Generalized Numerical Radius of Real Quaternion Matrices with Symmetric Function

In the paper the generalized numerical radiuses of real quaternion matrices with symmetric function are defined and theirs inequalities are given.

Coupling mechanism of THM fields and SLG phases during the gas extraction process and its application in numerical analysis of gas occurrence regularity and effective extraction radius

The analysis of the coupling mechanism of thermal-hydraulic-mechanical(THM)fields,and solid-liquidgas(SLG)phases during gas extraction process is of profound significance to explore its numerical application in the gas occurrence regularity and its effective extraction radius.In this study,the Hudi coal mine in Qinshui basin is taken as the research area,the influencing factors of gas occurrence were analyzed,the differences in overburden load for gas pressure distribution and the factors influencing the effective extraction radius were further discussed by using the COMSOL software.The results show that the derivation of mathematical model in gas extraction shows that the process is a process the THM fields restrict each other,and the SLG phases influence each other.The longer the extraction time,the larger the influencing range of borehole,and the better the extraction effect.The larger the diameter of borehole,the larger the effective extraction radius,and the influence on gas extraction effect is smaller in the early stage and larger in the late stage.The borehole arrangement should be flexibly arranged according to the actual extraction situation.The higher the porosity,the higher the permeability,the better the gas extraction effect.The larger the overburden load of reservoir,the stronger the effective stress,which will result in the more severe the strain,and the closure of pore and fracture,which in turn will lead to the decrease of permeability and slow down the gas extraction.The relationship among extraction time,borehole diameter,negative pressure of gas extraction,permeability with effective extraction radius is exponential.This study has important theoretical and practical significance for clarifying and summarizing the gas occurrence regularity and its engineering practice.

A Note on Numerical Radius Operator Spaces

In this paper, we first study some -completely bounded maps between various numerical radius operator spaces. We also study the dual space of a numerical radius operator space and show that it has a dual realization. At last, we define two special numerical radius operator spaces and which can be seen as a quantization of norm space E.

On y-numerical Radius and Its Stability

Let A be an n×n complex matrix,and let y =(α1,...,αn) be an n-dimensional complex vector.The y-numerical radius of A,denoted by ry(A),is defined follows:r_y(A) = max {|sum form i=1 to n α_ix_i~* Ax_i|:x_i~* x_i = 1,x_i ∈ C^n},where Cn is an n-dimensional vector space over complex field C.In this paper we studynorm properties and stability of y-numerical radius.

Wind-sand flow simulation and radius optimization of highway embankment under different vertical curve radius

It is of great practical value to explore the correlation between the vertical curve radius of desert highway and the increase of sand accumulation in local lines,and to select the appropriate vertical curve radius for reducing the risk of sand accumulation.In this study,three-dimensional models of desert highway embankments with different vertical curve radii were constructed,and Fluent software was used to simulate the wind-sand flow field and sand accumulation distribution of vertical curve embankments.The results show that:(1)Along the direction of the road,the concave and the convex vertical curve embankments have the effect of collecting and diverging the wind-sand flow,respectively.When the radius of the concave vertical curve is 3000 m,5000 m,8000 m,10000 m and 20000 m,the wind velocity in the middle of the vertical curve is 31.76%,22.58%,10.78%,10.53%and 10.44%,higher than that at both ends.When the radius of the convex vertical curve is 6500 m,8000 m,10000 m,20000 m and 30000 m,the wind velocity at both ends of the vertical curve is 14.06%,9.99%,6.14%,3.22%and 2.41%,higher than that in the middle.The diversion effect also decreases with the increase of the radius.(2)The conductivity of the concave and convex vertical curve embankments with different radii is greater than 1,which is the sediment transport roadbed.The conductivity increases with the increase of radius and gradually tends to be stable.When the radius of the concave and convex vertical curves reaches 8000 m and 20000 m respectively,the phenomenon of sand accumulation is no longer serious.Under the same radius condition,the concave vertical curve embankment is more prone to sand accumulation than the convex one.(3)Considering the strength of the collection and diversion of the vertical curve embankment with different radii,and the sand accumulation of the vertical curve embankment in the desert section of Wuma Expressway,the radius of the concave vertical curve is not less than 8000 m,and the radius of the convex vertical curve is not less than 20000 m,which can effectively reduce the sand accumulation of the vertical curve embankment.In the desert highway area,the research results of this paper can provide reference for the design of vertical curve to ensure the safe operation of desert highway.

