Related papers: Special Classes of CR Singularities I
We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…
We give a presentation of Simple Type Theory as a clausal rewrite system in Polarized deduction modulo.
The similarity renormalization group procedure formulated in terms of effective particles is briefly reviewed in a series of selected examples that range from the model matrix estimates of its numerical accuracy to issues of the Poincare…
We introduce and study categorical realizations of quivers. This construction generalizes comma categories and includes representations of quivers on categories, twisted representations of quivers and bilinear pairings as special cases. We…
We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.
In this work, singular surfaces are obtained from smooth orientable closed surfaces by applying three basic simple loop operations, collapsing operation, zipping operation and double loop identification, each of which produces different…
We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.
A hierarchy of normalized classes of generalized Burgers equations is studied. The equivalence groupoids of these classes are computed. The equivalence groupoids of classes of linearizable generalized Burgers equations are related to those…
This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the…
We construct flat metrics in a given conformal class with prescribed singularities of real orders at marked points of a closed real surface. The singularities can be small conical, cylindrical, and large conical with possible translation…
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
We study the classes of filters F on N such that the weak and strong F-convergence of sequences in l1 coincide. We study also an analogue of l1 weak sequential completeness theorem for filter convergence.
Main results are, firstly, a generalization of the Conley-Zehnder index from ODEs to the delay equation at hand and, secondly, the equality of the Morse index and the clockwise normalized Conley-Zehnder index.
In this paper, we give the explicit bounds for the data of objects involved in some basic theorems of Singularity theory: the Inverse, Implicit and Rank Theorems for Lipschitz mappings, Splitting Lemma and Morse Lemma, the density and…
We extend the validity of the Penrose singularity theorem to spacetime metrics of regularity $C^{1,1}$. The proof is based on regularisation techniques, combined with recent results in low regularity causality theory.
The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation…
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
We establish the existence of Springer isomorphisms for reductive group schemes over general base schemes. For this, we first study centralizers of fiberwise regular sections of reductive group schemes, and we establish their flatness in…
We present a theorem which generalizes the classical Euler's theorem on congruencies: if $(a,m)=1$ then $a^ \phi(m) \equiv 1 (mod m)$ for the case when $a$ and $m$ are not relatively primes.
A great number of articles widen a known scientific result $P(a)$ (such as: a theorem, an inequality, or a math/physics/chemical etc. proposition or formula) by a simple recurrence procedure and using, in the proof, the proposition $P(a)$…