# Browse Dept. of Mathematics by Title

• (2003)
Let R be a model of an o-minimal theory T. We define the "T-levels" of R and explore their connection to tame substructures of R , subject to a few easily satisfied assumptions. This leads to results about the ...

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• (2009)
In this dissertation, we study the Tarry-Escott problem and some related diophantine systems over Z and over some quadratic fields. We give infinitely many solutions of the Tarry-Escott problem over Zi of degrees 2, ...

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• (1999)
S. Ramanujan's last letter to G. H. Hardy contains the definition of mock theta functions, a list of 17 mock theta functions, and 5 identities related to mock theta functions. Also, Ramanujan's lost notebook contains many ...

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• (2001)
In Chapter 6, we have discuss matricially holomorphic mappings between two TROs. We show that the Mobius transformation is matricially holomorphic.

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• (2017-07-07)
This thesis includes four chapters. In Chapter 1, we briefly introduce the history and the main results of the topics of this thesis: the distribution of $k$-free numbers and the derivative of the Riemann zeta-function, ...

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• (1967)

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• (1998)
On page 54, Ramanujan recorded certain summations of theta functions, which may be called the "circular summations of theta functions." In Chapter 7, we discuss these identities with elementary proofs.

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• (1992)
We consider three separate topics in nonlinear optimization, one theoretical topic and two algorithmic topics. Each of these topics deals with a broad class of nonlinear optimization problems. We first introduce and analyze ...

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• (1958)

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• (1953)

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• (1966)

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• (1976)

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• (2010-08-20)
Proving the existence or nonexistence of structures with specified properties is the impetus for many classical results in discrete mathematics. In this thesis we take this approach to three different structural questions ...

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• (2009)
In the second chapter we study the Multiplicative Partition Function. In the third chapter we study an analog of the abc conjecture for arithmetical functions in r variables over a field K of characteristic zero.

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• (2000)
In the last chapter we consider the problem of determining how large an integer M should be so that almost every subset of {l, ..., N} of size M contains at least one arithmetic progression of length k. We also investigate ...

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• (1986)
In chapter 1 we investigate the A(,s)(n,d) problem in the Plotkin Region. The problem is to finding the maximum number of codewords in a code on an alphabet with s symbols that has length n and minimum Hamming distance d. ...

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• (1984)
In this dissertation we present a number of new results in combinatorial number theory. Chapter I discusses a generalization of B(,2)-sequences which are used in Chapter II and Chapter III to obtain short interval results ...

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• (1993)
New results are proved on several problems in extremal graph theory.

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• (1953)

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• (1959)

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