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Abstract  

Let A and k be positive integers. We study the Diophantine quadruples

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\{ k,A^2 k + 2A,(A + 1)^2 k + 2(A + 1),d\}$$ \end{document}
. We prove that if d is a positive integer such that the product of any two distinct elements of the set increased by 1 is a perfect square, then
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\begin{gathered} d = (4A^4 + 8A^3 + 4A^2 )k^3 + (16A^3 + 24A^2 + 8A)k^2 \hfill \\ + (20A^2 + 20A + 4)k + (8A + 4) \hfill \\ \end{gathered}$$ \end{document}
when 3 ≦ A ≦ 10. This extends a theorem obtained by Dujella [7] for A = 1, and also, a classical theorem of Baker and Davenport [2] for A = k = 1.

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Arbuscular mycorrhizal (AM) fungi are obligatory biotrophic symbionts living in the roots of most terrestrial plants. AM fungi (AMF) have a positive effect on plant growth and plant nutrition, especially under stress conditions.  The aim of the present study was to observe the relationship between the mycorrhizal dependency and nutrient uptake of host plants and the rate of AMF colonization in a pot experiment. The degree of host growth responses to AMF colonization is expressed as mycorrhizal dependency (MD).  The pot trial was set up with a sterilized calcareous chernozem soil from Nagyhörcsök (Hungary) in a growth chamber under controlled climatic conditions. Tomato (Lycopersicon esculentum L.) plants were inoculated with Glomus claroideum (BEG23) , Glomus fasciculatum (BEG53), Glomus geosporum (BEG11), Glomus mosseae (BEG12) strains and a Glomus mosseae AMF culture produced by authors. The dry biomass production, the micro- and macronutrient concentrations of the shoots and the parameters of the mycorrhizal infection were determined. Each AM fungi species or isolate caused different and distinct changes in host plant growth and nutrient uptake. The biomass production of tomato increased significantly in the presence of AM symbiosis. The mean values of MD, calculated from shoot dry matter, varied between 36% and 55%. Mycorrhizal inoculation improved the P, N and K uptake of tomato. The highest values for root colonization, frequency of infection or arbuscular richness were found in the root of tomato inoculated with the two Glomus mosseae strains. The highest MD and nutrient contents appeared in the shoot of tomato treated withour Glomus mosseae strain, which may indicate a stronger affinity (compatibility) between the symbiotic partners. The results confirmed that the selected AMF strains are applicable in sustainable horticulture.

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Naturalization is the introduction and establishment of a nonnative species with sustainable populations in a novel environment. The success of nonnative species may be influenced by their relatedness to the native flora. Darwin proposed that if a nonnative plant species is introduced into an environment without native congeners, the nonnative species will have a greater chance of becoming naturalized. To test Darwin’s naturalization hypothesis, we compiled a Kentucky plant database consisting of 821 vascular plant species and subsequently selected species traits and distribution information to determine the effect of congeneric species and traits on the probability of successful naturalization and invasion. The predictors used include reproductive traits, growth form, abundance, habitat type, native congeners, and biogeographical origin. We fit three sets of generalized linear mixed models (GLMMs) with a binomial family and a logit link. Backward selection based on minimizing the Akaike Information Criterion (AIC) was used in the analyses. Our results from these three sets of models clearly indicate that the validity of Darwin’s hypothesis is invasion stage dependent. More specific, the naturalized and invasive models (predicting the probability of being naturalized and invasive respectively) did not support Darwin’s naturalization hypothesis. The number of native congeners had no effect on the likelihood that a particular species would naturalize and become invasive. Our results suggest that Darwin’s naturalization hypothesis is more relevant during the early stage of establishment as demonstrated by the native model (predicting the probability of being native) and it becomes irrelevant during the late stages of invasion as indicated by the naturalized and invasive models. Thus, it can be generalized that biotic interactions, especially competition, is a critical determinant of initial success for nonnative species in the recipient communities. Once established, the fate of non-native species during the late stages of invasion may be more related to other factors such as biogeographic origin and habitat conditions. Furthermore, we found reproductive traits such as flowering phenology and flower type are associated with invasion success. We also recognized contrasting traits between native and nonnative species, indicating niche differentiation between these two groups of species. Niche overlapping was found as well among species regardless of the status of being native or otherwise. Our study provides a novel approach to advance the understanding of phylogenetic relatedness between nonnative species and native flora by integrating traits and niche concepts at the regional scale.

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Abstract  

Positron lifetime spectra were measured as a function of the time for metallocene polyethylene (mPE), poly(methyl methacrylate) (PMMA), polyamide (PA), and polycarbonate (PC). A decrease in o-Ps intensity with the elapsed time was observed in mPE and PC measured at room temperature and in PMMA measured at 225 K. Formation of free radicals has been supposed to be one of the causes of this effect. The effect of maleic-anhydride (maH) grafted copolymers and its ionomers in mPE/PA blends was also studied. The change in the positron lifetime distribution with increasing maH and the ionomer content revealed an enhanced interaction between mPE and PA phase and the decrease of dispersed mPE particles, which reflected good compatibility of the blend.

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Abstract  

The recombination of hydrogen and oxygen in technical gaseous waste of nuclear power plants in enlarged scale experiment has been studied on the basis of our previous work.1 The catalyst and its best operating conditions for recombination of hydrogen and oxygen determined in a small scale experiment were demonstrated and tested. The results show that the data obtained in an enlarged scale experiment agreed well with that of in a small scale test. The recombination rate of H2 and O2 was higher than 98.3% and 99.98% respectively. After recombination, the residual concentrations of H2 and O2 in waste gas were O2<3 ppm, H2<400 ppm. The Pd-Al2O3 catalyst and operating conditions determined for gaseous waste processing of nuclear power plants were satisfactory.

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Abstract  

A laser-induced optical fiber fluorimetry has been reported for the analysis of ultralow level of uranium. The fluorescence spectrometer includes five major components: a pulsed nitrogen laser, optical fibers, an optrode, a detector, and a boxcar. The fluorescence intensity of uranyl ions is linear with respect to the concentration of uranium. The detection limit of uranium in 1M phosphoric acid is 24 ppb. This technique can be used for the remote, on-line measurement of low level uranium.

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Abstract  

Laser-induced optical fiber fluorimetry has been first used to analyze uranium(VI) concentration in the kinetic studies on the extraction of uranium(VI) between 0.5 mol/l H3PO4 solution and HDEHP-cyclohexane system with a Lewis cell. The effects of stirring speed, temperature and concentrations of uranium(VI) and HDEHP on the rate of extraction were examined. These data show that the extraction rate of uranium(VI) in this system is controlled by the chemical reaction at the interface. The rate equations and the rate constants of forward and reverse extraction are obtained. The mechanism of the extraction is discussed.

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Abstract  

The recombination of hydrogen and oxygen in technical gaseous waste of nuclear power plants has been studied. A highly efficient catalyst for reacting H2 with O2 to form water was prepared. Various operating conditions and factors affecting the recombination of H2 and O2 were tested and the best conditions were determined. Results show that the Pd–Al2O3 catalyst prepared had very good characteristics. The recombination rate of H2 and O2 was higher than 98.3% and 99.9%, respectively. After recombination, residual concentrations of H2 and O2 in waste gas were O2<3 ppm, H2<400 ppm. The Pd–Al2O3 catalyst and operating conditions determined for gaseous waste processing of nuclear power plants were satisfactory.

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