相关论文: Lens sequences
We introduce the $k$-bonacci polyominoes, a new family of polyominoes associated with the binary words avoiding $k$ consecutive $1$'s, also called generalized $k$-bonacci words. The polyominoes are very entrancing objects, considered in…
A nearly linear recurrence sequence (nlrs) is a complex sequence $(a_n)$ with the property that there exist complex numbers $A_0$,$\ldots$, $A_{d-1}$ such that the sequence $\big(a_{n+d}+A_{d-1}a_{n+d-1}+\cdots +A_0a_n\big)_{n=0}^{\infty}$…
Recurrent neural networks (RNNs) are capable of learning features and long term dependencies from sequential and time-series data. The RNNs have a stack of non-linear units where at least one connection between units forms a directed cycle.…
Subdivision schemes are iterative methods for the design of smooth curves and surfaces. Any linear subdivision scheme can be identified by a sequence of Laurent polynomials, also called subdivision symbols, which describe the linear rules…
Additional remarks and questions for transseries. In particular: properties of composition for transseries; the recursive nature of the construction of R[[[ x ]]]; modes of convergence for transseries. There are, at this stage, questions…
We study screening of optical singularities in random optical fields with two widely different length scales. We call the speckle patterns generated by such fields speckled speckle, because the major speckle spots in the pattern are…
We give a very brief introduction to the machinery of spectral sequences, including the spectral sequence of a bicomplex. We then briefly introduce a generalisation of the spectral sequences of a bicomplex to the spectral sequences of…
In this paper, we have constructed the higher order k-bonacci matrices and studied some of their basic properties. We have also shown that these matrices satisfying some new and interesting relations in k-bonacci recurrence. This is the…
We survey and prove properties a family of recurrences bears in relation to integer representations, compositions, the Pascal triangle, sums of digits, Nim games and Beatty sequences.
This paper introduces a new construction of subcomplexes associated with a truncated multicomplex. Inspired by the machinery of spectral sequences, this construction yields a collection of interrelated subcomplexes whose differentials…
Light traveling through a liquid crystal with disclinations perceives a geometrical background which causes lensing effects similar to the ones predicted for cosmic objects like global monopoles and cosmic strings. In this article we…
We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either…
Six families of generalized hypergeometric series in a variable $x$ and an arbitrary number of parameters are considered. Each of them is indexed by an integer $n$. Linear recurrence relations in $n$ relate these functions and their product…
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…
Measurements from galaxies spanning a broad range of morphology reveal a linear scaling of enclosed dark to luminous mass that is not anticipated by standard galaxy formation cosmology. The linear scaling is found to extend from the inner…
This is the first of several monographs to be devoted to the optics of accelerated systems. They are being published for the benefit of those who may wish to have another way of looking at kineoptical problems, and also to demonstrate that…
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the…
The goal of this article is to understand some interesting features of sequences of arbitrage operations, which look relevant to various processes in Economics and Finances. In the second part of the paper, analysis of sequences of…
We define a so-called square $k$-zig-zag shape as a part of the regular square grid. Considering the shape as a $k$-zig-zag digraph, we give values of its vertices according to the number of the shortest paths from a base vertex. It…