EXTRACTION OF CHARACTERISTIC ROOTS ON BESSEL-NEUMANN’S MIXED EQUATIONS

This paper discusses the problem of the extraction of characteristic roots on Bessel-Neumann's mixed equations. It gives the expressions and the evaluation of the minimum root. The advantage of the method has no use for the table of the multi-figure number Bessel function and it does not need computer but can calculate all the characteristic roots The precision of these roots is still high.

Studies on the Root Characteristics of Maize Varieties of Different Eras

Experiment was conducted at the Gongzhuling Experimental Station of Institute of Crop Sciences, Chinese Academy of Agricultural Sciences, Jilin Province, China, during 2009-2010. Six representative varieties of maize （Baihe in the 1950s, Jidan 101 in the 1960s, Zhongdan 2 in the 1970s, Yedan 13 in the 1980s, Zhengdan 958 in the 1990s, and Xianyu 335 in the 2000s） were each planted under two different densities （52 500 and 82 500 plants ha-~） and two different nitrogen application levels （150 and 300 kg ha-l）. Root characteristics and distribution among soil layers were studied by the field root digging method. The results showed that root mass increased with the process of the growth and development of the plant, and it peaked at kernel filling stage, and decreased at maturity due to the root senesces. Root mass of different maize varieties from the 1950s to 1980s had a trend of increase, while it decreased for the modern varieties. Root length and root surface areas had the similar changing trend. The study suggested that early maize varieties may have root redundancy, and reducing root redundancy may be a direction for variety improvement for high yield. Root characteristics were affected by nitrogen application level and density; modern varieties were more suitable for higher fertilizer application level and density conditions. Root characteristics distribution among soil layers decreased by an exponent equation, but the regression coefficients of different varieties were different. Though the root length density （RLD） of every soil layer of different varieties also decreased by an exponent equation, there were large variations of RLD in every part of a layer.

Fusarium pseudograminearum and F.culmorum affect the root system architecture of bread wheat

Yield losses of bread wheat due to crown rot can be more severe when drought conditions occur during the grain-filling period.Root architecture characteristics are important for soil exploration and belowground resource acquisition and are essential for adaptation to water-limited environments.Traits such as root angle,length and density have been strongly associated with acquisition efficiency and contribute to yield stability of the crop.The impact of crown rot pathogens on wheat root architecture is poorly understood.We examined differences in root angle,length and number,as well as dry root weight of the crown rot-susceptible bread wheat cultivar,Livingston inoculated with one of two crown rot pathogens Fusarium culmorum or Fusarium pseudograminearum in a transparent-sided root observation chamber.Significant adverse impacts on plant health and growth were revealed by visual discolouration of the leaf sheaths;fresh and dry shoot weight;leaf area of the oldest and the youngest fully expanded leaf and leaf number.Values of most recorded root system measurements were reduced when inoculated with either F.culmorum or F.pseudograminearum.In contrast,root angle was increased in the presence of F.culmorum but was not significantly changed by F.pseudograminearum.The development of whiteheads and grain losses in bread wheat caused by crown rot have previously been associated with blockages of the vascular systems.The method employed here was able to identify differences in the pathogen impacts on roots,which were not detected using previous systems.This research indicates that in the presence of F.culmorum and F.pseudograminearum infection,not only reductions in the size and biomass of the shoot system but also changes in the length,biomass and architecture of the root system could play an important role in yield loss.

Identification of quantitative trait loci and epistasis for root characteristics and root exudations in maize (Zea mays L.) under deficient phosphorus

The phosphorus uptake （PU） in above-ground parts of plant, root characteristics and root exudations as well as the quantitative trait loci （QTLs） associated with these characteristics were determined for a F2：3 population derived from the cross of two contrasting maize （Zea mays L.） genotypes, 082 and Yel07. A total of 241 F2：3 families were evaluated in replicated trials under deficient phosphorus conditions in 2007 at two sites （Kaixian County and Southwest University, Chongqing, P. R. China）. The results show pleiotropy and close linkage among QTLs. Four common regions in different environments were in bnlg100- bnlg1268b （bins 1.02） for QTL of H＋, bnlg1268a-umc1290a （bins 1.09） for QTL of AP （acid phospbatase activity）, dupssrl5- P 1MT/a （bins 6.06） for QTLs of PU （phosphorus uptake） and RW （root weight）, and P IM3/d-P1M3/g （bins9.04） for QTLs of PU and AP. These QTLs are non-environment or minor QTLs x environment. By epistatic analysis, three main QTLs and eighteen QTLs x QTLs interactions were detected for the seven measured characteristics. These QTLs may affect trait expression by epistatic interaction with the other loci, and make a substantial contribution to phosphorus utilization efficiency, which should be considered when breeding maize varieties with high P efficiency. Two regions were detected in dupssrl 5- P1MT/a （bins 6.06） for QTL of RW and P1M3/d- P 1M3/g （bins 9.04） for QTL of PU and AP. They were detected in two different environments and by two methods of QTL analysis, which were useful for marker-assisted selection.

Biological Characteristics of Root Rot Pathogen on Sambucus chinensis

Effects of different media,pH values,temperatures,carbon and nitrogen sources on mycelial growth and sporulation of root rot pathogen on Sambucus chinensis was determined in the paper.The results showed that root rot pathogen on S.chinensis was identified as Fusariumsp.The mycelial growth and sporulation of Fusariumsp.in PSA medium was the best;the optimal temperature for mycelial growth and sporulation was from 25℃ to 30℃ and the optimal temperature was 28℃;the suitable pH values for mycelial growth and sporulation was from 5 to 7,and the optimum pH value was 6;the absence or presence of carbon sources had significant effect on growth of Fusariumsp.;sucrose was the best carbon source utilized in mycelial growth,while lactose was the worst; KNO3 was the best nitrogen source utilized in mycelial growth,while（NH4） 2 SO4 was the worst one.

Negative Effects of Oxytetracycline on Wheat (Triticum aestivum L.) Growth, Root Activity, Photosynthesis, and Chlorophyll Contents

A solution culture experiment was performed to investigate the effects of oxytetracycline （OTC） on wheat （Triticum aestivum L.） growth, chlorophyll contents, and photosynthesis at five levels of 0, 10, 20, 40, and 80 mmol L-1 OTC. OTC is toxic to wheat. The wheat growth, especially wheat root was significantly decreased. Further OTC also significantly decreased root activity, chlorophyll contents, and photosynthetic parameters except for intercellular CO2 concentrations. The different responses of indicators such as root number, root activity and so on to OTC were also observed. The IC50 values for the tested indicators to OTC ranged from 7.1 to 113.4 mmol L-1 OTC. The order of indicator sensitivity to OTC was root number stomatal conductance chlorophyll a total chlorophyll photosynthetic rates total surface area transpiration rate chlorophyll b fresh weight of root dry weight of root total length dry weight of shoot = fresh weight of shoot total volume. The root number was more sensitive than other indicators with the IC50 value of 7.1 mmol L-1 OTC, and could be taken as the sensitive indicator to predict the hazards of OTC to wheat.

Effect of plough pans on the growth of soybean roots in the black-soil region of northeastern China

Plough pans （PPs）, common in the black-soil region of northeastern China, have significant effects on the root systems of crops. We conducted a field experiment to study the distribution of soybean roots under the influence of PPs. The soybean roots showed compensatory growth above the PP, with higher root length and weight in soil with a PP compared to those without a PP. Roots were heavier and longer in the 15-75 cm soil layer without a PP than with a PP. Soil porosity was lower in the PP and the soil below the PP, which likely decreased the oxygen content of the soil and induced more growth of roots above the PP. The PP is also likely to decrease infiltration of rain-water and hinder the migration of nitrate downward, which in turn increased the density and length of soybean root hairs, which, hence, promoted growth.

Shoot and root traits in drought tolerant maize(Zea mays L.) hybrids

This study aimed to investigate the differences in shoot and root traits, and water use and water use efficiency（WUE） in drought tolerant（DT） maize（Zea mays L.） hybrids under full and deficit irrigated conditions. A two-year greenhouse study was conducted with four hybrids（one conventional hybrid, 33D53AM, two commercial DT hybrids, P1151 AM, N75H, and an experimental hybrid, Exp HB） grown under two water regimes（I（100） and I（50）, referring to 100 and 50% of evapotranspiration requirements）. Under water stress, the hybids P1151 AM, N75, and Exp HB showed more drought tolerance and had either greater shoot dry weight or less dry weight reduction than the conventional hybrid（33 D53 AM）. However, these three hybrids responded to water stress using different mechanisms. Compared with the conventional hybrid, the two commercial DT hybrids（P1151 AM and N75H） had a smaller leaf area, shoot dry weight, and root system per plant. As a result, these hybrids used less water but had a higher WUE compared with the conventional hybrid. In contrast, the experimental hybrid（ExpHB） produced more shoot biomass by silking stage at both irrigation levels than all other hybrids, but it had relatively lower WUE. The hybrids demonstrated different drought response mechanisms that may require different irrigation management strategies. More investigation and validation are needed under field conditions and in different soil types.

Evolution of Root Characters of Soybean Varieties Developed in Different Years

It was studied that the evolution of root characteristics among 42 soybean varieties developed in Heilongjiang and Jilin Province in different years. The results showed that there were differences on the root characteristics among soybean varieties. From 1950s to 1990s, root fresh weight, root volume, root surface, root dry weight, lateral root length of main root characters tendedly increased with the variable development

水稻根系性状的遗传研究

采用双回交试验设计系统研究了水稻６个根系性状的遗传。结果表明：各性状表现为数量遗传，只受细胞核基因控制。６个性状的加性效应及显性效应均达显著以上统计水平，其中平均根长、根数、根基粗的加性率较高达４０％左右。上位性效应对各性状尤其是根重、根中粗具有不可忽视的影响，其中又以加性×加性、显性×显性的贡献较大，只有平均根长符合加性一显性模型。各性状的显性及上位性效应值基本上均为正值。因而既可以利用各根系性状的正向杂种优势，也可以选育根系发达的纯系品种。６个性状中平均根长、根数、根基粗的狭义遗传力在５５％上下，育种中的选择效果比较好；根中粗、最长根长、根重的狭义遗传力为４０％左右，利用杂种优势的潜力比较大，选育纯系品种的育种方案中应在较高世代选择为宜。

Optimal feedback gains of a delayed proportional-derivative(PD) control for balancing an inverted pendulum

In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a systematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost characteristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial values around the origin are fixed. The main results are checked by numerical simulation.

Comprehensive Study on the Estimation of the Variance Components of Traverse Nets

This paper advances a new simplified formula for estimating variance components ,sums up the basic law to calculate the weights of observed values and a circulation method using the increaments of weights when estimating the variance components of traverse nets,advances the charicteristic roots method to estimate the variance components of traveres nets and presents a practical method to make two real and symmetric matrices two diagonal ones.

Changes in soil properties and erodibility of gully heads induced by vegetation restoration on the Loess Plateau, China

Soil erosion on the Loess Plateau of China is effectively controlled due to the implementation of several ecological restoration projects that improve soil properties and reduce soil erodibility. However, few studies have examined the effects of vegetation restoration on soil properties and erodibility of gully head in the gully regions of the Loess Plateau. The objectives of this study were to quantify the effects of vegetation restoration on soil properties and erodibility in this region. Specifically, a control site in a slope cropland and 9 sites in 3 restored land-use types （5 sites in grassland, 3 in woodland and 1 in shrubland） in the Nanxiaohegou watershed of a typical gully region on the Loess Plateau were selected, and soil and root samples were collected to assess soil properties and root characteristics. Soil erodibility factor was calculated by the Erosion Productivity Impact Calculator method. Our results revealed that vegetation restoration increased soil sand content, soil saturated hydraulic conductivity, organic matter content and mean weight diameter of water-stable aggregate but decreased soil silt and clay contents and soil disintegration rate. A significant difference in soil erodibility was observed among different vegetation restoration patterns or land-use types. Compared with cropland, soil erodibility decreased in the restored lands by 3.99% to 21.43%. The restoration patterns of Cleistogenes caespitosa K. and Artemisia sacrorum L. in the grassland showed the lowest soil erodibility and can be considered as the optimal vegetation restoration pattern for improving soil anti-erodibility of the gully heads. Additionally, the negative linear change in soil erodibility for grassland with restoration time was faster than those of woodland and shrubland. Soil erodibility was significantly correlated with soil particle size distribution, soil disintegration rate, soil saturated hydraulic conductivity, water-stable aggregate stability, organic matter content and root characteristics （including root average diameter, root length density, root surface density and root biomass density）, but it showed no association with soil bulk density and soil total porosity. These findings indicate that although vegetation destruction is a short-term process, returning the soil erodibility of cropland to the level of grassland, woodland and shrubland is a long-term process （8-50 years）.

Successful vegetative propagation by stem cuttings of Tetraena mongolica Maxim.

Techniques have been developed for the vegetative propagation of Tetraena mongolica,a rare and endangered species endemic to the western Ordos Plateau in the northcentral portion of China.The purpose of the study was to investigate the rooting characteris-tics of the plant species from the aspects of length and ages of cuttings,external hormone concentration,leaf retention,cutting orientations,and cutting positions.The results obtained from the experiments indicated that the rooting ratio of 2-year or 3-year old cuttings was larger than more than of 4-year old cuttings.The influence of external hormone concentration on rooting was ob-vious;the rooting ratio of cuttings was increased by external hormone treatment,especially when treated by ABT1(ABT No.1 Rooting Powder) 50 mg/L for 3 hours,in which case,the rooting ratio reached 91 percent.Leaf retention influenced rooting sig-nificantly;the rooting rate of cuttings became greater as the leaf retention increased.There was no significant difference in rooting capability between south and north orientations of the ortets.The rooting ratio of the cuttings obtained from the distal portions of shoots was significantly larger than those obtained from the middle and the basal portions of the shoots.On day three after treat-ment,calluses started appearing at the incisions of some cuttings dipped in 500 mg/L IAA(indole acetic acid).Most cuttings were healed or swelled,and 6 percent of cuttings rooted on day 6 after treatment.Higher rooting period occurred 7-10 days after the experiment was set up.

Stability test of fractional-delay systems via integration

This paper focuses on the stability testing of fractional-delay systems. It begins with a brief introduction of a recently reportedalgorithm, a detailed demonstration of a failure in applications of the algorithm and the key points behind the failure. Then,it presents a criterion via integration, in terms of the characteristic function of the fractional-delay system directly, for testingwhether the characteristic function has roots with negative real parts only or not. As two applications of the proposed criterion,an algorithm for calculating the rightmost characteristic root and an algorithm for determining the stability switches, are proposed.The illustrative examples show that the algorithms work effectively in the stability testing of fractional-delay systems.

SOLUTION TO FRACTIONAL ORDER HYBRID NON-HOMOGENEOUS ORDINARY DIFFERENTIAL EQUATION

In this paper, we study a fractional order hybrid non-homogeneous ordinary diffe- rential equation. We gain r^ae^rt for the a order derivatives of both Riemann-Liouville type and Caputo type of function f（t） = e^rt by letting integral lower limit of fractional derivative be -∞. It is first time for us to use the traditional eigenvalue method to solve fractional order ordinary differential equation. However, the law of the number of mutually independent arbitrary constants in general solutions to fractional order hy- brid non-homogeneous ordinary differential equation and general ordinary differential equation are very different.