查询词典 condition of equilibrium

According to the existence results of general equilibrium problems and vector equilibrium problems have been studied more and more. Inspired and motivated by these research results, this paper is devoted to study systematically a class of equilibrium problems, which is unify and extension of a large number of known equilibrium problems and variational inequalities problems. The research is carried on from three aspects.Firstly, in finitely continuous topological spaces, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and we derive some existence results of a solution for the system of generalized vector quasi-equilibrium problems via the maximal element theorems in product finitely continuous topological spaces.Secondly, in complete metric spaces, we provide the Ekeland variational principle to equilibrium problems with set-valued maps. And via the Ekeland variational principle, existence results for vector equilibrium problem with set-valued maps and the system of vector equilibrium problem with set-valued maps.

针对一般的均衡问题和向量均衡问题解的存在性，已有许多研究成果，受这些成果的启发，本文主要从理论上较为系统地研究了一类均衡问题，它统一和推广了许多已有的均衡问题和变分不等式问题，研究分有三个方面；首先，在有限连续拓扑空间中，我们提出了四类广义向量拟均衡系，并借助于有限连续拓扑空间中的极大元定理讨论了这四类均衡系问题的解的存在性问题，然后，在完备度量空间中，我们给出了关于集值均衡问题的Ekeland变分原理，并利用Ekeland变分原理分别讨论了集值向量均衡问题和集值向量均衡系问题的解的存在性。

By applying game theory and contraction mapping theorem, a sufficient condition for the existence and uniqueness of Nash equilibrium in a multi-person non-cooperative game is proposed. Another implication in the sense of game theory is presented for the stability condition of supply-demand equilibrium in traditional economic theory. It can demonstrate the stability condition for supply-demand equilibrium in economic theory. So the stable supply-demand equilibrium of cobweb model in economics is in fact equivalent to the Nash equilibrium in game theory. That is a brand-new explanation for the conclusion in traditional economic theory.

应用博弈论中的有关理论与压缩映象定理寻求一类多ISP非合作对策纳什均衡存在、唯一的充分条件，给出了传统经济理论中供求均衡稳定性条件的对策论意义，证明了经济理论中的供求均衡稳定性条件；说明了经济学中蛛网模型的稳定供求均衡实际上就是对策理论中的纳什均衡，从而给出了传统经济理论中关于这一结论的新解释。

The effectiveness of the equilibrium credit rationing behavior to our monetary policy mainly express in following aspects: The first, the creation of the equilibrium credit rationing behavior influence the National Central Bank's activity of adjusting the control of foundational monetary directly; The second, the existence of the equilibrium credit rationing behavior inevitably influence the effectiveness of the National Central Bank controls the policy of the market interest rate; The third, the equilibrium credit rationing behavior would influence the monetary multiplicator; The fourth, the existence of the equilibrium credit rationing behavior would result the partition of the credit market.

均衡性信贷配给对我国货币政策的影响主要表现在以下几个方面：第一，均衡信贷配给的产生直接影响中央银行调控基础货币投放的主动性；第二，均衡信贷配给的存在必然影响中央银行控制市场利率政策的效力；第三，均衡性信贷配给影响货币乘数；第四，信贷配给的存在导致信贷市场的分割。

In the many foundation work, two methods that based on the equilibrium thought have been paid much attention: One is from partial equilibrium to general equilibrium; the other is from the static equilibrium to dynamic equilibrium.

在众多的开创性工作中，有两条基于均衡思想的思路最值得关注：一是从局部均衡到一般均衡的思路，二是从静态均衡到动态均衡的思路。

The result indicates that the potential-pH equilibrium diagram, solution's practical pH and metal corrosion's measured potential at corresponding temperature must be used when potential-pH equilibrium diagram is used. And also the potential-pH equilibrium diagram in Fe—H〓O system at different temperature is gathered and classified. According to thermodynamics data, the relation equation of water ionization equilibrium constant K〓 and of ammoniac equilibrium constant K〓 to temperature T is respectively derived.

二、高温电位-pH平衡图的应用与高温溶液实际pH值的计算对高温电位-pH平衡图的应用方法和溶液的高温实际pH值进行了分析和计算，指出在用电位—pH图进行分析时，必须使用相应温度下的电位—pH图、该温度下溶液的实际pH值和金属腐蚀电位测量值，并对各种温度下Fe—H〓O体系的电位－pH图进行了收集归类。

For the infective subsystem, we obtain the existent condition of the subsystem equilibrium point and the uniqueness of the positive equilibrium point by the no infectious subsystem's conclusion and the image analysis. The partial stability of the subsystem equilibrium points is discussed by analyzing eigenvalue. The condition that the system has no limit cycle is obtained by the Dulac function.

