Stirling numbers of second kind S(n,k) denotes the number ways partitioning a set n elements into k nonempty sets. There are many types stirling which studied up to now. In this study, we use extended defined for arbitrary reals. First, define relation between and q-B-splines by using property that divided differences have representation with q-B-splines. addition, derive identities on q-integr...

Let F (x) = f1x + f2x + · · · be a formal power series over a field ∆. Let F (0)(x) = x and, for q = 1, 2, . . . , define F (q)(x) = F (q−1)(F (x)). The obvious algorithm for computing the first n terms of F (q)(x) is by the composition analogue of repeated squaring. This algorithm has complexity about log2 q times that of a single composition. Brent [1] showed that the factor log2 q can be eli...

In this paper we introduce a new form of decomposition of graphs, the (P, Q)-decomposition. We first give an optimal algorithm for finding the 1-decomposition of a graph which is a special case of the (P, Q)-decomposition which was first introduced in [21]. We then examine the connections between the 1-decomposition and well known forms of decomposition of graphs, namely, modular and homogeneou...

The ferromagnetic q-state Potts model on three-dimensional lattices: a study for real values of q Abstract We study the phase diagram of the ferromagnetic q-state Potts model on the various three-dimensional lattices for integer and non-integer values of q > 1. Our approach is based on a thermodynamically self-consistent Ornstein-Zernike approximation for the two-point correlation functions. We...

We extend results of Videla and Fukuzaki to define algebraic integers in large classes of infinite algebraic extensions of Q and use these definitions for some of the fields to show first-order undecidability. In particular, we show that the following propositions hold. (1) For any rational prime q and any positive rational integer m, algebraic integers are definable in any Galois extension of ...

In this paper, we study the desingularization problem in the first qWeyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first q-Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first q-Weyl closure of a given q-difference operator. As an application, we certify that s...

We show that the first order theory of the Σ2 s-degrees is undecidable. Via isomorphism of the s-degrees with the Q-degrees, this also shows that the first order theory of the Π2 Q-degrees is undecidable. Together with a result of Nies, the proof of the undecidability of the Σ2 s-degrees yields a new proof of the known fact (due to Downey, LaForte and Nies) that the first order theory of the c....

in this study, analysis is presented in two steps. in the first step, the theoretical s-wave displacement spectra, conditioned by frequency-independent q, was fitted with the observed displacement spectra. therefore corner frequency, moment magnitude and frequency-independent q for each record were estimated simultaneously and the estimate of error is given in the root-mean-square sense over al...

Let q be a power of 2. We show by representation theory that there exists a q × q unitary matrix of multiplicative order q + 1 whose powers generate q + 1 complex pairwise mutually unbiased bases in C. When q is a power of an odd prime, there is a q × q unitary matrix of multiplicative order q+1 whose first (q+1)/2 powers generate (q+1)/2 complex pairwise mutually unbiased bases. We also show h...