A Note on Systems of Linear Equations

This note is a comment on reference [1] and a generalization of the method there presented. We consider a system of m linear equations in n unknowns x_1, x_2,...x_n (1) Σ^(n)_(j=1) a_(ij)x_j = c_i i=1, 2,...m, a_(ij), c_i real or A∙x=c in matrix notation. We distinguish three cases: (I) There is no finite vector x satisfying (1) (inconsistent case); (II) There is a unique vector x satisfying (1); (III) There are an infinity of vectors x satisfying (1), such that their endpoints lie on some line, plane, or higher-dimensional linear manifold

An Ermerging Model for a New System of Education in New York State

This document has been written to serve two distinct but related purposes. First, it is an attempt to describe a set of educational experiences which will be developed by a consortium of county-wide agencies to meet the existing as well as the emerging needs of learners in Rockland County, New York. To this end, a theoretical operational construct is explicated and the implementation strategies and tactics which are felt to insure a high degree of success for the program relative to realities extant in Rockland County are outlined. Second, an extended rationale reflecting the status of the American society, the value systems operating within that society, the history and current condition of the United States educational institution, and a preview of what the future needs of the United States may be, have been addressed and documented so that the system of alternative education suggested by the design of the consortium can be seen in its widest context. Without detailing the particular design outlined within the dissertation it should be noted that educational policy of the future must place the role of education within the broad context of societal goals. This demands a structure which encourages a unified approach that utilizes the expertise and the commitment of all people living in the society. To this end, a process has been established to aid a community design and implement a system of education which will be responsive to their ideals and their desires. The first step is to have the neighborhood, the city, the county, or whatever group is being involved in the project, to fully analyze their problems. They must then develop a set of approaches, priorities and goals that constitute their responses to local conditions. Finally, the concerned citizens must create an administrative structure that will pull together the various elements in the society to attack problems in their full breadth. Naturally, cooperation among all the society\u27s institutions is needed to solve basic problems. The schools must learn to work not only with other elements of local government, but also with the larger community in order to enhance their key role

Abnormal flowers and pattern formation in floral

“From our acquaintance with this abnormal enabled to unveil the secrets that normal us, and to see distinctly what, from the regular we can only infer.” - J. W. von Goethe (1790

Genetic interactions among floral homeotic genes of Arabidopsis

We describe allelic series for three loci, mutations in which result in homeotic conversions in two adjacent whorls in the Arabidopsis thaliana flower. Both the structure of the mature flower and its development from the initial primordium are described by scanning electron microscopy. New mutations at the APETALA2 locus, ap2-2, ap2-8 and ap2-9, cause homeotic conversions in the outer two whorls: sepals to carpels (or leaves) and petals to stamens. Two new mutations of PISTILLATA, pi-2 and pi-3, cause second and third whorl organs to differentiate incorrectly. Homeotic conversions are petals to sepals and stamens to carpels, a pattern similar to that previously described for the apetala3-1 mutation. The AGAMOUS mutations, ag-2 and ag-3, affect the third and fourth whorls and cause petals to develop instead of stamens and another flower to arise in place of the gynoecium. In addition to homeotic changes, mutations at the APETALA2, APETALA3 and PISTILLATA loci may lead to reduced numbers of organs, or even their absence, in specific whorls. The bud and flower phenotypes of doubly and triply mutant strains, constructed with these and previously described alleles, are also described. Based on these results, a model is proposed that suggests that the products of these homeotic genes are each active in fields occupying two adjacent whorls, AP2 in the two outer whorls, PI and AP3 in whorls two and three, and AG in the two inner whorls. In combination, therefore, the gene products in these three concentric, overlapping fields specify the four types of organs in the wild-type flower. Further, the phenotypes of multiple mutant lines indicate that the wild-type products of the AGAMOUS and APETALA2 genes interact antagonistically. AP2 seems to keep the AG gene inactive in the two outer whorls while the converse is likely in the two inner whorls. This field model successfully predicts the phenotypes of all the singly, doubly and triply mutant flowers described

Smallholder Farming Under Increasingly Difficult Circumstances: Policy and Public Investment Priorities for Africa

