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Summary LetX be a centered stationary Gaussian stochastic process with ad-dimensional parameter (d2),F its spectral measure, (x denotes the Euclidean norm ofx). We consider regularizations of the trajectories ofX by means of convolutions of the formX (t)=( *X)(t) where stands for an approximation of unity (as tends to zero) satisfying certain regularity conditions.The aim of this paper is to recover the local time ofX at a given levelu, as a limit of appropriate normalizations of the geometric measure of theu-level set of the regular approximating processesX . A part of the difficulties comes from the fact that the geometric behavior of the covariance of the Gaussian processX can be a complex one as approaches O.The results are onL 2-convergence and include bounds for the speed of convergence.L presults may be obtained in similar ways, but almost sure convergence or simultaneous convergence for the various values ofu do not seem to follow from our methods. In Sect. 3 we have included examples showing a diversity of geometric behaviors, especially in what concerns the dependence on the thickness of the set in which the covariance of the original processX is irregular.Some technical results of analytic nature are included as appendices in Sect. 4.  相似文献   
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Semiclassical calculations are carried out by two methods for the problem of collision-induced predissociation of electronically excited I2. The first method is that of surface-hopping with the Landau-Zener model. The second method is similar to surface-hopping, except that analytic continuation of the adiabatic potential energy surfaces replaces the Landau-Zener model. Results of the calculations by the two methods compare favorably with each other and with experiment. The possible advantages of the second method are discussed.Camille and Henry Dreyfus Teacher-Scholar, Alfred P. Sloan Research Fellow.  相似文献   
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The theory of first-order kinetic collection efficiencies at the double channel electrode is developed for the following two schemes: (I) A±n1e→B (at the generator electrode), B→kP (in solution), B±n2e→Y (at the detector electrode), (II) A±n1e→B, B→kA, B±n2e→Y. The exact expressions for the kinetic collection efficiencies are obtained as ascending and asymptotic series with respect to the kinetic parameter. Further, approximate formulae in exponential forms are given, which hold within an error of about 2% for conventional electrode geometry. Finally, the validity of the approximate procedure, which has been used previously to obtain the kinetic collection efficiencies for fast homogeneous reactions, is discussed in comparison with the present theory.  相似文献   
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Treatment of a solution of excess PCl(3) and PS (PS = "proton sponge" = 1,8-dimethylamino naphthalene) with arachno-4-CB(8)H(14) (1) in CH(2)Cl(2), followed by hydrolysis of the reaction mixture, resulted in the isolation of the eleven-vertex diphosphacarbaborane nido-7,8,9-P(2)CB(8)H(10) (2) (yield 34%) as the main product. Other products isolated from this reaction were the phosphacarboranes nido-7,8,9,10-P(3)CB(7)H(8) (3) (yield 5%) and closo-2,1-PCB(8)H(9) (4) (yield 15%). Compound 2 can be deprotonated by PS in CH(2)Cl(2) or NaH in diethyl ether to give the [nido-7,8,9-P(2)CB(8)H(9)](-) (2(-)()) anion, which gives back the original compound, 2, upon re-protonation. Thermal rearrangement of anion 2(-) (Na(+) salt) at 350 degrees C for 2 h produced the isomeric [nido-7,8,10-P(2)CB(8)H(9)](-) (5(-)()) anion, which was isolated as a PPh(4)(+) salt (yield 86%). Multinuclear ((1)H, (11)B, (31)P, and (13)C), two-dimensional [(11)B-(11)B] COSY, (1)H{(11)B(selective)}, (1)H{(31)P(selective)}, and gradient-enhanced ([(1)H-(13)C] HSQC) magnetic resonance measurements led to complete assignments of all resonances which are in excellent agreement with the structures proposed. Coupling constants, (1)J((31)P,(13)C), (2)J((31)P,C,(1)H), and (1)J((31)P,(31)P), were calculated using the DFT method B3LYP/6-311+G(d,p). The molecular geometries of all compounds were optimized ab initio at a correlated level of theory (RMP2(fc)) using the 6-31G basis set, and their correctness was assessed by comparison of the experimental (11)B and (13)C chemical shifts with those calculated by the GIAO-SCF/II//RMP2(fc)/6-31G method. The computations also include the structures and chemical shieldings of the still unknown isomers [nido-7,10,8-P(2)CB(8)H(9)](-) (6(-)) and [nido-7,9,8-P(2)CB(8)H(9)](-) (7(-)).  相似文献   
