Let Rm be the (unique) universal homogeneous m-edge-coloured countable complete graph (m ≥ 2), and Gm its group of colourpreserving automorphisms. The group Gm was shown to be simple by John Truss. We examine the automorphism group of Gm, and show that it is the group of permutations of Rm which induce permutations on the colours, and hence an extension of Gm by the symmetric group of degree m....

In 1929, Zermelo proposed a probabilistic model for ranking by paired comparisons and showed that this model produces a unique ranking of the objects under consideration when the outcome matrix is irreducible. When the matrix is reducible, the model may yield only a partial ordering of the objects. In this paper, we analyze a natural extension of Zermelo’s model resulting from a singular pertur...

An integro-differential equation satisfied by an eigenvalue density defined as the logarithmic derivative of the average inverse characteristic polynomial of a Wilson loop in two dimensional pure Yang Mills theory with gauge group SU(N) is derived from two associated complex Burgers’ equations, with viscosity given by 1/(2N). The Wilson loop does not intersect itself and Euclidean space-time is...

The study determined the willingness and capacity of poultry farmers to pay for extension services in Nasarawa State, Nigeria. At this research used a sample size of 120 poultry farmers. Simple descriptive statistics, Kuppuswamy scale and Logit regression model were used data analysis. The results showed that majority of the poultry farmers (87.5%) indicated their willingness to pay for extensi...

We examine the uniqueness of equilibrium states for natural extension a topologically exact, non-uniformly expanding, local homeomorphism with Hölder continuous potential function. do this by applying general techniques developed Climenhaga and Thompson, show there is condition on decompositions which guarantees unique state exists. then how to apply these results certain partially hyperbolic a...

A simple method, primer specific and mispair extension analysis (PSMEA) with pfu DNA polymerase was developed for genotyping. PSMEA is based on the unique properties of 3'-->5' exonuclease proofreading activity. In the presence of an incomplete set of dNTPs, pfu was found to be extremely discriminative in nucleotide incorporation and proofreading at the initiation step of DNA synthesis, complet...

As is well known, a continuous parameter process with mutually independent random variables is not jointly measurable in the usual sense. This paper proposes an extension of the usual product measure-theoretic framework, using a natural “one-way Fubini” property. When the random variables are independent even in a very weak sense, this property guarantees joint measurability and defines a uniqu...

Class field theory relates abelian extensions of a given number field K to certain generalized ideal class groups ofK. The fundamental tool for doing this is Frobenius elements, and the Artin map obtained from them. Recall from lecture 24 that if L/K is an abelian extension (i.e., a Galois extension with abelian Galois group), and p is a prime of OK unramified in OL, then we defined Fr(p) ∈ Gal...

Usually a coherence multiplexing system uses delay-filters at the transmitter and receiver to perform the code. An extension to other filter types is described. Using a continuous source the signal-to-beat noise ratio is proportional to the square of the inverse of the number of simultaneous users. A further extension is made by using a pulsed source and by replacing the filters by banks of fil...

The purpose of the study was to examine compliance of extension personnel in Imo state agricultural extension service delivery system of Nigeria. A purposive and multi-stage random sampling was used to select 105 extension personnel from the three agricultural zones of the state. Data generated were analyzed using descriptive statistics such as frequencies and percentages, as well as mean score...