New alfalfa varieties are constantly being introduced into the marketplace. The number of varieties available for low-elevation desert areas in Arizona in the non-dormant class is over50. New varieties are introduced each year and unbiased yield comparisons are helpful to the grower to base the decision of whether or not to sow a new variety. The study reported here is part of the on-going effort to evaluate alfalfa variety performance in Arizona. A summary of alfalfa variety trials conducted by the University of Arizona can be found online at http://ag.arizona.edu/pubs/crops/az1267.pdf.

New alfalfa varieties are constantly being introduced into the marketplace. The number of varieties available for low-elevation desert areas in Arizona in the non-dormant class is aver50. New varieties are introduced each year and unbiased yield comparisons are helpful to the grower to base the decision of whether or not to sow a new variety. The study reported here is part of the ongoing effort to evaluate alfalfa variety performance in Arizona. A summary of alfalfa variety trials conducted by the University of Arizona can be found online at http://ag.arizona.edu/pubs/crops/az1267.pdf.

Small grain varieties are evaluated each year by University of Arizona personnel. The purpose of these tests is to characterize varieties in terms of yield and other attributes. Variety performance varies greatly from year to year and several site-years are necessary to adequately characterize the yield potential of a variety. A summary of small grain variety trials conducted by the University of Arizona can be found online at http://ag.arizona.edu/pubs/crops/az1265.pdf.

M. Tech. Chemistry. / Determines if specific terpenes might play a role in triggering the lenticel's self-defense reaction.

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In this paper we consider the action of the mapping class group of a surface on the space of homomorphisms from the fundamental group of a surface into PSU(1,1). Goldman conjectured that when the surface is closed and of genus bigger than one, the action on non-Teichmuller connected components of the associated moduli space (i.e. the space of homomorphisms modulo conjugation) is ergodic. One approach to this question is to use sewing techniques which requires that one considers the action on the level of homomorphisms, and for surfaces with boundary. In this paper we consider the case of the one-holed torus with boundary condition, and we determine regions where the action is ergodic. This uses a combination of techniques developed by Goldman, and Pickrell and Xia. The basic result is an analogue of the result of Goldman's at the level of moduli.

The motivating question behind this body of research is Smale’s 17th problem: Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average, in polynomial time with a uniform algorithm? While certain aspects and viewpoints of this problem have been solved, the analog over the real numbers largely remains open. This is an important question with applications in celestial mechanics, kinematics, polynomial optimization, and many others. Let A = {α_1, . . . , α_n+k } ⊂ Zn. The A-discriminant variety is, among other things, a tool that can be used to categorize polynomials based on the topology of their real solution set. This fact has made it useful in solving aspects and special cases of Smale’s 17th problem. In this thesis, we take a closer look at the structure of the A-discriminant with an eye toward furthering progress on analogs of Smale’s 17th problem. We examine a mostly ignored form called the Horn uniformization. This represents the discriminant in a compact form. We study properties of the Horn uniformization to find structural properties that can be used to better understand the A-discriminant variety. In particular, we use a little known theorem of Kapranov limiting the normals of the A-discriminant amoeba. We give new O(n^2) bounds on the number of components in the complement of the real A-discriminant when k = 3, where previous bounds had been O(n^6) or even exponential before that. We introduce new tools that can be used in discovering various types of extremal A-discriminants as well as examples found with these tools: a family of A-discriminant varieties with the maximal number of cusps and a family that appears to asymptotically admit the maximal number of chambers. Finally we give sage code that efficiently plots the A-discriminant amoeba for k = 3. Then we switch to a non-Archimedean point of view. Here we also give O(n^2) bounds for the number of connected components in the complement of the non- Archimedean A-discriminant amoeba when k = 3, but we also get a bound of O(n^(2(k−1)(k−2)) )when k > 3. As in the real case, we also give a family exhibiting O(n^2) connected components asymptotically. Finally we give code that efficiently plots the p-adic A-discriminant amoeba for all k ≥ 3. These results help us understand the structure of the A-discriminant to a degree, as yet, unknown. This can ultimately help in solving Smale’s 17th problem as it gives a better understanding of how complicated the solution set can be.

This dissertation deals with the classification of varieties according to their Mal'cev properties. In general the so called Mal'cev-type theorems illustrate an interplay between first order properties of a given class of algebras and the lattice properties of the congruence lattices of algebras of the considered class. CHAPTER 1. A survey of some notational conventions, relevant definitions and auxiliary results is presented. Several examples of less frequently used algebras are given together with the important properties of some of them. The term algebra T(X) and useful results concerning 'term' operations are established. A K-reflection is defined and a connection between a K-reflection of an algebra and whether a class K satisfies an identity of the algebra is established. CHAPTER 2. The Mal'cev-type theorems are presented in complete detail for varieties which are congruence permutable, congruence distributive, arithmetical, congruence modular and congruence regular. Several examples of varieties which exhibit these properties are presented together with the necessary verifications. CHAPTER 3. A general scheme of algorithmic character for some Mal'cev conditions is presented. R. Wille (1970) and A. F. Pixley (1972) provided algorithms for the classification of varieties which exhibit strong Mal'cev properties. This chapter is largely devoted to a modification of the Wille-Pixley schemes. It must be noted that this modification is quite different from all such published schemes. The results are the same as in Wille's scheme but slightly less general than in Pixley's. The text presented here, however is much simpler. As an example, the scheme is used to confirm Mal'cev's original theorem on congruence permutable varieties. Finally, the so-called Chinese var£ety is defined and Mal'cev conditions are established for such a variety of algebras . CHAPTER 4. A comprehensive survey of literature concerning Mal'cev conditions is given in this chapter. / Thesis (M.Sc.)-University of Natal, Durban, 1991.

Diss. Alnarp : Sveriges lantbruksuniversitet, 2005.