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$Top(X)$ within $\px$ ]{When lattices meet topology: $Top(X)$ within $\px$.}
$Top(X)$ within $\px$ lattices meet topology
2012/2/29
For a non-empty set $X$, the collection $Top(X)$ of all topologies on $X$ sits inside the Boolean lattice $\PP(\PP(X))$ (when ordered by set-theoretic inclusion) which in turn can be naturally identif...
Expansion of $k$-Schur functions for maximal $k$-rectangles within the affine nilCoxeter algebra
$k$-Schur functions $k$-rectangles affine nilCoxeter algebra Combinatorics
2011/9/14
Abstract: We give several explicit combinatorial formulas for the expansion of $k$-Schur functions indexed by maximal $k$-rectangles, $s_R^{(k)}$, in terms of the standard basis of the affine nilCoxet...
A chaotic system under periodic forcing can develop a periodically
visited strange attractor. We discuss simple models in which the phenomenon,
quite easy to see in numerical simulations, can be com...
Intrinsic branching structure within random walk on $\mathbb{Z}$
random walk branching process random environment invariant density
2011/1/17
In this paper, we reveal the branching structure for a non-homogeneous random walk with bounded
jumps. The ladder time T1, the first hitting time of [1,∞) by the walk starting from 0, could be expres...
Gaussian Relay Channel Capacity to Within a Fixed Number of Bits
Gaussian Relay Channel Capacity Fixed Number of Bits
2010/11/24
In this paper, we show that the capacity of the three-node Gaussian relay channel can be achieved to within 1 and 2 bit/sec/Hz using compress-and-forward and amplify-and-forward relaying, respectively...
On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics (math-ph)
2010/11/10
A gradient-holonomic approach for the Lax type integrability analysis of differentialdiscrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied, the rela...
A time-dependent Poisson random field model for polymorphism within and between two related biological species
A time-dependent Poisson random field model polymorphism biological species
2010/11/12
We derive a Poisson random field model for population site polymorphisms differences within and between two species that share a relatively recent common ancestor. The model can be either equilibrium ...
Any l-state solutions of the Woods-Saxon potential in arbitrary dimensions within the new improved quantization rule
Woods-Saxon potential improved quantization rule Pekeris approximation
2010/12/13
The approximated energy eigenvalues and the corresponding eigenfunctions of the spherical
Woods-Saxon effective potential in D dimensions are obtained within the new improved quantization rule for al...
Numerical relations within cubes and the estimation of central tendency
Interpolation Experimental design Shifting operator
2010/9/10
The discovery of relationships connecting data in cubical array is pertinent to data analysis. New equations that interrelate data at the vertices, edges, and sides of a cube are obtained by the shift...
Integral Mean Estimates for Polynomials whose Zeros are within a Circle
Polynomials Zeros of order $m$ Inequalities Polar derivatives
2010/1/22
Let be a polynomial of degree . Zygmund [11] has shown that for In this paper, we have obtained inequalities in the reverse direction for the polynomials having a zero of order at the origin. W...
The Extension of Majorization Inequalities within the Framework of Relative Convexity
Relative convexity Majorization Abel summation formula
2008/6/26
Some of the basic inequalities in majorization theory (Hardy-Littlewood-Pólya, Tomic-Weyl and Fuchs) are extended to the framework of relative convexity.
The Asymptotic Behavior of the Ruin Probability within a Random Horizon
Asymptotics extended regular variation class finite time ruin probability renewal model
2007/12/11
Subject to the assumption that the common distributionof claim sizes belongs to the extended regular variation class,the present work obtains a simple asymptotic formula for the ruinprobability within...