The notion of an∞-generalized Fibonacci sequence has been introduced in [6], and studied in [1], [7], [9]. This class of sequences defined by linear recurrences of infinite order is an extension of the class of ordinary (weighted) r-generalized Fibonacci sequences (r-GFS, for short) with r finite defined by linear recurrences of r order (for example, see [2], [3], [4], [5], [8] etc.) More preci...

We give explicit solutions to two longstanding problems on coupled second–order recurrences.

Divide-and-conquer functions satisfy equations in F(z), F(z2), F(z4) . . .. Their generated sequences are mainly used in computer science, and they were analyzed pragmatically, that is, now and then a sequence was picked out for scrutiny. By giving several classes of ordinary generating functions togetherwith recurrences, we hope to helpwith the analysis of many such sequences, and try to class...

[1] The recurrence intervals for 194 repeating clusters on the Calaveras fault follow a power-law decay relation with elapsed time after the 1984 M6.2 Morgan Hill, California, mainshock. The decay rates of repeating aftershocks in the immediate vicinity of a high-slip patch that failed during the mainshock systematically exceed those that are farther away. The trend between relative moment and ...

In this paper we study some combinatorial properties of the antichains of a garland, or double fence. Specifically, we encode the order ideals and the antichains in terms of words of a regular language, we obtain several enumerative properties (such as generating series, recurrences and explicit formulae), we consider some statistics leading to Riordan matrices, we study the relations between t...

In this paper we find a general approach to find closed forms of sums of products of arbitrary sequences satisfying the same recurrence with different initial conditions. We apply successfully our technique to sums of products of such sequences with indices in (arbitrary) arithmetic progressions. It generalizes many results from literature. We propose also an extension where the sequences satis...

This paper shows that, even at the most basic level (namely, in combination with only ¬,∧,∨), the parallel, countable branching and uncountable branching recurrences of computability logic validate different principles. MSC: primary: 03B47; secondary: 03B70; 68Q10; 68T27; 68T15.

A solution to get the problem off, have you found it? Really? What kind of solution do you resolve the problem? From what sources? Well, there are so many questions that we utter every day. No matter how you will get the solution, it will mean better. You can take the reference from some books. And the recurrent events data analysis for product repairs disease recurrences and other applications...

1. There is growing interest in improving the biodiversity of urban and suburban areas. Here we report on the effectiveness of a very simple intervention that may be used to boost flower and pollinator abundance; the sowing of plots of wildflowers in amenity grasslands. The abundance of flowers, bumblebees (Bombus spp.), and hoverflies (Syrphidae) was surveyed in 30 such plots, either 1 or 2 ye...

Y. ZOU∗,¶, M. C. ROMANO†,‡, M. THIEL†, N. MARWAN∗ and J. KURTHS∗,†,§ ∗Potsdam Institute for Climate Impact Research, P. O. Box 60 12 03, 14412 Potsdam, Germany †Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom ‡Institute of Medical Sciences, Foresterhill, University of Aberdeen, Aberdeen AB25 2ZD, United Kingdom §Department of Phy...