Related papers: Un th\'eor\`eme de Bloch presque complexe
It is well known that iterates of quasi-compact operators converge towards a spectral projection, whereas the explicit construction of the limiting operator is in general hard to obtain. Here, we show a simple method to explicitly construct…
In this paper we prove the probabilistic continuous complexity conjecture. In continuous complexity theory, this states that the complexity of solving a continuous problem with probability approaching 1 converges (in this limit) to the…
Let $k$ be a perfect field of characteristic $p > 0$, $W_n = W_n(k)$. For separated $k$-schemes of finite type, we explain how rigid cohomology with compact supports can be computed as the cohomology of certain de Rham-Witt complexes with…
The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it…
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.
We have defined almost separable space. We show that like separability, almost separability is $c$ productive and converse also true under some restrictions. We establish a Baire Category theorem like result in Hausdorff, Pseudocompacts…
We present an algebro-geometric proof of the K-semistability of the projective plane.
We give an elementary proof of an analogue of Fej\'er's theorem in weighted Dirichlet spaces with superharmonic weights. This provides a simple way of seeing that polynomials are dense in such spaces.
We introduce and study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfeld double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the algebraic structure of the triple,…
We establish an explicit quasi-isomophism of complexes, which is homogeneous in graded situation, from a given Cech complex of modules of generalized fractions.
We compute here the Borel complexity of the relation of isometry between separable Banach spaces, using results of Gao, Kechris and Weaver.
We generalize Rado's extension theorem to complex spaces.
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
We prove that a locally bounded and differentiable in the sense of Gateaux function given in a finite-dimensional commutative Banach algebra over the complex field is also differentiable in the sense of Lorch.
Approximation theorems for algebraic stacks over a number field $k$ are studied in this article. For G a connected linear algebraic group over a number field we prove strong approximation with Brauer-Manin obstruction for the classifying…
We prove that the Bredon homology or cohomology of the partition complex with fairly general coefficients is either trivial or computable in terms of constructions with the Steinberg module. The argument involves developing a theory of…
We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.
Based on the probability distribution observed in complex systems and an assumption that the probability distributions of complex systems satisfy a new generalized multiplication, it is proved that the statistical theory of complex systems…
By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their…