abstract INERT SUBGROUPS AND CENTRALIZERS OF INVOLUTIONS IN LOCALLY FINITE SIMPLE GROUPS &uml / Ozyurt, Erdal Ph. D., Department of Mathematics Supervisor: Prof. Dr. Mahmut Kuzucuo&amp / #728 / glu September 2003, 68 pages A subgroup H of a group G is called inert if [H : H Hg] is finite for all g 2 G. A group is called totally inert if every subgroup is inert. Among the basic properties of inert subgroups, we prove the following. Let M be a maximal subgroup of a locally finite group G. If M is inert and abelian, then G is soluble with derived length at most 3. In particular, the given properties impose a strong restriction on the derived length of G. We also prove that, if the centralizer of every involution is inert in an infinite locally finite simple group G, then every finite set of elements of G can not be contained in a finite simple group. In a special case, this generalizes a Theorem of Belyaev&amp / #8211 / Kuzucuo&amp / #728 / glu&amp / #8211 / Se&cedil / ckin, which proves that there exists no infinite locally finite totally inert simple group.

This thesis focuses on the past, present, and future of food sustainability on Maui. It begins by explaining ancient Hawaiian agriculture and how this complex system of agriculture was deeply rooted in the customs and traditions of the Hawaiian people. The second section explores how this sustainable agricultural system changed after the arrival of Captain Cook in 1778. After western settlement, land that was once a communal resource became privatized. As land ownership shifted, the traditional subsistence agricultural system of Hawai’i began to change. Export crops such as sugar cane and pineapple became more widespread. As these crops shifted the way land was utilized in Hawai’i, the islands reduced the amount of crops grown for local consumption and became increasingly reliant on imported foods. The last section stresses the necessity of increasing the production of locally grown food on Maui. It discusses the locally grown food movement that has developed on Maui, and addresses the obstacles that prevent more food from being grown locally. Lastly, it suggests strategies to increase the amount of food produced for local consumption so that Maui can secure a more sustainable agricultural future.

The proton exchange membrane fuel cells should have three major advantages: 1. micro-phase separation, 2. mechanical properties and 3. thermal stability. According to the recent literature and the material of core benzene ring poly (arylene ether)s studied by our group, this paper synthesize a series of the locally and densely sulfonated polymer. We use core benzene ring as the diol monomer and the containing CF3 groups as the fluorine monomer to synthesis poly (arylene ether)s via nucleophilic displacement reactions, and then use the different concentrations synthesized sulfonated polymer by sulfonic acid reaction. According to NMR¡¦s result we confirmed that the structure of synthetic materials is correct. By using GPC we get that the KP1, KP2, and KP3¡¦s molecular weight about 20000 (g/mol) ; The thermal stability up to 530OC for 5% loss in TGA under nithtrogen, to prove thisseries of polymer excellent thermal stability. After sulfonation, SKP1, SKP2 and SKP3¡¦s decomposition temperature decreased about 200OC ~ 250OC ranging with increasing degree of sulfonation. By DSC analysis, K1, K2 and K3 monomer's Tg followed up with the increase of the benzene ring number, however, the polymer does not have any apparent peak. About the Proton conductive, SKP2C IEC 2.23mequiv / g, water uptake 94%, the highest proton conductivity can be as high as 68.2 mS / cm, has been similar to Nafion 117 of 70 mS / cm.

High-dimensional data take place from digital image processing, gene expression micro arrays, neuronal population activities to financial time series. Dimensionality Reduction - extracting low dimensional structure from high dimension - is a key problem in many areas like information processing, machine learning, data mining, information retrieval and pattern recognition, where we find some data reduction techniques. In this thesis we will give a survey about modern data reduction techniques, representing the state-of-the-art of theory, methods and application, by introducing the language of mathematics there. This needs a special care concerning the questions of, e.g., how to understand discrete structures as manifolds, to identify their structure, preparing the dimension reduction, and to face complexity in the algorithmically methods. A special emphasis will be paid to Principal Component Analysis, Locally Linear Embedding and Isomap Algorithms. These algorithms are studied by a research group from Vilnius, Lithuania and Zeev Volkovich, from Software Engineering Department, ORT Braude College of Engineering, Karmiel, and others. The main purpose of this study is to compare the results of the three of the algorithms. While the comparison is beeing made we will focus the results and duration.

