Root Systems Lie Algebras

A root system is any collection of vectors that has properties that satisfy the roots of a semi simple Lie algebra. If g is semi simple, then the root system A, (Q) can be described as a system of vectors in a Euclidean vector space that possesses some remarkable symmetries and completely defines the Lie algebra of g. The purpose of this paper is to show the essentiality of the root system on the Lie algebra. In addition, the paper will mention the connection between the root system and Ways chambers. In addition, we will show Dynkin diagrams, which are an integral part of the root system.

Soil physical properties and maize root growth under different tillage systems in the North China Plain

The standard cultivation system in the North China Plain is double cropping of winter wheat and summer maize. The main effects of this cultivation system on root development and yield are decreases in soil nutrient content and depth of the plow layer under either long-term no-tillage or rotary tillage before winter wheat sowing and no tillage before summer maize sowing. In this study, we investigated the combined effects of tillage practices before winter wheat and summer maize sowing on soil properties and root growth and distribution in summer maize. Zhengdan 958(ZD958) was used as experimental material, with three tillage treatments: rotary tillage before winter wheat sowing and no tillage before summer maize sowing(RTW + NTM), moldboard plowing before winter wheat sowing and no tillage before summer maize sowing(MPW + NTM), and moldboard plowing before winter wheat sowing and rotary tillage before summer maize sowing(MPW + RTM).Tillage practice showed a significant(P < 0.05) effect on grain yield of summer maize. Grain yields under MPW + RTM and MPW + NTM were 30.6% and 24.0% higher, respectively, than that under RTW + NTM. Soil bulk density and soil penetration resistance decreased among tillage systems in the order RTW + NTM > MPW + NTM > MPW + RTM. Soil bulk densities were 3.3% and 515% lower in MPW + NTM and MPW + RTM, respectively, than that in RTW + NTM, and soil penetration resistances were respectively 17.8% and 20.4% lower,across growth stages and soil depths. Root dry matter and root length density were highest under MPW + RTM, with the resulting increased root activity leading to a yield increase of summer maize. Thus the marked effects of moldboard plowing before winter-wheat sowing on root length density, soil penetration resistance, and soil bulk density may contribute to higher yield.

An in vitro study on the efficacy of removing calcium hydroxide from curved root canal systems in root canal therapy

To compare the efficacy of various irrigants(citric acid, ethylenediaminetetraacetic acid(EDTA) and Na OCl) and techniques in removing Ca(OH)2in two types of curved root canal systems, simulated root canals with specific curvatures were used to investigate the effects of different irrigants and instruments on Ca(OH)2removal. The optimal methods were verified on extracted human teeth. Simulated root canals were assigned to one of two groups based on the irrigation solution: 10% citric acid or2.5% Na OCl. Each group was divided into four subgroups according to the technique used to remove Ca(OH)2. The percentage of Ca(OH)2removal in different sections of root canals was calculated. On the basis of the results obtained for the simulated canals, 10% citric acid and 17% EDTA were applied to remove Ca(OH)2from the extracted human teeth with curved root canal systems. The teeth were scanned by micro computed tomography to calculate the percentage of Ca(OH)2removal in the canals.In simulated root canals, we found that 10% citric acid removed more Ca(OH)2than 2.5% NaOCl in the 0–1 mm group from the apex level(Po0.05). Ultrasonic and Endo Activator activation significantly removed more Ca(OH)2than a size 30 K file in the apical third(Po0.05). However, there were no significant differences in any sections of the canals for 10% citric acid or 17%EDTA in removing Ca(OH)2in extracted human teeth. We concluded that it was effective to remove residual Ca(OH)2using the decalcifying solution with Endo Activator or Passive Ultrasonic Irrigation in a curved root canal system. A protocol for Ca(OH)2removal was provided based on the conclusions of this study and the methods recommended in previous studies.

