一类奇异扩散方程解的渐近性质

讨论了一类奇异扩散方程ut=Δu^m＋f（u）具齐次Neumann边值条件解的渐近性质.结果表明：1）若f（u）=-u^α,且u（x,t）是该问题在QT上的解,则t≤T0,此处T0=（max u0 x∈Ω）^1-α/（1-α） ;2）存在正常数c1,δ1,c2,δ2,使得‖▽u^m‖L^2（Ω）≤c1e^-δ1t以及‖u‖L^2（Ω）≤c2e^-δ2t.     

一类可降阶二阶变系数齐次线性方程的求解问题

目的讨论了一种特殊二阶变系数齐次线性方程的求解问题。方法利用降阶法研究了变系数二阶线性微分方程u(x)y″+v(x)y′+w(x)y=0的可解性。结果得到了一个可解的条件:如果微分算子u(x)(d~2)/(dx~2)+v(x)d/(dx)+w(x)刚好可以分解为(pd/(dx)+q)(rd/(dx)+s),那么方程是可积的。结论给出了求通解的方法和通解表达式。     

关于不定方程1/x+1/y+1/z +1/w+1/xyzw=0的一点注记

利用初等方法研究了不定方程1/x＋1/y＋1/z＋1/w＋1/xyzw=1/z＋1/w以及1/x＋1/y＋1/z=1/w＋1/xyzw的正整数解问题,分别给出了它们的全部正整数解的公式：（x,y,z,w）=[（n＋k,n（n＋k）-d]/k,n2（n＋k）2-n（n＋k）d-k/kd,n）其中n,k,d为正整数,     

关于不定方程1/x＋1/y＋1/z＋1/w＋1/xyzw=0的一点注记

利用初等方法研究了不定方程1/x＋1/y＋1/z＋1/w＋1/xyzw=1/z＋1/w以及1/x＋1/y＋1/z=1/w＋1/xyzw的正整数解问题,分别给出了它们的全部正整数解的公式：（x,y,z,w）=[（n＋k,n（n＋k）-d]/k,n2（n＋k）2-n（n＋k）d-k/kd,n）其中n,k,d为正整数,     

一类带有非线性边界条件和Hardy项的凸凹非线性问题

通过对偶喷泉定理,证明了当参数λ很小且1< q< 2 < p ≤ 2*=2N/N-2,0 ≤μ≤μ*时,方程-△u+u-μu/｜χ｜2=｜u｜p-2 u∈Ω、{0}δu/δv=λ｜u｜q-2u u∈δΩ有无穷多个解.     

预测冬季不同结构大棚内气象要素值的不同数学模型比较研究

[目的]为有效调节大棚内的光照、气温和湿度提供理论依据。[方法]对3种常见结构塑料大棚内外150cm的冬季光照、气温和湿度等气象要素进行对比观测、分析,建立预测不同结构大棚气象要素值的多种数学模型。[结果]单栋塑料大棚的光照预测模型以多项式y=-0.0006x3＋0.0029x2＋0.7404x＋0.0799最为确切,气温预测模型以乘幂y=0.7593x1.1554最为确切,相对湿度预测模型以多项式y=0.00000003x5-0.0001x4＋0.0131x3-0.8732x2＋29.823-347.99最为确切;3连栋塑料大棚的光照预测模型以多项式y=-0.0005x2＋0.47061x-0.015最为确切,气温预测模型以指数函数y=4.6629e0.089x最为确切,相对湿度预测模型以多项式y=-0.0004x3＋0.0136x2＋0.2051x＋35.056最为确切;6连栋塑料大棚的光照预测模型以直线y=0.3996x＋0.0536,最为确切,气温预测模型以指数函数y=4.6227e0.0897x最为确切,相对湿度预测模型以多项式y=-0.00008x3＋0.089x2＋0.6459x＋21.191最为确切。[结论]建立了冬季以棚外气象要素值预测不同结构大棚内气象要素值的数学模型。     

关于一类合作椭圆系统的正解

通过上下解方法和极大值原理, 证明了当ε很小时, 椭圆系统-Δu=(e)F/(e)u(x, u, v)+εg(x) x∈Ω -Δv=(e)F/(e)v(x, u, v)+εh(x) x∈Ω u＞0, v＞0 x∈Ω u=v=0x∈(e)Ω的极小正解的存在性, 其中Ω是RN上的有界光滑区域; F∈C1(Ω-×(R+)2, R+); g,h∈C1(Ω-);ε是正参数. 此外, 也证明了当ε很大时该系统无解.     

关于一类合作椭圆系统的正解

通过上下解方法和极大值原理, 证明了当ε很小时, 椭圆系统-Δu=(e)F/(e)u(x, u, v) εg(x) x∈Ω -Δv=(e)F/(e)v(x, u, v) εh(x) x∈Ω u＞0, v＞0 x∈Ω u=v=0x∈(e)Ω的极小正解的存在性, 其中Ω是RN上的有界光滑区域; F∈C1(Ω-×(R )2, R ); g,h∈C1(Ω-);ε是正参数. 此外, 也证明了当ε很大时该系统无解.     

正交Euler-Lagrange型三次方程的Ulam稳定性

研究了正交Euler-Lagrange型三次方程Ef（x,y）f（mx＋y）＋f（mx-y）-mf（x＋y）-mf（x-y）-2m（m2-1）f（x）=0在混合型积和函数F（x,y）=ε{xEpypE＋（xE2p＋yE2p）}和泛函H（x,y）限制下的Ulam稳定性.     

关于Diophantine方程的一类求解问题

对于正整数a,设δ(a)是a的约数和,证明了Diophantine方程δ(x3)=y2没有正整数解(x,y)适合x=4p,其中p是奇素数.     

Levels of Germinable Seed in Topsoil and Yak Dung on an Alpine Meadow on the North-East Qinghai-Tibetan Plateau

In order to clarify the interactive mechanism between grazing yak and alpine meadow on the Qinghai-Tibetan Plateau,our study assessed seed density（by species） in the topsoil of alpine meadow with different grazing intensities in the Tianzhu area,north-eastern margins of the Qinghai-Tibetan Plateau and their rates of occurrence in yak dung.Seed density in the topsoil of the lightly grazed,moderately grazed,heavily grazed and extremely grazed alpine meadows in November,2010 were 1 551,1 692,2 660 and 1 830 grains m-2,while in the same meadows in April,2011 densities were 1 530,2 404,2 530 and 2 692 grains m-2,respectively.In the cold season pasture,mean seed density in yak dung from November to April in the lightly grazed,moderately grazed,heavily grazed and extremely grazed sites were 121,127,187,and 120 grains kg-1of dry yak dung.The proportion of total seed numbers in yak dung to soil seed bank in lightly grazed,moderately grazed,heavily grazed and extremely grazed alpine meadow was 1.40,2.62,0.69,and 0.90%.12 species out of the 47 were not found in topsoil but were found in yak dung,10 species out of 45 were not found in yak dung but were found in the topsoil.Endozoochorous dispersal by yaks is therefore very important for soil seed bank and plant biodiversity and population dynamics in alpine meadows.     

Yeast-Derived β-1,3-Glucan Substrate Significantly Increased the Diversity of Methanogens During In vitro Fermentation of Porcine Colonic Digesta

