查询词典 lower bound

Both upper bound formula and lower bound formula of the global truncation error of Euler method have been derived theoretically.After making certain approximat e processing,the derived upper formula changes into current upper bound formula.

从理论上推导出了欧拉方法的整体截断误差的上限公式和下限公式，作一定的近似后，得到的整体截断误差上限公式就变为现用的整体截断误差上限公式。

Quasi-convex relaxation algorithm, which aims to solve ordinary constraint global optimization problems, is produced by a combination of branch-and-bound method with quasi-convex lower bound and quasi-concave upper bound functions developed from quasi convex-concave extension. This algorithm extends the interval algorithm with box constraint to general constraint global optimization problem.

利用拟凸-凹扩张中构造出的函数的拟凸下界函数和拟凹上界函数，与分枝定界方法相结合，建立了求一般约束全局优化问题的拟凸松弛算法，这一算法是将盒子约束的区间算法推广到一般约束优化问题中。

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

We establish a relation between μ and the stucture of the group G, and obtain the lower bound of the ratio by the mininal prime divisor of the order and commutator of the group G, and give a necessary and sufficient condition under which this lower bound is attained.

第一部分，记有限群G的阶与不可约特征标个数的比值为μ，我们研究了一般的非交换有限群G的结构和μ之间的关系，通过群G的阶的最小素因子和换位子群G′的最小素因子得到了μ的一个下界，同时给出了达到下界的一个充分必要条件。

Secondly, the author gives some exact values of mb(2 q) for some values of b, which impliesthat the above lower bound is not only the lower bound but also the infimum.

其次，对于部分b值，给出了m_b（2，q）的确切值，从而说明了上面给出的下界值不仅是下界而且是下确界。

Lower order and proximate lower order of Dirichlet setries and random Dirichlet setries convergent on left half plane;2. The present paper gives lower side bitangent Laplace Stieltjes transformation and integral,θ linear lower order and proximate lower order of the analytic function defined by this transformation.

给出下侧二重 Laplace- Stieltjes变换与积分以及由该变换所定义的解析函数 f的θ线性下级与准确下级的定义；通过引入递减负实数列{λ- m}与{μ- n}，建立 f的θ线性下级存在的充要条件及其θ线性下级的下型与θ线性下级及其系数与指数的关系。

The stack type reactor according to the present invention comprises an upper block including at least two inlets through which different kinds of raw substances are entered and a lower channel communicated in fluid with the inlets and formed a lower surface thereof; and an unit block including an upper channel corresponding to the lower channel of the upper block and formed on an upper surface thereof, the unit block including a lower channel formed a lower surface thereof and communicated in fluid with the upper channel via a connecting flow passage penetrating therethrough.

根据本发明的堆叠式反应器包括：上部块，其包括至少两个允许各种原料物质进入的入口以及与该入口流体连通且形成于该上部块下表面的下部通道；和单元块，其包括与上部块的下部通道对应且形成于单元块上表面上的上部通道，该单元块包括形成于单元块下表面且经由穿透其中的连接流道流体连通上部通道的下部通道。

The results show that upper bainite of 9Cr2Mo Steel and GCr15 steel is feathery and the upper bainite carbide is lamellar or claviform. The upper bainite carbide distributes between the subunits of bainite ferrites by and large parallelly to the axis of bainite ferrites. Lower bainite of 9Cr2Mo Steel and GCr15 steel is in bamboo leaf shape and the lower bainite carbide is in shred or fibre shape. The lower bainite carbide distributes between the bainite ferrites, furthermore, the angles between lower bainite carbonide and the principal axis of the lower bainite ferrites are unequal.

结果表明，9Cr2Mo钢和GCr15钢的上贝氏体组织呈羽毛状，上贝氏体碳化物呈长短不一的薄片状或短棒状，分布在铁素体亚片条或亚单元之间，其排列与贝氏体铁素体片条轴向大体上平行分布；下贝氏体组织呈竹叶状或针状，下贝氏体碳化物呈细片状或纤维状等形状，分布在铁素体片中间，大多数与片条的主轴方向交角排列，但角度不等。

