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There exists no distance-regular graph with intersection array {55,36,11;1,4,45}
distance-regular graph intersection array
2010/11/12
We prove that a distance-regular graph with intersection array $\{55,36,11;1,4,45\}$ does not exist. This intersection array is from the table of feasible parameters for distance-regular graphs in "Di...
The theory of valued difference fields $(K, \sigma, v)$ depends on how the valuation $v$ interacts with the automorphism $\sigma$. Two special cases have already been worked out - the isometric case,...
Trajectory averaging for stochastic approximation MCMC algorithms
Trajectory averaging MCMC algorithms
2010/11/18
The subject of stochastic approximation was founded by Robbins and Monro [Ann. Math. Statist. 22 (1951) 400--407]. After five decades of continual development, it has developed into an important area...
Ramsey theory for words over a finite alphabet was unified in the work of Carlson and Furstenberg-Katznelson. Carlson, in the same work, outlined a method to extend the theory for words over an infin...
On the conjugacy of pure imaginary elements of quaternion algebras and Cayley algebras
quaternion algebras Cayley algebras
2010/11/9
In the quatenions ($\H$, $\H'$, $\H^{C}$) and octonions ($\gC$, $\gC^\prime$, $\gC^C$), we show some results on the conjugacy of two pure imaginary non-zero elements with same norm.
The Prouhet-Tarry-Escott problem for Gaussian integers
The Prouhet-Tarry-Escott problem Gaussian integers
2010/11/11
Given natural numbers $n$ and $k$, with $n>k$, the Prouhet-Tarry-Escott (PTE) problem asks for distinct subsets of $\Z$, say $X=\{x_1,...,x_n\}$ and $Y=\{y_1,...,y_n\}$, such that \[x_1^i+...+x_n^i=y...
A probabilistic algorithm approximating solutions of a singular PDE of porous media type
A probabilistic algorithm approximating solutions singular PDE
2010/11/19
The object of this paper is a one-dimensional generalized porous media equation (PDE) with possibly discontinuous coefficient $\beta$, which is well-posed as an evolution problem in $L^1(\mathbb{R})$...
Operator system structures on the unital direct sum of C*-algebras
Operator system structures direct sum of C*-algebras
2010/11/11
This work is motivated by R\u{a}dulescu's result on the comparison of C*-tensor norms on C*(F_n)\otimes C*(F_n).
For unital C*-algebras A and B, there are natural inclusions of A and B into the unit...
Tight Bounds for Mixing of the Swendsen-Wang Algorithm at the Potts Transition Point
the Swendsen-Wang Algorithm the Potts Transition Point
2010/11/19
We study two widely used algorithms for the Potts model on rectangular subsets of the hypercubic lattice Z^d - heat bath dynamics and the Swendsen-Wang algorithm - and prove that, under certain circu...
Congruences for Andrews' spt-function modulo powers of 5, 7 and 13
Andrews' spt-function math
2010/11/15
Congruences are found modulo powers of 5, 7 and 13 for Andrews' smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan's partition congruences modulo powers of 5, 7 a...
Gromov-Witten invariants and rational curves on Grassmannians
Gromov-Witten invariants rational curves on Grassmannians
2010/11/15
We study the enumerative significance of the s-pointed genus zero Gromov-Witten invariant on a homogeneous space X. For that, we give an interpretation in terms of rational curves on X.
On Pseudo-Convex Partitions of a Planar Point Set
On Pseudo-Convex Partitions Planar Point Set
2010/11/15
Aichholzer et al. [{\it Graphs and Combinatorics}, Vol. 23, 481-507, 2007] introduced the notion of pseudo-convex partitioning of planar point sets and proved that the pseudo-convex partition number ...
On summable form of Poisson-Mehler kernel for big q-Hermite and Al-Salam-Chihara polynomials
Poisson-Mehler kernel big q-Hermite Al-Salam-Chihara polynomials
2010/11/15
Using special technique of expansion of the ratio of densities we obtain simple closed forms for certain kernels analogous to Poisson-Mehler, also asymmetric, for certain values of parameters, proving...
Fluid Simulations with Localized Boltzmann Upscaling by Direct Simulation Monte-Carlo
Localized Boltzmann Upscaling Simulation Monte-Carlo
2010/11/18
In the present work, we present a novel numerical algorithm to couple the Direct Simulation Monte Carlo method (DSMC) for the solution of the Boltzmann equation with a finite volume like method for t...
A numerical stability investigation of strong ZND detonations for Majda's model
numerical stability investigation ZND Majda's model
2010/11/12
We carry out a systematic numerical stability analysis of ZND detonations of Majda's model with Arrhenius-type ignition function, a simplified model for reacting flow, as heat release and activation ...