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121.
Modifying the shape of FB-spline curves 总被引:1,自引:0,他引:1
FB-spline curves are the unification of recently developed trigonometric CB-spline and hyperbolic HB-spline curves, including the classical B-spline curves. These generalized curves overcome some restrictions of B-spline curves and allow to design some important curves like helix, cycloids or catenary. Their properties, however, have been studied only theoretically. In this paper practical shape modification algorithms of FB-spline curves are discussed, including the geometrical effects of the alteration of shape parameters, which are essential from the users’ point of view. 相似文献
122.
123.
Singlet and triplet calculations, including configuration interaction, are reported for H2CSi, HCSiH and CSiH2, and for the transition state on both surfaces. 相似文献
124.
Imre Brny 《Discrete Mathematics》1982,40(2-3):141-152
The following theorem is proved. If the sets
and a εn+1i=1 conv Vi, then there exist elements vi ε Vi (i=1…,n+1) such that a ε conv{v1,…,vn+1}. This is generalization of Carathéodory's theorem. By applying this and similar results some open questions are answered. 相似文献
125.
Imre Bucsi György Szöllsi Tibor Bartók Mihály Bartók 《Reaction Kinetics and Catalysis Letters》2005,85(2):361-366
Summary The first identification of aluminium containing oxonium cations having chiral atomic groups is described which may play a role in enantioselective hydrogenation of ethyl pyruvate using Pt-alumina catalyst in AcOH. The structure these cations at m/z = 509 and m/z = 567 is: [O{Al(OAc)2}2Al(OPy.OLt)]+ and [O(AlOAc.OLt)2Al(OPy)2]+ 相似文献
126.
An IP system is a functionn taking finite subsets ofN to a commutative, additive group Ω satisfyingn(α∪β)=n(α)+n(β) whenever α∩β=ø. In an extension of their Szemerédi theorem for finitely many commuting measure preserving transformations, Furstenberg and Katznelson showed that ifS i ,1≤i≤k, are IP systems into a commutative (possibly infinitely generated) group Ω of measure preserving transformations of a probability space (X, B, μ, andA∈B with μ(A)>0, then for some ø≠α one has μ(? i=1 k S i({α})A>0). We extend this to so-called FVIP systems, which are polynomial analogs of IP systems, thereby generalizing as well joint work by the author and V. Bergelson concerning special FVIP systems of the formS(α)=T(p(n(α))), wherep:Z t →Z d is a polynomial vanishing at zero,T is a measure preservingZ d action andn is an IP system intoZ t . The primary novelty here is potential infinite generation of the underlying group action, however there are new applications inZ d as well, for example multiple recurrence along a wide class ofgeneralized polynomials (very roughly, functions built out of regular polynomials by iterated use of the greatest integer function). 相似文献
127.
Summary Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation
ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>m>1$
be an integer, $B_m$ the set of all unit vectors of $\Bbb R^m$ pointing in the direction of a nonzero integer vector of the
cube $[-1,\,1]^m$. Denote by $s_m$ the radius of the largest ball contained in the convex hull of $B_m$. We determine the
exact value of $s_m$ and obtain the asymptotic equality $s_m\sim\frac{2}{\sqrt{\log m}}$. 相似文献
128.
Let K Rd be a sufficiently round convex body (the ratio
of the circumscribed ball to the inscribed ball is bounded by a
constant) of a sufficiently large volume.
We investigate the randomized integer convex hull
IL(K) = conv (K L), where L is a randomly translated and rotated
copy of the integer lattice Zd.
We estimate the expected number
of vertices of IL(K), whose behaviour is similar to the
expected number of vertices of the convex hull of Vol K
random points in K. In the planar case we also
describe the expectation of the missed area
Vol (K \ IL(K)). Surprisingly, for K a
polygon, the behaviour in this case
is different from the convex hull of random points. 相似文献
129.
Margit Imre 《Acta Mathematica Hungarica》1964,15(1-2):115-121
Ohne Zusammenfassung
Vorgelegt von
L. Fejes Tóth 相似文献
130.
Let Σ be a finite alphabet, Σ* the free monoid generated by Σ and χ the length of χ ∈ Σ*. For any integer k0, fk(χ) (tk(χ)) is χ if χ < k + 1, and it is the prefix (suffix) of χ of length k, othewise. Also let mk+1(χ) = {νχ = uνw and ν = k+1}. For χ, y ε Σ* define χ ~ k+1y iff fk(χ) = fk(y), tk(χ) = tk(y) and mk+1(χ) = mk+1(y). The relation ~k+1 is a congruence of finite index over Σ*. An event E ? Σ* is (k+1)-testable iff it is a union of congruence classes of ~k+1. E is locally testable (LT) if it is k+1-testable for some k. (This definition differs from that of [6] but is equivalent.)We show that the family of LT events is a proper sub-family of star-free events of dot-depth 1. LT events and k-testable events are characterized in terms of (a) restricted star-free expressions based on finite and cofinite events; (b) finite automata accepting these events; (c) semigroups; and (d) structural decomposition of such automata. Algorithms are given for deciding whether a regular event is (a) LT and (b) k+1-testable. Generalized definite events are also characterized. 相似文献