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Mathematics and Natural Sciences

Using CPLEX
 Date Added:
 03/28/2009
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 5
CPLEX is optimization software developed and sold by ILOG, Inc. It can be used to solve a variety of different optimization problems in a variety of computing environments. Here we will discuss only its use to solve “linear programs” and will discuss only its use in interactive mode. 
Using Approximate Secant Equations in Limited Memory Methods for Multilevel Unconstrained...
 Date Added:
 09/29/2011
 Hits:
 1
The properties of multilevel optimization problems defined on a hierarchy
of discretization grids can be used to define approximate secant equations, which describe
the secondorder behavior of the objective function. Following earlier work by
Gratton and Toint (2009) we introduce a quasiNewton method (with a linesearch). 
Upper Bounds for RLinear Resolvents
 Date Added:
 09/29/2011
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 1
We discuss upper bounds for the resolvent of an Rlinear operator in Cd. Mathematics Subject Classification (2010). 47A10. Real linear operator, resolvent operator, spectrum. The resolvent ? ? (?I ? A)?1 of a d × d complex matrix A is a matrix valued function with rational elements. Thus, in particular, all singularities are poles of at most order d, and the following lower and upper bound hold1 dist(?, ?(A)) dist(?, ?(A))d , (1.1) where ?(A) denotes the set of eigenvalues of A.

Universality of Random Matrices and Local Relaxation Flow
 Date Added:
 09/14/2011
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 1
Consider the Dyson Brownian motion with parameter ?, where
? = 1, 2, 4 corresponds to the eigenvalue flows for the eigenvalues of symmetric,
hermitian and quaternion selfdual ensembles. For any ? ? 1, we
prove that the relaxation time to local equilibrium for the Dyson Brownian
motion is bounded above by N ?? for some ? >0. 
Units of Group Algebras of NonAbelian Groups of Order 16 and Exponent...
 Date Added:
 09/28/2011
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 1
Let U(KG) be the unit group of the group algebra KG of the field K over the
group G and V (KG) be the normalized unit group of KG. It is well known
that V (KG) = KG?1 where G is a finite pgroup and K is a field of characteristic
p. Sandling in [9], provides a basis for V (FpG) where G is an abelian
pgroup and Fp is the Galois field of pelements.