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# Divergence points with fast growth orders of the partial quotients in continued fractions

Acta Mathematica Hungarica
Authors: B. Wang and J. Wu

## Abstract

This paper is concerned with the divergence points with fast growth orders of the partial quotients in continued fractions. Let S be a nonempty interval. We are interested in the size of the set of divergence points

\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} $$E_\varphi (S) = \left\{ {x \in [0,1):{\rm A}\left( {\frac{1} {{\varphi (n)}}\sum\limits_{k = 1}^n {\log a_k (x)} } \right)_{n = 1}^\infty = S} \right\},$$ \end{document}
where A denotes the collection of accumulation points of a sequence and φ: ℕ → ℕ with φ(n)/n → ∞ as n → ∞. Mainly, it is shown, in the case φ being polynomial or exponential function, that the Hausdorff dimension of E φ(S) is a constant. Examples are also given to indicate that the above results cannot be expected for the general case.

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# Packing dimensions of homogeneous perfect sets

Acta Mathematica Hungarica
Authors: X. Wang and J. Wu

## Abstract

In [10], the notion of homogeneous perfect sets as a generalization of Cantor type sets is introduced and their Hausdorff and lower box-counting dimensions are studied. In this paper, we determine their exact packing and upper box-counting dimensions based on the length of their fundamental intervals and the gaps between them. Some known results concerning the dimensions of Cantor type sets are generalized.

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# Subsolidus phase diagram of binary system in the perovskite type layer compounds ( n -CnH2n+1NH3)2MnCl4

Journal of Thermal Analysis and Calorimetry
Authors: K. Wu and J. Zhang

## Abstract

The thermotropic phase transitions in the perovskite type layer compound (n-C10H21NH3)2MnCl4 and (n-C14H29NH3)2MnCl4 were synthesized and, at the same time, a series of their mixtures C10Mn-C14Mn were prepared. The experimental binary phase diagram of C10Mn-C14Mn was established by differential thermal analysis (DTA), IR and X-ray diffraction. In the phase diagram new material (n-C10H21NH3)(n-C14H29NH3)MnCl4 and two eutectoid invariants were observed, two eutectic points temperatures are about 29.8 and 27.9°C. Contrasting other similar system, there are three noticeable solid solution ranges (α, β, γ) at the left and right boundary and middle of the phase diagram.

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# On the Sum of Exponential Divisors of an Integer

Acta Mathematica Hungarica
Authors: Y.-F. Pétermann and J. Wu
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# Mapping of STS markers developed from drought tolerance candidate genes and preliminary analysis of their association with yield-related traits in common wheat (Triticum aestivum)

Cereal Research Communications
Authors: J. Chen, G. Hu, J. Zhang, C. Chu, and Y. Wu

Drought is a severe abiotic stress that affects wheat production worldwide. In order to identify candidate genes for tolerance to water stress in wheat, sequences of 11 genes that have function of drought tolerance in other plant species were used to identify the wheat ortholog genes via homology searching in the wheat EST database. Atotal of 11 primer pairs were identified and amplified PCR products in wheat. Of them, 10 STS markers were mapped on 11 chromosomes in a set of nulli-tetrasomic lines of ‘Chinese Spring’ wheat; six were mapped on chromosomes 1A, 1B, 4B, 7A, 2B and 5D, respectively, in a spring wheat mapping population (POP1). The marker XTaABH1 mapped on 7A in POP1 was the only one mapped but characterized in a winter wheat mapping population (POP2) for grain yield, kernel weight and diameter, and height in four-field trials applied different water stress or irrigation. The marker XTaABH1 was significantly associated with grain yield under rainfed condition, with kernel weight under terminal stress and non-irrigation conditions, with kernel diameter and height under non-irrigated condition. The STS primers, map information and marker-trait association produced in the currently study would be of interest to researchers working on drought tolerance.

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# Analysis of developmental genetics for phenylalanine content in indica-japonica hybrid rice ( Oryza sativa L.) across environments

Cereal Research Communications
Authors: X. Zhang, C. Shi, J. Wu, S. Yue, and Y. Qi

Developmental genetics of phenylalanine content in indica-japonica hybrid rice ( Oryza sativa L.) have been studied through 7 indica rice crossed with 5 japonica rice by using the developmental genetic models and corresponding statistical approaches for quantitative traits of triploid seeds in cereal crops. The unconditional genetic model was used to analyze the cumulative genetic effects (from flowering to a specific time) along the developmental stages, and the conditional genetic model was used to analyze the genetic effects in one specially developmental stage from one filling time to another time ( t -1→ t ). Results showed that phenylalanine content of indica-japonica hybrid rice was simultaneously controlled by the triploid endosperm effects, cytoplasm effects, diploid maternal effects and their genotype × environment interaction effects. Endosperm dominance effect, maternal additive effect and cytoplasmic effect were more important at the initial stage of rice development than endosperm additive effect and maternal dominance effect. With regard to the components of heritability, maternal and cytoplasm general heritability and their interaction heritability were higher for phenylalanine content at all 5 developmental stages. Respectively, it occupied 68.3, 92.4, 100.0, 100.0 and 78.9% among all the component of heritability. It was suggested that improving the phenylalanine content of indica-japonica hybrid rice would be more efficient when selection was based on maternal plants at early generations in rice breeding program.

