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Classical Teichmüller theory provides links between complex analytic and dynamical quantities defined on Riemann surfaces with conformal hyperbolic metrics. More precisely, properties of the geodesic ...
We provide a natural interpretation of the secondary Euler characteristic and generalize it to higher Euler characteristics. For a compact oriented manifold of odd dimension, the
secondary Euler char...
Closed Form Summation for Classical Distributions: Variations on Theme of De Moivre
Binomial distribution Stirling's formula his- tory of probability Pearson curves Stein's identity mean absolute deviation.
2015/7/14
De Moivre gave a simple closed form expression for the mean
absolute deviation of the binomial distribution. Later authors showed
that similar closed form expressions hold for many of the other cl...
Some Critical Support for Power Laws and their variations
Some Critical Support Power Laws their variations Adaptation and Self-Organizing Systems
2012/4/26
The paper "Critical Truths About Power Laws" (Science, 335, pp665-666) by MPH Stumpf MPH and MA Porter is commented.
Abstract: We study variations of the G_2 structure on the unit tangent sphere bundle, introduced in [Alb2,AlbSal1,AlbSal2] and now called gwistor space. We analize the equations of calibration and coc...
The Fuglede-Kadison determinant, theme and variations
Determinant Fuglede-Kadison determinant Banach algebra
2011/8/25
Abstract: We review the definition of determinants for finite von Neumann algebras, due to Fuglede and Kadison (1952), and a generalisation for appropriate groups of invertible elements in Banach alge...
Sections hyperplanes à singularités simples et exemples de variations de structure de Hodge
Sections hyperplanes à singularités exemples de variations de structure de Hodge
2011/1/20
We construct smooth complex projective varieties of dimension 3 to 6 with variations of Hodge structure, by generalizing an example of J. Carlson and C. Simpson in dimension 2. Then, we study some of ...
Oscillator Variations of the Classical Theorem on Harmonic Polynomials
Oscillator Variations Classical Theorem Harmonic Polynomials
2011/1/21
We study two-parameter oscillator variations of the classical theorem on har-monic polynomials, associated with noncanonical oscillator representations of sl(n, F) and o(n, F).
Composition Functionals in Fractional Calculus of Variations
Fractional calculus of variations Composition of functionals Fractional Euler–Lagrange equations
2010/12/6
We prove Euler–Lagrange and natural boundary necessary optimality conditions for fractional problems of the calculus of variations which are given by a composition of functionals. Our approach uses th...
Interpretations of the Beurling–Lax–Halmos Theorem on invariant subspaces of the unilateral shift are explored using the language of Hilbert modules. Extensions and consequences are considered in both...
Variations on Fintushel-Stern Knot Surgery on 4-manifolds
Fintushel-Stern Knot Surgery 4-manifolds
2010/3/1
We discuss some consequences Fintushel-Stern `knot surgery' operation coming from its handlebody description. We give some generalizations of this operation and give a counterexample to their conjectu...
On a Non-Standard Convex Regularization and the Relaxation of Unbounded Integral Functionals of the Calculus of Variations
Non-Standard Convex Regularization Integral Functionals Calculus of Variations
2009/1/20
The analysis of the relationships between the functional $F^{(\infty)}(\Omega,\cdot) \colon u \in W^{1,\infty}(\Omega) \mapsto \inf$ $\{\liminf_h \int_\Omega f(\nabla u_h)dx : \{u_h\}$ $\subseteq W^{1...
We consider the stability of solutions of variational problems with respect to perturbations of the integrand, raised by S. M. Ulam [A Collection of Mathematical Problems, Interscience, Los Alamos, 1...
Some Inequalities for Spectral Variations
Spectral variation Unitarily invariant norm Hadamard product Relative perturbation theorem
2008/6/27
Over the last couple of decades, significant progress for the spectral variation of a matrix has been made in partially extending the classical Weyl and Lidskii theory [11,17] to normal matrices and e...