Case study of performance assessment of overlapping shield tunnels with a small curve radius

Due to the network planning of subways and their surrounding structures,increasingly more overlapping shields with a small curve radius have been constructed. A newly constructed upper tunnel partly overlaps a lower one, leading to the extremely complex uplift of the lower tunnel caused by the construction of a new tunnel. Based on the shield-driven project that runs from the Qinghe Xiaoyingqiao Station to the Qinghe Station in Beijing, which adopts the reinforcement measures of interlayer soil grouting and steel supports on site, in this study, the uplift pattern of the lower tunnel and the stress characteristics of steel supports were investigated through numerical simulations and on-site monitoring.The study results show that among all tunnel segments, the first segment of the shield witnesses a maximum uplift displacement that increases with the horizontal space between tunnels. On using either interlayer soil grouting or steel-ring bracing reinforcement, the uplift of the tunnel lining exceeds the control value;by contrast,when these two measures are jointly applied, the uplift of the tunnel lining does not exceed a maximum value of 4.87 mm, which can satisfy the requirements of deformation control. Under these two joint measures, the soil strength between two stacked shield tunnels can be enhanced and the uplift deformation can be restricted with the interlayer soil grouting. Also, the segmental deformation and overall stability of the existing tunnel can be controlled with the temporary steel supports.The deformation of circumferential supports and segments is closely related to each other, and the segmental uplift is controlled by H-shaped steel supports. With the increase in the horizontal space between twin shields, the effect of the construction would gradually weaken, accompanied by a gradual reduction of the stresses of steel supports. These findings provide a valuable reference for the engineering design and safe construction of overlapping shield tunnels with a small curve radius.

Numerical simulation of enhancing coalbed methane recovery by injecting CO_2 with heat injection

The technology used to enhance coalbed methane(CBM) recovery by injecting CO_2(CO_2-ECBM) with heat, combining heat injection with CO_2 injection, is still in its infancy; therefore, theoretical studies of this CO_2-ECBM technology should be perused. First, the coupling equations of the di usion–adsorption–seepage–heat transfer fields of gas are established. The displacement processes under di erent pressures and temperatures are simulated by COMSOL. Finally, the displacement effects, a comparison of the CO_2 storage capacity with the CH_4 output and the e ective influencing radius of CO_2 injection are analyzed and discussed. The results show that(1) the displacement pressure and temperature are two key factors influencing the CH_4 output and the CO_2 storage capacity, and the increase in the CO_2 storage capacity is more sensitive to temperature and pressure than the CH_4 output.(2) The gas flow direction is from the injection hole to the discharge hole during the displacement process, and the regions with high velocity are concentrated at the injection hole and the discharge hole.(3) A reduction in the CH_4 concentration and an increase in the CO_2 concentration are obvious during the displacement process.(4) The e ective influencing radius of injecting CO_2 with heat increases with the increase in time and pressure. The relationship between the e ective influencing radius and the injection time of CO_2 has a power exponential function, and there is a linear relationship between the functional coe cient and the injection pressure of CO_2. This numerical simulation study on enhancing CBM recovery by injecting CO_2 with heat can further promote the implementation of CO_2-ECBM project in deep coal seams.

Numerical simulation of the temperature fields of stainless steel with different roller parameters during twin-roll strip casting

The temperature field of stainless steel during twin-roll strip casting was simulated by experiment and a finite element （FE） model. By comparing the measured result with the simulated values, it is found that they fit close to each other, which indicates this FE model is effective. Based on this model, the effects of roll gap （t） and roll radius （R） on solidification were simulated. The simulated results give the relationship between t or R and the position of the freezing point. The larger the t is and the smaller the R is, the closer the position of the freezing point is to the exit.

