Collineation group as a subgroup of the symmetric group

Let $\Psi$ be the projectivization (i.e., the set of one-dimensional vector subspaces) of a vector space of dimension $\ge 3$ over a field. Let $H$ be a closed (in the pointwise convergence topology) subgroup of the permutation group $\mathfrak{S}_{\Psi}$ of the set $\Psi$. Suppose that $H$ contains the projective group and an arbitrary self-bijection of $\Psi$ transforming a triple of collinear points to a non-collinear triple. It is well-known from \cite{KantorMcDonough} that if $\Psi$ is finite then $H$ contains the alternating subgroup $\mathfrak{A}_{\Psi}$ of $\mathfrak{S}_{\Psi}$. We show in Theorem \ref{density} below that $H=\mathfrak{S}_{\Psi}$, if $\Psi$ is infinite.Comment: 9 page

Physiological indicators and yield of the Chinese cabbage cultivated at different soil water tensions

The development and yield of Chinese cabbage is influenced by soil moisture. The objective of this study was to evaluate the physiological indicators, development, and yield of Chinese cabbage (Brassica rapa subsp. pekinensis (Lour.) Rupr.) grown at different soil water tension ranges. Two experiments were conducted (2016–2017) in the Olericulture Sector of the Federal University of Technology of Paraná. Two cultivars of the Chinese cabbage, Eikoo and Kinjitsu, and four soil water tension ranges 13–17, 23–27, 33–37, and 43–47 kPa were studied. Eikoo presented higher relative chlorophyll index, photosynthesis, and fresh leaf mass than did Kinjitsu. Physiological indicators transpiration (5.8 mmol H2O m-2 s -1 ), photosynthesis (14.5 µmol CO2 m-2 s -1 ), stomatal conductance (0.31 mol H2O m-2 s -1 ), and WUE (39.4 kg m-3 ) were higher at 13–17 kPa soil water tension. Soil water tension ranges with high water restrictions reduced the fresh leaf mass of both cultivars. Fresh leaf mass decreased by 236.2 and 191.7 g plant-1 in the highest soil water tension range in 2016 and 2017, respectively, when compared with the fresh leaf mass at the 13–17 kPa tension range. The lowest water consumption was observed at the 13–17 kPa tension range. The year 2017 resulted in higher internal CO2 concentration, transpiration rate, fresh leaf mass, number of irrigations and water consumption compared to the year 2016. Thus, the irrigation regime for the most optimal Chinese cabbage cultivation should maintain the soil water tension range at 13–17 kPa

Biochemical parameters of silver catfish (Rhamdia quelen) after transport with eugenol or essential oil of Lippia alba added to the water

The transport of live fish is a routine practice in aquaculture and constitutes a considerable source of stress to the animals. The addition of anesthetic to the water used for fish transport can prevent or mitigate the deleterious effects of transport stress. This study investigated the effects of the addition of eugenol (EUG) (1.5 or 3.0 mu L L-1) and essential oil of Lippia alba (EOL) (10 or 20 mu L L-1) on metabolic parameters (glycogen, lactate and total protein levels) in liver and muscle, acetylcholinesterase activity (AChE) in muscle and brain, and the levels of protein carbonyl (PC), thiobarbituric acid reactive substances (TBARS) and nonprotein thiol groups (NPSH) and activity of glutathione-S-transferase in the liver of silver catfish (Rhamdia quelen; Quoy and Gaimard, 1824) transported for four hours in plastic bags (loading density of 169.2 g L-1). The addition of various concentrations of EUG (1.5 or 3.0 mu L L-1) and EOL (10 or 20 mu L L-1) to the transport water is advisable for the transportation of silver catfish, since both concentrations of these substances increased the levels of NPSH antioxidant and decreased the TBARS levels in the liver. In addition, the lower liver levels of glycogen and lactate in these groups and lower AChE activity in the brain (EOL 10 or 20 mu L L-1) compared to the control group indicate that the energetic metabolism and neurotransmission were lower after administration of anesthetics, contributing to the maintenance of homeostasis and sedation status.Fundacao de Amparo a Pesquisa do Estado do Rio Grande do Sul (FAPERGS/PRONEX) [10/0016-8]; Conselho Nacional de Pesquisa e Desenvolvimento Cientifico (CNPq) [470964/2009-0]; Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES); CNPqinfo:eu-repo/semantics/publishedVersio

