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Hierarchy Structure of Graphs and Weighted Condensations
Hierarchy Structure Graphs Weighted Condensations
2010/11/1
By natural way the hierarchy structure is introduced on directed graphs with weighted adjacencies. Embedded system of algebras of subsets of the set of vertices of such digraph and it's consolidation...
Application of Tree-like Structure of Graph to Matrix Analysis
Application Tree-like Structure Matrix Analysis
2010/11/1
Formulas for matrix determinants, algebraic adjunctions, characteristic polynomial coefficients, components of eigenvectors are obtained in the form of signless sums of matrix elements products taking...
This paper is withdrawn by the authors.
Cohomology on Toric Varieties and Local Cohomology with Monomial Supports
Cohomology Toric Varieties Local Monomial Supports
2010/11/1
We study the local cohomology modules H^i_B(R) for a reduced monomial ideal B in a polynomial ring R=k[X_1,...,X_n]. We consider a grading on R which is coarser than the Z^n-grading such that each com...
Nonuniformizable skew cylinders. A counterexample to the simultaneous uniformization problem
Nonuniformizable skew cylinders counterexample
2010/10/29
At the end of 1960-ths Yu.S.Ilyashenko stated the problem: is it true that for any one-dimensional holomorphic foliation with singularities on a Stein manifold leaves intersecting a transversal disc ...
Mirror symmetry and actions of braid groups on derived categories
Mirror symmetry actions braid groups derived categories
2010/10/29
Talk given at Harvard, January 1999, published in the Proceedings of the Harvard Winter School on mirror symmetry, vector bundles and lagrangian cycles, 1999, International Press. Surveys the joint wo...
Selfdual Einstein metrics and conformal submersions
Selfdual Einstein metrics conformal submersions
2010/10/29
Weyl derivatives, Weyl-Lie derivatives and conformal submersions are defined, then used to generalize the Jones-Tod correspondence between selfdual 4-manifolds with symmetry and Einstein-Weyl 3-manif...
Polynomial hulls and H-infinity control for a hypoconvex constraint
Polynomial hulls H-infinity control hypoconvex constraint
2010/10/29
We say that a subset of C^n is hypoconvex if its complement is the union of complex hyperplanes. Let D be the closed unit disk in C, T the unit circle. We prove two conjectures of Helton and Marshall...
Problems on geometric structures of projective embeddings
geometric structures projective embeddings
2010/10/29
This is a survey of our research on geometric structures of projective embeddings and includes some topics of our talks in several symposia during 1990-99. We clarify our main problem, which is to co...
Connections in Poisson Geometry I: Holonomy and Invariants
Connections Poisson Geometry I Holonomy Invariants
2010/11/1
We discuss contravariant connections on Poisson manifolds. For vector bundles, the corresponding operational notion of a contravariant derivative had been introduced by Izu Vaisman. We show that thes...
The Bisognano-Wichmann Theorem for Charged States and the Conformal Boundary of a Black Hole
The Bisognano-Wichmann Theorem Charged States Conformal Boundary
2010/11/2
Recent applications of Operator Algebras to Quantum Field Theory on a Curved Spacetime show that the incremental entropy associated with a quantum black hole, due the addition of a short range charge...
Let $p(z)$ be a monic polynomial of degree $n$, with complex coefficients, and let $q(z)$ be its monic factor. We prove an asymptotically sharp inequality of the form $\|q\|_{E} \le C^n \|p\|_E$, whe...
In this paper, we will define the inner-product and the norm in taxicab geometry and then we will discuss this inner-product geometrically.
On the Validity of the Borel-Hirzebruch Formula for Topological Actions
Lie group actions characteristic classes cohomology classifiying spaces weights
2010/3/4
We defined an equivalence among group actions and find sufficient conditions for actions of compact connected Lie groups on Euclidean spaces for which the topological version of the Borel-Hirzebruch f...
We construct an exact differential sequence which indicates certain relations between curvature, local flatness, torsion and simplicity of higher order connections. Our formulas are expressed explicit...