the renewable energy resources such as wind power have recently attracted more researchers’ attention. it is mainly due to the aggressive energy consumption, high pollution and cost of fossil fuels. in this era, the future fluctuations of these time series should be predicted to increase the reliability of the power network. in this paper, the dynamic characteristics and short-term predictabili...

The random Fibonacci sequence is defined by t1 = t2 = 1 and tn = ±tn−1 + tn−2, for n > 3, where each ± sign is chosen at random with probability P (+) = P (−) = 12 . Viswanath has shown that almost all random Fibonacci sequences grow exponentially at the rate 1.13198824 . . . . We will consider what happens to random Fibonacci sequences when we remove the randomness; specifically, we will choos...

Multiple sequential recurrences are one of themost important characteristics of superficial transitional cell carcinoma of the bladder, more than 50% of the patients will have recurrences (reappearance of a new superficial tumor). When in the same subject recurrent events are considered and these observed events are clustered into groups, independence between the clustered survival times cannot...

Let S be a set with n elements. The set of all subsets of S has elements. By a partition of S we mean a disjoint set of nonempty subsets (called blocks) whose union is S. The set of all partitions of S has elements, where is the nth Bell number and where denotes the Stirling number of the second kind. For example, We have recurrences ([1,2,3]) and asymptotics where is defined by. If U and V are...

We present a new master theorem for the study of divide-and-conquer recursive deenitions, which improves the old one in several aspects. In particular, it provides more information, frees us from technicalities like oors and ceilings, and covers a wider set of toll functions and weight distributions, stochastic recurrences included.

Based on the analysis of the Vr index from data from geomagnetic observatories in China and four geomagnetic observatories abroad, temporal-spatial distribution characteristics of Vr index were analyzed. The Vr index showed 27-day solar-cycle recurrences and significant seasonal variation. It also increased with latitude. Meanwhile, both local-time dependence and an obvious dusk-dawn asymmetry ...

A recurrence is a recursive description of a function, usually of the form F : IN→ IR, or a description of such a function in terms of itself. Like all recursive structures, a recurrence consists of one or more base cases and one or more recursive cases. Each of these cases is an equation or inequality, with some function value f (n) on the left side. The base cases give explicit values for a (...

Bousquet-Mélou and Petkovšek investigated the generating functions of multivariate linear recurrences with constant coefficients. We will give a reinterpretation of their results by means of division theorems for formal power series, which clarifies the structural background and provides short, conceptual proofs. In addition, extending the division to the context of differential operators, the ...

This paper introduces a new simplified version of the countable branching recurrence ◦ |א0 of Computability Logic, proves its equivalence to the old one, and shows that the basic logic induced by ◦ |א0 (i.e., the one in the signature {¬,∧,∨, ◦ |א0 , ◦| א}) is a proper superset of the basic logic induced by the uncountable branching recurrence ◦ | (i.e., the one in the signature {¬,∧,∨, ◦ | , ◦|...

Logical theories have been developed which have allowed temporal reasoning about eventualities (a la Galton) such as states, processes, actions, events, processes and complex eventualities such as sequences and recurrences of other eventualities. This paper presents the problem of coincidence within the framework of a first order logical theory formalizing temporal multiple recurrence of two se...