Related papers: A note on V-binomials recurrence for Lucas compani…
In this paper, we study the combinatorial sum $$\sum_{k\equiv r(\mbox{mod }m)}{n\choose k}a^k.$$ By studying this sum, we obtain new congruences for Lucas quotients of two infinite families of Lucas sequences. Only for three Lucas…
In this work, we made a generalization that includes all bicomplex Fibonacci-like numbers such as; Fibonacci, Lucas, Pell, etc.. We named this generalization as bicomplex Horadam numbers. For bicomplex Fibonacci and Lucas numbers we gave…
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
The purpose of these notes is to give a categorical presentation/analysis of homotopy type theory. The notes are incomplete as they stand (October 2017). The chapter on univalent tribes is missing. The references are not always connected to…
For an integer \( k \geq 2 \), the sequence of \( k \)-generalized Lucas numbers is defined by the recurrence relation \( L_n^{(k)} = L_{n-1}^{(k)} + \cdots + L_{n-k}^{(k)} \) for all \( n \geq 2 \), with initial conditions \( L_0^{(k)} = 2…
We discuss the problem of Poincare recurrences in area-preserving maps and the universality of their decay at long times. The work is related to to the results presented in Refs. [1,2].
Up to now, most planet search projects have concentrated on F to K stars. In order to considerably widen the view, we have stated a survey for planets of old, nearby brown dwarfs and very low mass stars. Using UVES, we have observed 26…
The reduced Burau representation $V_n$ of the braid group $B_n$ is obtained from the action of $B_n$ on the homology of an infinite cyclic cover of the $n$-punctured disc. In this note, we calculate $H_*(B_n;V_n)$ as a module over the…
We study log-concavity properties of real sequences $(a_n)_{n \ge 0}$ satisfying a $d$-th order linear recurrence whose coefficients are linear functions of $n$; the so-called P-recursive (or holonomic) sequences. Writing the recurrence in…
A theory of Galois co-objects for von Neumann bialgebras is introduced. This concept is closely related to the notion of comonoidal W*-Morita equivalence between von Neumann bialgebras, which is a Morita equivalence taking the…
Motivated by the resemblance of a multivariate series identity and a finite analogue of Euler's pentagonal number theorem, we study multiple extensions of the latter formula. In a different direction we derive a common extension of this…
We use a sample of z~3 Lyman Break Galaxies (LBGs) to examine close pair clustering statistics in comparison to LCDM-based models of structure formation. Samples are selected by matching the LBG number density and by matching the observed…
A model for verifying a consistency of the next-to-leading order hadronic contributions to the muon anomalous magnetic moment with those of the leading order is proposed. A part of the next-to-leading order hadronic contributions related to…
We search for transient sources in a sample of ULXs from the 3XMM-DR4 release of the XMM-Newton Serendipitous Source Catalogue in order to find candidate neutron star ULXs alternating between an accreting state and the propeller regime, in…
We provide an informal response to James P. Lloyd's recent arXiv preprint (arXiv:1306.6627v1) "The Mass Distribution of Subgiant Planet Hosts", accepted for publication by Astrophysical Journal Letters.
The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in the past. The main questions are, as usual, about existence…
We use observations of the Luminous Blue Variable (LBV) P Cygni spanning seven decades, along with signal processing methods, to identify a periodicity in the stellar luminosity. We find a distinct period of $4.7 \pm 0.3$ years together…
A thorough search for Ultraluminous X-ray source candidates within the Local Volume is made. The search spatially matches potential ULXs detected in X-ray images or cataloged in the literature with galaxies tabulated in the Catalog of…
Let $a$ and $b$ be relatively prime integers. Then the first Lucas sequence $\left(U_n\right)_{n\geq0}$ and the second Lucas sequence $\left(V_n\right)_{n\geq0}$ are defined respectively by $U_{n+2}=aU_{n+1}+bU_{n},\, U_0=0,\,U_1=1$ and…
This thesis is about the study of Diophantine equations involving binary recurrent sequences with arithmetic functions. Various Diophantine problems are investigated and new results are found out of this study. Firstly, we study several…