利用“等”与“不等”的辩证关系解题

数学中的“等”与“不等”都是绝对存在的．从表面上看，“等”与“不等”是对立的，但如果着眼于“等”与“不等”的关系，会发现它们之间相互联系的另一面．可以这样说，任何数学变换都是“等”与“不等”之间的周旋．许多数学问题若能很好利用它们之间的辩证关系，在解题中可以起到出奇制胜、化难为易之功效．本文以几个常见的典型例题，

初中数学中的“相等”与“不等”

在数学中，“相等”已是我们认识数学、学习数学的一种最为常用的手段了。然而，在现实生活中，“不等”现象却更多于“相等”现象。那么，如何利用我们熟悉的“相等”去解决数学中的不等问题呢？

“不等”的助词化及其动因

"不等"一词在现代汉语中较常见,其用法复杂。在句中,"不等"除了可以直接做谓语,还时常黏附于一组有"数量"区别的语言项,或某个数量范围之后,其句法位置趋于固化,语义也有相对弱化趋势。基于汉语语料库考察,这个词在实际运用中存在一定的"助词化"倾向。

不同应变率加载下硅的高压相变行为

高压相变是凝聚态物理、地球与行星科学、材料科学等领域关注的核心问题之一,而加载应变率是相变动力学过程的重要影响因素。由于动态加载下物质相结构原位诊断技术的不足以及宽广加载应变率下物质高压相变系统实验研究的缺失,难以开展基于原子尺度物理机制的相变动力学过程建模和数值模拟研究。由于硅的高压相极其丰富,且拥有大量亚稳相,动力学因素在其高压相变过程中发挥着至关重要的作用,因此,硅是研究高压相变动力学的理想材料,对普适相变动力学过程的理论建模具有重要意义。以硅为例,介绍其在准静态、中等应变率和高应变率加载下的相变行为,探讨加载应变率对其高压相变行为的影响。

内观认知疗法对医学生焦虑水平、自我效能感和应对方式的干预及机制

目的:探究内观认知疗法对医学生焦虑水平、自我效能感和应对方式的影响,并考察医学生内观认知疗法干预、自我效能感、应对方式和焦虑水平间的关系,以期为医学生心理健康教育工作和NCT疗法的作用机制研究提供理论支持。方法:采用随机数字表法将70名符合筛选标准的研究对象随机分配到内观认知疗法组和心理健康教育组,每组35人。内观认知疗法组接受为期7天的内观认知疗法干预,心理健康教育组接受相同时间的常规心理健康教育,最终共68人完成试验(内观认知疗法组34人,心理健康教育组34人)。干预前后使用SAS、GSES、SCSQ量表对两组研究对象进行测评。结果:①干预前,内观认知疗法组与心理健康教育组在焦虑,自我效能感,积极和消极应对方式得分上均不存在显著差异。②干预后,内观认知疗法组焦虑得分显著降低(t=5.835;P<0.01),自我效能感和积极应对方式得分均显著升高(t=2.289,4.668;P<0.05),消极应对方式得分不存在显著差异,干预前后心理健康教育组在上述所有量表得分中均不存在显著差异。③干预后,内观认知疗法组自我效能感和积极应对方式得分显著高于心理健康教育组(t=2.653,3.122;P<0.01),焦虑得分显著低于心理健康组(t=2.562;P<0.05)。④中介效应检验方面,内观认知疗法既可以直接影响医学生焦虑水平(β=-0.293,95%CI=-3.755~0.008),也可以通过自我效能感的中介作用(β=-0.307,95%CI=-0.612~-0.028)、积极应对方式的中介作用(β=0.140,95%CI=-0.293~-0.004)及自我效能感和积极应对方式的链式中介作用(β=0.222,95%CI=-0.553~-0.022)间接影响医学生焦虑水平。结论:内观认知疗法是一种能够有效降低医学生焦虑水平的干预手段,既能直接缓解焦虑,也能通过提高医学生自我效能感水平,改善积极应对方式间接降低医学生焦虑水平。

A Multifunctional Chiral Metasurface with Asymmetric Transmission and Linear-Polarization Conversion

In this paper,a multifunctional chiral metasurface is presented to achieve asymmetric transmission(AT)and linear-polarization conversion(LPC).The designed metasurface consists of a cross swords-like shape and two holes in the lower side of the unit cell.In the frequency band from 8.3 GHz to 10.4 GHz,AT is realized with more than 90%efficiency and the same chiral metasurface transforms linear polarized wave into its orthogonal counterpart with high efficiency.For LPC,the polarization conversion ratio(PCR)is greater than 95%.The proposed metasurface is stable against the incident angles of striking electromagnetic(EM)waves up to 60°for both operations of AT and LPC.

