The fractional integrated process has been widely studied since the seminal work of Granger and Joyeus (1980). However, most of the tests for fractional integration are time-domain tests. This paper contributes to the ∗We would like to thank Jianqing Fan, N.H. Chan and Yin-Wong Cheung for helpful comments. We also thank Carrella Ernesto and Lumpkin Samuel Mcspadden for able research assistance....

‎In this paper‎, ‎we investigate the number of 1-factors of a‎ ‎generalized Petersen graph $P(N,k)$ and get a lower bound for the‎ ‎number of 1-factors of $P(N,k)$ as $k$ is odd‎, ‎which shows that the‎ ‎number of 1-factors of $P(N,k)$ is exponential in this case and‎ ‎confirms a conjecture due to Lovász and Plummer (Ann‎. ‎New York Acad‎. ‎Sci‎. ‎576(2006)‎, ‎no‎. ‎1‎, ‎389-398).

For a finite group $G$‎, ‎let $Cent(G)$ denote the set of centralizers of single elements of $G$‎. ‎In this note we prove that if $|G|leq frac{3}{2}|Cent(G)|$ and $G$ is 2-nilpotent‎, ‎then $Gcong S_3‎, ‎D_{10}$ or $S_3times S_3$‎. ‎This result gives a partial and positive answer to a conjecture raised by A‎. ‎R‎. ‎Ashrafi [On finite groups with a given number of centralizers‎, ‎Algebra‎ ‎Collo...

‎an  oriented perfect path double cover (oppdc) of a‎ ‎graph $g$ is a collection of directed paths in the symmetric‎ ‎orientation $g_s$ of‎ ‎$g$ such that‎ ‎each arc‎ ‎of $g_s$ lies in exactly one of the paths and each‎ ‎vertex of $g$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎maxov{'a} and ne{v{s}}et{v{r}}il (discrete‎ ‎math‎. ‎276 (2004) 287-294) conjectured that ...

Birth order has been examined over a wide variety of dimensions in the context of modern populations. A consistent message has been that it is better to be born first. The analysis of birth order in this paper is different in several ways from other investigations into birth order effects. First, we examine the effect of birth order in an egalitarian, small-scale, kin-based society, which has n...

The celebrated Traub’s method involving Banach space-defined operators is extended. main feature in this study involves the determination of a subset original domain that also contains Traub iterates. In smaller domain, Lipschitz constants are too. Hence, finer analysis developed without usage additional conditions. This methodology applies to other methods. examples justify theoretical results.