Abstract Loop quantum cosmology leads to a difference equation for the wave function of a universe. In the semiclassical limit, small-scale oscillations must be suppressed by choosing parameters of general solutions appropriately. For anisotropic models this is not possible to do numerically by trial and error; instead, it is shown here for the Bianchi I LRS model how this can be done analytica...

To shift the path of integration to the left, one needs at least meromorphic continuation to some half-plane R s > r− δ as well as some information on the growth and the distribution of the poles of Φr. Assuming the Riemann hypothesis, Egami and Matsumoto[4] described the behavior for the case r = 2. In addition to the RH, parts of their results depend on unproved assumptions on the distributio...

Abstract: This is the first of two articles devoted to a exposition of the generatingfunction method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp’s character method. An alternative approach to the construction of tensor-product generating functions ...

The neighbourhood polynomial G , is generating function for the number of faces of each cardinality in the neighbourhood complex of a graph. In other word $N(G,x)=sum_{Uin N(G)} x^{|U|}$, where N(G) is neighbourhood complex of a graph, whose vertices are the vertices of the graph and faces are subsets of vertices that have a common neighbour. In this paper we compute this polynomial for some na...

A composition of an integer constrained to have decreasing then increasing parts is called concave. We prove that the generating function for the number of concave compositions, denoted v(q), is a mixed mock modular form in a more general sense than is typically used. We relate v(q) to generating functions studied in connection with “Moonshine of the Mathieu group” and the smallest parts of a p...

This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in the companion article. Although the Kac-Walton algorithm provides a method for constructing a fusion generating function from the corresponding tensor-produ...

A single server queue with Bernoulli vacation has been considered. In addition the admission to queue is based on a Bernoulli process and the server gives two type of services. For this model the probability generating function for the number of customers in the queue at different server's state are obtained using supplementary variable technique. Some performance measures are calculated. Some ...

Kazemi (2014) introduced a new version of bucket recursive trees as another generalization of recursive trees where buckets have variable capacities. In this paper, we get the $p$-th factorial moments of the random variable $S_{n,1}$ which counts the number of subtrees size-1 profile (leaves) and show a phase change of this random variable. These can be obtained by solving a first order partial...

Most of people knows the following problem, What is the next term ? What expression would give us the general term ? It would be nice to have a formula to generate all the terms in the sequence. how do we find the formula? here is the way to become a 'genius' at MENSA tests.

In this paper correspondence between experimental data for packet delay and two theoretical types of distribution is investigated. Statistical tests have shown that only exponential distribution can be used for the description of packet delays in global network. Precision experimental data to within microseconds are gathered by means of the RIPE Test Box. Statistical verification of hypothesis ...