Related papers: Classification of near-normal sequences
We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…
For every positive integer $n$, we find a complete classification for planar graphs according to the collection of numbers of common neighbours for every $n$-tuple of distinct vertices. Our results expand the literature on planar graphical…
Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family…
In this paper the problem of finding a normal form of triangles and plane quadrilaterals up to similarity is considered. Several normal forms for triangles and a normal form for quadrilaterals of special case are described. Normal forms of…
The categories with noninvertible morphisms are studied analogously to the semisupermanifolds with noninvertible transition functions. The concepts of regular n-cycles, obstruction and the regularization procedure are introduced and…
In the present paper we construct normal numbers in base $q$ by concatenating $q$-ary expansions of pseudo polynomials evaluated at the primes. This extends a recent result by Tichy and the author.
In this paper, we introduce two types of general classes of even and odd $q$-Lidstone polynomial sequences. We prove essential properties related to them like the matrix and determinate form representation, the generating function,…
New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an $n$-point subset of the plane is…
We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in the case of symmetric n-ary…
Let $L=(L_d)_{d \in \mathbb N}$ be any ordered probability sequence, i.e., satisfying $0 < L_{d+1} \le L_d$ for each $d \in \mathbb N$ and $\sum_{d \in \mathbb N} L_d =1$. We construct sequences $A = (a_i)_{i \in \mathbb N}$ on the…
It is formally constructed a normal form for a class of real-formal surfaces defined near a CR Singularity.
Let A be an exact category, that is, an extension-closed full subcategory of an abelian category. Firstly, we give some necessary and sufficient conditions for A to have almost split sequences. Then, we study when an almost split sequence…
In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
We use the theory of q-characters to establish a number of short exact sequences in the category of finite-dimensional representations of the quantum affine groups of types A and B. That allows us to introduce a set of 3-term recurrence…
Given a real number $0.a_1a_2 a_3\dots$ that is normal to base $b$, we examine increasing sequences $n_i$ so that the number $0.a_{n_1}a_{n_2}a_{n_3}\dots$ are normal to base $b$. Classically it is known that if the $n_i$ form an arithmetic…
We give a canonical form of m-by-2-by-2 spatial matrices for equivalence over any field.
We look at thin interpolating sequences and the role they play in uniform algebras, Hardy spaces, and model spaces.
We define a class of "algebraic" random matrix channels for which one can generically compute the limiting Shannon transform using numerical techniques and often enumerate the low SNR series expansion coefficients in closed form. We…
Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian…
This paper establishes new restrictions for attainable enhanced principal rank characteristic sequences (epr-sequences). These results are then used to classify two related families of sequences that are attainable by a real symmetric…