Related papers: Berezovsky number
The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.
Binomial versions of the Andrews-Gordon-Bressoud identities are given.
In this paper, we define the truncated Bernoulli-Carlitz numbers and the truncated Cauchy-Carlitz numbers as analogues of hypergeometric Bernoulli numbers and hypergeometric Cauchy numbers, and as extensions of Bernoulli-Carlitz numbers and…
The numbers of even and odd permutations with a given ascent number are investigated using an operator that was previously introduced by the author. Their difference is called a signed Eulerian number. By means of the operator the…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
This paper provides a non-standard analogue of Bezout's theorem. This is acheived by showing that, in all characteristics, the notion of Zariski multiplicity coincides with intersection multiplicity when we consider the full families of…
Methods to solve a node discovery problem for a social network are presented. Covert nodes refer to the nodes which are not observable directly. They transmit the influence and affect the resulting collaborative activities among the persons…
In this note, we observe several properties of arithmetic divisors on the projective line over Z and give their Zariski decompositions.
The purpose of the present paper is to investigate the decay of Bernstein numbers of the embedding from $B^t_{p_1,q}((0,1)^d)$ into the space $L_{p_2}((0,1)^d) $. The asymptotic behaviour of Bernstein numbers of the identity $id:…
In this expository article, the real numbers are defined as infinite decimals. After defining an ordering relation and the arithmetic operations, it is shown that the set of real numbers is a complete ordered field. It is further shown that…
We survey 25 years of research on decidability issues for Petri nets. We collect results on the decidability of important properties, equivalence notions, and temporal logics.
We prove sharp radial estimates using Besov spaces. We also prove the propagation of singularities in Besov spaces.
Real data show that interdependent networks usually involve inter-similarity. Intersimilarity means that a pair of interdependent nodes have neighbors in both networks that are also interdependent (Parshani et al \cite{PAR10B}). For…
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
In this paper we investigate the value of a social network with respect to the probability mechanism underlying its structure. Specifically, we compute the value for small world and scale free networks. We provide evidence in support of the…
In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable properties as…
The networks formed from the links between telephones observed in a month's call detail records (CDRs) in the UK are analyzed, looking for the characteristics thought to identify a communications network or a social network. Some novel…
Web services substitution is one of the most challenging tasks for automating the composition process of multiple Web services. It aims to improve performances and to deal efficiently with Web services failures. Many existing solutions have…
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
Wordnets are semantic networks containing nouns, verbs, adjectives, and adverbs organized according to linguistic principles, by means of semantic relations. In this work, we adopt a complex network perspective to perform a comparative…