Consider a linear regression model with a two-dimensional control vector (x_1, x_2) and an m-dimensional response vector y = (y_1, . . . , y_m). The components of y are correlated with a known covariance matrix. Based on the assumed regression model, there are two problems of interest. The first one is to estimate unknown control vector x_c corresponding to an observed y, where xc will be estimated by the classical estimator. The second one is to obtain a suitable estimation of the control vector x_T corresponding to a given target T = (T_1, . . . , T_m) on the expected responses. Consideration in this work includes the deviation of the expected response E(y_i) from its corresponding target value T_i for each component and defines the optimal control vector x, say x_T , to be the one which minimizes the weighted sum of squares of standardized deviations within the range of x. The objective of this study is to find c-optimal designs for estimating x_c and x_T , which minimize the mean squared error of the estimator of xc and x_T respectively. The comparison of the difference between the optimal calibration design and the optimal design for estimating x_T is provided. The efficiencies of the optimal calibration design relative to the uniform design are also presented, and so are the efficiencies of the optimal design for given target vector relative to the uniform design.

We look from a new point of view at the definition and basic properties of the Lebesgue measure and integral on Euclidean spaces, on abstract spaces, and on locally compact Hausdorff spaces. We use mini sums to give all of them a unified treatment that is more efficient than the standard ones. We also give Fubini's theorem a proof that is nicer and uses much lighter technical baggage than the usual treatments.

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This study investigates the determinants that influence adult Kentuckians’ preference to buy organic and/or locally grown food based on their age, gender, income, education level and metropolitan versus nonmetropolitan living status. Ajzen’s theory of planned behavior (TPB) provides the conceptual framework of the research and the appropriateness of the theory. Data for this analysis are from a 2009 Kentucky statewide survey. The analysis shows that: There is a significant difference in food purchasing habits of Metropolitan and Nonmetropolitan adult Kentuckians; the factors associated with the purchase of organic and locally grown foods are different; and, those who purchased locally grown and organic foods shared similar beliefs.

Let G be a locally compact group, w be a continuous weight function on G, and L^1(G,w) be the corresponding Beurling algebra. In this thesis, we study weak amenability of L^1(G,w) and of its centre ZL^1(G,w) for non-commutative locally compact groups G. We first give examples to show that the condition that characterizes weak amenability of L^1(G,w) for commutative groups G is no longer sufficient for the non-commutative case. However, we prove that this condition remains necessary for all [IN] groups G. We also provide a necessary condition for weak amenability of L^1(G,w) of a different nature, which, among other things, allows us to obtain a number of significant results on weak amenability of l^1(F_2,w) and l^1((ax+b),w). We then study the relation between weak amenability of the algebra L^1(G,w) on a locally compact group G and the algebra L^1(G/H,^w) on the quotient group G/H of G over a closed normal subgroup H with an appropriate weight ^w induced from w. We give an example showing that L^1(G,w) may not be weakly amenable even if both L^1(G/H,^w) and L^1(H,w|_H) are weakly amenable. On the other hand, by means of constructing a generalized Bruhat function on G, we establish a sufficient condition under which weak amenability of L^1(G,w) implies that of L^1(G/H,^w). In particular, with this approach, we prove that weak amenability of the tensor product of L^1(G_1,w_1) and L^1(G_2,w_2) implies weak amenability of both Beurling algebras L^1(G_1,w_1) and L^1(G_2,w_2), provided the weights w_1, w_2 are bounded away from zero. However, given a general weight on the direct product G of G_1 and G_2, weak amenability of L^1(G,w) usually does not imply that of L^1(G_1,w|_{G_1}), even if both G_1, G_2 are commutative. We provide an example to illustrate this. While studying the centres ZL^1(G,w) of L^1(G,w), we characterize weak amenability of ZL^1(G,w) for connected [SIN] groups G, establish a necessary condition for weak amenability of ZL^1(G,w) in the case when G is an [FC] group, and give a sufficient condition for the case when G is an [FD] group. In particular, we obtain some positive results on weak amenability of ZL^1(G,w) for a compactly generated [FC] group G with a polynomial weight w. Finally, we briefly discuss the derivation problem for weighted group algebras and present a partial solution to it.