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61.
H. Beiro da Veiga 《Mathematical Methods in the Applied Sciences》1995,18(4):295-306
We consider the equations of motion to slightly compressible fluids and we prove that solutions converge, in the strong norm, to the solution of the equations of motion of incompressible fluids, as the Mach number goes to zero. From a physical point of view this means the following. Assume that we are dealing with a well-specified fluid, so slightly compressible that we assume it to be incompressible. Our result means that the distance between the (continuous) trajectories of the real and of the idealized solution is ‘small’ with respect to the natural metric, i.e. the metric that endows the data space. 相似文献
62.
63.
H. Beirão da Veiga 《Journal of Mathematical Fluid Mechanics》2014,16(3):539-550
In this notes we consider the stationary Stokes system in a bounded, connected, three-dimensional smooth domain, with homogeneous Dirichlet boundary condition. Proofs also apply to the n-dimensional case, and to other boundary conditions, like Navier-slip ones. We say here that a solution is classical if all derivatives appearing in the equations are continuous up to the boundary. It is well known, for long time, that solutions of the Stokes system are classical if the external forces belong to the H?lder space \({C^{0,\; \lambda}(\bar{\Omega})}\) . It is also well known that, in general, solutions are not classical in the presence of continuous external forces. Hence, a very challenging problem is to find Banach spaces, strictly containing the H?lder spaces \({C^{0,\; \lambda}(\bar{\Omega})}\) such that solutions to the Stokes problem corresponding to forces in the above space are classical. We prove this result for external forces in a suitable functional space, denoted \({{\rm C}_*(\bar{\Omega})}\) , introduced in references Beirão da Veiga (On the solutions in the large of the two-dimensional flow of a non-viscous incompressible fluid, 1982) and Beirão da Veiga (J Differ Equ 54(3):373–389, 1984) in connection with the Euler equations. 相似文献
64.
Hugo Beir?o da Veiga Petr Kaplicky Michael R??i?ka 《Journal of Mathematical Fluid Mechanics》2011,13(3):387-404
This article is concerned with the global regularity of weak solutions to systems describing the flow of shear thickening
fluids under the homogeneous Dirichlet boundary condition. The extra stress tensor is given by a power law ansatz with shear
exponent p≥ 2. We show that, if the data of the problem are smooth enough, the solution u of the steady generalized Stokes problem belongs to W1,(np+2-p)/(n-2)(W){W^{1,(np+2-p)/(n-2)}(\Omega)} . We use the method of tangential translations and reconstruct the regularity in the normal direction from the system, together
with anisotropic embedding theorem. Corresponding results for the steady and unsteady generalized Navier–Stokes problem are
also formulated. 相似文献
65.
L. C. Rodrigues M. M. Silva H. I. M. Veiga J. M. S. S. Esperança M. Costa M. J. Smith 《Journal of Solid State Electrochemistry》2012,16(4):1623-1629
In this paper, the preparation and purification of an amorphous polymer network, poly[oxymethylene-oligo(oxyethylene)], designated
as aPEO, are described. The flexible CH2CH2O segments in this host polymer combine appropriate mechanical properties, over a critical temperature range from −20 to 60 °C,
with labile salt-host interactions. The intensity of these interactions is sufficient to permit solubilisation of the guest
salt in the host polymer while permitting adequate mobility of ionic guest species. We also report the preparation and characterisation
of a novel polymer electrolyte based on this host polymer with lithium tetrafluoroborate, LiBF4, as guest salt. Electrolyte samples are thermally stable up to approximately 250 °C and completely amorphous above room temperature.
The electrolyte composition determines the glass transition temperature of electrolytes and was found to vary between −50.8
and −62.4 °C. The electrolyte composition that supports the maximum room temperature conductivity of this electrolyte system
is n = 5 (2.10 × 10−5 S cm−1 at 25 °C). The electrochemical stability domain of the sample with n = 5 spans about 5 V measured against a Li/Li+ reference. This new electrolyte system represents a promising alternative to LiCF3SO3 and LiClO4-doped PEO analogues. 相似文献
66.
The perovskite-type manganites LaMn1−xZnxO3 (0.05x0.40), synthesized by the liquid-mix technique, show orthorhombic symmetry (S.G. Pbnm) as shown by the Rietveld analysis from X-ray diffraction data. Mn and Zn cations occupy the octahedral sites of the perovskite structure and are placed at random. The variation of magnetic susceptibility with temperature show a complex behaviour that can be understood in terms of spin-glass: frustration and competition of both antiferro- and ferromagnetic interactions. This behaviour has been confirmed from a.c. susceptibility data. Resistivity measurements show semiconductor behaviour in all cases with activations energies of about 0.2 eV. Magnetocaloric effect of these perovskites has been studied and a ΔSmax of about 0.12 J kg−1 K−1 was obtained for the x=0.05 sample at 120 K for a field up to 1 T. Finally, no magnetoresistance response was found. 相似文献
67.
