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  • Author or Editor: J. Wu x
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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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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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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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The stability behaviour of a thin-film superconductor under a localized release of thermal disturbance is investigated. Two-dimensional conjugate film/substrate conduction equation with anisotropic thermal conductivity of the film, and Joule heat are employed to investigate effects of substrate and thermal properties on the intrinsic stability and quenching recovery. To consider the thermal boundary resistance between film and substrate, an interfacial-layer model (ILM) with very low diffusivity and an acoustic mismatch model (AMM) are employed. Results show that the thermal boundary resistance influences strongly the intrinsic stability. Thermal boundary resistance increases intrinsic stability if the thermal conductivity of the substrate or the disturbance energy is large. Higher Biot numbers and thermal conductivity ratios of film to substrate in longitudinal direction influence stability favorably. We demonstrate also that operation of a film/substrate system, such as YBCO/MgO, is either intrinsically stable or irrecoverably unstable.

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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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Garlic is widely used as food flavouring, and China is the world's largest garlic producer and exporter. To develop a convenient technique for evaluation of garlic cultivars would be worthwhile, and it would have wide application in such a huge market. In this research, 3D front-face fluorescence data of 8 garlic cultivars were recorded, and independent component analysis was used to decompose the overall fluorescence spectra into six independent components. The first, second, and fourth independent components showed a big difference among the cultivars, and the chemical fluorophores behind these three components were specified as protein, vitamin B6, and ATP, respectively, as fluorescent markers for evaluation. The result showed that all 8 cultivars cluster separately. The cultivar “YNQJ” have the highest quality in terms of protein and vitamin B6, “NXYC” and “SDHB” have the highest content of ATP, while “SXXA” is the poorest in terms of protein and ATP, and “HNJZ” has the lowest content of vitamin B6. Therefore, rapid evaluation of garlic cultivars can be accomplished successfully by using only the proportion values of three properly selected fluorescent markers.

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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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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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