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1.
The purpose of this article is to establish conditions under which a positive quadratic differential form is topologically equivalent to its principal part defined by Newton polyhedra. The problem is to study the simultaneous behavior of two foliations in the plane having a common point as a singularity. 2000 Mathematics Subject Classification. Primary: 37C15; Secondary: 34C20, 34A34. The first author was partially supported by FAPESP Grant No. 03/03107-9 and by CNPq Grant No. 306992/2003-5, Brazil. The second author was supported by CNPq-Brazil Grant No. 154150/01-1 and PROCAD-Brazil No. 092/01. The third author was supported by PRONEX No. 76.97.1080/00 and Fapesp-Brazil under Grant No. 97/10735-3.  相似文献   
2.
Lithium–sulfur (Li–S) batteries are recognized as promising candidates for next-generation electrochemical energy storage systems owing to their high energy density and cost-effective raw materials. However, the sluggish multielectron sulfur redox reactions are the root cause of most of the issues for Li–S batteries. Herein, a high-efficiency CoSe electrocatalyst with hierarchical porous nanopolyhedron architecture (CS@HPP) derived from a metal–organic framework is presented as the sulfur host for Li–S batteries. The CS@HPP with high crystal quality and abundant reaction active sites can catalytically accelerate capture/diffusion of polysulfides and precipitation/decomposition of Li2S. Thus, the CS@HPP sulfur cathode exhibits an excellent capacity of 1634.9 mAh g−1, high rate performance, and a long cycle life with a low capacity decay of 0.04% per cycle over 1200 cycles. CoSe nanopolyhedrons are further fabricated on a carbon cloth framework (CC@CS@HPP) to unfold the electrocatalytic activity by its high electrical conductivity and large surface area. A freestanding CC@CS@HPP sulfur cathode with sulfur loading of 8.1 mg cm−2 delivers a high areal capacity of 8.1 mAh cm−2 under a lean electrolyte. This work will enlighten the rational design of structure–catalysis engineering of transition-metal-based nanomaterials for diverse applications.  相似文献   
3.
    
In this paper, we consider augmented Lagrangian (AL) algorithms for solving large-scale nonlinear optimization problems that execute adaptive strategies for updating the penalty parameter. Our work is motivated by the recently proposed adaptive AL trust region method by Curtis et al. [An adaptive augmented Lagrangian method for large-scale constrained optimization, Math. Program. 152 (2015), pp. 201–245.]. The first focal point of this paper is a new variant of the approach that employs a line search rather than a trust region strategy, where a critical algorithmic feature for the line search strategy is the use of convexified piecewise quadratic models of the AL function for computing the search directions. We prove global convergence guarantees for our line search algorithm that are on par with those for the previously proposed trust region method. A second focal point of this paper is the practical performance of the line search and trust region algorithm variants in Matlab software, as well as that of an adaptive penalty parameter updating strategy incorporated into the Lancelot software. We test these methods on problems from the CUTEst and COPS collections, as well as on challenging test problems related to optimal power flow. Our numerical experience suggests that the adaptive algorithms outperform traditional AL methods in terms of efficiency and reliability. As with traditional AL algorithms, the adaptive methods are matrix-free and thus represent a viable option for solving large-scale problems.  相似文献   
4.
Globally Optimal Estimates for Geometric Reconstruction Problems   总被引:2,自引:2,他引:2  
We introduce a framework for computing statistically optimal estimates of geometric reconstruction problems. While traditional algorithms often suffer from either local minima or non-optimality—or a combination of both—we pursue the goal of achieving global solutions of the statistically optimal cost-function. Our approach is based on a hierarchy of convex relaxations to solve non-convex optimization problems with polynomials. These convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation. The technique is applied to a number of classical vision problems: triangulation, camera pose, homography estimation and last, but not least, epipolar geometry estimation. Experimental validation on both synthetic and real data is provided. In practice, only a few relaxations are needed for attaining the global optimum.  相似文献   
5.
Extrusion is a basic operation allowing the generation of higher intrinsic dimension polyhedra. The paper gives closed formulas both to generate a (d+1)-dimensional polyhedron obtained by affine extrusion of a (d)-dimensional polyhedron, and to generate by rotational extrusion. Algorithms for the boundary evaluation when a decompositive representation is given are also discussed.

