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181.
Xin-rong Cong 《国际计算机数学杂志》2018,95(2):316-328
The high-order accurate compact finite difference scheme which belongs to the finite difference methods is constructed to solve the system of partial differential equations with random noise. The error analysis and stability analysis are given and then the numerical simulation is executed. The simulation results verify the theoretical analysis results and have the faster computation speed and higher accuracy. 相似文献
182.
Crack propagation in metals has long been recognized as a stochastic process. As a consequence, crack propagation rates have been modeled as random variables or as random processes of the continuous. On the other hand, polynomial chaos is a known powerful tool to represent general second order random variables or processes. Hence, it is natural to use polynomial chaos to represent random crack propagation data: nevertheless, no such application has been found in the published literature. In the present article, the large replicate experimental results of Virkler et al. and Ghonem and Dore are used to illustrate how polynomial chaos can be used to obtain accurate representations of random crack propagation data. Hermite polynomials indexed in stationary Gaussian stochastic processes are used to represent the logarithm of crack propagation rates as a function of the logarithm of stress intensity factor ranges. As a result, crack propagation rates become log-normally distributed, as observed from experimental data. The Karhunen–Loève expansion is used to represent the Gaussian process in the polynomial chaos basis. The analytical polynomial chaos representations derived herein are shown to be very accurate, and can be employed in predicting the reliability of structural components subject to fatigue. 相似文献
183.
Several estimation techniques assume validity of Gaussian approximations for estimation purposes. Interestingly, these ensemble methods have proven to work very well for high-dimensional data even when the distributions involved are not necessarily Gaussian. We attempt to bridge the gap between this oft-used computational assumption and the theoretical understanding of why this works, by employing some recent results on random projections on low dimensional subspaces and concentration inequalities. 相似文献
184.
We assume a financial market governed by a diffusion process reverting to a stochastic mean which is itself governed by an unobservable ergodic diffusion, similar to those observed in electricity and other energy markets. We develop a moment method algorithm for the estimation of the parameters of both the observable process and the unobservable stochastic mean. Our approach is contrasted with other methods for parameter estimation of partially observed diffusions, and applications to the modelling of interest rates and commodity prices are discussed. 相似文献
185.
A recently proposed Bayesian model selection technique, stochastic model specification search, is carried out to discriminate between two trend generation hypotheses. The first is the trend-stationary hypothesis, for which the trend is a deterministic function of time and the short run dynamics are represented by a stationary autoregressive process. The second is the difference-stationary hypothesis, according to which the trend results from the cumulation of the effects of random disturbances. A difference-stationary process may originate in two ways: from an unobserved components process adding up an integrated trend and an orthogonal transitory component, or implicitly from an autoregressive process with roots on the unit circle. The different trend generation hypotheses are nested within an encompassing linear state space model. After a reparameterisation in non-centred form, the empirical evidence supporting a particular hypothesis is obtained by performing variable selection on the model components, using a suitably designed Gibbs sampling scheme. The methodology is illustrated with reference to a set of US macroeconomic time series which includes the traditional Nelson and Plosser dataset. The conclusion is that most series are better represented by autoregressive models with time-invariant intercept and slope and coefficients that are close to boundary of the stationarity region. The posterior distribution of the autoregressive parameters provides useful insight on quasi-integrated nature of the specifications selected. 相似文献
186.
The coordinated supplier selection and customer order scheduling in the presence of supply chain disruption risks is studied for single and multiple sourcing strategies. Given a set of customer orders for products, the decision maker needs to select a single supplier or a subset of suppliers for purchasing parts required to complete the customer orders, and schedule the orders over the planning horizon, to mitigate the impact of disruption risks. The suppliers are located in different geographic regions and the supplies are subject to different types of disruptions: to random local disruptions of each supplier individually, to random regional disruptions of all suppliers in the same region simultaneously and to random global disruptions of all suppliers simultaneously. For any combination of suppliers hit by different types of disruptions, a formula for calculating the corresponding disruption probability is developed. The obtained combinatorial stochastic optimization problem is formulated as a mixed integer program with conditional value-at-risk as a risk measure. The problem objective is either to minimize expected worst-case cost or to maximize expected worst-case customer service level, i.e., the expected worst-case fraction of customer orders filled on or before their due dates. The risk-averse solutions that optimize worst-case performance of a supply chain under disruptions risks are compared for the two sourcing strategies and the two objective functions. Numerical examples and computational results are presented and some managerial insights on the choice between the two sourcing strategies are reported. 相似文献
187.
This paper presents a stochastic mixed-integer linear programming approach for solving the self-scheduling problem of a price-taker thermal and wind power producer taking part in a pool-based electricity market. Uncertainty on electricity price and wind power is considered through a set of scenarios. Thermal units are modelled by variable costs, start-up costs and technical operating constraints, such as: forbidden operating zones, ramp up/down limits and minimum up/down time limits. An efficient mixed-integer linear program is presented to develop the offering strategies of the coordinated production of thermal and wind energy generation, having as a goal the maximization of profit. A case study with data from the Iberian Electricity Market is presented and results are discussed to show the effectiveness of the proposed approach. 相似文献
188.
Modeling electrochemical impedance spectroscopy is usually done using equivalent electrical circuits. These circuits have parameters that need to be estimated properly in order to make possible the simulation of impedance data. Despite the fitting procedure is an optimization problem solved recurrently in the literature, rarely statistical significance of the estimated parameters is evaluated. In this work, the optimization process for the equivalent electrical circuit fitting to the impedance data is detailed. First, a mathematical development regarding the minimization of residual least squares is presented in order to obtain a statistically valid objective function of the complex nonlinear regression problem. Then, the optimization method used in this work is presented, the Differential Evolution, a global search stochastic method. Furthermore, it is shown how a population-based stochastic method like this can be used directly to obtain confidence regions to the estimated parameters. A sensitivity analysis was also conducted. Finally, the equivalent circuit fitting is done to model synthetic experimental data, in order to demonstrate the adopted procedure. 相似文献
189.
Mineral concentrators are designed from preliminary geological data, and are therefore subject to geological uncertainty. This uncertainty has a demonstrable impact on the mining lifecycle, and has motivated stochastic strategic mine planning algorithms. The current paper describes how these algorithms may be extended to consider mineral processing operations in conjunction with open-pit mining operations. In particular, the paper describes an effective way to incorporate variable concentrator feed grade into these algorithms, which is the first step toward more elaborate representations of mineral concentrators. The resulting framework will be able to connect geological data to alternate configurations of the downstream resources, hence comparing the benefit of each configuration, and the corresponding capital investments. Sample computations are presented, comparing the net present value and utilisation for several different mineral processing capacities. 相似文献
190.
In this paper, the function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is investigated. Firstly, according to the stability theory of fractional-order systems and tracking control, a controller is designed. At the same time, based on the orthogonal polynomial approximation, the method of transforming stochastic error system into an equivalent deterministic system is given. Thus, the stability of the stochastic error system can be analyzed through its equivalent deterministic one. Finally, to demonstrate the effectiveness of the proposed scheme, the function projective synchronization between integer-order Lorenz system and stochastic fractional-order Chen system is studied. 相似文献