No-splitting property and boundaries of random groups

We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on trees. This implies that their Gromov boundaries, defined at density less than 1/2, are Menger curves.Comment: 20 page

Property (T)(T) for noncommutative universal lattices

We establish a new spectral criterion for Kazhdan's property $(T)$ which is applicable to a large class of discrete groups defined by generators and relations. As the main application, we prove property $(T)$ for the groups $EL_n(R)$, where $n\geq 3$ and $R$ is an arbitrary finitely generated associative ring. We also strengthen some of the results on property $(T)$ for Kac-Moody groups from a paper of Dymara and Januszkiewicz (Invent. Math 150 (2002)).Comment: 47 pages; final versio

Ferromagnetism and Electronic Structure of (Ga,Mn)As:Bi and (Ga,Mn)As Epitaxial Layers

The photoreflectance (PR) spectroscopy was applied to study the band-structure in GaAs:Bi, (Ga,Mn)As and (Ga,Mn)As:Bi layers with the 4% of Mn and 1 % of Bi content and, as a reference, undoped GaAs layer. All films were grown by low temperature (LT) MBE on semi-insulating (001) GaAs substrates. Photoreflec-tance studies were supported by Raman spectroscopy and high resolution X-ray diffractometry (XRD) measurements. Magnetic properties of the films were characterized with a superconducting quantum in-terference device (SQUID) magnetometer. Our findings were interpreted in terms of the model, which as-sumes that the mobile holes residing in the valence band of GaAs and the Fermi level position determined by the concentration of valence-band holes. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3533

Finite covers of random 3-manifolds

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this model of random 3-manifold, we are able to compute the probabilities that the resulting manifolds have finite covers of particular kinds. Our results contrast with the analogous probabilities for groups coming from random balanced presentations, giving quantitative theorems to the effect that 3-manifold groups have many more finite quotients than random groups. The next natural question is whether these covers have positive betti number. For abelian covers of a fixed type over 3-manifolds of Heegaard genus 2, we show that the probability of positive betti number is 0. In fact, many of these questions boil down to questions about the mapping class group. We are lead to consider the action of mapping class group of a surface S on the set of quotients pi_1(S) -> Q. If Q is a simple group, we show that if the genus of S is large, then this action is very mixing. In particular, the action factors through the alternating group of each orbit. This is analogous to Goldman's theorem that the action of the mapping class group on the SU(2) character variety is ergodic.Comment: 60 pages; v2: minor changes. v3: minor changes; final versio

6-Benzylaminopurine Alleviates the Impact of Cu2+ Toxicity on Photosynthetic Performance of Ricinus communis L. Seedlings

Copper (Cu) is an essential element involved in various metabolic processes in plants, but at concentrations above the threshold level, it becomes a potential stress factor. The effects of two different cytokinins, kinetin (KIN) and 6-benzylaminopurine (BAP), on chlorophyll a fluorescence parameters, stomatal responses and antioxidation mechanisms in castor (Ricinus communis L.) under Cu2+ toxicity was investigated. Ricinus communis plants were exposed to 80 and 160 MCuSO4 added to the growth medium. Foliar spraying of 15 M KIN and BAP was carried out on these seedlings. The application of these cytokinins enhanced the tissue water status, chlorophyll contents, stomatal opening and photosynthetic efficiency in the castor plants subjected to Cu2+ stress. The fluorescence parameters, such as Fm, Fv/Fo, Sm, photochemical and non-photochemical quantum yields, energy absorbed, energy trapped and electron transport per cross-sections, were more efficiently modulated by BAP application than KIN under Cu2+ toxicity. There was also effective alleviation of reactive oxygen species by enzymatic and non-enzymatic antioxidation systems, reducing the membrane lipid peroxidation, which brought about a relative enhancement in the membrane stability index. Of the various treatments, 80 M CuSO4 + BAP recorded the highest increase in photosynthetic efficiency compared to other cytokinin treatments. Therefore, it can be concluded that BAP could effectively alleviate the detrimental effects of Cu2+toxicity in cotyledonary leaves of R. communis by effectively modulating stomatal responses and antioxidation mechanisms, thereby enhancing the photosynthetic apparatus’ functioning

Isoperimetric Inequalities in Simplicial Complexes

In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high dimensional Laplacian defined by Eckmann. In particular, we present a Cheeger-type inequality, and a high-dimensional Expander Mixing Lemma. As a corollary, using the work of Pach, we obtain a connection between spectral properties of complexes and Gromov's notion of geometric overlap. Using the work of Gunder and Wagner, we give an estimate for the combinatorial expansion and geometric overlap of random Linial-Meshulam complexes

Improvement of growth, yield, seed production and phytochemical properties of satureja khuzistanica jamzad by foliar application of boron and zinc

Satureja khuzistanica Jamzad is a valuable and endemic medicinal plant. Boron and zinc are essential elements for the vegetative and reproductive growth of plants and have significant effects on yield, essential oil composition and the seed production of plants. To investigate the effects of the foliar application of zinc and boron on the growth, yield, seed production and phytochemical properties of S. khuzistanica, a study was conducted in a factorial experiment with three replicates in two consecutive years based on a randomized complete block design. The foliar application of boron (B) at three concentrations (control or distilled water, 0.4% and 0.8% as H3BO3) and zinc (Zn) at three concentrations (control or distilled water, 0.3% and 0.6% as ZnSO4) was carried out. Our results showed that the foliar application of B resulted in a significant increase in the fresh and dry weights of plants, the dry weight of stems, drug yield, seed yield, seed germination and 1000-seed weight. At the same time, the application of B resulted in a significant decrease in seed emptiness. The fresh and dry weights of plants, drug yield, seed yield, 1000-seed weight and seed germination were also significantly improved by Zn foliar spraying compared to the control. Application of 0.8% B resulted in a significant decrease in seed emptiness by 14.16% and 22.37%, as compared to the control. The foliar spraying of B and Zn improved the total phenolic content, the essential oil content and the yield and antioxidant activity of S. khuzistanica. Moreover, B application generally concentrated more carvacrol in the essential oil (in the first experimental year). In contrast, no significant differences were observed between Zn treatments in carvacrol content and total flavonoids. The use of several microelements, such as B and Zn, could improve both the quantity and quality of S. khuzistanica. Additionally, improvement of seed set and seed quality by the foliar spraying of Zn and B may be useful for growing plants in arid and semi-arid areas

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy