The SPAMS Schedule - Fall 1997

The literature on river networks and eroding landscapes is rather full of wild conjectures, crazy models and a modicum of reasonable science. I will discuss how we have mostly added to the first 2 of these 3 elements. A starting point will be Hack's Law which relates areas of drainage basins to stream lengths. We will then briefly look at other observables such as stream order and shapes of basins. Power laws are abundant in the study of topography and I will survey the present list of scaling ansatzs and scaling laws connecting various exponents. We will then delve into a few simple lattice models that have been proposed to simulate the action of fluvial erosion, diffusion and avalanching on landscapes. We'll see the results of one in particular and compare its statistics with those of some real landscapes. Finite-size scaling will show its usefulness and we will find a possible extension for Hack's law - this is a nice result and it remains to be seen how deep it is... at this point everyone will lose concentration and we will get stuck into dahl and excellent mathematical discussions.

The "four point property" that characterizes those positive, real matrices which are realizeable as weighted trees is generalized to allow edge weights to take values in any cancellative abelian monoid satisfying several additional requirements.

I will also briefly mention an application of this result to the problem of distinguishing humans, and chimpanzees from gorillas.

The talk will be very accessible.

Abstract: "The standard blah that is actually quite fascinating and sadly is probably ignored by most readers who are really only interested in the future contents of their stomachs etc"

OK - clearly I have no idea what the talk will be on. It will however be amazingly interesting....

Certain combinatorial problems seem to only allow a solution using topological methods. The necklace splitting problem is an example of such a problem.

We will give lots of examples and discuss some fundamental properties beginning with the interpretation of the mobius function of a partially ordered set as the Euler characteristic of a simplicial complex. This is aimed at students in any area of applied math.

ABSTRACT (translated from Swedish Chef) In 1920 A.E. Boycott observed an intriguing phenomenon in a gravity settling suspension of heavy particles. By tilting the container he achieved a significant reduction in the separation time and an entirely unexpected flow configuration. About 60 years later these phenomena were analyzed from first principles. Using today's models for hydrodynamic suspensions a qualitative explanation can be obtained from a proper scaling of the terms in the momentum equation. A hydrodynamic model for suspension flows will be presented followed by some simple examples of gravity induced flows.

(see, we have some taste -> the abstract was left untouched)

In 1920 A.I. Buycutt oobserfed un intreegooing phenumenun in a grefeety settleeng soospenseeun ooff heefy perteecles. Bork Bork Bork! By teelting zee cunteeener he-a echeeefed a seegnifficunt redoocshun in zee sepereshun teeme-a und un inturely unexpected floo cunffeegooreshun. Ebuoot 60 yeers leter zeese-a phenumena vere-a unelyzed frum furst preenciples. Bork Bork Bork! Useeng tudey's mudels fur hydrudynemeec soospenseeuns a qooeleetetife-a ixpluneshun cun be-a oobteeened frum a pruper sceleeng ooff zee terms in zee mumentoom iqooeshun. A hydrudynemeec mudel fur soospenseeun floos veell be-a presented fullooed by sume-a seemple-a ixemples ooff grefeety indooced floos. Bork Bork Bork!

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  this_week's_SPAMster = Dmitri_Betaneli;

  Title = Wavelets_and_PDE's;

  Time = 5pm_Thursday_Oct_30_in_2-338;

  Abstract = Ways_to_improve_computational_perfromance_using
        multi-resolution_analysis;

  if (Food == post_SPAMs && Food != SPAM)
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      eat_heartily();
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Mathematicians have been interested in rigorous methods for attaching values to sums of divergent series for centuries. A gaggle of different methods exist, due to Abel, Borel, Cesaro, Hausdorff and many others, each with applicability to particular classes of series. Their rigor within these classes is measured by their success in providing the correct analytic continuations of functions defined by such series beyond their domains of convergence.

We'll concentrate on one method, due to Cesaro, with long-standing applications to Fourier Theory. Its key ingredient is a natural transformation of the sequence of partial sums, and its domain of applicability is, roughly, alternating series of polynomial growth. By adding an extra idea of smoothing, viewing the natural transformation as an operator, and considering its spectrum of eigenvalues and eigenvectors, we will show how to extend this domain significantly to include series defining zeta functions. We'll then discuss various properties of this new extended-Cesaro approach, including its connection with Bernoulli numbers and the Euler-MacLaurin sum formula, the question of metric-dependence, and a power-scaling-invariance property. The possibility of applying this operator-theory approach to other summation schemes may also rear its ugly head briefly at the end.

The discussion will be really elementary - lots of genuine series with actual numbers, and only functions of one variable.

The famous 48 preludes and fugues by J.S. Bach were written, in part, to demonstrate the versatility and usefulness of equal temperament, a tuning method for musical instruments that enables composers to write in different scales. Bach wrote four fugues starting on each note of the western music scale (two in the major and two in the minor). The fact that the scale he was writing for contained 12 notes was no historical accident. Indeed, using the theory of continued fractions, we will show that there is a mathematical reason underlying the use of the 12 note scale (and for that matter other scales such as the Chinese 5 note scale). No musical knowledge will be assumed for the purposes of the talk, although attendees will be required to perform on musical instruments in order to be eligible for the food following the talk.

Let's share some knowledge about orthogonal polynomials. There is a measure-free and easily accessible way to this popular and important topic. This tool is called the Umbral Method. Come to learn about it !!!