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81.
We present a single grid error estimation technique based on the derivation of a continuous equation for the discretization error. It is developed in the context of finite-volume methods for arbitrary meshes. The key issue of the evaluation of the source term is addressed through the use of a reconstruction operator. Using a higher order accurate evaluation of this term and solving the error equation with the same numerical methods and on the same computational grid as the primal problem leads to a higher order accurate error prediction. The methodology is presented in detail and its properties of asymptotic exactness and superconvergence are illustrated on several cases, including an application of practical engineering complexity. Also presented is the derivation of a powerful criterium for driving any adaptive procedure.  相似文献   
82.
利用可调谐激光吸收光谱技术(TDLAS),扫描多条吸收谱线以实现气体温度分布的测量。文章给出了温度分布测量的原理和方程离散化的方法,在气体浓度和压力均匀时,利用带约束最小二乘法计算得到温度分布。根据HITRAN中6 330 cm-1附近的4条CO谱线的参数,建立了温度在300和600 K时,路径长度均为55 cm的两段温度分布模型,模拟了测量误差与温度区间长度约束条件的影响。结果表明随着测量误差的增大和约束条件的减弱,计算结果误差相应增大。在5%的测量误差下,计算结果的最大误差为11%,平均误差为2.2%。以管式炉中的高温段和室温下的低温段作为两段温度分布模型进行试验。利用6 330 cm-1处的垂直腔面发射激光二极管(VCSEL)扫描得到的4条CO谱线,通过背景信号的三次多项式拟合得到基线,求出温度分布计算所需的光谱吸收率积分值。在四种情况下, 计算温度分布结果与模型误差分别为7.3%,6.5%,4.7%和2.7%。  相似文献   
83.
This study provides operational guidance for building naïve Bayes Bayesian network (BN) models for bankruptcy prediction. First, we suggest a heuristic method that guides the selection of bankruptcy predictors. Based on the correlations and partial correlations among variables, the method aims at eliminating redundant and less relevant variables. A naïve Bayes model is developed using the proposed heuristic method and is found to perform well based on a 10-fold validation analysis. The developed naïve Bayes model consists of eight first-order variables, six of which are continuous. We also provide guidance on building a cascaded model by selecting second-order variables to compensate for missing values of first-order variables. Second, we analyze whether the number of states into which the six continuous variables are discretized has an impact on the model’s performance. Our results show that the model’s performance is the best when the number of states for discretization is either two or three. Starting from four states, the performance starts to deteriorate, probably due to over-fitting. Finally, we experiment whether modeling continuous variables with continuous distributions instead of discretizing them can improve the model’s performance. Our finding suggests that this is not true. One possible reason is that continuous distributions tested by the study do not represent well the underlying distributions of empirical data. Finally, the results of this study could also be applicable to business decision-making contexts other than bankruptcy prediction.  相似文献   
84.
对于一个多类别的网络均衡问题,可以通过计算某个辅助问题的容量限制约束相应的乘子向量得到有效收费.本文通过计算拉格朗日函数的鞍点来计算乘子向量.借助于广义拉格朗日函数的稳定性和Uzawa算法非精确解的收敛性,得到鞍点序列的收敛性.其中离散化方法用于最小化广义拉格朗日函数的计算.  相似文献   
85.
SINGULARINTEGRALOPERATORSANDSINGULARQUADRATUREOPERATORSASSOCIATEDWITHSINGULARINTEGRALEQUATIONSOFTHEFIRSTKINDANDTHEIRAPPLICATI...  相似文献   
86.
We study optimal control problems for semilinear elliptic equations subject to control and state inequality constraints. Both boundary control and distributed control problems are considered with boundary conditions of Dirichlet or Neumann type. By introducing suitable discretization schemes, the control problem is transcribed into a nonlinear programming problem. Necessary conditions of optimality are discussed both for the continuous and the discretized control problem. It is shown that the recently developed interior point method LOQO of [35] is capable of solving these problems even for high discretizations. Four numerical examples with Dirichlet and Neumann boundary conditions are provided that illustrate the performance of the algorithm for different types of controls including bang–bang controls.  相似文献   
87.
88.
Semidefinite programs are convex optimization problems arising in a wide variety of applications and are the extension of linear programming. Most methods for linear programming have been generalized to semidefinite programs. Just as in linear programming, duality theorem plays a basic and an important role in theory as well as in algorithmics. Based on the discretization method and convergence property, this paper proposes a new proof of the strong duality theorem for semidefinite programming, which is different from other common proofs and is more simple.  相似文献   
89.
We study the optimal discretization error of stochastic integrals driven by a multidimensional continuous Brownian semimartingale. In the previous works a pathwise lower bound for the renormalized quadratic variation of the error was provided together with an asymptotically optimal discretization strategy, i.e. for which the lower bound is attained. However the construction of the optimal strategy involved the knowledge about the diffusion coefficient of the semimartingaleunder study. In this work we provide a model-adaptive asymptotically optimal discretization strategy that does not require any prior knowledge about the model. We prove the optimality for quite general class of discretization strategies based on kernel techniques for adaptive estimation and previously obtained optimal strategies that use random ellipsoid hitting times.  相似文献   
90.
The auxiliary linear problems are presented for all discretization levels of the Hirota-Ohta system. The structure of these linear problems coincides essentially with the structure of Nonlinear Schrödinger hierarchy. The squared eigenfunction constraints are found which relate Hirota-Ohta and Kulish-Sklyanin vectorial NLS hierarchies.  相似文献   
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