The β-1,3-glucan from yeast has been extensively examined for its immuno-enhancing effects in animals.However,investigation on the relationship among β-glucan,gut microbiota and immune-modulating effects remains limited particularly in pigs.Considering the critical roles of gut methanogens in the microbial fermentation,energy metabolism and disease resistance,we investigated the phylogenetic diversity of methanogens from fermented cultures of porcine colonic digesta with（G） or without（N） yeast β-glucan based on sequences of the archaeal 16S rRNA gene.A total of 145 sequences in the G library were assigned into 8 operational taxonomic units（OTUs） with the majority of sequences（114/145） related to strains Methanobrevibacter millerae or Methanobrevibacter gottschalkii with high identities ranging from 97.9 to 98.6%,followed by 23 sequences to Methanobrevibacter ruminantium,2 sequences to Methanobrevibacter smithii and one sequence to Methanobrevibacter wolinii.The 142 sequences in the N library were assigned to 2 OTUs with most sequences（127/142） related to strains M.millerae or M.gottschalkii with sequence identities ranging from 97.9 to 98.5%,and 15 sequences related to M.gottschalkii with 97.9% identity.Shannon diversity index showed that the G library exhibited significantly higher archaeal diversity（P0.05） and Libshuff analysis indicated the differences in the community structure between the two libraries were significant（P0.0001）.In conclusion,the current study provides evidence that addition of yeast β-glucan significantly increased the diversity of methanogens in in vitro fermented porcine colonic digesta.     

Influences of Cold Storage at 5℃ for Different Durations on Oviposition of Female Silkworm Moths

In order to investigate the resistance of female silkworm moths to cold storage and their copulation and oviposition after cold storage, copulation and ovipo- sition experiments of Liangguang 2 silkworms and Guican 1 female silkworm moths were conduced under cold storage at 5 ~C for different durations. The results indi- cated that, after cold storage at 5 ~C with relative humidity of 75%, the resistance of female silkworm moths to cold storage varied with different varieties; to be specific, 9-Fu and 7.Xiang, parent silkworm varieties of Liangguang 2 with ancestry of mul- tivoltinism, were relatively resistant to cold storage, and their copulation capability was still at a high level after cold storage for 72 h. Oviposition capability also varied with different varieties and durations; to be specific, under 5 ~C conditions, between two parent silkworm varieties of Liangguang 2, female silkworm moths of 9-Fu achieved the best results within cold storage duration of 24 h, female silkworm moths of 7.Xiang achieved the best results within cold storage duration of 72 h; be- tween two parent silkworm varieties of Guican 1, female silkworm moths of Xinhang achieved the best results without cold storage, female silkworm moths of 826 achieved the best results within cold storage duration of 48 h.     

Strategies and Suggestions for the Development of Mechanized Rapeseed Production in Sichuan

Mechanization is the future direction of rapeseed production in Sichuan. A series of technology tests for rapeseed mechanized production have been carried out in terms of variety selection, key agronomic measures and machinery in the main production area of Sichuan in recent years. In the research, the agronomic techniques, including variety selection for mechanical production, key agronomic measures and mechanical harvesting were analyzed. Based on the present condi- tions, strategy and suggestions for the development of mechanized rapeseed produc- tion in Sichuan also were presented.     

Effects of Grafting on Root Exudates of Cucumber and Rhizosphere Environment under Copper Stress

[Objective] This study to aimed to investigate the effects of Cu stress on root exudates and microbial activities in rhizosphere of grafted and ungrafted cucum-ber seedlings, and therefore to elucidate the microbial mechanism of grafting for in-creasing cucumber plants tolerance to Cu stress [Method] Four treatments： （1） un-grafted seedlings ＋ test soil （U0）; （2） ungrafted seedlings ＋ test soil ＋ CuSO4·5H2O （U1）; （3） grafted seedlings ＋ test soil （G0）; （4） grafted seedlings ＋ test soil ＋ Cu-SO4·5H2O （G1） were set in the pot culture experiment. The contents of free amino acids, organic acids, phenolic acid and sugars, microbial population and enzyme ac-tivity in the four treatment were measured, respectively. [Result] The secretion of amino acids and organic acids were increased under Cu stress. The amino acids secretions of grafted seedlings roots were obviously higher than ungrafted seedlings except for Phe and Val. At the same time, the secretion of oxalic acid, malic acid, acetic acid, citric acid, cinnamic acid, ρ-hydroxybenzoic acid and benzoic acid of grafted seedlings were significantly higher than ungrafted seedlings as wel . There-fore, more Cu2＋ were restricted in soil by chelating, complexing and precipitation with root exudates, and its toxicity was decreased. The soil microbial biomass C and N in grafted cucumber rhizosphere were significantly higher than those in ungrafted cu-cumber rhizosphere, whereas basal respiration and metabolic quotient were signifi-cantly lower. Under Cu stress, the numbers of actinomyces and nitrogen fixing bac-teria decreased and the number of fungi increased significantly, whereas there was no significant difference in amounts of bacteria. The numbers of bacteria, actino-myces, and nitrogen fixing bacteria in grafted cucumber rhizosphere were significant-ly higher than those in ungrafted cucumber rhizosphere, but the number of fungi was opposite. The activities of soil urease, phosphatase, sucrase and catalase in grafted cucumber rhizosphere were significantly higher than those in ungrafted cu-cumber rhizosphere. [Conclusion] These indicated that the soil microbial environment and soil enzymes activities were improved by grafting under Cu stress, and as a re-sult, the adaptability of cucumber to Cu stress was improved.     