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# Synthesis and Thermal Decomposition of the Macrocyclic Dinuclear Ni(II) Complex

Journal of Thermal Analysis and Calorimetry
Authors: W. Yan, C. Ma, J. Wu, W. Zhang, and D. Jang

## Abstract

Crystal of the complex Ni2L (ClO4)2 was obtained by reaction of Ni(ClO4)2 and macrocyclic ligand H2L, where L2– is the dinucleating macrocycle with two 2,6-di(aminomethyl)-4-methyl phenolate entities combined by the same two lateral chains, –(CH2)2–NH–(CH2)2–, at the amino nitrogens. The thermal decomposition processes of the title complex were studied in a dynamic atmosphere of dry argon using TG-DTG. The kinetic analysis of the first and second thermal decomposition steps were performed via the TG-DTG curves, and the kinetic parameters were obtained from analysis of the TG-DTG curves with integral and differential methods. The most probable kinetic function was suggested by comparison of the kinetic parameters.

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# Thermal runaway evaluation of α-methylstyrene and trans -β-methylstyrene with benzaldehyde

Journal of Thermal Analysis and Calorimetry
Authors: S. Lin, J. Tseng, M. Lee, T. Wu, and C. Shu

## Abstract

Styrene is an important chemical in the petrochemical industry. In recent years, there have been sporadic releases, runaway reactions, fires, and thermal explosion accidents incurred by styrene and its derivatives worldwide. The purpose of this study was to estimate the impact of styrene and its derivatives of α-methylstyrene (AMS) and trans-β-methylstyrene (TBMS) contacting with benzaldehyde. Experiments were carried out to evaluate the thermokinetic parameters estimated by differential scanning calorimetry (DSC) and thermal activity monitor III (TAM III). TAM III was used to determine the fundamental thermokinetics under various isothermal temperatures, 80, 90 and 100°C. This autocatalytic reaction was demonstrated in thermal curves. After styrene was contacted with benzaldehyde, the exothermic onset temperature (T 0) and the total heat of reaction (Q total) were altered by DSC tests. When benzaldehyde is mixed with AMS and TBMS, the reaction time will be shorter but the enthalpy reduced, as revealed by TAM III tests. As AMS and TBMS, respectively, were contacted with benzaldehyde, both exothermic phenomena were changed during the reaction excursion. According to the results of this research, an operator should dictate the oxygen concentration in order to avoid any potential hazards during handling and transportation.

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# Spatial pattern of water controlled wetland communities on the Sanjiang Floodplain, Northeast China

Community Ecology
Authors: D. Zhou, H. Gong, Z. Luan, J. Hu, and F. Wu

The study site is the Honghe National Nature Reserve, a Ramsar designated site on the Sanjiang Plain in Northeast China. We present results regarding the spatial pattern and structure of plant communities in these most important natural but continually diminishing freshwater wetlands of China to help promote both protection and restoration. By investigating three ecological levels (landscape, ecosystem and community), this paper quantifies the characteristics of spatial pattern with the aim to identify specific ecological correlations with different hydrogeomorphic features. Specifically, the research involves hierarchical mapping of vegetation types by use of remote sensed data, and the coupling of landscape indices with fluvial topographic zones that have been deduced by GIS from DEM. Statistics from historical survey data are also used to measure the degradation of marshes as well as the historical change of the hydrological regime. We found that dominant is the Calamagrostis angustifolia — Carex spp. community type, a wet meadow and marsh complex within the prevailing landscape mosaic of shrubland and meadow. The results suggest that the sites’ hydro-geomorphic character has decisive influence on plant community structure and composition. There is only limited direct human interference in the sites and, as a consequence, the spatial pattern of vegetation distribution is natural. However, changes to the hydrological regime as the result of extensive irrigation activity in the surrounding area has led to rapid degradation of marsh wetlands within the sites, which threatens the ecological status in this storehouse of “Natural Genes” in the reserve.

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# Genotypic and environmental variation in grain protein components and their relations to beta-amylase and beta-glucanase activity in malting barley

Cereal Research Communications
Authors: D. Xue, J. Dong, F. Wu, and G. Zhang

Eight malting barley cultivars were used to investigate the cultivar and environmental effects on grain protein components and the relationships between protein fractions and β -amylase or β -glucanase activity. The results showed there was a great variation for three protein fraction (albumin, hordein and glutelin) contents over cultivars and locations, and a distinct difference in each protein fraction content between the locations for a given cultivars. Correlation analysis indicated that β -amylase activity was significantly correlated with three protein fraction contents and there was a negative correlation between glutelin content and β -amylase activity, but β -amylase activity positively correlated with albumin or hordein content. Furthermore, there was a significant positive correlation between total protein content and β -glucanase activity, and we found the hordein and glutelin content did not show correlated with β -glucanase activity but the albumin content was a significantly negative correlation with β -glucanase activity.

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