The conjugacy classes of fixed point free elements in GLn(F) and SLn(F)

AbstractIf there is a least positive integer m such that Am=I for an element A of GLn(F), then we call A a fixed point free element of order m. In the present paper, we determine the formula of the conjugacy classes of fixed point free elements in GLn(F) and SLn(F) completely

Model Simulation of Cucumber Yield and Microclimate Analysis in a Semi-closed Greenhouse in China

Adequate greenhouse environmental management is very important for improving resource use efficiency and increasing vegetable yield. The objective of this study was to explore suitable climate and cultivation management for cucumber to achieve high yield and build optimal yield models in semi-closed greenhouses. A fruit cucumber cultivar Deltastar was grown over 4 years in greenhouse and weekly data of yields (mean, highest and lowest) and environmental variables, including total radiation, air temperature, relative humidity, and carbon dioxide (CO2) concentration were collected. Regression analyses were applied to develop the relationships and build best regression models of yields with environmental variables using the first 2 years of data. Data collected in years 3 and 4 were used for model validation. Results showed that total radiation, nutrient, temperature, CO2 concentration, and average nighttime relative humidity had significant correlations with cucumber yields. The best regression models fit the mean, lowest, and highest yields very well with R2 values of 0.67, 0.66, and 0.64, respectively. Total radiation and air temperature had the most significant contributions to the variations of the yields. Our results of this study provide useful information for improving greenhouse climate management and yield forecast in semi-closed greenhouses

Exogenous glutathione improves high root-zone temperature tolerance by modulating photosynthesis, antioxidant and osmolytes systems in cucumber seedlings

To investigate the physiological responses of plants to high root-zone temperature (HT, 35 °C) stress mitigated by exogenous glutathione (GSH), cucumber (Cucumis sativus L.) seedlings were exposed to HT with or without GSH treatment for 4 days and following with 4 days of recovery. Plant physiological variables, growth, and gene expression related to antioxidant enzymes and Calvin cycle were quantified. The results showed that HT significantly decreased GSH content, the ratio of reduced to oxidized glutathione (GSH/GSSG), chlorophyll content, photosynthesis and related gene expression, shoot height, stem diameter, as well as dry weight. The exogenous GSH treatment clearly lessened the HT stress by increasing the above variables. Meanwhile, HT significantly increased soluble protein content, proline and malondialdehyde (MDA) content as well as O2•− production rate, the gene expression and activities of antioxidant enzymes. The GSH treatment remarkably improved soluble protein content, proline content, antioxidant enzymes activities, and antioxidant enzymes related gene expression, and reduced the MDA content and O2•− production rate compared to no GSH treatment in the HT condition. Our results suggest that exogenous GSH enhances cucumber seedling tolerance of HT stress by modulating the photosynthesis, antioxidant and osmolytes systems to improve physiological adaptation

Thermoelectric Transport in Nanocomposites.

Thermoelectric materials which can convert energies directly between heat and electricity are used for solid state cooling and power generation. There is a big challenge to improve the efficiency of energy conversion which can be characterized by the figure of merit

Effects of Heat Shock on Photosynthetic Properties, Antioxidant Enzyme Activity, and Downy Mildew of Cucumber (Cucumis sativus L.)

Heat shock is considered an abiotic stress for plant growth, but the effects of heat shock on physiological responses of cucumber plant leaves with and without downy mildew disease are still not clear. In this study, cucumber seedlings were exposed to heat shock in greenhouses, and the responses of photosynthetic properties, carbohydrate metabolism, antioxidant enzyme activity, osmolytes, and disease severity index of leaves with or without the downy mildew disease were measured. Results showed that heat shock significantly decreased the net photosynthetic rate, actual photochemical efficiency, photochemical quenching coefficient, and starch content. Heat shock caused an increase in the stomatal conductance, transpiration rate, antioxidant enzyme activities, total soluble sugar content, sucrose content, soluble protein content and proline content for both healthy leaves and downy mildew infected leaves. These results demonstrate that heat shock activated the transpiration pathway to protect the photosystem from damage due to excess energy in cucumber leaves. Potential resistance mechanisms of plants exposed to heat stress may involve higher osmotic regulation capacity related to an increase of total accumulations of soluble sugar, proline and soluble protein, as well as higher antioxidant enzymes activity in stressed leaves. Heat shock reduced downy mildew disease severity index by more than 50%, and clearly alleviated downy mildew development in the greenhouses. These findings indicate that cucumber may have a complex physiological change to resist short-term heat shock, and suppress the development of the downy mildew disease

On the invariants of root subgroups of finite classical groups

We show that invariant fields Fq(X1, . . . , Xn)G are purely transcendental over Fq if G are root subgroups of finite classical groups. The key step is to find good similar groups of our groups. Moreover, the invariant rings of the root subgroups of special linear groups are shown to be polynomial rings, and their corresponding Poincare series are presented.Показано, що iнварiантнi поля Fq(X1, . . . , Xn)G є чисто трансцендентними над Fq, якщо G — кореневi пiдгрупи скiнченних класичних груп. Ключовим мiсцем доведення є знаходження гарних подiбних груп для наших груп. Крiм того, показано, що iнварiантнi кiльця кореневих пiдгруп спецiальних лiнiйних груп є полiномiальними кiльцями. Також наведено вiдповiднi ряди Пуанкаре

Dynamics of Endomorphism of Finite Abelian Groups

We study the dynamics of endomorphisms on a finite abelian group. We obtain the automorphism group for these dynamical systems. We also give criteria and algorithms to determine whether it is a fixed point system

Structure of unitary groups over finite group rings and its application

summary:In this paper, we determine all the normal forms of Hermitian matrices over finite group rings $R=F_{q^2}G$, where $q=p^{\alpha }$, $G$ is a commutative $p$-group with order $p^{\beta }$. Furthermore, using the normal forms of Hermitian matrices, we study the structure of unitary group over $R$ through investigating its BN-pair and order. As an application, we construct a Cartesian authentication code and compute its size parameters

Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups

summary:Let $F$ be a finite field of characteristic $p$ and $K$ a field which contains a primitive $p$th root of unity and ${\rm char} K\neq p$. Suppose that a classical group $G$ acts on the $F$-vector space $V$. Then it can induce the actions on the vector space $V\oplus V$ and on the group algebra $K[V\oplus V]$, respectively. In this paper we determine the structure of $G$-invariant ideals of the group algebra $K[V\oplus V]$, and establish the relationship between the invariant ideals of $K[V]$ and the vector invariant ideals of $K[V\oplus V]$, if $G$ is a unitary group or orthogonal group. Combining the results obtained by Nan and Zeng (2013), we solve the problem of vector invariant ideals for all classical groups over finite fields

Symplectic inner product graphs and their automorphisms

A new graph, called the symplectic inner product graph $Spi\big(2\nu,q\big)$, over a finite field $\mathbb{F}_q$ is introduced. We show that $Spi\big(2\nu,q\big)$ is connected with diameter $4$ if and only if $\nu\geq2$ and the automorphism group of $Spi\big(2\nu,q\big)$ is determined. Two necessary and sufficient conditions for two vertices of $Spi\big(2\nu,q\big)$ and two edges of $Spi\big(2\nu,q\big)$ respectively are in the same orbit under the action of the automorphism group of $Spi\big(2\nu,q\big)$ are obtained