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961.
Let n and d be two positive integers.By Bn,d we denote the graph obtained by identifying an endvertex of path Pd with the center of star Sn-d+1,where n ≥ d + 1.By Cn,d we denote the graph obtained by identifying an endvertex of Pd-1 with the center of Stare Sn-d,and the other endvertex of Pd-1 with the center of S3 where n ≥ d + 3.By En,d,k we denote the graph obtained by identifying the vertex vk of P(v1 - v2 - ··· - vd+1) with the center of Sn-d.In this paper,we completely characterize all trees T which have diameter at least d(d ≥ 3) and satisfy the following conditions:(i) Z(Bn,d) ≤ Z(T) ≤ Z(En,d,3) for n = d + 3;(ii) Z(Bn,d) ≤ Z(T) ≤ Z(Cn,d) for n ≥ d + 4. 相似文献
962.
A. Stoimenow 《数学学报(英文版)》2012,28(3):515-528
We introduce a method to compute the girth of knots, defined by Hernndez and Lin, using the Jones and BrandtLickorishMillettHo polynomial. We determine the girth of all knots up to 10 crossings. 相似文献
963.
Shang-wang Tan 《Discrete Mathematics》2010,310(5):1026-1212
The spectrum of weighted graphs is often used to solve the problems in the design of networks and electronic circuits. We first give some perturbational results on the (signless) Laplacian spectral radius of weighted graphs when some weights of edges are modified; we then determine the weighted tree with the largest Laplacian spectral radius in the set of all weighted trees with a fixed number of pendant vertices and a positive weight set. Furthermore, we also derive the weighted trees with the largest Laplacian spectral radius in the set of all weighted trees with a fixed positive weight set and independence number, matching number or total independence number. 相似文献
964.
Florian Pfender 《Journal of Graph Theory》2010,64(3):206-209
For a graph G, let t(G) denote the maximum number of vertices in an induced subgraph of Gthat is a tree. Further, for a vertex v∈V(G), let t(G, v) denote the maximum number of vertices in an induced subgraph of Gthat is a tree, with the extra condition that the tree must contain v. The minimum of t(G) (t(G, v), respectively) over all connected triangle‐free graphs G(and vertices v∈V(G)) on nvertices is denoted by t3(n) (t(n)). Clearly, t(G, v)?t(G) for all v∈V(G). In this note, we solve the extremal problem of maximizing |G| for given t(G, v), given that Gis connected and triangle‐free. We show that and determine the unique extremal graphs. Thus, we get as corollary that $t_3(n)\ge t_3^{\ast}(n) = \lceil {\frac{1}{2}}(1+{\sqrt{8n-7}})\rceilFor a graph G, let t(G) denote the maximum number of vertices in an induced subgraph of Gthat is a tree. Further, for a vertex v∈V(G), let t(G, v) denote the maximum number of vertices in an induced subgraph of Gthat is a tree, with the extra condition that the tree must contain v. The minimum of t(G) (t(G, v), respectively) over all connected triangle‐free graphs G(and vertices v∈V(G)) on nvertices is denoted by t3(n) (t(n)). Clearly, t(G, v)?t(G) for all v∈V(G). In this note, we solve the extremal problem of maximizing |G| for given t(G, v), given that Gis connected and triangle‐free. We show that and determine the unique extremal graphs. Thus, we get as corollary that $t_3(n)\ge t_3^{\ast}(n) = \lceil {\frac{1}{2}}(1+{\sqrt{8n-7}})\rceil$, improving a recent result by Fox, Loh and Sudakov. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 206–209, 2010 相似文献
965.
The energy of a graph is defined as the sum of the absolute values of all the eigenvalues of the graph. Let
denote the set of trees on n vertices and diameter d,
. Yan and Ye [Appl. Math. Lett. 18 (2005) 1046–1052] have recently determined the unique tree in
with minimal energy. In this article, the trees in
with second-minimal energy are characterizedAMS Subject Classification: 05C50, 05C35 相似文献
966.
967.
Ionut Cardei Mihaela Cardei Lusheng Wang Baogang Xu Ding-Zhu Du 《Journal of Global Optimization》2006,36(3):391-399
In the design of wireless networks, techniques for improving energy efficiency and extending network lifetime have great importance, particularly for defense and civil/rescue applications where resupplying transmitters with new batteries is not feasible. In this paper we study a method for improving the lifetime of wireless networks by minimizing the length of the longest edge in the interconnecting tree by deploying additional relay nodes at specific locations. This optimization problem, known as the Bottleneck Steiner Tree Problem (BSTP), asks to find a Steiner tree for n terminals with at most k Steiner points such that the length of the longest edge in the tree is minimized. We present a ratio-
polynomial time approximation algorithm for BSTP, where
is an arbitrary positive number. 相似文献
968.
Rodrigo Bissacot Eric Ossami Endo Aernout C.D. van Enter 《Stochastic Processes and their Applications》2017,127(12):4126-4138
We consider the ferromagnetic Ising model with spatially dependent external fields on a Cayley tree, and we investigate the conditions for the existence of the phase transition for a class of external fields, asymptotically approaching a homogeneous critical external field. Our results extend earlier results by Rozikov and Ganikhodjaev. 相似文献
969.
Hongxia Chen Hao Zhou Ran Tao Jianzhong Ye Wenjun Li 《Natural product research》2018,32(18):2221-2224
Three polysaccharides, LTPS-1, LTPS-21 and LTPS-31 were isolated and purified from the seed cakes of lacquer tree using DEAE-52 cellulose and Sephadex G-200 column chromatography. The total sugar contents of LTPS-1, LTPS-21 and LTPS-31 were 931.8, 958.2 and 895.1 g kg?1, respectively. LTPS-1 (3.48 kDa) was mainly composed of rhamnose, arabinose, glucose and galactose in a ratio of 35.36:5.06:1:2. LTPS-21 (11.4 kDa) was mainly composed of rhamnose, arabinose, mannose and galactose in a ratio of 41.93:21.8:1.01:9.24. LTPS-31 (19.49 kDa) was mainly composed of rhamnose, arabinose and mannose in a ratio of 38.31:16.44:1.1. IR analysis suggested they contained lower sulphuric acids, the LTPS-21 and LTPS-31 belonged to β-type polysaccharide. Among the three polysaccharides, LTPS-21 exhibited the strongest reducing power, scavenging activity on ABTS and hydroxyl radicals. These findings suggested that polysaccharides from the seed cakes could be potentially developed as natural functional ingredients in the food and cosmetic industry. 相似文献
970.
The goal of this paper is to provide a more detailed explanation of the principles how special formulas that characterize properties of trend of time series can be formed and how they are interpreted. Then we show how these formulas can be used in a tectogrammatical tree that construes special sentences of natural language, using which information on behavior of time series is provided. We also outline the principles of mining this information. The last part is devoted to application of the theory of intermediate quantifiers to mining summarized information on time series also in sentences of natural language. 相似文献