Significance-based optimization of processing parameters for thin-walled aluminum alloy tube NC bending with small bending radius

Thin-walled aluminum alloy tube numerical control （NC） bending with small bending radius is a complex process with multi-factor coupling effects and multi-die constraints. A significance-based optimization method of the parameters was proposed based on the finite element （FE） simulation, and the significance analysis of the processing parameters on the forming quality in terms of the maximum wall thinning ratio and the maximum cross section distortion degree was implemented using the fractional factorial design. The optimum value of the significant parameter, the clearance between the tube and the wiper die, was obtained, and the values of the other parameters, including the friction coefficients and the clearances between the tube and the dies, the mandrel extension length and the boost velocity were estimated. The results are applied to aluminum alloy tube NC bending d50 mm×1 mm×75 mm and d70 mm×1.5 mm×105 mm （initial tube outside diameter D0 × initial tube wall thickness t0 × bending radius R）, and qualified tubes are produced.

Numerical simulation on the shape of liquid surface of TIG full-penetrated weld pool

Based on the analysis of the three-dimensional liquid surface behavior of TIG penetrated weld pool,the three-dimensional shape models of weld pool with different values of the back fusion zone radius RB were obtained.The effects of arc on the penetrated weld pool were studied by numerical simulation with finite elements analysis software Surface Evolver.The results show that the size and shape of the back weld pool are not affected obviously by the arc,and the top surface of the weld pool is lowered by arc.From pulse background to pulse peak,the increase of the arc voltage(or the arc light intensity) is due to two factors.One is the increase of the current,and the other is the lowering of the top weld pool surface.

Norm Properties of Y-numerical Radii

Given an n×n complex matrix A and an n-dimensional complex vector y=(ν1 , ··· , νn ), the y-numerical radius of A is the nonnegative quantity ry(A)=max{n∑j=1ν*jAx︱:Axj︱: x*jxj=1,xj ∈Cn}.Here Cn is an n-dimensional linear space overthe complex field C. For y = (1, 0, ··· , 0) it reduces to the classical radius r(A) =max {|x*Ax|: x*x=1}.We show that ry is a generalized matrix norm if and only ifn∑j=1νj≠ 0.Next, we study some properties of the y-numerical radius of matrices andvectors with non-negative entries.

Effects of process parameters on numerical control bending process for large diameter thin-walled aluminum alloy tubes

Numerical control(NC) bending experiments with different process parameters were carried out for 5052O aluminum alloy tubes with outer diameter of 70 mm, wall thickness of 1.5 mm, and centerline bending radius of 105 mm. And the effects of process parameters on tube wall thinning and cross section distortion were investigated. Meanwhile, acceptable bending of the 5052O aluminum tubes was accomplished based on the above experiments. The results show that the effects of process parameters on bending process for large diameter thin-walled aluminum alloy tubes are similar to those for small diameter thin-walled tubes, but the forming quality of the large diameter thin-walled aluminum alloy tubes is much more sensitive to the process parameters and thus it is more difficult to form.

Analysis of Cutter Radius Compensation

Cutter radius compensation （CRC） is a very important function of numerical control（NC） system. We refer to a large number of NC information and sum up the CRC function. We illustrate how to realize rough machining ＆ finish machining by the same program, machining matching surface by the same program, simplify pro- gramming methods, realize direct programming by parts contour, remove machining allowance by the increase of CRC value, control the parts size precision by adjusting the CRC value, state the essence of the CRC, and elucidate the physical meaning of the CRC value.

Solving Large Scale Unconstrained Minimization Problems by a New ODE Numerical Integration Method

In reference [1], for large scale nonlinear equations , a new ODE solving method was given. This paper is a continuous work. Here has gradient structure i.e. , is a scalar function. The eigenvalues of the Jacobian of;or the Hessian of , are all real number. So the new method is very suitable for this structure. For quadratic function the convergence was proved and the spectral radius of iteration matrix was given and compared with traditional method. Examples show for large scale problems (dimension ) the new method is very efficient.

Gas-solid coupling analysis and numerical simulation of the dynamic process of gas drainage

Based on the basic theory of gas seepage and coal seam deformation, using the numerical simulation method, this paper established the gas-solid coupling model of gas drainage from borehole. Using multi-physical coupling analysis software, the authors studied the stress change conditions around the drainage borehole, the influence of the gas drainage effect caused by the drilling gap, and the gas drainage effect under the conditions of different borehole radius and different permeabilities. The results show that the effective drainage radius is 1.03 m during 30 days of drainage. The effect of the diameter change of the drainage borehole is limited, but the influence of coal seam permeability is much bigger. After the same drainage period, the greater the permeability of coal seam is, the bigger the drainage radius is. For a low permeability coal seam, coal miners should take pressure-relief measures and increase the permeability to improve the drainage effects before draining gas through drilling.

