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A subset of {1,2,3,...}^n whose non-computability leads to the existence of a Diophantine equation whose solvability is logically undecidable
Hilbert’s Tenth Problem logically undecidable Diophantine equation Logic
2011/9/22
Abstract: Let B(n)={(x_1,...,x_n) \in {1,2,3,...}^n: for each positive integers y_1,...,y_n the conjunction
(\forall i,j,k \in {1,...,n} (x_i+x_j=x_k ==> y_i+y_j=y_k)) AND
\forall i,j,k \in {1,......
Existence of Gibbs measure for a model of T-tessellations
Gibbs measure model of T-tessellations
2011/1/20
Some man-made landscapes, such as plots of land may be viewed as Ttessellations,that is a tessellations of a subset of the plane, where all vertices are degree three and with one flat angle. Adamczyk ...
Existence of doubling measures via generalised nested cubes
doubling measures via generalised nested cubes
2010/11/9
Using generalised dyadic cubes and the mass distribution principle, we give a straightforward new proof for the existence of doubling measures in complete doubling metric spaces.
Existence of isoperimetric regions in contact sub-Riemannian manifolds
isoperimetric regions sub-Riemannian manifolds
2010/11/9
We prove existence of regions minimizing perimeter under a volume constraint in contact sub-Riemannian manifolds such that their quotient by the group of contact transformations preserving the sub-Rie...
Existence of Spherically Symmetric Initial Data with Zero Energy, Unit Mass, and Virial less than - 1/2 for the Relativistic Vlasov-Poisson Equation with Attractive Coupling
Zero Energy Unit Mass
2010/11/19
In a recent paper, Kiessling and Tahvildar-Zadeh proved that any spherically symmetric classical solution of the attractive relativistic Vlasov-Poisson equation launched by sufficiently regular initi...
Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems with Discontinuous Mappings
Generalized vector quasi-equilibrium problem Upper semi-continuity Lower semi-contin-uity Fixed point Existence
2007/12/12
Let $X,Y$ be two finite-dimensional topological vector spaces, $Z$ a Hausdorff topological vector space, $K\subset X$ and $D\subset Z$ be two nonempty sets, $C$ be a pointed, closed, and convex cone i...