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Algebraic boundaries of Hilbert's SOS cones
Positive polynomials K3 surfaces Hilbert's SOS cones
2011/8/31
Abstract: We study the geometry underlying the difference between non-negative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and quaternary q...
Approximate Parametrization of Space Algebraic Curves
Approximate Parametrization Space Algebraic Curves Algebraic Geometry
2011/8/30
Abstract: Given a non-rational real space curve and a tolerance $\epsilon>0$, we present an algorithm to approximately parametrize the curve. The algorithm checks whether a planar projection of the sp...
Algebraic Structures using Natural Class of Intervals
Algebraic Structures Natural Class of Intervals General Mathematics
2011/8/23
Abstract: This book has eleven chapters. Chapter one describes all types of natural class of intervals and the arithmetic operations on them. Chapter two introduces the semigroup of natural class of i...
On the degree of a Kloosterman sum as an algebraic integer
cyclotomic field Kloosterman sum
2011/8/22
Abstract: The maximal degree over rational numbers that an n-dimensinonal Kloosterman sum defined over a finite field of characteristic p can achieve is known to be (p-1)/d where d=gcd(p-1,n+1). Wan h...
Revisiting special relativity: A natural algebraic alternative to Minkowski spacetime
Special Relativity, Geometric algebra, Clifford algebra, Lorentz transformation,Minkowski
2011/9/2
Minkowski famously introduced the concept of a space-time continuum in 1908, merging three dimensional space with an imaginary time dimension represented by ict, a framework which naturally produced t...
Revisiting special relativity: A natural algebraic alternative to Minkowski spacetime
Special Relativity Geometric algebra Clifford algebra Lorentz transformation
2011/7/28
Revisiting special relativity: A natural algebraic alternative to Minkowski spacetime.
Super Distributions, Analytic and Algebraic Super Harish-Chandra pairs
Super Distributions Analytic Algebraic Super Harish-Chandra pairs
2011/7/27
Abstract: The purpose of this paper is to extend the theory of Super Harish-Chandra pairs, originally developed by Koszul for Lie supergroups, to analytic and algebraic supergroups, in order to obtain...
Compress-and-Forward Scheme for a Relay Network: Approximate Optimality and Connection to Algebraic Flows
Compress-and-Forward Scheme Relay Network Approximate Optimality Connection Algebraic Flows
2011/1/17
We study a wireless relay network, with a single source and a single destination.Our main result is to show that an appropriate compress-and-forward scheme supports essentially the same reliable data ...
Algebraic arctic curves in the domain-wall six-vertex model
Algebraic arctic domain-wall six-vertex model
2011/1/20
The arctic curve, i.e. the spatial curve separating ordered (or ‘frozen’) and disordered (or ‘temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root...
Note on a relation between Randic index and algebraic connectivity
Randi´ c index algebraic connectivity edge connectivity diameter
2011/2/24
A conjecture of AutoGraphiX on the relation between the Randi´c index R and the algebraic connectivity a of a connected graph G is:R a n − 3 + 2p2 2 ! / 2(1 − cos n ) with ...
Let Q(α) and Q(β) be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, Q(β) → Q(α). The algorithm is particularly efficient if the number of isomorphisms is o...
An improvement upon unmixed decomposition of an algebraic variety
unmixed decomposition weakly non-degenerate conditions
2011/1/18
Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Sever...
Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
Quantum-to-Classical Correspondence Hubbard-Stratonovich Dynamical Systems
2011/3/2
We propose a Lie-algebraic duality approach to analyze non-equilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of Hubbard-St...
Vanishing of algebraic Brauer-Manin obstructions
Hasse principle weak approximation Brauer-Manin obstruction
2011/1/18
Let X be a smooth geometrically integral algebraic variety over a number field k with finitely generated geometric Picard group. We prove that under certain conditions, certain algebraic Brauer-Manin ...
An algebraic analysis of the two state Markov model on tripod trees
Phylogenetics Identi ability Invariant Two-State-Model
2011/3/1
Methods of phylogenetic inference use more and more complex models to generate trees from data. However, even simple models and their implications are not fully understood.Here, we investigate the two...