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Line bundles and the Thom construction in noncommutative geometry
Line bundles Thom construction noncommutative geometry
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2011/1/19
The idea of a line bundle in classical geometry is transferred to noncommutative geometry by the idea of a Morita context. From this we can construct Z and N graded algebras, the Z graded algebra bein...
Geometry of free cyclic submodules over ternions
Geometry of free cyclic submodules ternions
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2011/1/19
Given the algebra T of ternions (upper triangular 2 ×2 matrices)over a commutative field F we consider as set of points of a projective line over T the set of all free cyclic submodules of T2. This se...
Universal Hyperbolic Geometry II: A pictorial overview
Universal Hyperbolic Geometry II pictorial overview
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2011/1/18
This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished...
Geometry and Energy of Non-abelian Vortices
Geometry Energy of Non-abelian Vortices
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2011/3/4
We study pure Yang–Mills theory on × S2, where is a compact Riemann surface, and invariance is assumed under rotations of S2. It is well known that the self-duality equations in this set-up reduce...
Geometry of maximum likelihood estimation in Gaussian graphical models
Geometry of maximum likelihood estimation Gaussian graphical models
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2011/1/21
We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to nd exact lower bounds on the number of observations...
Quantum Gravity coupled to Matter via Noncommutative Geometry
Quantum Gravity Matter Noncommutative Geometry
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2011/3/2
We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construc-tion which encodes the kinematics of quantum gravity.
Integral geometry for the taxicab metric
Integral geometry taxicab metric
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2011/3/1
Classical integral geometry takes place in Rn equipped with the Euclidean metric. We begin to develop integral geometry for Rn equipped with the taxicab metric (induced by the 1-norm).
Tracing light propagation to the intrinsic accuracy of space-time geometry
relativity gravitation space-time geometry weak field approximations light propagation
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2011/3/4
Advancement in astronomical observations and technical instrumentation requires coding light
propagation at high level of precision; this could open a new detection window of many subtle relativistic...
The comparison of geometry skills learning in dynamic geometry educational places based on algebraic and traditional (static) educational places in Iran educational system
geometry dynamic educational traditional
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2010/9/26
With development in communication and information technology and fast distribution of personal computers, the use of technology in training has improved. The foundation of mathematics educational fiel...
Weakly regular T2 symmetric spacetimes. The global geometry of future developments
regular T2 symmetric spacetimes global geometry future developments
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2011/3/4
Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum
Einstein spacetimes with T2–symmetry, establish the global well-posedness of the initial value
problem for Eins...
Weakly regular T2 symmetric spacetimes. The global geometry of future developments
regular T2 symmetric spacetimes global geometry of future developments
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2011/3/4
Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum
Einstein spacetimes with T2–symmetry, establish the global well-posedness of the initial value
problem for Eins...
Virial Theorem and Hypervirial Theorem in a spherical geometry
Viral Theorem Perturbation Theory Spherical geometry
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2011/2/25
In the paper, we obtain the Virial Theorem and Hypervirial Theorem in a spherical geometry.
The Hypervirial Theorem and Hellmann-Feynman Theorem are used to formulate a perturbation
theorem without ...
Basic Riemannian Geometry and Sobolev Estimates used in Symplectic Topology
Basic Riemannian Geometry Sobolev Estimates used Symplectic Topology
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2011/2/22
This note collects a number of standard statements in Riemannian geometry and in Sobolevspace
theory that play a prominent role in analytic approaches to symplectic topology. These
include relations...
The Convex Geometry of Linear Inverse Problems
The Convex Geometry Linear Inverse Problems
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2011/1/4
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimensi...
Transport barrier for the radial diffusion due to the ExB drift motion of guiding centers in cylindrical confinement geometry
Transport barrier for the radial diffusion ExB drift motion cylindrical confinement geometry
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2010/12/28
We consider the radial transport of test particles due to the E×B drift motion in the guiding center approximation. In a configuration where the magnetic field is constant and uniform in linear device...