Related papers: On Some Generalisations of Gauss Sequences
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.
We generalize the result about the congruence subgroup property for GGS-groups to the family of multi-GGS-groups; that is, all multi-GGS-groups except the one defined by the constant vector have the congruence subgroup property. Even if the…
We motivate and explore the possibility that extra SU(N) gauge groups may exist independently of the Standard Model groups, yet not be subgroups of some grand unified group. We study the running of the coupling constants as a potential…
Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…
The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \int d{\bf H} [P({\bf H})] \ln [P({\bf H})], with suitable constraints. Here we construct and analyze…
We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or…
An \emph{evolving Shelah-Spencer process} is one by which a random graph grows, with at each time $\tau \in {\bf N}$ a new node incorporated and attached to each previous node with probability $\tau^{-\alpha}$, where $\alpha \in (0,1)…
In this paper, we investigate seemingly unrelated regression (SUR) models that allow the number of equations (N) to be large, and to be comparable to the number of the observations in each equation (T). It is well known in the literature…
Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…
We present a concise survey of the running of gauge couplings in realistic models of gauge-Higgs grand unification in a slice of AdS$_5$ space and investigate their potential unification. Besides unifying the gauge groups of the Standard…
A sequence $A$ of elements an additive group $G$ is {\it incomplete} if there exists a group element that {\it can not} be expressed as a sum of elements from $A$. The study of incomplete sequences is a popular topic in combinatorial number…
Linear recurrence equations with constant coefficients define the power series coefficients of rational functions. However, one usually prefers to have an explicit formula for the sequence of coefficients, provided that such a formula is…
The Fermat numbers have many notable properties, including order universality, coprimality, and definition by a recurrence relation. We use arbitrary elliptic curves and rational points of infinite order to generate sequences that are…
In this paper we attack the Erdos-Straus conjecture by means of the structure of its solutions, extending and improving the results of a previous paper. Using previous results and supported by the works of Elsholtz and Tao and Monks and…
For many types of graphs, criteria have been discovered that give necessary and sufficient conditions for an integer sequence to be the degree sequence of such a graph. These criteria tend to take the form of a set of inequalities, and in…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
Generalized quantum cluster algebras introduced in [1] are quantum deformation of generalized cluster algebras of geometric types. In this paper, we prove that the Laurent phenomenon holds in these generalized quantum cluster algebras. We…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
This note is a response to one of the problems posed by Kwa\'sniewski in [1,2], see also [3] i.e. GCD-morphic Problem III. We show that any GCD-morphic sequence $F$ is at the point product of primary GCD-morphic sequences and any…
We prove some unique prime factorization results for tensor products of type $II_1$ factors of the form $\Gamma_q(\mathbb{C}, S \otimes H)$ arising from symmetric independent copies with sub-exponential dimensions of the spaces $D_k(S)$ and…