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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Coordinate Systems And Bounded Isomorphisms, David R. Pitts, David R. Pitts
Coordinate Systems And Bounded Isomorphisms, David R. Pitts, David R. Pitts
Department of Mathematics: Faculty Publications
For a Banach D-bimoduleMover an abelian unital C*-algebraD, we define E1(M) as the collection of norm-one eigenvectors for the dual action of D on the Banach space dual M#. Equip E1(M) with the weak*-topology. We develop general properties of E1(M). It is properly viewed as a coordinate system for M when M C, where C is a unital C*-algebra containing D as a regular MASA with the extension property; moreover, E1(C) coincides with Kumjian’s twist in the context of C*-diagonals. We identify the C*-envelope of a subalgebra A of a C*-diagonal when D A C. For triangular subalgebras, each containing …
Reversals And Transpositions Over Finite Alphabets, A. J. Radcliffe, A. D. Scott, E. L. Wilmer
Reversals And Transpositions Over Finite Alphabets, A. J. Radcliffe, A. D. Scott, E. L. Wilmer
Department of Mathematics: Faculty Publications
Extending results of Christie and Irving, we examine the action of reversals and transpositions on finite strings over an alphabet of size k. We show that determining reversal, transposition, or signed reversal distance between two strings over a finite alphabet is NP-hard, while for “dense” instances we give a polynomial-time approximation scheme. We also give a number of extremal results, as well as investigating the distance between random strings and the problem of sorting a string over a finite alphabet.
Pseudo-Codewords Of Cycle Codes Via Zeta Functions, Ralf Koetter, Wen-Cheng W. Li, Pascal O. Vontobel, Judy L. Walker
Pseudo-Codewords Of Cycle Codes Via Zeta Functions, Ralf Koetter, Wen-Cheng W. Li, Pascal O. Vontobel, Judy L. Walker
Department of Mathematics: Faculty Publications
Cycle codes are a special case of low- density parity-check (LDPC) codes and as such can be decoded using an iterative message-passing decod- ing algorithm on the associated Tanner graph. The existence of pseudo-codewords is known to cause the decoding algorithm to fail in certain instances. In this paper, we draw a connection between pseudo- codewords of cycle codes and the so-called edge zeta function of the associated normal graph and show how the Newton polyhedron of the zeta function equals the fundamental cone of the code, which plays a crucial role in characterizing the performance of iterative de- coding …
Weak Solutions To The Cauchy Problem Of A Semilinear Wave Equation With Damping And Source Terms, Petronela Radu
Weak Solutions To The Cauchy Problem Of A Semilinear Wave Equation With Damping And Source Terms, Petronela Radu
Department of Mathematics: Faculty Publications
In this paper we prove local existence of weak solutions for a semilinear wave equation with power-like source and dissipative terms on the entire space ℝn. The main theorem gives an alternative proof of the local in time existence result due to J. Serrin, G. Todorova and E. Vitillaro, and also some extension to their work. In particular, our method shows that sources that are not locally Lipschitz in L2 can be controlled without any damping at all. If the semilinearity involving the displacement has a “good” sign, we obtain global existence of solutions.
Matrix Model Superpotentials And Calabi–Yau Spaces: An A-D-E Classification, Carina Curto
Matrix Model Superpotentials And Calabi–Yau Spaces: An A-D-E Classification, Carina Curto
Department of Mathematics: Faculty Publications
We use F. Ferrari’s methods relating matrix models to Calabi-Yau spaces in order to explain Intriligator and Wecht’s ADE classification of N = 1 superconformal theories which arise as RG fixed points of N = 1 SQCD theories with adjoints. The connection between matrix models and N = 1 gauge theories can be seen as evidence for the Dijkgraaf–Vafa conjecture. We find that ADE superpotentials in the Intriligator–Wecht classification exactly match matrix model superpotentials obtained from Calabi-Yau’s with corresponding ADE singularities. Moreover, in the additional Ô, Â, Dˆ and Ê cases we find new singular geometries. These ‘hat’ geometries are …