Effects of Different Tillage Systems on Soil Properties,Root Growth,Grain Yield,and Water Use Efficiency of Winter Wheat (Triticum aestivum L.) in Arid Northwest China

Studies on root development, soil physical properties, grain yield, and water-use efficiency are important for identifying suitable soil management practices for sustainable crop production. A field experiment was conducted from 2006 through 2008 in arid northwestern China to determine the effects of four tillage systems on soil properties, root development, water-use efficiency, and grain yield of winter wheat （Triticum aestivum L.）. The cultivar Fan 13 was grown under four tillage systems：conventional tillage （CT） without wheat stubble, no-tillage without wheat stubble mulching （NT）, no-tillage with wheat stubble standing （NTSS）, and no-tillage with wheat stubble mulching （NTS）. The soil bulk density （BD） under CT system increased gradually from sowing to harvest, but that in NT, NTSS, and NTS systems had little change. Compared to the CT system, the NTSS and NTS systems improved total soil water storage （0-150 cm） by 6.1-9.6 and 10.5- 15.3% before sowing, and by 2.2-8.9 and 13.0-15.1% after harvest, respectively. The NTSS and NTS systems also increased mean dry root weight density （DRWD） as compared to CT system. The NTS system significantly improved water-use efficiency by 17.2-17.5% and crop yield by 15.6-16.8%, and the NTSS system improved that by 7.8-9.6 and 7.0-12.8%, respectively, compared with the CT system. Our results suggested that Chinese farmers should consider adopting conservation tillage practices in arid northwestern China because of benefits to soil bulk density, water storage, root system, and winter wheat yield.

Study on the Root Systems for Different Types of Winter Wheat

Root growth traits for different wheat types varied during the growth cycle. The root system of 93 Zhong 6, which is a dwarf, big-ear variety, reached its highest density at anthesis, while the root density of Zhoumai 13, a medium-type variety, demonsrated its highest value during the node elongation stage and decreased rapidly at later growth stages, which resulted in lower yield. The root density of Zhongyu 6 and 98 Zhong 18, high yield potential, multiple ears varieties, did not show observable variation in their root systems during their growth cycles.

GPR Survey for Fir(Abies alba)and Spruce(Picea abies)Root Systems in Different Locations in the Western Carpathians Mts.(Poland)

The aim of the GPR research was a non-invasive inspection of the root systems arrangement of selected trees(fir Abies alba and spruce Picea abies),in the Silesian Beskids Landscaped Park and Zywiec Beskids Landscaped Park(Carpathian Mountains,Poland).Field research has been done using RAMAC/GPR with 800 MHz shielded antennas.The survey was conducted by linear profiling to a depth of 2 m.The survey was carried out around the designated trees in 6 meters×6 meters grids.Base points for X(S-N)and Y(W-E)axis were set in corners of each grid.Parallel GPR traverses were conducted within each study area,at intervals of 0.20 m.The maps of the research areas show existing trees and stumps within the GPR sections,with ±1 m error.GPR data analysis was carried out in 2D and 3D systems.Major findings from the GPR survey concluded that the firs(Abies alba),have a "vertical" root system type(with the roots dominant at depths of 0.2-0.8 meters),concentrically away from the tree trunk at a distance of about 1 m to about 2 m,and the spruces(Picea abies),have a "cloud" root system type(at a depth of 10-100 cm),with a few clear,thicker roots extending from the trunk.

