Intersection theorems for systems of finite vector spaces

AbstractA theorem of Erdös, Ko and Rado states that if S is an n-element set and F is a family of k-element subsets of S, k⩽ 12n, such that no two members of F are disjoint, then …F… ⩽ (n - 1k - 1). In this paper we investigate the analogous problem for finite vector spaces.Let F be a family of k-dimensional subspaces of an n-dimensional vector space over a field of q elements such that members of F intersect pairwise non-trivially. Employing a method of Katona, we show that for n ⩾ 2k, …F… ⩽ (k/n) [nk]q. By a more detailed analysis, we obtain that for n ⩾ 2k + 1, …F… ⩽ [n - 1k - 1]q, which is a best possible bound. The argument employed is generalized to the problem of finding a bound on the size of F when its members have pairwise intersection dimension no smaller than r. Again best possible results are obtained for n ⩾ 2k + 2 and n ⩾ 2k + 1, q ⩾ 3. Application of these methods to the analogous subset problem leads to improvement on the Erdös-Ko-Rado bounds

Mouse Chromosome 11

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46996/1/335_2004_Article_BF00648429.pd

Control of Dye Aggregation and Electron Injection for Highly Efficient Porphyrin Sensitizers Adsorbed on Semiconductor Films with Varying Ratios of Coadsorbate

We report the photovoltaic performances and kinetics of femtosecond fluorescence for three zinc-porphyrin sensitizers (YD0-YD2) coadsorbed with chenodeoxycholic acid (CDCA) at three molar ratios on nanocrystalline semiconductor (TiO(2) or Al(2)O(3)) films. The addition of CDCA improved the efficiencies of YD0 and YD1 so that their maximum performance occurred at a dye/CDCA ratio of 1:2, but the presence of CDCA had a negative effect for YD2. Porphyrin aggregation on TiO(2) surfaces not only accelerates the rate of intermolecular energy transfer but also increases the rate of interfacial electron injection, so that the electron injection yields (Phi(inj)) are balanced by these two important factors. As a result, Phi(inj) increased slightly with increasing amount of CDCA for both YD0 and YD1, but decreased for YD2; for this reason, the presence of CDCA failed to improve the photovoltaic performance for YD2, unlike for YD0 and YD1. The cell performances were optimized on TiO(2) films of similar to 10-mu m thickness with a scattering layer of similar to 4-mu m thickness: the efficiencies 4 if power conversion of YD1 and YD2 are slightly smaller than, but near, that of N719, being 6.5% and 6.8%, respectively, compared to 7.3%. Without a scattering layer on the films, the performance of N719 was degraded significantly (6.3%), whereas the efficiencies of YD1 and YD2 decreased only slightly (6.4% and 6.6%), making this series of green sensitizers promising candidates for future light-penetrable photovoltaic applications

On the chromatic number of q-Kneser graphs

We show that the q-Kneser graph $qK_{2k:k}$ (the graph on the k-subspaces of a 2k-space over GF(q), where two k-spaces are adjacent when they intersect trivially), has chromatic number $q^k + q^{k-1}$ for k = 3 and for k <q log q - q. We obtain detailed results on maximal cocliques for k = 3. Keywords: Chromatic number – q-analog of Kneser grap

Synthesis and characterization of porphyrin sensitizers with various electron-donating substituents for highly efficient dye-sensitized solar cells

A series of porphyrin dyes with an electron-donating group (EDG) attached at a meso-position (YD1-YD8) have been designed and synthesized for use as sensitizers in dye-sensitized solar cells (DSSC). The nature of the EDG exerts a significant influence on the spectral, electrochemical and photovoltaic properties of these sensitizers. Absorption spectra of porphyrins having an amino group show broadened Soret band and red-shifted Q bands with respect to those of reference porphyrin YD0. This phenomenon is more pronounced for porphyrins YD7 and YD8 that have a pi-conjugated triphenylamine at the meso-position opposite the anchoring group. Upon introduction of an EDG at the meso-position, the potential for the first oxidation alters significantly to the negative whereas that for the first reduction changes inappreciably, indicating a decreased HOMO-LUMO gap. Results of density-functional theory (DFT) calculations support the spectroelectrochemical data for a delocalization of charge between the porphyrin ring and the amino group in the first oxidative state of diarylamino-substituted porphyrins YD1-YD4, which exhibit superior photovoltaic performance among all porphyrins under investigation. With long-chain alkyl groups on the diarylamino substituent, YD2 shows the best cell performance with J(SC) = 13.4 mA cm(-2), V(OC) = 0.71 V, and FF = 0.69, giving an overall efficiency 6.6% of power conversion under simulated one-sun AM1.5 illumination

LZF1, a HY5-regulated transcriptional factor, functions in Arabidopsis de-etiolation

We surveyed differential gene expression patterns during early photomorphogenesis in both wild-type and mutant Arabidopsis defective in HY5, an influential positive regulator of the responses of gene expression to a light stimulus, to identify light-responsive genes whose expression was HY5 dependent. These gene-expression data identified light-regulated zinc finger protein 1 (LZF1), a gene encoding a previously uncharacterized C2C2-CO B-box transcriptional regulator. HY5 has positive trans-activating activity toward LZF1 and binding affinity to LZF1 promoter in vivo. HY5 is needed but not sufficient for the induction of LZF1 expression. Anthocyanin content is significantly diminished in lzf1 under far red, which is the most efficient light for the induction of LZF1. The expression of PAP1/MYB75 is elevated in plants overexpressing LZF1, which leads to the hyperaccumulation of anthocyanin in transgenic Arabidopsis. The transition from etioplast to chloroplast and the accumulation of chlorophyll were notably compromised in the lzf1 mutant. We provide molecular evidence that LZF1 influences chloroplast biogenesis and function via regulating genes encoding chloroplast proteins. In the absence of HY5, mutation of LZF1 leads to further reduced light sensitivity for light-regulated inhibition of hypocotyl elongation and anthocyanin and chlorophyll accumulation. Our data indicate that LZF1 is a positive regulator functioning in Arabidopsis de-etiolation