Related papers: Special Classes of CR Singularities I
There are proven few analogues of the Theorem of Moser using The Approximation Theorem of Artin.
Let a real-analytic manifold $M$ formally (holomorphically) equivalent to the following model…
It is constructed a normal form for a class of real-smooth surfaces M\subset\mathbb{C}^{2} defined near a degenerate CR singularity.
It is formally constructed a normal form for a class of real-formal surfaces defined near a CR Singularity.
In the classification of real singularities by Arnold et al. (1985), normal forms, as representatives of equivalence classes under right equivalence, are not always uniquely determined. We describe the complete structure of the equivalence…
It is constructed a Formal Normal Form for a Special Class of Real-Smooth Submanfolds in $\mathbb{C}^{2N}$.
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
Owing to the analogy between the Connes-Kreimer theory of the renormalization and the integrable systems, we derive the differential equations of the unit mass for the renormalized character $\phi_+$ and the counter term $\phi_-$. We give…
In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.
The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…
We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.
We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by…
We prove an infinite analogue of the main theorem of discrete Morse theory formulated in terms of discrete Morse matchings. Our theorem holds under the assumption that the given Morse matching induces finitely many equivalence classes of…
We prove that every simplicial complex is the dual complex of some simple normal crossing divisor in a smooth variety. As an application, we simplify and extend the results of Kapovich--Koll\'ar (math.AG:1109.4047) on the existence of…
We develop a technique for normalization for $\infty$-type theories. The normalization property helps us to prove a coherence theorem: the initial model of a given $\infty$-type theory is $0$-truncated. The coherence theorem justifies…
To any finite simplicial complex X, we associate a natural filtration starting from Chari and Joswig's discrete Morse complex and abutting to the matching complex of X. This construction leads to the definition of several homology theories,…
In this article, we prove a class of normal dilation matrices affirming the Marcus-de Oliveira conjecture.
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…
For strongly connected, pure $n$-dimensional regular CW-complexes, we show that {\it evenness} (each $(n{-}1)$-cell is contained in an even number of $n$-cells) is equivalent to generalizations of both cycle decomposition and…
Imposing some conditions on derivatives of the known functions, using the Fiber Contraction Theorem we prove the existence of $C^1$ solutions of a class of iterative functional equations which involves iterates of the unknown functions and…