geq 0$ where $M$ is an Einstein (locally) symmetric space of compact type and not a spherical space form when $k = 0.$

Abstract:
Within the framework of the ODE/IM correspondence, we show that the minimal conformal field theories with c<1 emerge naturally from the monodromy properties of certain families of ordinary differential equations.

Abstract:
We give an simple criterion for ODE equivalence in identical edge homogeneous coupled cell networks. This allows us to give a simple proof of Theorem 10.3 of Aquiar and Dias "Minimal Coupled Cell Networks", which characterizes minimal identical edge homogeneous coupled cell networks. Using our criterion we give a formula for counting homogeneous coupled cell networks up to ODE equivalence. Our criterion is purely graph theoretic and makes no explicit use of linear algebra.

Abstract:
An overview of the authors results is given. Property C for ODE is defioned, It is proved that the pair of Sturm-Liouville operators has property C. This property is applied to many inverse problems. Some well-known results, such as uniqueness of the recovery of the potential from scattering data, from the spectral function and from two spectra are proved in a new short way based on property C. Many new results are obtained. In particular, it is proved that a compactly supported potential can be uniquely recovered from the phase shift of s-wave alone, known at all energies, without knowledge of bound states and norming constants. The fixed-energy phase shifts known at some values of the angular momentum determine a compactly supported potential uniquely. Mixed data inverse problems are studied. Analysis of the Newton-Sabatier procedure is given. It is shown that this procedure is a parameter-fitting procedure rather than an inversion method. Other results on inverse problems are obtained.

Abstract:
In this paper, we generate asymmetric Fourier kernels as solutions of ODE's. These kernels give many previously known kernels as special cases. Several applications are considered.

Abstract:
We use generalized Gaussian quadratures for exponentials to develop a new ODE solver. Nodes and weights of these quadratures are computed for a given bandlimit $c$ and user selected accuracy $\epsilon$, so that they integrate functions $e^{ibx}$, for all $|b|\le c$, with accuracy $\epsilon$. Nodes of these quadratures do not concentrate excessively near the end points of an interval as those of the standard, polynomial-based Gaussian quadratures. Due to this property, the usual implicit Runge Kutta (IRK) collocation method may be used with a large number of nodes, as long as the method chosen for solving the nonlinear system of equations converges. We show that the resulting ODE solver is symplectic and demonstrate (numerically) that it is A-stable. We use this solver, dubbed Band-limited Collocation (BLC-IRK), in the problem of orbit determination. Since BLC-IRK minimizes the number of nodes needed to obtain the solution, in this problem we achieve speed close to that of explicit multistep methods.

Abstract:
We present some results on the existence of fast and heteroclinic solutions of an ODE connected with travelling wave solutions of a Fisher-Kolmogorov's equation. In particular, we present a variational characterization of the minimum speed of propagation.