Production Performance of Root Systems of Four Forage Legume Species and Their Development Characteristics in Loess Plateau,China

Production performance of four forage legumes species of Medicago sativa,Onobrychis viciifolia,Lotus corniculatus and Galega officinalis were determined,including plant height,above-ground biomass per unit area,tillers per unit area,fertile tillers per unit area,shoot /leaf ratio and fresh /dry matter weight ratio,and the distribution characteristics of their root systems in 0- 100 cm soil layers with 10 cm interval were studied. Results showed that the average aboveground fresh biomass(4 a and 5 a) of four forage legumes species successively were L. corniculatus 】 M. sativa 】 O. viciifolia 】 G. officinalis. The average plant heights in two years successively were O. viciifolia 】 M. sativa 】 G. officinalis 】 L. corniculatus. Tillers per unit area of four forage legume species in two years successively were M. sativa 】 L. corniculatus 】 O. viciifolia 】 G. officinalis. Fertile tillers per unit area in two years were O. viciifolia 】 M. sativa 】 L. corniculatus 】 G. officinalis. Average shoot /leaf ratio in two years were G. officinalis 】 M. sativa 】 O. viciifolia 】 L. corniculatus. Average moisture contents of four forage legume species in two years successively were G. officinalis 】 L. corniculatus 】 M. sativa = O. viciifolia. The distribution characteristics of root systems of four forage legumes species in 0- 100 cm soil layers were as follows: the root weights of M. sativa in 0- 40 cm soil layers accounted for about 98. 3% of total root weight,that of O. viciifolia in 0- 30 cm soil layers was 85. 8%,that of L. corniculatus in 0- 10 cm soil layers was 80%,and that of G. officinalis in 0- 40 cm soil layers was 81. 4%. The results suggested that L. corniculatus was suited to plant in slighter degraded pasture to control water and soil erosion in early stage,G. officinalis with strong lateral roots was adapted to degraded grassland in the Loess Plateau where soil nutrient was poor,while O. viciifolia and M. sativa with potentially strong main root were fit for water and soil conservation in the losses plateau for long term.

Renormalization of Tripartite Entanglement in Spin Systems with Dzyaloshinskii–Moriya Interaction

Quantum entanglement represents a fundamental feature of quantum many-body systems. We combine tripartite entanglement with quantum renormalization group theory to study the quantum critical phenomena. The Ising model and the Heisenberg X X Z model in the presence of the Dzyaloshinskii–Moriya interaction are adopted as the research objects. We identify that the tripartite entanglement can signal the critical point. The derivative of tripartite entanglement shows singularity as the spin chain size increases. Furthermore, the intuitive scaling behavior of the system selected is studied and the result allows us to precisely quantify the correlation exponent by utilizing the power law.

Spin-star environment assisted entanglement generation in weakly coupled bipartite systems

We study the entanglement evolution in a weakly coupled bipartite system with a large energy level difference under the influence of spin-star environments. The subsystems can be coupled to a pure state or a thermal equilibrium state spin-star environment. Our results show that, in the case of the coupling strength being less than the energy level difference of the subsystems （weakly coupled）, the spin-star environment can always be used to assist the entanglement generation of the bipartite system.

Thermodynamics around magnetic phase transitions in alternating double-chain spin systems

The thermodynamics and quantum phase transitions of two typically alternating double-chain systems are investigated by Green＇s function theory.（i） For the completely antiferromagnetic（AFM） alternating double-chain, the low-temperature antiferromagnetism with gapped behavior is observed, which is in accordance with the experimental result. In a magnetic field, we unveil the ground state phase diagram with zero plateau, 1/2 plateau, and polarized ferromagnetic（FM） phases,as a result of the intra-cluster spin-singlet competition. Furthermore, the Gr ¨uneisen ratio is an excellent tool to identify the quantum criticality and testify various quantum phases.（ii） For the antiferromagnetically coupled FM alternating chains,the 1/2 magnetization plateau and double-peak structure of specific heat appear, which are also observed experimentally.Nevertheless, the M–h curve shows an anomalous behavior in an ultra-low field, which is ascribed to the effectively weak Haldane-like state, demonstrated by the two-site entanglement entropy explicitly.

The Number of Irreducible Subsystems in the Classical Irreducible Root Systems

Let Φ be an irreducible root system of classical type. In t his short note, we study the irreducible subsystems of Φ and compute the nu mber of irreducible subsystems of any rank k in Φ.

