Date: May 19, 2009

Math department picture 2009

The Tulane Mathematics Department as of April 27, 2009. Unfortunately but naturally, a few people are missing.

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Date: May 16, 2009

Using the Google Chart API

The following graph is dedicated to my brother Benjamin.

read more »

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Date: May 13, 2009

A trick for playing a multivariate integral

For suitable functions f the integral

$$ \int_0^{\infty} \int_0^{\infty} \ldots \int_0^{\infty} \frac{dx_1 dx_2 \cdots dx_n}{(f(x_1) + f(x_2) + \ldots + f (x_n))^{k+1}} $$

is equal to

$$ \frac{1}{k!} \int_0^{\infty} t^k \left( \int_0^{\infty} e^{- t f(x)} dx \right)^n dt . $$

To see why this is true, start with the last integral and write the n-th power of the inner integral as a multiple integral over variables x1, …, xn. Then change order of integration and evaluate read more »

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Des Herrn Geburt

Der Mensch war Gottes Bild.
Weil dieses Bild verloren,
Wird Gott, ein Menschenbild,
In dieser Nacht geboren.

Author: 
Andreas Gryphius
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Positivity of Szegö's rational function

Errata and addenda are contained in an additional document.

Abstract

We consider the problem of deciding whether a given rational function has a power series expansion with all its coefficients positive. Introducing an elementary transformation that preserves such positivity we are able to provide an elementary proof for the positivity of Szegö's function

$$ \frac{1}{(1-x)(1-y)+(1-y)(1-z)+(1-z)(1-x)} $$
Download:
application/pdf icon
positivity.pdf
application/pdf icon
positivity-addendum.pdf

I Am Not Yours

I am not yours, not lost in you,
Not lost, although I long to be
Lost as a candle lit at noon,
Lost as a snowflake in the sea.

You love me, and I find you still
A spirit beautiful and bright,
Yet I am I, who long to be
Lost as a light is lost in light.

Oh plunge me deep in love -- put out
My senses, leave me deaf and blind,
Swept by the tempest of your love,
A taper in a rushing wind.

Author: 
Sarah Teasdale
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Nothing Gold Can Stay

Nature's first green is gold,
Her hardest hue to hold.
Her early leaf's a flower;
But only so an hour.
Then leaf subsides to leaf.
So Eden sank to grief,
So dawn goes down to day.
Nothing gold can stay.

Author: 
Robert Lee Frost
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The Sin of Omission

It isn't the thing you do dear,
It's the thing you leave undone
That gives you a bit of a heartache
At setting of the sun.

The tender word forgotten,
The letter you did not write,
The flowers you did not send, dear,
Are your haunting ghosts at night.

The stone you might have lifted
Out of a brother's way;
The bit of heartsome counsel
You were hurried too much to say;

The loving touch of the hand, dear,
The gentle, winning tone
Which you had no time nor thought for
With troubles of your own.

Those little acts of kindness
So easily out of mind, read more »

Author: 
Margaret E. Sangster
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Date: Dec 10, 2007

StuVo talk on nonstandard analysis

These are complementary notes for a StuVo talk I gave at Technische Universität Darmstadt, 10 December 2007. While this text is supposed to be informal in nature, any corrections as well as suggestions are very welcome. read more »

Attachment: 
application/pdf icon
nonstandard.pdf
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Date: Oct 12, 2007

Hiring a secretary

Imagine you want to hire exactly one secretary. There is a fixed number, say, N persons available for this job and you may invite each of them for an interview. However, you have to tell each one right after the interview if you will hire her. Now, what is your strategy? read more »

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