> Dear Colleagues,
>
> We have a very unusual Colloquium in the Math Department.
>
>
> Sonja Petrovic
>
>
> Sonja is a graduating student from Mathematics Program who has written
> an Honors Project under the direction of Professor John Graef. Other
> members of the Committee are R. Smith, B. Belinskiy, and N. Ozbek.
>
> Sonja will give a Colloquium presentation based on her paper on August
> 7, Thursday, at 3:30, EMCS Room 422 . The title of her paper is
>
> Oscillation of Solutions of Dynamic Equations on Time Scales: the
> Sturm-Picone Comparison Theorem
>
> Abstract. Presented here are the basic properties of time scales and
> operations on them. We consider two generalized derivatives on time
> scales, namely, the delta and nabla derivatives.  We further discuss
> integration on time scales with respect to both of these derivatives.
> The delta derivative, an equivalent of the forward difference operator
> on $\Bbb Z$, is described in more detail.  The analogous results for
> nabla derivative, the equivalent of a backward difference on $\Bbb Z$,
> follow similarly.  Finally, we focus on second order dynamic
> equations, which are the time-scale equivalents of second order
> differential and difference equations on their respective domains.
>
> The particular problem we study in this paper is a generalized version
> of the well-known Sturm-Picone Comparison Theorem.  We focus on the
> second order delta-derivative self-adjoint equations of a particular
> form and derive the analogous result for time scales.  The result is
> proved directly, avoiding the usual Riccati type transformations.  The
> possibility for further research stems from the final result which may
> be considered for a more general form of self-adjoint equations that
> includes not only delta, but also the nabla derivative, and also some
> nonlinear  cases.
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