Interacted Effect of Arbuscular Mycorrhizal Fungi and Polyamines on Root System Architecture of Citrus Seedlings

Either arbuscular mycorrhizal fungi （AMF） or polyamines （PAs） may change root system architecture （RSA） of plants, whereas the interaction of AMF and PAs on RSA remains unclear. In the present study, we studied the interaction between AMF （Paraglomus occultum） and exogenous PAs, including putrescine （Put）, spermidine （Spd） and spermine （Spin） on mycorrhizal development of different parts of root system, plant growth, RSA and carbohydrate concentrations of 6-m-old citrus （Citrus tangerine Hort. ex Tanaka） seedlings. After 14 wk of PAs application, PA-treated mycorrhizal seedlings exhibited better mycorrhizal colonization and numbers of vesicles, arbuscules, and entry points, and the best mycorrhizal status of taproot, first-, second-, and third-order lateral roots was respectively found in mycorrhizal seedlings supplied with Put, Spd and Spm, suggesting that PAs might act as a regulated factor of mycorrhizal development through transformation of root sucrose more into glucose for sustaining mycorrhizal development. AMF usually notably increases RSA traits （taproot length, total length, average diameter, projected area, surface area, volume, and number of first-, second-, and third-order lateral roots） of only PA-treated seedlings. Among the three PA species, greater positive effects on RSA change and plant biomass increment of the seedlings generally rank as Spd〉Spm〉Put, irrespective of whether or not AMF colonization. PAs significantly changed the RSA traits in mycorrhizal but not in non-mycorrhizal seedlings. It suggests that the application of PAs （especially Spd） to AMF plants would optimize RSA of citrus seedlings, thus increasing plant growth （shoot and root dry weight）.

A Study of Tensile Strength Tests of Arborous Species Root System in Forest Engineering Technique of Shallow Landslide

One experiment was conducted, through tensile tests of Albazzia and Eucalypt roots culled from the fields. The other experiment was conducted, by testing anti-drawing strength of these root systems in the Albazzia and Eucalypt lands. These two experiments had an aim to give insights into the maximum tensile strength and anti-drawing strength of the root systems. Results indicated that the maximum tensile strength of root system is in an exponential relation with the diameter of root system while the maximum tensile strength is positively correlative with the diameter of root system. Anti-drawing force of root system together with root diameter, length, and soil bulk density are folded into a regression equation in an attempt to figure out the static friction coefficient between root system and its ambient soil.

Electron Spin Resonance(ESR)Spectroscopy of the Transition-metal Complexes and Clusters I.Systematic Investigations of Real-and Complex-Orbital Methods for Calculating the d-Orbital Energies of a Low-spin(S=1/2)nd^5(t_2~5,~2T_2)(n=3

On the basis of the first paper’s theoretical derivations and concrete instance calculations of the energies of the d orbitals for a low spin ( S =1/2) nd 5(t 2 5, 2T 2)(n =3, 4, 5) system, the major results reported in this paper contain the following two respects: explicit relationships between the coefficients of the real and complex Kramers doublets have been derived by using two types of the expressions of the principal components of the g tensors in real and complex orbital representations obtained in the first paper; the use of these relationships of the real and complex orbital coefficients has carried out a series of mathematical demonstrations on the agreement of the real and complex orbital methods .

Optimal root system strategies for desert phreatophytic seedlings in the search for groundwater

