Thesis (M.Sc. (Agronomy )) --University of Limpopo, 2007 / Intercropping is the growing of two or more crops simultaneously on the same field, and it is a common traditional practice among resource-poor farmers throughout the Limpopo Province of South Africa. Field studies were conducted at two locations in the province namely, the University of Limpopo experimental farm at Syferkuil, and a farmer’s field at Dalmada during the 2002/2003 growing season, to determine patterns of nodulation in cowpea and lablab varieties under sole culture and in an intercropping system with maize, variety SNK2147 and also to assess biomass accumulation and grain yielding abilities of the component crops in the system. The experiments were established as a randomized complete block design with three replications at each location. Treatments examined were sole maize, two cowpea cultivars: Bechuana white and Glenda; two lablab cultivars, Rongai and Common. The legumes were intercropped alternately within 90 cm inter-row spacing of maize, thus creating a distance of 45 cm between the maize and the legume rows. Cropping system had no effect on cowpea grain yield at Syferkuil, but at Dalmada cowpea yield was reduced. Maize grain yield was significantly affected by the cropping system at both Syferkuil and Dalmada. At both locations, the yields of all the intercropped maize were lower than those of the sole crop maize. The dry matter production of different cropping systems was generally similar during the different sampling dates. / the National Research Foundation,and the Gauteng Department of Agriculture Conservation and Environment

We study projective completions of affine algebraic varieties (defined over an algebraically closed field K) which are given by filtrations, or equivalently, integer valued `degree like functions' on their rings of regular functions. For a polynomial map P := (P_1, ..., P_n): X -> K^n of affine varieties with generically finite fibers, we prove that there are completions of the source such that the intersection of completions of the hypersurfaces {P_j = a_j} for generic (a_1, ..., a_n) in K^n coincides with the respective fiber (in short, the completions `do not add points at infinity' for P). Moreover, we show that there are `finite type' completions with the latter property, i.e. determined by the maximum of a finite number of `semidegrees', by which we mean degree like functions that send products into sums. We characterize the latter type completions as the ones for which ideal I of the `hypersurface at infinity' is radical. Moreover, we establish a one-to-one correspondence between the collection of minimal associated primes of I and the unique minimal collection of semidegrees needed to define the corresponding degree like function. We also prove an `affine Bezout type' theorem for polynomial maps P with finite fibers that admit semidegrees corresponding to completions that do not add points at infinity for P. For a wide class of semidegrees of a `constructive nature' our Bezout-type bound is explicit and sharp.

We study projective completions of affine algebraic varieties (defined over an algebraically closed field K) which are given by filtrations, or equivalently, integer valued `degree like functions' on their rings of regular functions. For a polynomial map P := (P_1, ..., P_n): X -> K^n of affine varieties with generically finite fibers, we prove that there are completions of the source such that the intersection of completions of the hypersurfaces {P_j = a_j} for generic (a_1, ..., a_n) in K^n coincides with the respective fiber (in short, the completions `do not add points at infinity' for P). Moreover, we show that there are `finite type' completions with the latter property, i.e. determined by the maximum of a finite number of `semidegrees', by which we mean degree like functions that send products into sums. We characterize the latter type completions as the ones for which ideal I of the `hypersurface at infinity' is radical. Moreover, we establish a one-to-one correspondence between the collection of minimal associated primes of I and the unique minimal collection of semidegrees needed to define the corresponding degree like function. We also prove an `affine Bezout type' theorem for polynomial maps P with finite fibers that admit semidegrees corresponding to completions that do not add points at infinity for P. For a wide class of semidegrees of a `constructive nature' our Bezout-type bound is explicit and sharp.

Due to the exponential growth of the dimension of the space of tensors V_(1)⊗• • •⊗V_(n), any naive method of representing these tensors is intractable on a computer. In practice, we consider feasible subspaces (subvarieties) which are defined to reduce the storage cost and the computational complexity. In this thesis, we study two such types of subvarieties: the third secant variety of the product of n projective spaces, and tensor network states. For the third secant variety of the product of n projective spaces, we determine set-theoretic defining equations, and give an upper bound of the degrees of these equations. For tensor network states, we answer a question of L. Grasedyck that arose in quantum information theory, showing that the limit of tensors in a space of tensor network states need not be a tensor network state. We also give geometric descriptions of spaces of tensor networks states corresponding to trees and loops.

The theme of this thesis is a comparison of the yield capability naked and hulled oat varieties. The work is divided into two sections. The first half of this thesis is devoted to literature search. The second part of this thesis describes the actual experiment, which was carried out in 2012 on the farm school University of South Bohemia (České Budějovice). 10 varieties of oats, 4 of them naked varieties and 6 hulled varieties, was used for this experiment. Highest average yield of hulled varieties reached Vok variety (3.85 tons per ha) and of naked varieties with a yield of 3.43 tons per hectare the Otakar variety. The average thousand grain weight was in naked varieties 28,7 grams and 33,4 grams hulled varieties. Number of grains per panicle reached 57 grains on average in nude varieties and 55 grains on average in hulled varieties. in nude varieties averaged 57 grains and 55 grains of hulled varieties.