对染病子系统，利用无病子系统所得结论及图像分析法，得到了系统平衡点的存在条件，正平衡点的存在唯一性；利用特征根方法判断了系统平衡点的局部稳定性；利用Dulac函数得到了系统不存在极限环的条件；利用极限方程理论得到了系统疾病消除平衡点和地方病平衡点的全局稳定性。

The results show that the addition of certain manganese in high chromium cast iron leads to a re-partitioning of alloy elements between austenite and carbide and a dropping in equilibrium phase transformation temperature although it's inappreciable for the influence of manganese on mass fractions of every phase in this cast iron. There is about 87 percent ledeburite under thermodynamic equilibrium condition and 23 to 32 percent M7C3 type carbide under thermodynamic non-equilibrium condition in the microstructure of 3C-l5Cr-4Mn-0.75Si system high chromium cast iron. Furthermore, the improvement of austenite stability and hardenability of manganese alloyed high chromium cast iron may been expected because there is a substitution between manganese and chromium that has been suggested by thermodynamic calculations.

结果表明，锰虽然对高铬铸铁中的各相数量影响不大，但一定数量的锰存在促使合金元素在奥氏体和碳化物两相中的重新分配，并降低平衡相的转变温度；在平衡条件下3C-15Cr-4Mn-0.75Si系高铬铸铁中菜氏体数量约占87%，而非平衡条件下M7C3型碳化物数量在23%-32%之间，且奥氏体中锰铬互替现象保证了奥氏体的稳定性和加锰高铬铸铁的淬透性。

The results show that the addition of certain manganese in high chromium cast iron leads to a re-partitioning of alloy elements between austenite and carbide and a dropping in equilibrium phase transformation temperature although it＇s inappreciable for the influence of manganese on mass fractions of every phase in this cast iron. There is about 87 percent ledeburite under thermodynamic equilibrium condition and 23 to 32 percent M7C3 type carbide under thermodynamic non-equilibrium condition in the microstructure of 3C-15Cr-4Mn-0.75Si system high chromium cast iron. Furthermore, the improvement of austenite stability and hardenability of manganese alloyed high chromium cast iron may been expected because there is a substitution between manganese and chromium that has been suggested by thermodynamic calculations.

结果表明，锰虽然对高铬铸铁中的各相数量影响不大，但一定数量的锰存在促使合金元素在奥氏体和碳化物两相中的重新分配，并降低平衡相的转变温度；在平衡条件下3C-15Cr-4Mn-0.75Si系高铬铸铁中莱氏体数量约占87％，而非平衡条件下M7C2型碳化物数量在23％～32％之间，且奥氏体中锰铬互替现象保证了奥氏体的稳定性和加锰高铬铸铁的淬透性。

Secondly, by linearizing the system at the unique positive equilibrium solution and analyzing the associated characteristic equation, it is found that the positive equilibrium solution is asymptotically stable when the delay equals to zero and when it is increased to certain critical value, the positive equilibrium solution will loss the stability and a spatially heterohomogeneous periodic solution will bifurcate from this positive equilibrium solution.

通过在系统唯一的正平衡解处线性化系统和分析相应的特征方程，发现在时滞等于零时该正平衡解是渐近稳定的，当时滞逐渐增大到某个临界值时该正平衡解将失去稳定性而且在该平衡解处分支出空间非齐次的周期解。

In this method, an interim variable is defined by combining one variable of each subsystem. The interim variable is used to construct the sliding-mode function and the total control law can be derived to guarantee the equilibrium point is reachable in finite time. Using LaSalle invariance theorem, it can be proved further that the equilibrium field only includes one equilibrium point and the equilibrium point is asymptotically stable.

该方法将各个子系统的一个变量进行组合定义成一个中间变量，然后从这个中间变量出发构造滑模函数，通过求取总的控制量保证中间变量在有限时间内收敛到平衡点；进一步利用LaSalle不变性原理证明该收敛域内只有一个平衡点且是渐近稳定的。

Researches reveal that students who suffer from corporal punishment tend to resort to violence in their future life.

研究表明遭受过肉体惩罚的孩子倾向于在他们今后的人生中使用暴力。

Total sugar of sarcocarp and chlorophyll of pericarp increased firstly, and then decreased afterward along with altitude; Titratable acidity, ascorbicacid and anthocyanin of pericarp were increased along with altitude; The content of protein increased firstly and decreased afterward along with altitude; Carotenoid of pericarp were decreased along with altitude.

果肉总糖和果皮叶绿素含量随海拔高度升高先升高后降低；可滴定酸、维生素C和果皮花青苷含量均随海拔升高而升高；蛋白质在1720m处最大，1420m处最小；果皮类胡萝卜素随海拔升高而降低。