Desert phreatophytes are greatly dependent on groundwater, but how their root systems adapt to different groundwater depths is poorly understood. In the present study, shoot and root growths of Alhagi sparsifolia Shap. seedlings were studied across a gradient of groundwater depths. Leaves, stems and roots of different orders were measured after 120 days of different groundwater treatments. Results indicated that the depth of soil wetting front and the vertical distribution of soil water contents were highly controlled by groundwater depths. The shoot growth and biomass of A. sparsifolia decreased, but the root growth and rooting depth increased under deeper groundwater conditions. The higher ratios of root biomass, root/shoot and root length/leaf area under deeper groundwater conditions implied that seedlings of A. sparsifolia economized carbon cost on their shoot growths. The roots of A. sparsifolia distributed evenly around the soil wetting fronts under deeper groundwater conditions. Root diameters and root lengths of all orders were correlated with soil water availabilities both within and among treatments. Seedlings of A. sparsifolia produced finer first- and second-order roots but larger third- and fourth-order roots in dry soils. The results demonstrated that the root systems of desert phreatophytes can be optimized to acquire groundwater resources and maximize seedling growth by balancing the costs of carbon gain.

Construction of Rooting System during Camellia oleifera Tissue Culture

An rooting experiment of tissue culture plantlets was carried out with sterile plantlets obtained from the stem segments of a good clone of Camellia oleifera as materials. The results showed that basic medium and illumination condition are factors crucial to rooting of C. oleifera. With 1/4MS as basic medium, the treat- ment with the addition of 0.5 mg/L NAA and soaking in 2 000 mg/L KIBA, containing 30 mg/L sucrose and subjected to dark culture of 20 d was the optimal treat- ment, achieving a rooting rate of 86. 7%.

PID Stabilization of Linear Neutral Time-Delay Systems in a Numerical Approach

In this paper, the stabilization of neutral time-delay systems is investigated. An efficient numerical approach is presented in an algorithm to establish results so that stability of such systems is achieved and stabilizing PID parameters are determined directly. It is based on determining the rightmost characteristic roots and Nyquist plot. The Newton-Raphson’s iterative method based on Lambert W function is used for the calculation of these stabilizing roots directly from the closed-loop characteristic equation of the neutral time-delay system and then stability is checked by Nyquist plot and step response of closed-loop system. Two numerical examples are included to illustrate the effectiveness of the proposed approach.

Advances in experimental methods for root system architecture and root development

Plant roots play important roles in acquisition of water and nutrients, storage, anchoring, transport, and symbiosis with soil microorganisms, thus quantitative researches on root developmental processes are essential to understand root functions and root turnover in ecosystems,and at the same time such researches are the most difficult because roots are hidden underground. Therefore, how to investigate efficiently root functions and root dynamics is the core aspect in underground ecology. In this article, we reviewed some experimental methods used in root researches on root development and root system architecture, and summarized the advantages and shortages of these methods. Based on the analyses, we proposed three new ways to more understand root processes：（1） new experimental materials for root development;（2） a new observatory system comprised of multiple components, including many observatory windows installed in field, analysis software,and automatic data transport devices;（3） new techniques used to analyze quantitatively functional roots.

Entanglement and non-Markovianity of a spin-S system in a dephasing environment

We study the entanglement （measured by negativity） evolution and the non-Markovianity for the dynamical process of a spin-S system embedded in dephasing environments. The exact analytical solution is presented, which shows that the decoherence function governs the evolutions of coherence, entanglement, and the non-Markovianity of the correspond- ing dynamical processes. For Ohmic and sub-Ohmic reservoirs, the negativity decreases monotonically in time and the corresponding dynamics is Markovian. While for super-Ohmic reservoirs with non-monotonic decoherence function, the negativity appears as the phenomenon of revival and the corresponding dynamics is non-Markovian. The relation between non-Markovianity and the system dimension is studied.

Energy transfer and correlation dynamics in a three-quasi-spin-pigment system

In this paper, the effects of quantum and classical correlations on the excitation energy transfer in a three-quasi- spin-pigment system are investigated. We first study the dependence of the energy transfer efficiency on various initial correlations of the donor pigments, and find that the initial concurrence is crucial to the efficiency no matter whether the initial states are pure or mixed. We then demonstrate the dynamics of correlations of the system and observe the appearance of sudden death of quantum correlations in the donor pigments. The relation between the energy transfer efficiency and the dynamics of correlations in the donor pigments is also discussed.