Screening of Toxin Mutant of Dickeya zeae and Its Biological Characters

[Objective] This study aimed to screen toxin mutant of Dickeya zeae （Er- winia chrysanthemi pv. zeae） and investigate its biological characters. [Method] We obtained a toxin mutant strain D. zeae Ech7-3-42 by using acridine orange as a mutagenic agent and compared their biological characteristics and virulence between the toxin mutant and wild strain. [Result] There was no significant difference in pectin lyase, protease, cellulase and the production of extracellular polysaccharide and lipopolysaccharide, but significant difference in toxin biological activities and vir- ulence. Ech7-3-42 mutant did not produce toxin, as well as the loss of virulence on rice and HR on tobacco, but did not lose the ability to soft rot on potato. Mutant strain Ech7-3-42 can infect rice root and then enriched in the root neck and stalk, but it could not cause rice foot rot. Dickeya zeae （wild and mutant strain） could be detected by PCR in the root neck and below the 1-2 cm long stem area, but could not be detected in the leaves. [Conclusion] We believed that toxin may be one of the important factors for D. zeae virulence on rice.     

Induced in vitro Expression of Human Lactoferrin in Goat Mammary Gland Epithelial Cell

[Objective]The aim of this study was to explore the technical system of induced expression in vitro of goat mammary gland epithelial cell,and evaluate expression efficiency of mammary gland specific vector and foreign protein at the cell level.[Method]Goat mammary gland epithelial cell transfected by human lactoferrin gene was inducted by culturing in DMEM/F12 medium supplemented with 5 mg/L insulin,5 mg/L prolactin and 1 mg/L hydrocortisone.Supernatant was collected per 6 hours and concentrated.Expression situation of foreign protein were detected by SDS-PAGE and Western blotting.[Result]There was target protein expression in the induced culture medium,which molecular weight was about 42 kD.[Conclusion]The method used in this study can induce goat mammary gland epithelial cell to express foreign gene,it lays a foundation for researching heterologous expression of foreign gene and producing mammary gland bioreactor.     

Correlation Analysis of SPAD Value with Chlorophyll Content and Economic Yield Traits of Brassica napus L.

[Objective] The aim was to compare differences of SPAD value, chloro- phyll content, agronomic characters, economic characters and yield traits to analyze correlation of SPAD value with other indices and establish regression functions. [Method] Based on 34 Brassica napus L. varieties, SPAD value, chlorophyll content, agronomic characters, economic characters and yield traits were measured and re- gression functions were established according to correlations. [Result] SPAD value, chlorophyll content, agronomic and economic characters and yield traits all achieved significant level in differences among 34 varieties. Specifically, SPAD value was of extremely significant correlation with chlorophyll a and b, total chlorophyll and carotenoid, and the correlation from high to low was chl-b〉chl-z〉chl-a〉chl-x. SPAD value was of significantly positive correlation with total pod number per plant, plant height, seed number per pod, yield per plant and harvest yield, and of insignificant correlation with branch point height, effective branch number, pod density of main stem, and pod length. [Conclusion] It is simple and rapid to predict chlorophyll con- tent, economic characters and yields of Brassica napus L. with SPAD value and re- gression functions.     

