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     ON THE NUMBER OF SOLUTIONS OF THE CONGRUENCE sum from i=1 to k(x_i~2)≡o(MOD p) AND THE CLASS NUMBER OF Q(p~(1/2))
     关于同余式sum from i=1 to k(x_i~2)≡o(mod p)解的个数与二次域Q(p~(1/2))的类数
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     Infinitely Many W_0~(1,P)-Solutions to the Dirichlet Problem of Strongly Degenerate Elliptic Equations With Singularity
     具奇性的强退化椭圆型方程Dirichlet问题无穷多个W_0~(1,p)解(英文)
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     Global W~(k,p) Solutions of Strong Damped Nonlinear Wave Equations of Four Order
     四阶强阻尼非线性波动方程的整体W~(k,p)解
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     Global W~(1,p) solutions of semilinear pseudoparabolic equations
     半线性拟抛物方程的整体W~(1,p)解
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     The solutions of such a sequence of unconstrained minimization problems all exist, and they converge to the solution of the constrained minimization problem in a certain sense.
     这列无约束极小化问题(P_ε)的解都是存在的,并且在某种意义下收敛至原始约束极小化问题(P)的解,不仅如此,它们的性能指标也收敛至原始问题(P)解的性能指标。
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  相似匹配句对
     b) The solution of the inequality.
     (2)不等式;
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     THE ALCOHOLYSIS OF TRICHLOROSILANE
     三氯硅烷的甲醇
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     Magnetoelectrolysis technology
     磁电技术
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     G, Then G is p-solvable.
     则G是p-可
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     On the Solution of Diophantine Equation
     关于Diophantine方程的
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  p) solutions
It is also shown that the high energy n-p solutions cannot be continuously linked to the low energy ones if theS phaseshift for the singlet state is assumed positive throughout the considered energy interval.
      
Moreover, we show that the Newton Iteration Procedure can be applied in order to obtain a sequence of approximate (in W2,p) solutions for u0.
      
It also permits us to extend certain estimates for smooth solutions of degenerate two dimensional Monge-Ampère equations to W2,p solutions.
      
Plants of five species which varied in life span, persistence, and VAM responsiveness were grown in nutrientpoor soils in a glasshouse for 8 weeks and given weekly feedings with either high- or low-P solutions.
      
Cu and P carrier contents in64Cu and32P solutions were determined by the substoichiometric extractions with dithizone in CCl4 and with molybdic acid into MIBK in the series of the solutions adding various amounts of Cu or P carrier.
      
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We have proved equivalence between the problem of oblique derivative of the non-linear elliptic system(A) W_z=g(Z,W,W_z),|Z|<1 (A.1) |g(Z,W,W_z~1)-g(Z,W,W_z~2)|≤q_o|W_z~1-W_z~2,q_o=const<1 (A.2) and the problem P which consists in finding a solution W(z) of this system(A) in the unit disk K and satisfying on its boundary |z|=1 the condition R_a(Z~(-n)W_z)=0. We have constructed two integral operators F(ω) and F_1(ω) which satisfy the boundary conditions of problem P,established their complete continuity and...

We have proved equivalence between the problem of oblique derivative of the non-linear elliptic system(A) W_z=g(Z,W,W_z),|Z|<1 (A.1) |g(Z,W,W_z~1)-g(Z,W,W_z~2)|≤q_o|W_z~1-W_z~2,q_o=const<1 (A.2) and the problem P which consists in finding a solution W(z) of this system(A) in the unit disk K and satisfying on its boundary |z|=1 the condition R_a(Z~(-n)W_z)=0. We have constructed two integral operators F(ω) and F_1(ω) which satisfy the boundary conditions of problem P,established their complete continuity and differentiability,studied the norms of their differential operator π(ω)and π_1(ω).We have also proved the representation theorem of solution of the problem P W(Z)=(?) where ω=W_z,Φ(Z) is a analytic function in K,and satisfied cn the bou- ndary |Z|=1 the condition R_c[Z~(-n)Φ′(Z)]=0.

本文证明了广义一阶非线性椭圆型偏微分方程组——方程组(A)W_z=g(Z,W,W_z),|Z|<1, (A·1)|g(Z,W,W(_z~1))-g(Z,W,W(_z~2))|≤q_0|W(_z~1)-W(_z~2)|,q_0=const<1 (A·2)的斜微商问题等价于问题 P:在单位圆 K(|Z|<1)内寻找方程组(A)的一组解 W(Z),在|Z|=1上适合条件R_e[Z~(-n)W_z]=0。我们构造了适合问题 P 的边界条件的两个积分算子г(ω)与г_1(ω),建立了它们的全连续性与可微性,研究了其微分算子π(ω)与π_1(ω)的范数。我们还证明了问题 P 的解的表示定理W(Z)=(?),其中ω(Z)=W_z,Φ(Z)在 K 内解析,在|Z|=1上适合 R_e[Z~(-n)Φ'(Z)]=0。

A heuristic parameter estimation method for fault diagnosis is presented in this paper.Through applyingknowledge to diagnosis process,the performance of traditional parameter estimation method is improved in thefollowing two aspects:(1)The calculation labor for estimating the model parameters is reduced since theparameters estimated are reasonably limited to a small set.(2)The fault localization is more accurate as the equa-tions p=f~1(0) are solved under the guidance of the physical meanings(expressed as knowledge)...

A heuristic parameter estimation method for fault diagnosis is presented in this paper.Through applyingknowledge to diagnosis process,the performance of traditional parameter estimation method is improved in thefollowing two aspects:(1)The calculation labor for estimating the model parameters is reduced since theparameters estimated are reasonably limited to a small set.(2)The fault localization is more accurate as the equa-tions p=f~1(0) are solved under the guidance of the physical meanings(expressed as knowledge) of the system.Atthe last of the paper a simple illustrative example is given.

本文讨论故障诊断的启发式参数估计法.文中首先讨论了用知识选择待估模型参数,从而减少模型参数估计计算量的问题.接着讨论了在物理意义(体现为知识)下求解方程 p=f~(-1)(θ),从而减小 p 解范围,加强故障定位能力的问题.文末给出了一个用以说明所提方法的仿真算例.

This paper discussed the obstacle problem P:find u ∈K suchthat integral from n=Ω to (?u·?(v-u)dx)-integral from n=Ω(p(x,u)·(v-u)dx≥0(?v∈K)) andthe degenerate problem P: find u ∈K such that integral from n=Ω (g(|?u|~2)·?u·?(v - u)dx)≥integral from Ω(p(x,u)·(v - u)dx)(?v ∈K)), where K = {v∈H_0~1(Ω),v ≥ψ a. e. in Ω}, and found out the multiplicity of P and existenceof solution to P,based on the theory of locally minimizing and critical point.

本文讨论障碍问题P和拟线性退化问题P,应用局部极小化和临界点理论,得到了问题P的多解存在性和问题P解之存在性。

 
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