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1.
Francesca?PelosiEmail author Rida?T.?Farouki Carla?Manni Alessandra?Sestini 《Advances in Computational Mathematics》2005,22(4):325-352
It is shown that, depending upon the orientation of the end tangents t0,t1 relative to the end point displacement vector p=p1–p0, the problem of G1 Hermite interpolation by PH cubic segments may admit zero, one, or two distinct solutions. For cases where two interpolants exist, the bending energy may be used to select among them. In cases where no solution exists, we determine the minimal adjustment of one end tangent that permits a spatial PH cubic Hermite interpolant. The problem of assigning tangents to a sequence of points p0,...,pn in R3, compatible with a G1 piecewise-PH-cubic spline interpolating those points, is also briefly addressed. The performance of these methods, in terms of overall smoothness and shape-preservation properties of the resulting curves, is illustrated by a selection of computed examples. 相似文献
2.
3.
We introduce a general method in order to construct the nonchiral fusion rules which determine the operator content of the operator product algebra for rational conformal field theories. We are particularly interested in the models of the complementary D-like solutions of the modular invariant partition functions with cyclic center Z
N
. We find that the nonchiral fusion rules have a Z
N
-grading structure. 相似文献
4.
In this paper, numerical solutions of a reaction-diffusion chemotactic model of fractional orders for bacterial growth will
be present. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. We
compare the experimental result obtained with those obtained by simulation of the chemotactic model without fractional derivatives.
The results show that the solution continuously depends on the time-fractional derivative. The resulting solutions spread
faster than the classical solutions and may exhibit asymmetry, depending on the fractional derivative used. We present results
of numerical simulations to illustrate the method, and investigate properties of numerical solutions. The Adomian’s decomposition
method (ADM) is used to find the approximate solution of fractional ‘reaction-diffusion chemotactic model. Numerical results
show that the approach is easy to implement and accurate when applied to partial differential equations of fractional order. 相似文献
5.
The authors consider a model of ferromagnetic material subject to an electric current, and prove the local in time existence of very regular solutions for this model in the scale of Hk spaces. In particular, they describe in detail the compatibility conditions at the boundary for the initial data. 相似文献
6.
An adapted orthonormal frame (f1(ξ),f2(ξ),f3(ξ)) on a space curve r(ξ), ξ ∈ [ 0, 1 ] comprises the curve tangent \(\mathbf {f}_{1}(\xi ) =\mathbf {r}^{\prime }(\xi )/|\mathbf {r}^{\prime }(\xi )|\) and two unit vectors f2(ξ),f3(ξ) that span the normal plane. The variation of this frame is specified by its angular velocity Ω = Ω1f1 + Ω2f2 + Ω3f3, and the twist of the framed curve is the integral of the component Ω1 with respect to arc length. A minimal twist frame (MTF) has the least possible twist value, subject to prescribed initial and final orientations f2(0),f3(0) and f2(1),f3(1) of the normal–plane vectors. Employing the Euler–Rodrigues frame (ERF) — a rational adapted frame defined on spatial Pythagorean–hodograph curves — as an intermediary, an exact expression for an MTF with Ω1 = constant is derived. However, since this involves rather complicated transcendental terms, a construction of rational MTFs is proposed by the imposition of a rational rotation on the ERF normal–plane vectors. For spatial PH quintics, it is shown that rational MTFs compatible with the boundary conditions can be constructed, with only modest deviations of Ω1 about the mean value, by a rational quartic normal–plane rotation of the ERF. If necessary, subdivision methods can be invoked to ensure that the rational MTF is free of inflections, or to more accurately approximate a constant Ω1. The procedure is summarized by an algorithm outline, and illustrated by a representative selection of computed examples. 相似文献
7.
8.
In this paper, the Adomian’s decomposition method has been developed to yield approximate solution of the reaction-diffusion
model of fractional order which describe the evolution of the bacterium Bacillus subtilis, which grows on the surface of thin
agar plates. The fractional derivatives are described in the Caputo sense. The method introduces a promising tool for solving
many linear and nonlinear fractional differential equations. In these schemes, the solution takes the form of a convergent
series with easily computable components. Numerical results show that the approach is easy to implement and accurate when
applied to partial differential equations of fractional order. 相似文献
9.
Muhammad Imran Din Rida Khalid Fiza Akbar Ghazia Ahmad Jawayria Najeeb Zaib Un Nisa Hussain 《Soft Materials》2018,16(3):228-247
Hydrogels, having nanomaterials (e.g. nanoparticles and nanorods) incorporated inside their polymeric meshes, are generally called hybrid gels/hydrogels. These assemblies combine the properties of both hydrogels and nanomaterials in one system. These responsive hybrid hydrogels, particularly polymerized N-isopropylacrylamide (PoNip) polymeric gels, have been extensively exploited for various multi-disciplinary applications in the literature over the past two decades because of their unique and exquisite particulars. Next generation assemblies have been prepared by using the smart nature of these gels toward the general incentives (e.g. temperature, ionic strength, and pH) in the fields of nanocatalysis, water purification, drug delivery, photonics, and optics. This review presents an overview of the PoNip hybrid assemblies engineered over the past 7 years i.e. 2010–2016 and extensively discusses the interaction of the incorporated nanomaterial with the polymeric chains of the hydrogels as it is the most significant factor which makes these assemblies attractive for all the associated applications. Moreover, this article also describes the preparative routes, properties, classification, and applications of these hybrid hydrogels in the fields of medicine, environment, catalysis, and nanotechnology. 相似文献
10.
Algorithms are developed, based on topological principles, to evaluate the boundary and “internal structure” of the Minkowski sum of two planar curves. A graph isotopic to the envelope curve is constructed by computing its characteristic points. The edges of this graph are in one-to-one correspondence with a set of monotone envelope segments. A simple formula allows a degree to be assigned to each face defined by the graph, indicating the number of times its points are covered by the Minkowski sum. The boundary can then be identified with the set of edges that separate faces of zero and non-zero degree, and the boundary segments corresponding to these edges can be approximated to any desired geometrical accuracy. For applications that require only the Minkowski sum boundary, the algorithm minimizes geometrical computations on the “internal” envelope edges, that do not contribute to the final boundary. In other applications, this internal structure is of interest, and the algorithm provides comprehensive information on the covering degree for different regions within the Minkowski sum. Extensions of the algorithm to the computation of Minkowski sums in R3, and other forms of geometrical convolution, are briefly discussed. 相似文献