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The 2,2'-azobis(isobutyronitrile)(AIBN)-induced autoxidation of gamma-terpinene (TH) at 50 degrees C produces p-cymene and hydrogen peroxide in a radical-chain reaction having HOO* as one of the chain-carrying radicals. The kinetics of this reaction in cyclohexane and tert-butyl alcohol show that chain termination involves the formal HOO. + HOO. self-reaction over a wide range of gamma-terpinene, AIBN, and O2 concentrations. However, in acetonitrile this termination process is accompanied by termination via the cross-reaction of the terpinenyl radical, T., with the HOO. radical under conditions of relatively high [TH] (140-1000 mM) and low [O2] (2.0-5.5 mM). This is because the formal HOO. + HOO. reaction is comparatively slow in acetonitrile (2k approximately 8 x 10(7) M(-1) s(-1)), whereas, this reaction is almost diffusion-controlled in tert-butyl alcohol and cyclohexane, 2k approximately 6.5 x 10(8) and 1.3 x 10(9) M(-1) s(-1), respectively. Three mechanisms for the bimolecular self-reaction of HOO. radicals are considered: 1) a head-to-tail hydrogen-atom transfer from one radical to the other, 2) a head-to-head reaction to form an intermediate tetroxide, and 3) an electron-transfer between HOO. and its conjugate base, the superoxide radical anion, O2-.. The rate constant for reaction by mechanism (1) is shown to be dependent on the hydrogen bond (HB) accepting ability of the solvent; that by mechanism (2) is shown to be too slow for this process to be of any importance; and that by mechanism (3) is dependent on the pH of the solvent and its ability to support ionization. Mechanism (3) was found to be the main termination process in tert-butyl alcohol and acetonitrile. In the gas phase, the rate constant for the HOO. + HOO. reaction (mechanism (1)) is about 1.8 x 10(9) M(-1) s(-1) but in water at pH< or =2 where the ionization of HOO. is completely suppressed, this rate constant is only 8.6 x 10(5) M(-1) s(-1). The very large retarding effect of water on this reaction has not previously been explained. We find that it can be quantitatively accounted for by using Abraham's HB acceptor parameter, beta(2)(H), for water of 0.38 and an estimated HB donor parameter, alpha(2)(H), for HOO. of about 0.87. These Abraham parameters allow us to predict a rate constant for the HOO. + HOO. reaction in water at 25 degrees C of 1.2 x 10(6) M(-1) s(-1) in excellent agreement with experiment.  相似文献   
39.
The paper reports a study on the intercalation mechanism of NH2(CH2) n NH2 (withn=2, 4, 6, 8, 10) diamines in layered Zr(HOPO3)2·H2O, performed by titrating the host with aqueous solutions of amines at 80°C. The intercalation reactions occur stepwise according to the ‘moving boundary’ model, with the formation of a number of intermediate intercalation compounds of formula Zr(HOPO3)2·xNH2(CH2) n NH2 (0<x<1) before obtaining the fully intercalated ones (x=1). For each diamine the batch titration curve and a diagram of the phases involved in the interaclation reaction are reported. Twenty-two intercalation compounds have been isolated and characterized by their composition, XRD patterns and thermal behaviour, and information on the disposition of the guests within the interlayer region have been derived. At full intercalation the diamines form a monolayer of extended molecules with their axis inclined at 58° to the plane of the sheet. The terminal amino groups are protonated by the —POH groups of the host, thus each diamine binds adjacent layers and, in a sense, transforms a layered structure into a framework structure that may have an accessible or potentially accessible porosity. The intercalation compound Zr(HOPO3)2·0.5NH2(CH2)8NH2 is indeed able to include polar molecules such as water and short chain alkanols.  相似文献   
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The electronic absorption spectra of Ni, Zn and Mg hemiporphyrazine derivatives are presented and discussed together with theoretical results obtained by INDO/S computations. The absorption spectra of all the metal derivatives show marked red shifts of the lowest energy absorption bands with respect to those of the metal free hemiporphyrazine. The possible explanation that in metal derivatives low lying excited states with a fully conjugated π electron system are present is supported by theoretical computations.  相似文献   
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