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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars:Dirichlet is not just singular and bad
狄利克雷 单数 坏的
2023/4/27
QUASIHOMOGENEOUS THREE-DIMENSIONAL REAL ANALYTIC LORENTZ METRICS DO NOT EXIST
THREE-DIMENSIONAL LORENTZ METRICS
2015/10/14
We show that a germ of a real analytic Lorentz metric on R
3 which is locally homogeneous on an
open set containing the origin in its closure is necessarily locally homogeneous. We classifiy L...
We construct a hyperbolic group with a hyperbolic subgroup for which inclusion does not induce a map of the boundaries.
The unbounded dead end depth property is not a group invariant
group invariant depth property
2015/8/26
The dead-end depth of an element g of a group with finite generating set A is the distance from g to the complement of the radius d(1,g) closed ball, in the word metric d. We exhibit a finitely presen...
The Convergenceof an Euler Approximation of an Initial ValueProblemIs Not Always Obvious
Euler Approximation Initial ValueProblemIs Not Always Obvious
2015/8/26
The Convergenceof an Euler Approximation of an Initial ValueProblemIs Not Always Obvious.
The tricorn is the connectedness locus in the space of antiholomorphic quadratic polynomials z 7! z2 + c. We prove that the tricorn is not locally connected and not even pathwise connected, confirming...
Why We Can Not Surpass Capacity: The Matching Condition
Iterations coding system coding binary input
2015/8/21
We show that iterative coding systems can not surpass capacity using only quantities which naturally appear in density evolution. Although the result in itself
is trivial, the method which we apply s...
Dynamical system state need not have spectrum
Dynamic system nonlinear dynamical systems differential equation
2015/8/13
Recently there has been much study of nonlinear dynamical systems (differential equations) which have chaotic solutions. While there is not precise definition of what a chaotic solution is, it is gene...
In this paper, the quantum logical ‘or’ is analyzed from a physical perspective.
We show that it is the existence of EPR-like correlation states for the quantum
mechanical entity under consideration...
To Hash or Not to Hash Again?(In)Differentiability Results for H2 and HMAC
Indifferentiability Hash functions HMAC
2012/12/4
We show that the second iterate H2(M) = H(H(M)) of a random oracle H cannot achieve strong security in the sense of indifferentiability from a random oracle. We do so by proving that indifferentiabili...
Cannon-Thurston maps do not always exist
hyperbolic group Cannon–Thurston map Group Theory
2012/6/19
We construct an example of a hyperbolic group with a hyperbolic subgroup for which the Cannon-Thurston map does not exist. That is, inclusion does not induce a map of the boundaries.
Singularities and nonhyperbolic manifolds do not coincide
Semi-dispersing billiards hyperbolicity ergodicity local ergodicity invariant manifolds Chernov–Sinai Ansatz
2012/5/9
We consider the billiard flow of elastically colliding hard disks on the flat 2-torus and prove that no singularity manifold can locally coincide with a manifold describing future non-hyperbolicity of...
Not every object in the derived category of a ring is Bousfield equivalent to a module
Not every object derived category ring Bousfield equivalent module
2012/3/1
We consider the derived category of a specific non-Noetherian ring \Lambda, and show that there are objects in D(\Lambda) that are not Bousfield equivalent to any module. This answers a question posed...
Bergman completeness is not a quasi-conformal invariant
quasi-conformal invariant Bergman completeness Complex Variables
2011/9/22
Abstract: We show that Bergman completeness is not a quasi-conformal invariant for general Riemann surfaces.
A 1-dimensional Peano continuum which is not an IFS attractor
Fractal Peano continuum Iterated Function System IFS-attractor
2011/9/15
Abstract: Answering an old question of M.Hata, we construct an example of a 1-dimensional Peano continuum which is not homeomorphic to an attractor of IFS.