On the basis of experiment was performed an evaluation of yield production of the selected spectrum of naked and hulled oat varieties. There were compared time-tested varieties to new varieties registered in the list of recommended varieties in 2013. At the same time were compared methods of yield production of hulled oat and naked oat. After evaluation of real yield was informatively compared the amount of raw food materials obtained from naked oat with the oat rice obtained from hulled oat by hulling machine.

Let $\bk$ be a field of characteristic zero. A Pham-Brieskorn ring is a $\bk$-algebra of the form $B_{a_0,\dots,a_n} = \bk[X_0,\dots,X_n] / \lb X_0^{a_0} + \cdots + X_n^{a_n} \rb$, where $n \geq 2$ and $a_0, \dots, a_n$ are positive integers. A ring $B$ is rigid if the only locally nilpotent derivation $D : B \to B$ is the zero derivation. Consider the following conjecture. \begin{conjnonumber}\label{PBConjectureAbstract} Let $n \geq 2$, and let $B_{a_0, \dots, a_n} = \bk[X_0, \dots, X_n] / \langle X_0^{a_0} + \cdots + X_n^{a_n} \rangle$ be a Pham-Brieskorn ring. If $\min\{a_0, \dots,a_n \} \geq 2$ and at most one element $i$ of $\{0,\dots ,n\}$ satisfies $a_i = 2$, then $B_{a_0, \dots, a_n}$ is rigid. \end{conjnonumber} The $n = 2$ case of the Conjecture is known to be true. In this thesis, we make progress towards solving the above conjecture. Our main results are: \begin{enumerate}[\rm(1)] \item For any $n \geq 3$, in order to prove the above conjecture, it suffices to prove rigidity of $B_{a_0, \dots, a_n}$ in the cases where $\bk = \Comp$ and $\cotype(a_0, \dots, a_n) = 0$. \item For any $n \geq 2$, $X = \Proj B_{a_0, \dots, a_n}$ is a well-formed quasismooth weighted complete intersection if and only if $\cotype(a_0, \dots, a_n) = 0$. \item When $n = 3$ and $\cotype(a_0, a_1, a_2, a_3) = 0$, $B_{a_0, a_1, a_2, a_3}$ is rigid, except possibly in the cases where, up to a permutation of the $a_i$, $(a_0, a_1, a_2, a_3) \in \{(2,3,4,12), (2,3,5,30)\}$. \item We summarize the list of 3-dimensional Pham-Brieskorn rings $B_{a_0, a_1, a_2, a_3}$ for which rigidity is known. It follows in particular that if $B_{2,3,4,12}$ and $B_{2,3,5,30}$ are rigid then the $n = 3$ case of the above conjecture is true. \end{enumerate} In addition to the above, we develop techniques for proving rigidity of rings in general; prove rigidity of many Pham-Brieskorn rings whose dimension is greater than 3; give simple examples of rational projective surfaces with quotient singularities that have an ample canonical divisor and prove that the members of a certain family of singular hypersurfaces are not rational.

The International Potato Center (CIP) and Peruvian National Agricultural Research Institute (INIA) have invested a substantial amount of resources towards the development of improved potato varieties in Peru. These varieties are adaptable to the agro-ecologies of the Andes and have specific biotic and abiotic attributes. These efforts have led to the release of several prominent varieties including Canchan-INIA, Amarilis, Unica, Serranita and others. A 2013 household survey conducted by CIP was used to describe the diffusion of improved potato varieties in Peru. These data were also used to identify specific constraints to their adoption and dis-adoption. The assessment focused on a two-step adoption model, adoption and dis-adoption, by utilizing a Heckman Probit model to demonstrate two-steps of the adoption process. The Heckman Probit model was used to analyze variables affecting adoption and dis-adoption of improved varieties. Results suggest that adoption is region specific, time dependent, and in some cases relies on informal transmission methods. Risk to food insecurity and recurrent natural phenomena affect adoption and sometimes dis-adoption. Additionally, factors affecting a farmer's exposure to risk, such as information constraints and household head age, wealth, and social network were found to affect the adoption and dis-adoption of improved varieties. / Master of Science

Planting date is an important consideration when growing small grain varieties under reduced water use conditions. The objective of this study is to document interactions of planting date and varieties grown with a single irrigation near planting. Field studies were conducted at the Maricopa Agricultural Center during the 1988, 1989, and 1990 growing seasons. Six barley, durum, and wheat varieties were compared at four planting dates from November to February. Early November or early December planting dates were optimum. The relative performance of the varieties differed depending on the year and planting date. The highest yielding varieties over most planting dates were Solum and 6-39-1-1 (barleys), Mexicali (durum), and B85-277A and M83-39-18 (wheats). Improvement of barley, durum, and wheat genotypes for reduced water use conditions continues at the University of Arizona, and notable progress in durum and wheat performance has been achieved recently.

Yield trials were conducted at the Maricopa Agricultural Center during the 1990 -91 growing season. Barley, Durum and Wheat varieties as well as experimental lines from various seed companies were tested for yield performance. Gustoe and Sunbar 409 barleys, Turbo and Aldura durum wheats; and 911 and Klasic bread wheats were the highest yielding commercial varieties in this yield trial.