{"id":37,"date":"2016-01-06T13:05:39","date_gmt":"2016-01-06T18:05:39","guid":{"rendered":"https:\/\/my.vanderbilt.edu\/pastcolloquia\/?page_id=37"},"modified":"2016-01-06T13:05:39","modified_gmt":"2016-01-06T18:05:39","slug":"colloquia-spring-2000","status":"publish","type":"page","link":"https:\/\/my.vanderbilt.edu\/pastcolloquia\/colloquia-spring-2000\/","title":{"rendered":"Colloquia, Spring 2000"},"content":{"rendered":"\n\n
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<\/font>Vanderbilt Mathematics<\/font><\/a><\/font>
\n<\/font>Colloquia<\/font>
\n<\/font>Spring 2000<\/font><\/h1>\n

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\nJuly 27.
\nEdray Goins, of the
\nInstitute
\nfor Advanced Study, School of Mathematics<\/a>.
\nOn the Multiplicative Properties of the Sums of Squares.<\/b>
\nThe product of any two integers which are sums of two
\nsquares is again the sum of two squares, and, similarly, the product of
\nany two integers which are sums of four squares is again the sum of
\nfour squares. We give some thoughts on where these formulas come
\nfrom; we also discuss the multiplicative properties of the polynomials
\nax<\/i>2<\/sup>+bxy<\/i>+cy<\/i>2<\/sup>
\nby considering the product of three integers
\nexpressed in such a form. —
\nThis talk will be elementary and accessible to undergraduates.\n<\/p>\n

   <\/p>\n

May 16. Doron
\nLubinsky<\/a>, of the
\nUniversity
\nof Witwatersrand<\/a>,
\nJohannesburg, South Africa.
\nA Pade Look at Continued Fractions: Some old, some new.<\/b>
\nEvery formal power series admits a formal continued fraction
\nexpansion. This is the function theoretic analogue of the continued
\nfraction expansion of a positive real number. We discuss why they
\nare of practical and theoretical interest.
\n— The convergents to the continued fraction are also Pade
\napproximants, and we examine the convergence of the continued
\nfraction from a Pade perspective. In particular, we survey old and
\nnew convergence results, and the status of the Baker-Gammel-Wills
\nConjecture. Will it be killed by Ramanujan’s continued fraction?
\n\n<\/p>\n

   <\/p>\n

May 12.
\nQuintang Jiang,
\nof the
\nUniversity of Alberta<\/a>.
\nThe Design of Multiwavelets with Optimum Time-Frequency
\nResolution.<\/b>
\nIn this talk first we will discuss the procedure to design
\northogonal multiwavelets with good time-frequency resolution.
\nNext, we give formulas to compute the time-durations and
\nthe frequency-bandwidths of scaling functions and multiwavelets.
\nLater on we discuss the parameterization of symmetric orthogonal
\nmultifilter banks. Finally, we show some results of image
\ncompression with the optimal multiwavelets.
\n\n<\/p>\n

   <\/p>\n

May 4.
\nShinnosuke
\nOharu<\/a>, of
\nHiroshima University<\/a>.
\nContinuous and discrete models of phenotype evolution in
\nthe ecosystem of red tide plankton.<\/b>
\nHeterocapsa circularisquama are vegetative
\nplankton and form red tides because of active
\nproliferation in summer. Such red tides cause
\nmass mortality of bivalves. The coastal ocean is
\nconsidered complex multi-component fluid in
\nwhich the ecology of Heterocapsa is supported
\nby other living things and the physical states
\ndepending strongly upon seasonal variations of
\nair-sea interactions, weather, water temperature,
\nsalinity and water currents. Therefore it is not
\nstraightforward to elucidate the ecosystem of
\nHeterocapsa in the ocean from the point of view
\nof a sole field of biology as well as other separate
\nfields of natural science.\n<\/p>\n

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April 27.
\nBernd Schroeder<\/a>, of
\nLouisiana
\nTech University<\/a>.
\nUsing probabilistic formulas to predict the behavior of
\nsearch algorithms.<\/b><\/p>\n

Many problems in mathematics and in applications can be
\nformulated as constraint satisfaction problems. Among these
\nproblems are the question if a given ordered set has a fixed point
\nfree self-map, the question if a graph has a Hamiltonian Cycle,
\nthe n-queens problem, scheduling problems, etc. In particular,
\nconstraint satisfaction problems (we will give a general definition)
\nare NP-complete and thus any known solution procedure
\npotentially requires exponential effort. —
\nThe standard search algorithms that are used to solve such problems
\nare backtracking and forward checking. In addition to these main
\nparadigms there are refinements of each algorithm, which may
\nhave shorter search times. The problem now is that if a constraint
\nsatisfaction problem is presented, one would like to know in advance
\nwhich algorithm is the fastest to solve the problem. In this fashion
\none could automatically choose the “right” algorithm and save
\ncomputation time. —
\nThere are many approaches to this idea. The three main approaches
\nthe speaker is aware of are<\/p>\n