Effect of Metallothionein on Cell Cycle,Apoptosis Rate and Subsets Distribution of Lymphocytes in Peripheral Blood of Dairy Cattle under Heat Stress

[Objective] This study aimed to research the effect of metallothionein on cell cycle, apoptosis rate and subsets distribution of lymphocytes in peripheral blood of dairy cows under heat stress, so as to perfect the regulative mechanism re- searches of MT to anti-heat stress. [Method] Twenty lactating Chinese Holstein cows were randomly divided into four groups （A, B, C and D）, and injected with 0, 4.0, 8.0 and 12.0 mg Zn-metallothionein, respectively by intravenous route. Blood sam- ples were collected at 1＂, 16~, 31~, 46~ and 61~ day, and the dynamic changes of cell cycle, apoptosis rate and subsets distribution of lymphocytes were determined. [Result] The apoptosis rate of cells in group B and C was lower than those in group A by 26.63% （P〉0.05） and 24.84% （P〉0.05） respectively. The number of cells in the Gc/G1 phage in trial groups was increased and the number of cells in the S and GJM phages tended to decrease, but there were no significant differences （P〉 0.05）. The number of CD3~ T cell in three trial groups was greater than those in group A by 7.02% （P〉0.05）, 5.45% （P〉0.05） and 3.85% （P〉0.05） respectively, while the number of CD4~ T cell in trial groups was higher than those in control group by 31.04% （P〈0.05）, 35.68% （P〈0.05） and 39.34% （P〈0.05） respectively. The number of CD8＇ T cell and the levels of CD4＊/CD8~ in trial groups were increased observ- ably, but significant difference （P〈0.05） was observed in the levels of CD4~/CD8~ between groups A and C only. It demonstrated that exogenous Zn-metallothionein can decrease apoptosis rate, improve cell cycle and regulate subsets distribution of lymphocytes in dairy cattle in a dose-dependent manner. [Conclusion] This study will provide scientific basis for safe utilization of MT in dairy industry.     

Spatiotemporal Characteristics of Reference Evapotranspiration and Its Sensitivity Coefficients to Climate Factors in Huang-Huai-Hai Plain,China

Climate change will have important implications in water shore regions,such as Huang-Huai-Hai（3H） plain,where expected warmer and drier conditions might augment crop water demand.Sensitivity analysis is important in understanding the relative importance of climatic variables to the variation in reference evapotranspiration（ET 0）.In this study,the 51-yr ET 0 during winter wheat and summer maize growing season were calculated from a data set of daily climate variables in 40 meteorological stations.Sensitivity maps for key climate variables were estimated according to Kriging method and the spatial pattern of sensitivity coefficients for these key variables was plotted.In addition,the slopes of the linear regression lines for sensitivity coefficients were obtained.Results showed that ET 0 during winter wheat growing season accounted for the largest proportion of annual ET 0,due to its long phenological days,while ET 0 was detected to decrease significantly with the magnitude of 0.5 mm yr-1in summer maize growing season.Solar radiation is considered to be the most sensitive and primarily controlling variable for negative trend in ET 0 for summer maize season,and higher sensitive coefficient value of ET 0 to solar radiation and temperature were detected in east part and southwest part of 3H plain respectively.Relative humidity was demonstrated as the most sensitive factor for ET 0 in winter wheat growing season and declining relativity humidity also primarily controlled a negative trend in ET 0,furthermore the sensitivity coefficient to relative humidity increased from west to southeast.The eight sensitivity centrals were all found located in Shandong Province.These ET 0 along with its sensitivity maps under winter wheat-summer maize rotation system can be applied to predict the agricultural water demand and will assist water resources planning and management for this region.