不同植物生长调节剂对冬小麦生长及产量的影响

为考察不同植物生长调节剂对农作物生长状况及产量的影响,以氨基寡糖素、复硝酚钠和胺鲜酯为处理药剂,以复合肥(18-15-12)为药剂载体,于冬小麦播种前底施于土壤,测定了不同生育时期冬小麦的株高、主根长、须根数、分蘖数、叶片数、顶节长、穗长、旗叶长、颖果数等指标。结果表明:氨基寡糖素在冬小麦前期能促苗生根,中期能促叶、增加分蘖数,提高冬小麦产量;复硝酚钠主要表现在中后期能促进冬小麦株高和旗叶的生长;胺鲜酯在冬小麦前期对茎叶、须根数,在中期对顶节长、颖果数具有促进作用,但后期对顶节长、旗叶长和颖果数有抑制作用;复硝酚钠和胺鲜酯均会降低冬小麦产量。

Mechanisms of surface charge development of serpentine mineral

The electrokinetic behavior and surface dissolution of serpentine mineral were studied through Zeta potential measurements, dissolution experiments and X-ray photoelectron spectroscopy. The results show that serpentine has an iso-electric point （IEP） of 11.9, which is higher than that of other phyllosilicate minerals. Dissolution experiments show that the hydroxyl is easy to dissolve with respect to the magnesium cations in the magnesium oxide octahedral sheet. As a result of hydroxyl dissolution, the magnesium ions are left on serpentine surface, which is responsible for serpentine surface charge. The removal of magnesium ions from serpentine surface by acid leaching results in a decrease of serpentine IEP. Therefore, it has been clearly established that the surface charge developed at the serpentine/aqueous electrical interface is a function of the serpentine surface incongruent dissolution.

Exponential stability criteria on neural networks with continuously distributed delays

The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and the equivalent descriptor form, a delay-dependent stability criterion is established for the addressed systems. The condition is expressed in terms of a linear matrix inequality （LMI）, and it can be checked by resorting to the LMI in the Matlab toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the derivative of a time-varying delay being less than 1, which generalize and improve earlier methods. Finally, numerical examples are given to show the effectiveness of the obtained methods.

Development of transition condition for region with variable-thickness in isothermal local loading process

Using simple unequal-thickness billet combining isothermal local loading can control the metal flow and improve the cavity fill in manufacturing process of large-scale rib-web titanium alloy component with low cost and short cycle. The beveling transition pattern is well used for variable-thickness region of billet （VTRB） due to its simple and ample range of transition condition. The transition condition development in the local loading process has a significant influence on dynamic boundary of unrestricted portion of VTRB. With the help of reasonable assumptions, a mathematical model of transition condition development was established by theoretical analysis. The predicted results for local loading process of rib-web component using the established model were compared with the numerical and experimental ones, and the results indicated that the model of transition condition development is reasonable. Using the established model could deal with the dynamic boundary of unrestricted portion of VTRB well, and the model is suitable for the analysis of metal flow and cavity fill in local loading process of multi-ribs component.

STABILITY ANALYSIS AND COOPERATIVE CONTROL OF DISTRIBUTED MULTI-AGENT SYSTEM WITH SAMPLED COMMUNICATION

The cooperative control and stability analysis problems for the multi-agent system with sampled com- munication are investigated. Distributed state feedback controllers are adopted for the cooperation of networked agents. A theorem in the form of linear matrix inequalities（LMI） is derived to analyze the system stability. An- other theorem in the form of optimization problem subject to LMI constraints is proposed to design the controller, and then the algorithm is presented. The simulation results verify the validity and the effectiveness of the pro- posed approach.

Static Output Feedback H_∞ Controllers Design for Descriptor Linear Systems Based on LMI

This paper considers the design problem of static output feedback H ∞ controllers for descriptor linear systems with linear matrix inequality (LMI) approach. Necessary and sufficient conditions for the existence of a static output feedback H ∞ controller are given in terms of LMIs. Furthermore, the design method of H ∞ controllers is provided using the solutions to the LMIs.

FUZZY ROBUST H_∞ CONTROL OF UNCERTAIN NONLINEAR SYSTEM WITH TIME-DEALY

This paper addresses the problem of the fuzzy H ∞state feedback control for a class of uncertain nonlinear systems with time delay. The Takagi Sugeno (T S) mo del with time delay and parameter uncertainties is adopted for modeling of nonlinear system. The systematic design procedure for the fuzzy robust controller based on linear matrix inequality (LMI) is given. Some sufficient conditions are derived for the existence of fuzzy H ∞ state feedback controllers such that the closed loop system is asymptotically stable and the effect of the disturbance input on controlled output is reduced to a prescribed level. An example is given to demonstrate the effectiveness of the proposed method.

New criterion for delay-dependent absolute stability of Lurie system with interval time-varying delay

The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities （LMIs）. By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.

An Inequality Concerning the Center of Simplex's Circumscribed Sphere

Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…,n+1),then we have The equality holds if and only if A is a regular simplex.

On the Asymptotic Property of Solutions to Some Nonlinear Dissipative Wave Equations

In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.

On Several New Inequalities

In this paper, we find some new inequalities by Redheffer inequality, Jordan inequality and Jensen inequality. As application, we generalize one result which was given in [1].

Further Improvement of Klamkin Inequality

In this paper, we use a geometric identity in the n-dimensional Euclidean space En and give the further improveme nt of Klamkin inequality in the space En.

Plastic forming simulations of cold isostatic pressing of selective laser sintered components

A combined method of selective laser sintering （SLS） and cold isostatic pressing （CIP） was applied to manufacturing metal parts rapidly. Finite element method was used to predict final dimensions and decrease cost. The simulations of CIP of selective laser sintered parts were carried out by Drucker-Prager-Cap constitutive model with ABAQUS computer program. The property of metal powder was measured by CIP experiments. The results show the rubber bag and the friction coefficient have little influence on results of simulations. The parts only have uniform shrinkage and have no obvious distortion in shape. The results of simulations show a good agreement with the experimental results and the calculated results, indicating that the Drucker-Prager-Cap model is an effective model to simulate CIP process. The simulations could give a useful direction to forming process of the CIP of selective laser sintered components. K