Modification of Experimental Protocols for a Space Shuttle Flight and Applications for the Analysis of Cytoskeletal Structures During Fertilization, Cell Division , and Development in Sea Urchin Embryos

To explore the role of microgravity on cytoskeletal organization and skeletal calcium deposition during fertilization, cell division, and early development, the sea urchin was chosen as a model developmental system. Methods were developed to employ light, immunofluorescence, and electron microscopy on cultures being prepared for flight on the Space Shuttle. For analysis of microfilaments, microtubules, centrosomes, and calcium-requiring events, our standard laboratory protocols had to be modified substantially for experimentation on the Space Shuttle. All manipulations were carried out in a closed culture chamber containing 35 ml artificial sea water as a culture fluid. Unfertilized eggs stored for 24 hours in these chambers were fertilized with sperm diluted in sea water and fixed with concentrated fixatives for final fixation in formaldehyde, taxol, EGTA, and MgCl2(exp -6)H2O for 1 cell to 16 cell stages to preserve cytoskeletal structures for simultaneous analysis with light, immunofluorescence, and electron microscopy, and 1.5 percent glutaraldehyde and 0.4 percent formaldehyde for blastula and plueus stages. The fixed samples wre maintained in chambers without degradation for up to two weeks after which the specimens were processed and analyzed with routine methods. Since complex manipulations are not possible in the closed chambers, the fertilization coat was removed from fixation using 0.5 percent freshly prepared sodium thioglycolate solution at pH 10.0 which provided reliable immunofluorescence staining for microtubules. Sperm/egg fusion, mitosis, cytokinesis, and calcium deposition during spicule formatin in early embryogenesis were found to be without artificial alterations when compared to cells fixed fresh and processed with conventional methods

Expansion in perfect groups

Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an integer q, denote by Ga_q the subgroup of Ga consisting of the elements that project to the unit element mod q. We prove that the Cayley graphs of Ga/Ga_q with respect to the generating set S form a family of expanders when q ranges over square-free integers with large prime divisors if and only if the connected component of the Zariski-closure of Ga is perfect.Comment: 62 pages, no figures, revision based on referee's comments: new ideas are explained in more details in the introduction, typos corrected, results and proofs unchange

Quasars and their host galaxies

This review attempts to describe developments in the fields of quasar and quasar host galaxies in the past five. In this time period, the Sloan and 2dF quasar surveys have added several tens of thousands of quasars, with Sloan quasars being found to z>6. Obscured, or partially obscured quasars have begun to be found in significant numbers. Black hole mass estimates for quasars, and our confidence in them, have improved significantly, allowing a start on relating quasar properties such as radio jet power to fundamental parameters of the quasar such as black hole mass and accretion rate. Quasar host galaxy studies have allowed us to find and characterize the host galaxies of quasars to z>2. Despite these developments, many questions remain unresolved, in particular the origin of the close relationship between black hole mass and galaxy bulge mass/velocity dispersion seen in local galaxies.Comment: Review article, to appear in Astrophysics Update

Magnetoelectric ordering of BiFeO3 from the perspective of crystal chemistry

In this paper we examine the role of crystal chemistry factors in creating conditions for formation of magnetoelectric ordering in BiFeO3. It is generally accepted that the main reason of the ferroelectric distortion in BiFeO3 is concerned with a stereochemical activity of the Bi lone pair. However, the lone pair is stereochemically active in the paraelectric orthorhombic beta-phase as well. We demonstrate that a crucial role in emerging of phase transitions of the metal-insulator, paraelectric-ferroelectric and magnetic disorder-order types belongs to the change of the degree of the lone pair stereochemical activity - its consecutive increase with the temperature decrease. Using the structural data, we calculated the sign and strength of magnetic couplings in BiFeO3 in the range from 945 C down to 25 C and found the couplings, which undergo the antiferromagnetic-ferromagnetic transition with the temperature decrease and give rise to the antiferromagnetic ordering and its delay in regard to temperature, as compared to the ferroelectric ordering. We discuss the reasons of emerging of the spatially modulated spin structure and its suppression by doping with La3+.Comment: 18 pages, 5 figures, 3 table