A Hessenberg variety is a subvariety of the flag variety parametrized by two maps: a Hessenberg function on $[n]$ and a linear map on $\C^n$. We study regular nilpotent Hessenberg varieties in Lie type A by focusing on the Hessenberg function $h=(n-1,n,\ldots,n)$. We first state a formula for the $f^w_{n,1}$ which generates the local defining ideal $J_{w,h}$ for any $w\in\Ss_n$. Second, we prove that there exists a convenient monomial order so that $\lead(J_{w,h})$ is squarefree. As a consequence, we conclude that each codimension-1 regular nilpotent Hessenberg variety is locally Frobenius split (in positive characteristic). / Thesis / Master of Science (MSc)

No description available.

Given a quiver flag variety Y equipped with a tilting bundle E, a construction ofCraw, Ito and Karmazyn [CIK18] produces a closed immersion f_E : Y -> M(E), where M(E) is the fine moduli space of cyclic modules over the algebra End(E).In this thesis we present two classes of examples where f_E is an isomorphism. Firstly, when Y is toric and E is the tilting bundle from [Cra11]; this generalises the well-known fact that P^n can be recovered from the endomorphism algebra of \oplus_{0\leq i \leq n} O_{P^n}(i). Secondly, when Y = Gr(n, 2), the Grassmannian of 2-dimensional quotients of k^n and E is the tilting bundle from [Kap84]. In each case, we give a presentation of the tilting algebra A = End(E) by constructing a quiver Q' such that there is a surjective k-algebra homomorphism \Phi: kQ' -> A, and then give an explicit description of the kernel.

We define the phylogenetic model of a trivalent graph as a generalization of a binary symmetric model of a trivalent phylogenetic tree. If the underlining graph is a tree, the model has a parametrization that can be expressed in terms of the tree. The model is always a polarized projective toric variety. Equivalently, it is a projective spectrum of a semigroup ring. We describe explicitly the generators of this projective coordinate ring for graphs with at most one cycle. We prove that models of graphs with the same topological invariants are deformation equivalent and share the same Hilbert function. We also provide an algorithm to compute the Hilbert function, which uses the structure of the graph as a sum of elementary ones. Also, this Hilbert function of phylogenetic model of a graph with g cycles is meaningful for the theory of connections on a Riemann surface of genus g.

Current industry chilling practices with and without the application of 2 percent L-lactic acid were compared for their effectiveness at reducing levels of Salmonella, Yersinia enterocolitica, Campylobacter coli, and common indicator organisms used in industry (aerobic plate count APC, Escherichia coli, and coliforms) on pork variety meats. Pork livers, hearts, intestines, and stomachs were either inoculated individually with 1 of the 3 pathogens or not inoculated and subjected to 1 of 5 treatments: 1 (water wash + lactic acid spray + freeze), 2 (freeze), 3 (water wash + lactic acid spray + chill + freeze), 4 (chill + freeze), and 5 (water wash + freeze). Samples were analyzed between treatment steps and after 2 months, 4 months, and 6 months of frozen storage. Results of effects of the steps within treatments showed that reductions in levels of pathogens after the water wash and lactic acid spray were significantly different (P<0.05) across variety meats. Treatment of variety meats with water wash and lactic acid before chilling resulted in >/= 0.5 log CFU/sample (P<0.05) reductions when compared to chilling alone. Regardless of treatments, reductions in levels of Salmonella and Y. enterocolitica of 0.6-1.3 log CFU/sample were observed after freezing (0 degrees C) overnight. Freezing reduced C. coli by >/= 2.2 log CFU/sample regardless of previous treatment. Throughout 6 months of frozen storage, reductions were observed in levels of all microorganisms equal to or greater than 1.3 log CFU/sample. The greatest reductions were observed on samples treated with lactic acid (Treatments 1 and 3) (1.3-5.0 log CFU/sample) while the smallest reductions were reported for samples without any spray treatment (Treatments 2 and 4) (0.7-4.5 log CFU/sample). Large reductions were observed in levels of C. coli (2.9-5.0 log CFU/sample) for all treatments. The results of this study suggest that, while the application of a water wash followed by freezing reduced levels of pathogens by approximately 1 log CFU/sample, the application of lactic acid before chilling and freezing variety meats results in significantly larger (P<0.05) reductions in microorganisms. Results also show that aerobic plate counts, E. coli, and coliforms follow similar trends to the pathogens.

No description available.

Thesis (M. Sc.(Food science))-University of Pretoria, 2006. / Includes bibliographical references. Available on the Internet via the World Wide Web.

Cēgə Trouhèst is a three-movement work of about thirteen minutes duration. The text by the composer provides a vehicle for aural stimulation only. Cēgə Trouhèst is a continuum of resonances embellished by melodic and rhythmic passages. These embellishments along with other devices and the choice of instrumentation all contribute to the development of the varied timbres. The first two movements introduce the material to be employed in the third, which continues the idea of change exhibited in the text by modification and extraction. Timbre is the most important aspect of this work. It is exploited homophonically, contrapuntally, and through instrumental/vocal interchange and timbre modification of a single tone.

An e-pseudovariety is a class of finite regular semigroups closed under the taking of homomorphic images, regular subsemigroups and finite direct products. Chapter One consists of a survey of those results from algebraic semigroup theory, universal algebra and lattice theory which are used in the following two chapters. In Chapter Two, a theory of generalised existence varieties is developed. A generalised existence variety is a class of regular semigroups closed under the taking of homomorphic images, regular subsemigroups, finite direct products and arbitrary powers. Equivalently, a generalised e-variety is the union of a directed family of existence varieties. It is demonstrated that a class of finite regular semigroups is an e-pseudovariety if and only if the class consists only of the finite members of some generalised existence variety. The relationship between certain lattices of e-pseudovarieties and generalised existence varieties is explored and a usefu l complete surjective lattice homomorphism is found. A study of complete congruences on lattices of existence varieties and e-pseudovarieties forms Chapter Three. In particular it is shown that a certain meet congruence, whose description is relatively simple, can be extended to yield a complete congruence on a lattice of e-pseudovarieties of finite regular semigroups. Ultimately, theorems describing the method of construction of all complete congruences of lattices of e-pseudovarieties whose members are finite E-solid or locally inverse regular semigroups are proved.

No abstract added / African Languages / M.A. (African Languages)