objective to evaluate efficacy of extracorporeal shock wave lithotripsyfor treating ureteral stones in situ,investigate the cause of higher re-treatment rate.methods total of 687 patients with ureteral stone were received eswl between january 2000 and december 2004,included 455 male(66.2%) and 232 female(33.8%) patients,6 cases have bilateral ureteral calculi,12 cases have unilateral multiple calculi.hence,together 709 ureteral calculi were treated.patients upper ureteral calculi were treated in the supine position,for lower ureteral calculi patients were turned prone.to reduce eswl-induced renal trauma and pain,using lower energy source,adjusted power setting from 9.8 to 13.2kv,limited 1500 shock wavs per one session.no auxiliary procedure were used before eswl.the stone size was measured as the surface area of stone length by stone width on x-ray film.the interval between two treatment sessions was two weeks.results of 709 ureteral calculi,the overall stone free rate was 97.3%(690 calculi),re-treatment rate was 34.1%(292 calculi).according to the performed treatment sessions,one session 467 calculi,the mean stone size 37.27mm2,stone free rate 65.4%(464 calculi).two sessions 138 calculi,the mean stone size 62.48mm2,stone free rate 18.4%(131calculi).three sessions 52 calculi,the mean stone size 79.60mm2,stone free rate 7.1%(50calculi).four sessions 19 calculi,the mean stone size 101.63mm2,stone free rate 2.4%(17calculi).fivesessions 33 calculi,the mean stone size 119.33mm2,stone free rate 3.9%(28 calculi).overall 19 cases(2.7%)turned to other treatment modalities.of 335 upper ureteral calculi,303 achieved stone free (95.8%),re-treatment rate was 38.5%(129 calculi).of 374 lower ureteral calculi,369 achieved stone free(98.7%),re-treatment rate was 30.2%(113 calculi).the re-treatment rate of upper ureteral calculi was higher than lower ureteral calculi(p＜0.05,χ2=5.40).the difference of stone-free rate between upper and lower ureteral calculi was no significant(p＞0.05,χ2=0.15).conclusion eswl should be considered first line therapy for ureteral stone still.stone burden are the main variable of higher re-treatment rate,upper ureteral stone may moving with respiring during eswl.so efficinet shock wave was decreared,re-treatment rate become higher.

目的 评估体外震波碎石治疗输尿管结石的疗效，探讨再治疗率高的原因及输尿管结石的治疗选择。方法回顾2000年1月～2004年12月间eswl治疗输尿管结石的临床资料687例，男455例（66.2%），女232例（33.8%），平均年龄46.6岁（15～83岁）。有双侧输尿管结石6例，单侧多发性输尿管结石12例（4颗1例，3颗2例，2颗9例），共计输尿管结石709颗（含透光结石13颗）。应用上海爱申公司生产的desunit6030型碎石机，c臂x线球管做结石定位。上段输尿管结石（肾盂输尿管交界处至骶髂关节上缘）取仰卧位，下段输尿管结石（骶髂关节上缘下至输尿管口）取俯卧位。为减少eswl引起的肾损伤和疼痛，应用较低的能量，震波发生器电压从9.8～13.2kv，震波频率1.5s。每次治疗设定为1500次震波。治疗后3天摄腹部平片或b超，以后每隔7日重复检查。假如结石未碎或有残留结石最长径＞3mm以上，再次eswl，两次治疗的间隔时间为两周。结石的大小用x线片上的表面积（mm2表示。结果 709颗输尿管结石总的治愈率为97.3%（690颗），再治疗率34.1%（242颗）。其中一次治疗467颗，平均结石大小37.27mm2，治愈464颗（65.4%），3颗改治疗；两次治疗138颗，平均结石大小62.48mm2，治愈131颗（18.5%），7颗改治疗；第1和第2次治疗治愈率（1个月治愈率）为83.8%。3次治疗52颗，平均结石大小79.60mm2，治愈50颗（7.1%），2颗改治疗；4次治疗19颗，平均结石大小101.63mm2，治愈17颗（2.4%），2颗改治疗；5次及5次以上治疗33颗，平均结石大小119.33mm2，治愈28颗（3.9%），5颗改治疗。总计19颗（2.7%）结石改变治疗方式。上段输尿管结石335颗，治愈321颗（95.8%），再治疗129颗（38.5%）。下段输尿管结石374颗，治愈369颗（98.7%），再治疗113颗（30.2%）。经χ2检验，上、下段输尿管结石的再治疗率差异有显著性（χ2=5.40，p＜0.05），治愈率差异无显著性（χ2=0.15，p＞0.05）。不良反应：血压升高13例（1.9%），震波区域疼痛26例（3.8%），震波进入处皮肤点状淤血33例（4.8%），肉眼血尿128例（18.6%），均于第2、3天自行消失。结论 eswl目前仍是输尿管结石的第一线治疗，结石的大小是再治疗率高的主要因素。结石的位置有影响，上段输尿管结石可随呼吸移动，有效震波次数减少，再治疗率比下段输尿管结石高。eswl前注重病例筛选可降低再治疗率。

This paper presents the new bound theorems in structural limit analysis developed on the basis of the generalized variational principle. The approximate limit factors determined from the new bound theorems are closer to the exact limit factor than the ones obtained from the classical bound theorems.

本文给出在极限分析的一般变分原理[1]的基础上发展起来的极限乘子的新的上、下限定理[10]，由这个新的上、下限定理决定的极限乘子的上、下限比经典的上、下限定理给出的更为靠近准确解。

We have limited budget let me know if you can do this competitively.

我们有限的预算让我知道如果你能做到这一点竞争力。

We don't know how other critters breathe--lizards, for example.

我们还不知道诸如蜥蜴之类的动物如何呼吸。