小半径曲线盾构隧道施工变形特性研究

为深入探究小半径曲线盾构隧道开挖对地表沉降和管片结构变形的影响,采用ABAQUS有限元工具对曲线盾构隧道开挖过程进行了全面细致的模拟,分析了不同曲线半径和千斤顶推力比下盾构隧道施工过程中地表和管片结构的变形规律。研究结果表明:小半径曲线隧道施工较直线隧道地表沉降和管片结构变形明显增大;小半径曲线段盾构隧道横向地表沉降槽呈非对称分布,沉降槽向曲线内侧偏移,曲线半径越小,沉降、偏移越大;管片结构拱顶与拱底的水平变形受曲线半径影响不大,拱腰处受曲线半径影响较大。为控制地表不均匀沉降,建议小半径盾构隧道施工千斤顶内外侧推力比要尽可能控制在1∶1~1∶2;随着内外侧推力比的增大,拱腰外侧水平变形最大增长大于拱腰内侧。在设计和施工过程中,需特别关注曲线段管片的支护和结构设计,以减小变形差异对隧道安全和稳定性的影响。

Maps Preserving Numerical Radius or Cross Norms of Products of Self-adjoint Operators

Let H be a complex Hilbert space with dimH ≥3, Bs（H） the （real） Jordan algebra of all self-adjoint operators on H. Every surjective map Ф ： Bs（H）→13s（H） preserving numerical radius of operator products （respectively, Jordan triple products） is characterized. A characterization of surjective maps on Bs （H） preserving a cross operator norm of operator products （resp. Jordan triple products of operators） is also given.

Applying the Theory of Numerical Radius of Operators to Obtain Multi-observable Quantum Uncertainty Relations

Quantum uncertainty relations are mathematical inequalities that describe the lower bound of products of standard deviations of observables(i.e.,bounded or unbounded self-adjoint operators).By revealing a connection between standard deviations of quantum observables and numerical radius of operators,we establish a universal uncertainty relation for k observables,of which the formulation depends on the even or odd quality of k.This universal uncertainty relation is tight at least for the cases k=2 and k=3.For two observables,the uncertainty relation is a simpler reformulation of Schr?dinger’s uncertainty principle,which is also tighter than Heisenberg’s and Robertson’s uncertainty relations.

小半径隧道盾构施工对铁路桥梁的影响

随着城市轨道交通线网的完善,单一的直线型隧道已不能满足需求,而新建隧道也不可避免地近接建构筑物,势必危及建构筑物,甚至引发严重的安全问题。基于郑州地区某工程,运用有限元软件Midas GTS NX进行数值模拟,研究小半径隧道盾构施工期间隔离桩防护措施的作用效果,并结合监测数据验证数值计算的准确性。研究结果表明:1)在无隔离桩防护措施下,小半径盾构隧道施工会引起地表横向沉降变形,危及铁路线路运营安全;2)在隔离桩防护措施下,小半径盾构隧道施工对铁路桥梁的影响在可控范围内,能有效降低盾构隧道施工引起的铁路桥梁变形及其附加内力,有利于铁路线路的运营安全;3)监测数据与数值计算的对比表明,隔离桩防护措施对于保障铁路线路的运营安全是有效的。本文研究结果可为盾构隧道安全穿越铁路桥梁施工提供重要的工程实用价值。

长短径比对不对称转子泵性能的影响

为了提高泵的输送性能,改善受力情况,提出了一种不对称转子泵的新结构。建立了不对称转子的数学模型,并利用CFD数值模拟研究了转子长短径比对其性能的影响规律。结果表明:长短径比对泵腔内流体流动状况、流量脉动特性及转子受力影响显著。随着长短径比的增加,泵腔内流体流速逐渐增加,漩涡数量先减少后增多,主转子径向受力逐渐增大,在长短径比为1.52时的径向力均值相比于1.12时增大26.9%,容积效率的增加逐渐提高,出口流量的次级脉动得到有效抑制,流量脉动系数先减小后增大。当长短径比为1.28~1.44时,泵的容积效率较高,泵腔内部流动较平稳,转子受力情况较好。为采用不对称结构和调整长短径比来优化转子泵的设计提供了理论依据。