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A convexity theorem for noncommutative gradient flows


In this survey we shall prove a convexity theorem for gradient actions of reductive Lie groups on Riemannian symmetric spaces.


In the final section the theorem is applied to gradient actions on other homogeneous spaces and we show, that Hilgert's Convexity Theorem for moment maps can be derived from the results.


We observe that our methods clearly show that the restriction p>amp;gt;2n/n+1 is closely related to cancellation and size properties of the gradient of the Poisson kernel.


A new generalized gradient projection type algorithm for linearly constrained problems

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 Supersonic speed aircraft and guided aircraft missiles are subjected to rapid aerodynamic heating and rapid loading during their flight. For taking full advantage of the strength of structural materials in design, it is necessary to study the mechanical characteristics of metallic structural materials under rapid loading and heating. This paper describes a shorttime hightemperature tensile testing machine, which is capable of constantrate loading up to 85 kg/sec and heating at a rate up to 80℃/sec, the temperature... Supersonic speed aircraft and guided aircraft missiles are subjected to rapid aerodynamic heating and rapid loading during their flight. For taking full advantage of the strength of structural materials in design, it is necessary to study the mechanical characteristics of metallic structural materials under rapid loading and heating. This paper describes a shorttime hightemperature tensile testing machine, which is capable of constantrate loading up to 85 kg/sec and heating at a rate up to 80℃/sec, the temperature gradient within the gage length for a distance of 50 mm being less than 5℃. All the heating, temperaturecontrolling and stressstrain measuring processes are done automatically. Experiments such as rapid tension under high temperature, rapid heating under constant loading and shorttime creep can be carried out on this tester. Specimens of low carbon steel, R1T and 12F2A have been tested on it. Diagrams and tables have been included here and results from these tests have been preliminarily discussed.  高速飞机及飞航导弹在飞行过程中受到气动力的快速加热和快速加载.为了最充分地利用结构材料强度进行合理设计,必须研究金属结构材料在快速加载、快速加热下的力学性能.本文叙述了一种短时高温拉伸试验设备;这设备能以小于85 kg/s的速率对试件进行恒速加载,以小于80℃/s的速率进行快速升温;试件50mm标距内温度梯度小于5℃;整个加热控温过程和应力应变测量记录过程均系自动进行.在此设备上可进行高温快速拉伸和短时蠕变等实验,并已进行了低碳钢,等材料的短时拉伸、短时蠕变、恒裁等加热率的实验.文内列有图表,并对结果进行了初步讨论.  For various carbon and lowalloy steels with a wide range of the tensile strength, the effect of hydrogen on the apparent yield stress, which is a necessary exterior stress to produce the local macroscopi c plasti c deformation, was investigated with smooth tensile, bending, precracked type Ⅰ, type Ⅲ and combined type Ⅰ+Ⅲ specimens. The results show that the effect of hydrogen on the yield strength of a smooth tensile specimen is insignificant, the difference between the charged and uncharged specimens is... For various carbon and lowalloy steels with a wide range of the tensile strength, the effect of hydrogen on the apparent yield stress, which is a necessary exterior stress to produce the local macroscopi c plasti c deformation, was investigated with smooth tensile, bending, precracked type Ⅰ, type Ⅲ and combined type Ⅰ+Ⅲ specimens. The results show that the effect of hydrogen on the yield strength of a smooth tensile specimen is insignificant, the difference between the charged and uncharged specimens is less than 10％. However, for the smooth bending or precracked Ⅰtype specimen with a. tensile stress gradient, hydrogen can decrease the apparent yield stress considerably if the strength of steel and the amount of hydrogen entering into the specimen exceed their critical values. This is the cause of hydrogen induced delayed plastic deformation and hydrogen induced delayed cracking.The effect of hydrogen on the apparent yield stress increases with increasing strength of the steel and average hydrogen concentration in the specimen. The reduction of the apparent yield stress of charged precracked specimens is more evident than that of smooth bending ones. The hydrogen induced apparent yield stress reduction is a phenomenon controlled by hydrogen diffusion, it depends markedly on the strain rate and test temperature.For type Ⅲ cracked specimens, in which there is no hydrostatic stress the apparent torsional yield stress of the charged specimens does not decrease and K_(ⅢH)=K_(ⅢC). But hydrogen induced delayed plasticity and cracking can occur on the specific plane inclined at an angle of —45° to the original crack plane, For combined type Ⅰ+Ⅲ specimens, the apparent torsional yield stress can be decreased only when K_1 is so large that hydrogen induced delayed plasticity can occur under the action of K_1 itself.  利用光滑拉伸试样以及带有应力梯度的弯曲试样和预裂纹试样(Ⅰ型、Ⅲ型以及Ⅰ—Ⅲ复合型),研究了氢对产生局部宏观塑性变形所需外应力(称为表观屈服应力)的影响。结果表明,氢对低合金钢的屈服强度影响不大,但如试样中存在拉应力梯度,则当钢的强度和进入试样的氢浓度超过临界值后,氢能使表观屈服应力明显下降,这就是氢致滞后塑性变形的原因。氢致表观屈服应力的下降是由氢的扩散所控制的。它明显依赖加载速度和试验温度。但它随试验温度的变化不是单调的,在室温附近存在一个极值。对仅存在剪应力梯度的Ⅲ型裂纹试样,充氢后表观扭转屈服应力并不降低,沿原裂纹面也不产生滞后裂纹,即K_(ⅢH)=K_(ⅢC),但在和原裂纹面成45°的平面上却能产生氢致滞后塑性变形和裂纹。对Ⅰ—Ⅲ复合型试样,只有当恒定的K_Ⅰ大到足以单独就能产生滞后塑性变形时才能使表观扭转屈服应力开始下降。提出了一个氢使表观屈服应力下降的机构。  There are steep stress gradients in the surface layer of materials with strong texture and the metal workpieces after grinding、rolling and other surface treat ments, the main stress plane will no longer parallel to the surface of the sample and the stress profile in the surface layer is a three dimensional one. Hence such stress can not be measured by the usual xray diffraction method [1] [2] [3] [4]. On the basis of the previous work [5], a new method for measuring threedimensional stress and its profile... There are steep stress gradients in the surface layer of materials with strong texture and the metal workpieces after grinding、rolling and other surface treat ments, the main stress plane will no longer parallel to the surface of the sample and the stress profile in the surface layer is a three dimensional one. Hence such stress can not be measured by the usual xray diffraction method [1] [2] [3] [4]. On the basis of the previous work [5], a new method for measuring threedimensional stress and its profile along the depth of metal surface is presented, The measurements concerned must be done by means of the diffractometer equipped with a side inclination accessory.  各种具有强烈织构或经过磨削、轧制及其它表面处理的金属材料其表层往往存在激烈的应力梯度,应力主平面很可能不再平行于试样表面(σ_(13),σ_(23),σ_(33)≠0),所以表层呈三维应力的层深分布,不能再用常规的X射线应力测定方法来侧定其应力。在以往工作的基础上,本文介绍一种新的三维应力测定方法,与此同时,还提出了无损测定金属表层三维应力层深分布的新途径。有关试验在附有试样侧倾装置的衍射仪上进行。   << 更多相关文摘 
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