The representation used in the paper, based on simplicial complexes, is general and simple, and allows us to represent nonconvex, unconnected, unoriented, nonmanifold and unbounded linear polyhedra. A simplicial complex triangulating the extruded polyhedron is generated by independently extruding the simplices of the input object. The approach is very efficient because no a posteriori triangulation of the extruded polyhedron is required; furthermore, both the underlying complex and the adjacencies between cells are calculated by using closed formulas.  相似文献   

6.
应用罚函数求解二层线性优化问题的全局优化方法   总被引:3,自引:0,他引:3  
曹东 《控制与决策》1995,10(4):327-331
应用罚函数原理,将二层线性优化问题转化为目标函数带有罚函数子项的非线性优化问题,当罚系数大于某一数值时,库函数项为一精确项,该非线性优化问题用渐的进外逼近算法可求出其全局最优解。  相似文献   
7.
    
A displacement‐based continuous‐Galerkin finite element formulation for general polyhedra is presented for applications in nonlinear solid mechanics. The polyhedra can have an arbitrary number of vertices or faces. The faces of the polyhedra can have an arbitrary number of edges and can be nonplanar. The polyhedra can be nonconvex with only the mild restriction of star convexity with respect to the vertex‐averaged centroid. Conforming shape functions are constructed using harmonic functions defined on the undeformed configuration, thus requiring the use of a total‐Lagrangian finite element formulation in large deformation applications. For nonlinear applications with computationally intensive constitutive models, it is important to minimize the number of element quadrature points. For this reason, an integration scheme is adopted in which the number of quadrature points is equal to the number of vertices. As a first step toward verifying the element behavior in the general nonlinear setting, several linear verification examples are presented using both random Voronoi meshes and distorted hexahedral meshes. For the hexahedral meshes, results for the polyhedral formulation are compared to those of the standard trilinear hexahedral formulation. The element behavior in the nearly incompressible regime is also examined. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   
8.
    
The travelling salesman problem (TSP) with neighbourhoods extends the TSP to the case where each vertex of the tour is allowed to move in a given region. This NP-hard optimization problem has recently received increasing attention in several technical fields such as robotics, unmanned aerial vehicles, or utility management. In this paper, the problem is formulated as a non-convex mixed-integer nonlinear programme (MINLP) having the property that fixing all the integer variables to any integer values yield a convex nonlinear programme. This property is used to modify the global MINLP optimizer Couenne, improving by orders of magnitude its performance and allowing the exact solution of instances large enough to be useful in applications. Computational results are presented where neighbourhoods are either polyhedra or ellipsoids in ℝ2 or ℝ3 and with the Euclidean norm as distance metric.  相似文献   
9.
10.
    
ABSTRACT

This paper bestows a new swarm intelligence approach, Squirrel Search Algorithm (SSA) to solve Economic Load Dispatch (ELD) of the thermal unit by addressing the valve point loading effects and multiple fuel options. SSA inspires the foraging behavior of squirrels which is based on dynamic jumping and gliding strategies. The main intention of the ELD problem is to minimize the total generation cost of units while assuring various system constraints. Renovate strategy and selection rules are used in the SSA algorithm to handle the constraints appropriately. The practicability of the proposed algorithm is tested on six different power test systems having different sizes and intricacies. Simulation results ascertain that the proposed SSA approach outperforms the other existing heuristic optimization techniques in terms of solution quality, robustness, and computational efficiency. Consequently, the proposed SSA can be an efficient approach for solving the ELD problems with valve point loading impacts and multi-fuel options.  相似文献   
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