Agricultural and Food Policy,

Homo- And Hetero-dinuclear Complexes Of Cobalt

The work presented in this thesis concerns the synthesis and characterization of a series of novel phosphine-carbonyl complexes of cobalt. Chapters 2 and 3 outline mononuclear and homodinuclear cobalt complexes, chapters 4 and 5 discuss heterobimetallic complexes (CoM(CO){dollar}\sb{lcub}\rm n{rcub}{dollar}({dollar}\mu{dollar}-dppm){dollar}\sb2{dollar}) (M = Rh,n = 3; M = Mn or Re, n = 5), and finally chapters 6 and 7 discuss complexes containing the {dollar}\mu{dollar}-PPh{dollar}\sb2{dollar} group and the complex ((CO){dollar}\sb2{dollar}({dollar}\eta\sp1{dollar}-dppm) Co({dollar}\mu{dollar}-dppm)BH{dollar}\sb2{dollar}), respectively.;Introduction of CO into Co(II)/phosphine/NaBH{dollar}\sb4{dollar} reaction systems, previously shown to produce a number of interesting complexes, has provided a novel approach to the synthesis of phosphine-carbonyl complexes of cobalt. A number of complexes were isolated including the previously known (CoH(CO) (PPh{dollar}\sb3)\sb3{dollar}) and also (Co(CO) (PP){dollar}\sb2{dollar}) {dollar}\sp+{dollar} (PP = dppm or dppe). In addition isomers of {dollar}\{lcub}{dollar}Co(CO){dollar}\sb2{dollar}(dppm){dollar}\{rcub}\sb2{dollar}, were prepared by this method. By introduction of RhCl{dollar}\sb3\cdot{dollar} (H{dollar}\sb2{dollar}O){dollar}\sb{lcub}\rm n{rcub}{dollar} into the reaction system, the heterobimetallic complex (CoRh(CO){dollar}\sb3(\mu{dollar}-dppm){dollar}\sb2{dollar}) was isolated. Complexes (M(CO) (dppm){dollar}\sb2{dollar}) (Co(CO){dollar}\sb4{dollar}), isolated for M = Co, and observed by {dollar}\sp{lcub}31{rcub}{dollar}P and {dollar}\sp{lcub}13{rcub}{dollar}C in the case of M = Rh, were observed to lose CO in the formation of complexes (CoM(CO){dollar}\sb{lcub}\rm n{rcub}(\mu{dollar}-dppm){dollar}\sb2{dollar}) (M = Co, n = 4; M = Rh, n = 3). Similarly the (Co(CO)(dppm){dollar}\sb2{dollar}) {dollar}\sp+{dollar} cation reacted with other metal carbonyl anions (M(CO){dollar}\sb5{dollar}) {dollar}\sp-{dollar} (M = Mn or Re) to give the complexes ((CO){dollar}\sb2{dollar} ({dollar}\eta\sp1{dollar}-dppm) Co({dollar}\mu{dollar}-dppm)M(CO){dollar}\sb4{dollar}) and (CoM(CO){dollar}\sb5(\mu{dollar}-dppm){dollar}\sb2{dollar}).;The fluxionality of (CoM(CO){dollar}\sb{lcub}\rm n{rcub}(\mu{dollar}-dppm){dollar}\sb2{dollar}) (M = Co, n = 4; M = Rh, n = 3; M = Mn, n = 5) and protonated derivatives (Co{dollar}\sb2(\mu{dollar}-H) (CO){dollar}\sb4(\mu{dollar}-dppm){dollar}\sb2{dollar}) {dollar}\sp+{dollar} and (CoRh({dollar}\mu{dollar}-H) (CO){dollar}\sb3(\mu{dollar}-dppm){dollar}\sb2{dollar}) {dollar}\sp+{dollar} was investigated by variable temperature {dollar}\sp1{dollar}H, {dollar}\sp{lcub}13{rcub}{dollar}C and {dollar}\sp{lcub}31{rcub}{dollar}P NMR and four types of fluxionality were observed.;The reactivity of complexes (CoM(CO){dollar}\sb{lcub}\rm n{rcub}(\mu{dollar}-dppm){dollar}\sb2{dollar}) (M = Co, n = 4; M = Rh, n = 3) was investigated with a range of inorganic oxidizing agents and complexes (CoM ({dollar}\mu{dollar}-X) ({dollar}\mu{dollar}-CO)({dollar}\mu{dollar}-dppm){dollar}\sb2{dollar}(CO){dollar}\sb2{dollar}) {dollar}\sp{lcub}\rm n+{rcub}{dollar} (M = Co or Rh; X = Cl, n = 1; X = Br, n = 1; X = I, n = 1; X = S, n = 0) and (CoRh({dollar}\mu{dollar}-H) (CO){dollar}\sb{lcub}\rm n{rcub}{dollar}({dollar}\mu{dollar}-dppm){dollar}\sb2{dollar}) {dollar}\sp+{dollar} (M = Co, n = 4; M = Rh, n = 3) were characterized. The reactivity of (CoM(CO){dollar}\sb{lcub}\rm n{rcub}{dollar}({dollar}\mu{dollar}-dppm){dollar}\sb2{dollar}) towards olefins was demonstrated to be limited.;Surprising results from the Co(II)/dppm/NaBH{dollar}\sb4{dollar}/CO reaction systems were the isolation of complexes (Co{dollar}\sb2{dollar}({dollar}\mu{dollar}-H) ({dollar}\mu{dollar}-PPh{dollar}\sb2{dollar}) ({dollar}\mu{dollar}-dppm){dollar}\sb{lcub}\rm n{rcub}{dollar}(CO){dollar}\sb{lcub}\rm 6-2n{rcub}{dollar}) (n = 1 or 2) and (Ni{dollar}\sb2{dollar}({dollar}\mu{dollar}-PPh{dollar}\sb2{dollar}) ({dollar}\mu{dollar}-dppm){dollar}\sb2{dollar}(CO){dollar}\sb2{dollar}) {dollar}\sp+{dollar}, resulting from the cleavage of a P-C bond in dppm under very mild conditions, and the isolation of ((CO){dollar}\sb2{dollar}({dollar}\eta\sp1{dollar}-dppm) Co({dollar}\mu{dollar}-dppm) BH{dollar}\sb2{dollar}) containing the first structurally characterized simple metal-BH{dollar}\sb2{dollar} linkage