Michael O’Carroll Paulo A. Faria da Veiga Antônio Francisco Neto 《Communications in Mathematical Physics》2013,321(1):249-282
We consider a lattice SU(3) QCD model in 2 + 1 dimensions, with two flavors and 2 × 2 spin matrices. An imaginary time functional integral formulation with Wilson’s action is used in the strong coupling regime, i.e. small hopping parameter ${0 < \kappa \ll 1}$ , and much smaller plaquette coupling ${\beta, 0 < \beta \ll \kappa}$ . In this regime, it is known that the low-lying energy-momentum spectrum contains isolated dispersion curves identified with baryons and mesons with asymptotic masses ${m\approx-3\ln\kappa}$ and ${m_m\approx-2\ln\kappa}$ , respectively. We prove the existence of two (labelled by ±) two-baryon bound states for each of the total isospin sectors I = 0,1 and we obtain, in each case, the exact binding energies ${\epsilon_{I\,\pm} }$ (of order ${\kappa^2}$ ) which extend to jointly analytic function in ${\kappa}$ and β. We also prove that these points are the only mass spectrum up to slightly above the bound state masses. Precisely, we show, for ${\alpha_0=\frac 14, \alpha_1=\frac 1{12}, \alpha_2=\frac12, \alpha_3=\frac 34}$ and small ${\delta >0 }$ , that the bound state masses ${2m-\epsilon_{I\,\pm}}$ are the only points in the mass spectrum in ${(0,2m-\epsilon_{I\,\pm}+\delta \alpha_I\kappa^2)}$ , for I = 0,1, and in ${(0,2m-(1+\delta)\alpha_I\kappa^2)}$ , for I = 2,3. These results are exact and validate our previous results obtained in a ladder approximation. The method employs suitable two- and four-point correlations with spectral representations and a lattice Bethe-Salpeter equation. For I = 0,1, a quark, antiquark space-range one potential of order ${\kappa^2}$ is found to be the dominant contribution to the two-baryon interaction and the interaction of the individual quark isospins of one baryon with those of the other is described by permanents. A novel spectral free decomposition (but spectral representation motivated, for real κ and β) of the two-point correlation, after performing a complex extension, is a key ingredient in showing the joint analyticity of the binding energy. 相似文献
68.
Lourenço Beirão da Veiga David Mora Rodolfo Rodríguez 《Numerical Methods for Partial Differential Equations》2013,29(1):40-63
This article deals with the approximation of the bending of a clamped plate, modeled by Reissner‐Mindlin equations. It is known that standard finite element methods applied to this model lead to wrong results when the thickness t is small. Here, we propose a mixed formulation based on the Hellinger‐Reissner principle which is written in terms of the bending moments, the shear stress, the rotations and the transverse displacement. To prove that the resulting variational formulation is well posed, we use the Babu?ka‐Brezzi theory with appropriate t ‐dependent norms. The problem is discretized by standard mixed finite elements without the need of any reduction operator. Error estimates are proved. These estimates have an optimal dependence on the mesh size h and a mild dependence on the plate thickness t. This allows us to conclude that the method is locking‐free. The proposed method yields direct approximation of the bending moments and the shear stress. A local postprocessing leading to H1 ‐type approximations of transverse displacement and rotations is introduced. Moreover, we propose a hybridization procedure, which leads to solving a significantly smaller positive definite system. Finally, we report numerical experiments which allow us to assess the performance of the method. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
69.
We prove second-order convergence of the conservative variable and its flux in the high-order MFD method. The convergence
results are proved for unstructured polyhedral meshes and full tensor diffusion coefficients. For the case of non-constant
coefficients, we also develop a new family of high-order MFD methods. Theoretical result are confirmed through numerical experiments. 相似文献
70.
H. Beirão da Veiga 《Journal of Mathematical Fluid Mechanics》2009,11(2):258-273
In this paper we consider a class of stationary Navier–Stokes equations with shear dependent viscosity, in the shear thinning
case p < 2, under a non-slip boundary condition. We are interested in global (i.e., up to the boundary) regularity results, in dimension n = 3, for the second order derivatives of the velocity and the first order derivatives of the pressure. As far as we know,
there are no previous global regularity results for the second order derivatives of the solution to the above boundary value
problem.
We consider a cubic domain and impose the non-slip boundary condition only on two opposite faces. On the other faces we assume
periodicity, as a device to avoid effective boundary conditions. This choice is made so that we work in a bounded domain Ω
and simultaneously with a flat boundary. The extension to non-flat boundaries is done in the forthcoming paper [7], by following
ideas introduced by the author, for the case p > 2, in reference [5]. The results also hold in the presence of the classical convective term, provided that p is sufficiently close to the value 2.
相似文献