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181.
182.
183.
This is a companion paper to our polyhedral study [1] of the Vertex Separator (VS) Problem. Given an undirected graph G, the VS problem consists in identifying a minimum-weight vertex set whose removal disconnects G, subject to bounds on the size of the resulting components. In this paper, we describe versions of a branch-and-cut algorithm based on the results of that polyhedral study. It uses two families of cuts, symmetric and asymmetric, for which we develop polynomial-time greedy separation routines. A heuristic to generate feasible separators is also used. A computational experiment on several data sets from the literature compares the performance of three versions of our algorithm to that of the commercial MIP solver XPRESS. This experiment throws a sharp light on the role of cut density, known to software developers but never before documented in the literature. It convincingly shows that the practical usefulness of cuts in integer programming depends not only on their strength, but also on their sparsity: everything else being equal, the smaller the cut support, the better. The power of the inequalities proposed here is well illustrated by the computational tests on dense graphs. This is in accordance with the previous observation, since the support of these cuts tends to decrease with graph density.Research supported by the Brazilian agencies FAPESP (grant 01/14205–6), CAPES (grant BEX 04444/02–2) and CNPq (grants 302588/02–7 and Pronex 664107/97–4).Research supported by the National Science Foundation through grant #DMI-0098427 and by the Office of Naval Research through contract N00014-97-1-0196. 相似文献
184.
We study nonlinear stability of solitons under the action of external spatiotemporal perturbations. Previous results on stationary structures [Rizzato FB, de Oliveira GI, Chian AC-L. Nonlinear stability of solitons against strong external perturbations. Phys Rev E 2003;67:047601] are extended to show that the centroid of moving solitons may develop chaotic dynamics, which under certain circumstances affects the corresponding envelope dynamics of these modes and reduces their stability. Applications to plasmas and Bose–Einstein condensates are discussed. 相似文献
185.
Egon Schulte 《Discrete and Computational Geometry》2004,32(1):55-99
Chiral polyhedra in ordinary euclidean space E3 are nearly regular polyhedra; their
geometric symmetry groups have two orbits on the flags, such that adjacent flags are in distinct
orbits. This paper completely enumerates the discrete infinite chiral polyhedra in E3 with
finite skew faces and finite skew vertex-figures. There are several families of such
polyhedra of types {4,6}, {6,4} and {6,6}. Their geometry and combinatorics are
discussed in detail. It is also proved that a chiral polyhedron in E3 cannot be finite.
Part II of the paper will complete the classification of all chiral polyhedra in E3. All
chiral polyhedra not described in Part I have infinite, helical faces and again occur in
families. So, in effect, Part I enumerates all chiral polyhedra in E3 with finite faces. 相似文献
186.
Egon Balas 《Annals of Operations Research》2005,140(1):125-161
This is an overview of the significance and main uses of projection, lifting and extended formulation in integer and combinatorial
optimization. Its first two sections deal with those basic properties of projection that make it such an effective and useful
bridge between problem formulations in different spaces, i.e. different sets of variables. They discuss topics like projection
and restriction, the integrality-preserving property of projection, the dimension of projected polyhedra, conditions for facets
of a polyhedron to project into facets of its projections, and so on. The next two sections describe the use of projection
for comparing the strength of different formulations of the same problem, and for proving the integrality of polyhedra by
using extended formulations or lifting. Section 5 deals with disjunctive programming, or optimization over unions of polyhedra,
whose most important incarnation are mixed 0-1 programs and their partial relaxations. It discusses the compact representation
of the convex hull of a union of polyhedra through extended formulation, the connection between the projection of the latter
and the polar of the convex hull, as well as the sequential convexification of facial disjunctive programs, among them mixed
0-1 programs, with the related concept of disjunctive rank. Section 6 reviews lift-and-project cuts, the construction of cut
generating linear programs, and techniques for lifting and for strengthening disjunctive cuts. Section 7 discusses the recently
discovered possibility of solving the higher dimensional cut generating linear program without explicitly constructing it,
by a sequence of properly chosen pivots in the simplex tableau of the linear programming relaxation. Finally, section 8 deals
with different ways of combining cuts with branch and bound, and briefly discusses computational experience with lift-and-project
cuts.
This is an updated and extended version of the paper published in LNCS 2241, Springer, 2001 (as given in Balas, 2001).
Research was supported by the National Science Foundation through grant #DMI-9802773 and by the Office of Naval Research through
contract N00014-97-1-0196. 相似文献
187.
Mechthild Gall Maren Thomsen Christin Peters Ioannis V. Pavlidis Patrick Jonczyk Philipp P. Grünert Sascha Beutel Thomas Scheper Egon Gross Michael Backes Torsten Geißler Jakob P. Ley Jens‐Michael Hilmer Gerhard Krammer Gottfried J. Palm Winfried Hinrichs Uwe T. Bornscheuer 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2014,126(5):1463-1466
188.
Cristina Soltovski de Oliveira Marina Morena Pereira Andrade Tiago André Denck Colman Fernanda Janaina Oliveira Gomes da Costa Egon Schnitzler 《Journal of Thermal Analysis and Calorimetry》2014,115(1):13-18
In this study, samples of native waxy corn starch, waxy corn starch treated with HCl 0.15 mol L?1 at 20 and 50 °C, respectively, were analysed. The thermogravimetric curves showed similar behaviour with three main mass losses and a decrease in the thermal stability. The acid hydrolysis in low HCl concentration performed for 4 h caused a decrease in peak temperature (DSC), viscosity peak (RVA), gelatinisation enthalpy (DSC) and relative crystallinity (XRD), and an increase in the average roughness (NC-AFM). The X-ray diffraction patterns displayed the ‘A’ type for all the starch granules. 相似文献
189.
Klaus Bretterbauer Claudia Holzmann Egon Rubatscher Clemens Schwarzinger Albert Roessler Christian Paulik 《European Polymer Journal》2013
The synthesis and characterization of N1,N2,N3-trimethylmelamine based (meth)acrylates and their application as components of UV-curable lacquers is described. A pre-condensed oligomeric mixture with a degree of condensation up to five is obtained via a one-pot conversion. Dividing the synthesis into two steps gives access to the mostly monomeric tris(meth)acrylates in overall yields higher than 76%. In general, the prepared compounds can easily be applied on glass, metal, and polystyrene glass affording highly transparent, hard, and scratch resistant coatings after UV-curing. The UV-cured monomeric trimethylmelamine trisacrylate was fully characterized by means of hardness, gloss, scratch-, abrasion-, and chemical resistance. Remarkably, the trimethylmelamine trisacrylate does not release cancerogen formaldehyde even at 150 °C. 相似文献
190.
Egon Schulte 《Discrete and Computational Geometry》2005,34(2):181-229
A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral
polyhedra in ordinary euclidean space E3 with finite skew faces and finite skew vertex-figures; they occur in infinite families and are of types {4,6}, {6,4} and
{6,6}. Part II completes the enumeration of all discrete chiral polyhedra in E3. There exist several families of chiral polyhedra of types {∞,3} and {∞,4} with infinite, helical faces. In particular, there are no discrete chiral polyhedra with finite faces in addition to those described in Part I. 相似文献