相关论文: Lens sequences

The paper investigates the properties of a nonlinear recursive sequence which includes several ones studied formerly in the literature.

We continue the work begun in OEIS sequence A332636 which presents recursive sequences that have triangles that appear embedded in them. This paper i) generalizes the main result presented in A332636, ii) provides a complete set of…

One of the most popular and studied recursive series is the Fibonacci sequence. It is challenging to see how Fibonacci numbers can be used to generate other recursive sequences. In our article, we describe some families of integer…

The elegance and usefulness of a complex formulation of the basic lensing equations is demonstrated with a number of applications. Using standard tools of complex function theory, we present, for instance, a new proof of the fact that the…

We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.

Hidden symmetries, described by higher order in momenta integrals of motion that generate nonlinear algebras, are explored at the level of classical and quantum mechanics in a variety of physical systems related to conformal and…

Bidirectional transformation, also called lens, has played important roles in maintaining consistency in many fields of applications. A lens is specified by a pair of forward and backward functions which relate to each other in a consistent…

We investigate general properties of number sequences which allow explicit representation in terms of products. We find that such sequences form whole families of number sequences sharing similar recursive identities. Restricting to the…

We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also…

Lens spaces are a family of manifolds that have been a source of many interesting phenomena in topology and differential geometry. Their concrete construction, as quotients of odd-dimensional spheres by a free linear action of a finite…

We study a new type of sequences whose elements are defined in terms of the position, sign and magnitude of another element of the sequence. The name ultra-recursive comes from the fact that these sequences possess terms that are generated…

Refraction, traditionally viewed as a geometric event occurring at material interfaces, is now being re-examined through the lens of coherence. Recent studies in optics and photonics, including coherence tomography, Moire interference, and…

We introduce hypergeometric-type sequences. They are linear combinations of interlaced hypergeometric sequences (of arbitrary interlacements). We prove that they form a subring of the ring of holonomic sequences. An interesting family of…

We look at a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this…

In this paper we report on recent results by several authors, on the spectral theory of lens spaces and orbifolds and similar locally symmetric spaces of rank one. Most of these results are related to those obtained by the authors in [IMRN…

This paper presents a reinterpretation of a second-order linear recurrence sequence as a sequence of continuants derived from the convergents to a continued fraction. As a result, we are able to derive the generating function and Binet…

Lenses may be characterised as objects in the category of algebras over a monad, however they are often understood instead as morphisms, which propagate updates between systems. Working internally to a category with pullbacks, we define…

A persistence lens is a hierarchy of disjoint upper and lower level sets of a continuous luminance image's Reeb graph. The boundary components of a persistence lens's interior components are Jordan curves that serve as a hierarchical…

After giving an overview of the existing theory regarding the periods of sequences defined by linear recurrences over finite fields, we give explicit descriptions of the sets of periods that arise if one considers all sequences over…

The currently used linear and nonlinear lens inversion techniques are based on distortion estimators whose complicated source redshift dependence makes the influence of the redshift distribution of the sources difficult to take into account…