Spectral characteristics of normal and nutrient-deficient maize leaves

Reflectance, transmittance and absorbance spectra of normal and six types of mineral-deficient (N,P,K,S,Mg and Ca) maize (Zea mays L.) leaves were analyzed at 30 selected wavelengths along the electromagnetic spectrum from 500 to 2600 nm. Chlorophyll content and percent leaf moisture were also determined. Leaf thermograms were obtained for normal, N- and S- deficient leaves. The results of the analysis of variance showed significant differences in reflectance, transmittance and absorbance in the visible wavelengths among leaf numbers 3, 4, and 5, among the seven nutrient treatments, and among the interactions of leaves and treatments. In the reflective infrared wavelengths only treatments produced significant differences. The chlorophyll content of leaves was reduced in all deficiencies in comparison to controls. Percent moisture was increased in S-, Mg- and N- deficiencies. Positive correlation (r = 0.707) between moisture content and percent absorption at both 1450 and 1930 nm were obtained. Polynomial regression analysis of leaf thickness and leaf moisture content showed that these two variables were significantly and directly related (r = 0.894)

Regular obstructed categories and TQFT

A proposal of the concept of $n$-regular obstructed categories is given. The corresponding regularity conditions for mappings, morphisms and related structures in categories are considered. An n-regular TQFT is introduced. It is shown the connection of time reversibility with the regularity.Comment: 22 pages in Latex. To be published in J. Math. Phy

Spacetime as a Feynman diagram: the connection formulation

Spin foam models are the path integral counterparts to loop quantized canonical theories. In the last few years several spin foam models of gravity have been proposed, most of which live on finite simplicial lattice spacetime. The lattice truncates the presumably infinite set of gravitational degrees of freedom down to a finite set. Models that can accomodate an infinite set of degrees of freedom and that are independent of any background simplicial structure, or indeed any a priori spacetime topology, can be obtained from the lattice models by summing them over all lattice spacetimes. Here we show that this sum can be realized as the sum over Feynman diagrams of a quantum field theory living on a suitable group manifold, with each Feynman diagram defining a particular lattice spacetime. We give an explicit formula for the action of the field theory corresponding to any given spin foam model in a wide class which includes several gravity models. Such a field theory was recently found for a particular gravity model [De Pietri et al, hep-th/9907154]. Our work generalizes this result as well as Boulatov's and Ooguri's models of three and four dimensional topological field theories, and ultimately the old matrix models of two dimensional systems with dynamical topology. A first version of our result has appeared in a companion paper [gr-qc\0002083]: here we present a new and more detailed derivation based on the connection formulation of the spin foam models.Comment: 32 pages, 2 figure

Spectra of Normal and Nutrient-Deficient Maize Leaves

Reflectance, transmittance and absorptance spectral of normal and six types of nutrient-deficient (N, P, K, S, Mg, and Ca) maize (Zea mays L.) leaves were analyzed at 30 selected wavelengths from 500-2600 nm. The analysis of variance showed significant differences in reflectance, transmittance and absorptance in the visible wavelengths among leaf numbers 3, 4, and 5, among the seven treatments, and among the interactions of leaf number and treatments. In the infrared wavelengths only treatments produced significant differences. The chlorophyll content of leaves was reduced in all nutrient deficient treatments. Percent moisture was increased in S-, Mg-, and N-deficiencies. Positive correlations were obtained (r = 0.7) between moisture content and percent absorption at both 1450 and 1930 nm. Polynomial regression analysis of leaf thickness and leaf moisture content showed that these two variables were significantly and directly related (R = 0.894). Leaves from the P- and Ca-deficient plants absorbed less energy in the near infrared than the normal plants; S-, Mg-, K-, and N-deficient leaves absorbed more than the normal. Leaf thermograms were prepared on normal and S- and N-deficient leaves. Both S- and N-deficient leaves had higher temperatures than normal maize leaves

Invariants from classical field theory

We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. Applying our methods to several field theories such as abelian BF, Chern-Simons and 2-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S^3, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.Comment: 20 pages, 1 figure, to appear in J. Math. Phy