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911.
912.
For an integer N greater than 5 and a triple \({\mathfrak{a}}=[a_{1},a_{2},a_{3}]\) of integers with the properties 0<a i ≤N/2 and a i ≠a j for i≠j, we consider a modular function \(W_{\mathfrak{a}}(\tau)=\frac{\wp (a_{1}/N;L_{\tau})-\wp (a_{3}/N;L_{\tau})}{\wp (a_{2}/N;L_{\tau})-\wp(a_{3}/N;L_{\tau})}\) for the modular group Γ 1(N), where ?(z;L τ ) is the Weierstrass ?-function relative to the lattice L τ generated by 1 and a complex number τ with positive imaginary part. For a pair of such triples \({\mathfrak{A}}=[{\mathfrak{a}},{\mathfrak{b}}]\) and a pair of non-negative integers F=[m,n], we define a modular function \(T_{{\mathfrak{A}},F}\) for the group Γ 0(N) as the trace of the product \(W_{\mathfrak{a}}^{m}W_{\mathfrak{b}}^{n}\) to the modular function field of Γ 0(N). In this article, we study the integrality of singular values of the functions \(W_{\mathfrak{a}}\) and \(T_{{\mathfrak{A}},F}\) by using their modular equations. We prove that the functions \(T_{{\mathfrak{A}},F}\) for suitably chosen \({\mathfrak{A}}\) and F generate the modular function field of Γ 0(N), and from Shimura reciprocity and Gee–Stevenhagen method we obtain that singular values \(T_{{\mathfrak{A}},F}(\tau)\) for suitably chosen \({\mathfrak{A}}\) and F generate ring class fields. Further, we study the class polynomial of \(T_{{\mathfrak{A}},F}\) for Schertz N-system. 相似文献
913.
Brice Franke 《Extremes》2011,14(1):127-152
We investigate the recursive sequence Z
n
: = max {Z
n − 1,λ(Z
n − 1)X
n
} where X
n
is a sequence of iid random variables with exponential distributions and λ is a periodic positive bounded measurable function. We prove that the Césaro mean of the sequence λ(Z
n
) converges toward the essential minimum of λ. Subsequently we apply this result and obtain a limit theorem for the distributions of the sequence Z
n
. The resulting limit is a Gumbel distribution. 相似文献
914.
Two cellular embeddings i: G → S and j: G → S of a connected graph G into a closed orientable surface S are equivalent if there is an orientation-preserving surface homeomorphism h: S → S such that hi = j. The genus polynomial of a graph G is defined by
$
g\left[ G \right](x) = \sum\limits_{g = 0}^\infty {a_g x^g ,}
$
g\left[ G \right](x) = \sum\limits_{g = 0}^\infty {a_g x^g ,}
相似文献
915.
In this paper we formulate a continuous-time behavioral (à la cumulative prospect theory) portfolio selection model where the losses are constrained by a pre-specified upper bound. Economically
the model is motivated by the previously proved fact that the losses occurring in a bad state of the world can be catastrophic
for an unconstrained model. Mathematically solving the model boils down to solving a concave Choquet minimization problem with an additional upper bound. We derive the optimal solution explicitly for such a loss control model. The optimal
terminal wealth profile is in general characterized by three pieces: the agent has gains in the good states of the world,
gets a moderate, endogenously constant loss in the intermediate states, and suffers the maximal loss (which is the given bound
for losses) in the bad states. Examples are given to illustrate the general results. 相似文献
916.
In this paper, we consider a non-local PDE model with delay for population dynamics in ℝ
n
. First, we prove the existence and uniqueness of weak solutions under some suitable decayed assumptions on non-local term
at infinity. Then, we obtain the global attractor by proving ω-limit compactness property of the solution operator semigroup. 相似文献
917.
As evidence for his conjecture in birational log geometry, Kawamata constructed a family of derived equivalences between toric
orbifolds. In a previous paper, the authors showed that the derived category of a toric orbifold is naturally identified with
a category of polyhedrally-constructible sheaves on ℝ
n
. In this paper we investigate and reprove some of Kawamata’s results from this perspective. 相似文献
918.
The factors affecting performance of fractured wells are analyzed in this work. The static and dynamic geologic data of fractured
well and fracturing treatment parameters obtained from 51 fractured wells in sand reservoirs of Zhongyuan oilfield are analyzed
by applying the grey correlation method. Ten parameters are screened, including penetrability, porosity, net thickness, oil
saturation, water cut, average daily production, and injection rate, amount cementing front spacer, amount sand-carrying agent
and amount sand. With the novel Radial Basis Function neural network model based on immune principles, 13 parameters of 42
wells out of 51 are used as the input samples and the stimulation ratios as the output samples. The nonlinear interrelationship
between the input samples and output samples are investigated, and a productivity prediction model of optimizing fracture
design is established. The data of the rest 7 wells are used to test the model. The results show that the relative errors
are all less than 7%, which proves that the novel Radial Basis Function neural network model based on immune principles has
less calculation, high precision and good generalization ability. 相似文献
919.
It is well known that any Vitali set on the real line ? does not possess the Baire property. The same is valid for finite unions of Vitali sets. What can be said about infinite unions of Vitali sets? Let S be a Vitali set, S r be the image of S under the translation of ? by a rational number r and F = {S r : r is rational}. We prove that for each non-empty proper subfamily F′ of F the union ∪F′ does not possess the Baire property. We say that a subset A of ? possesses Vitali property if there exist a non-empty open set O and a meager set M such that A ? O \ M. Then we characterize those non-empty proper subfamilies F′ of F which unions ∪F′ possess the Vitali property. 相似文献
920.
Vitaly Maiorov 《Advances in Computational Mathematics》2010,32(2):239-253
We study geometrical properties of the ridge function manifold \(\mathcal{R}_n\) consisting of all possible linear combinations of n functions of the form g(a· x), where a·x is the inner product in \({\mathbb R}^d\). We obtain an estimate for the ε-entropy numbers in terms of smaller ε-covering numbers of the compact class G n,s formed by the intersection of the class \(\mathcal{R}_n\) with the unit ball \(B\mathcal{P}_s^d\) in the space of polynomials on \({\mathbb R}^d\) of degree s. In particular we show that for n?≤?s d???1 the ε-entropy number H ε (G n,s,L q ) of the class G n,s in the space L q is of order nslog1/ε (modulo a logarithmic factor). Note that the ε-entropy number \(H_\varepsilon(B\mathcal{P}_s^d,L_q)\) of the unit ball is of order s d log1/ε. Moreover, we obtain an estimate for the pseudo-dimension of the ridge function class G n,s. 相似文献
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