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61.
A subset S of vertices in a graph G=(V,E) is a connected dominating set of G if every vertex of V?S is adjacent to a vertex in S and the subgraph induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected domination number γc(G). The girth g(G) is the length of a shortest cycle in G. We show that if G is a connected graph that contains at least one cycle, then γc(G)≥g(G)−2, and we characterize the graphs obtaining equality in this bound. We also establish various upper bounds on the connected domination number of a graph, as well as Nordhaus–Gaddum type results. 相似文献
62.
李启宁 《数学年刊A辑(中文版)》2021,42(4):441-458
本文的目的是定义Hopf二重Ore扩张,讨论这种扩张的基本性质并研究Hopf 代数的分次与Hopf二重Ore扩张之间的关系.作者还研究了连通分次Hopf代数的结构及其Hopf二重Ore扩张的同调性质. 相似文献
63.
64.
Gertruda Gwó?d?-?ukawska 《Journal of Mathematical Analysis and Applications》2009,356(2):453-663
We develop the Hutchinson-Barnsley theory for finite families of mappings on a metric space endowed with a directed graph. In particular, our results subsume a classical theorem of J.E. Hutchinson [J.E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981) 713-747] on the existence of an invariant set for an iterated function system of Banach contractions, and a theorem of L. Máté [L. Máté, The Hutchinson-Barnsley theory for certain non-contraction mappings, Period. Math. Hungar. 27 (1993) 21-33] concerning finite families of locally uniformly contractions introduced by Edelstein. Also, they generalize recent fixed point theorems of A.C.M. Ran and M.C.B. Reurings [A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto and R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], and A. Petru?el and I.A. Rus [A. Petru?el, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] for contractive mappings on an ordered metric space. As an application, we obtain a theorem on the convergence of infinite products of linear operators on an arbitrary Banach space. This result yields new generalizations of the Kelisky-Rivlin theorem on iterates of the Bernstein operators on the space C[0,1] as well as its extensions given recently by H. Oruç and N. Tuncer [H. Oruç, N. Tuncer, On the convergence and iterates of q-Bernstein polynomials, J. Approx. Theory 117 (2002) 301-313], and H. Gonska and P. Pi?ul [H. Gonska, P. Pi?ul, Remarks on an article of J.P. King, Comment. Math. Univ. Carolin. 46 (2005) 645-652]. 相似文献
65.
本文引入了偏序集连通性的概念,给出了连通分支的构造,证明了偏序集可唯一地分解为连通分支的不交并,偏序集的连通子集是连通分支当且仅当它是分支并。 相似文献
66.
We prove that fractional k-factors can be transformed among themselves by using a new adjusting operation repeatedly. We introduce, analogous to Berge’s augmenting path method in matching theory, the technique of increasing walk and derive a characterization of maximum fractional k-factors in graphs. As applications of this characterization, several results about connected fractional 1-factors are obtained. 相似文献
67.
68.
R is any ring with identity. Let Spec r (R) (resp. Spec(R)) be the set of all prime right ideals (resp. all prime ideals) of R and let U r (eR) = {P ? Spec r (R) | e ? P}. In this article, we study the relationships among various ring-theoretic properties and topological conditions on Spec r (R) (with weak Zariski topology). A ring R is called Abelian if all idempotents in R are central (see Goodearl, 1991). A ring R is called 2-primal if every nilpotent element is in the prime radical of R (see Lam, 2001). It will be shown that for an Abelian ring R there is a bijection between the set of all idempotents in R and the clopen (i.e., closed and open) sets in Spec r (R). And the following results are obtained for any ring R: (1) For any clopen set U in Spec r (R), there is an idempotent e in R such that U = U r (eR). (2) If R is an Abelian ring or a 2-primal ring, then, for any idempotent e in R, U r (eR) is a clopen set in Spec r (R). (3) Spec r (R) is connected if and only if Spec(R) is connected. 相似文献
69.
R is any ring with identity. Let Spec r (R) (resp. Max r (R), Prim r (R)) denote the set of all right prime ideals (resp. all maximal right ideals, all right primitive ideals) of R and let U r (eR) = {P ? Spec r (R)| e ? P}. Let = ∪P?Prim r (R) Spec r P (R), where Spec r P (R) = {Q ?Spec r P (R)|P is the largest ideal contained in Q}. A ring is called right quasi-duo if every maximal right ideal is 2-sided. In this article, we study the properties of the weak Zariski topology on and the relationships among various ring-theoretic properties and topological conditions on it. Then the following results are obtained for any ring R: (1) R is right quasi-duo ring if and only if is a space with Zariski topology if and only if, for any Q ? , Q is irreducible as a right ideal in R. (2) For any clopen (i.e., closed and open) set U in ? = Max r (R) ∪ Prim r (R) (resp. = Prim r (R)) there is an element e in R with e 2 ? e ? J(R) such that U = U r (eR) ∩ ? (resp. U = U r (eR) ∩ ), where J(R) is the Jacobson of R. (3) Max r (R) ∪ Prim r (R) is connected if and only if Max l (R) ∪ Prim l (R) is connected if and only if Prim r (R) is connected. 相似文献
70.
Tatyana S. Turova 《Random Structures and Algorithms》2013,43(4):486-539
Consider the random graph on n vertices 1,…,n. Each vertex i is assigned a type xi with x1,…,xn being independent identically distributed as a nonnegative random variable X. We assume that EX3< ∞. Given types of all vertices, an edge exists between vertices i and j independent of anything else and with probability \begin{align*}\min \{1, \frac{x_ix_j}{n}\left(1+\frac{a}{n^{1/3}} \right) \}\end{align*}. We study the critical phase, which is known to take place when EX2 = 1. We prove that normalized by n‐2/3the asymptotic joint distributions of component sizes of the graph equals the joint distribution of the excursions of a reflecting Brownian motion with diffusion coefficient \begin{align*}\sqrt{{\textbf{ E}}X{\textbf{ E}}X^3}\end{align*}and drift \begin{align*}a-\frac{{\textbf{ E}}X^3}{{\textbf{ E}}X}s\end{align*}. In particular, we conclude that the size of the largest connected component is of order n2/3. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 43, 486–539, 2013 相似文献