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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...
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...
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...
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...
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...
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.
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).
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...
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...
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...
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...
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 ...
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...
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...
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...

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