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41.
Radial basis function (RBF)‐based parametric models for closed and open curves within the method of regularized stokeslets 下载免费PDF全文
The method of regularized Stokeslets (MRS) is a numerical approach using regularized fundamental solutions to compute the flow due to an object in a viscous fluid where inertial effects can be neglected. The elastic object is represented as a Lagrangian structure, exerting point forces on the fluid. The forces on the structure are often determined by a bending or tension model, previously calculated using finite difference approximations. In this paper, we study spherical basis function (SBF), radial basis function (RBF), and Lagrange–Chebyshev parametric models to represent and calculate forces on elastic structures that can be represented by an open curve, motivated by the study of cilia and flagella. The evaluation error for static open curves for the different interpolants, as well as errors for calculating normals and second derivatives using different types of clustered parametric nodes, is given for the case of an open planar curve. We determine that SBF and RBF interpolants built on clustered nodes are competitive with Lagrange–Chebyshev interpolants for modeling twice‐differentiable open planar curves. We propose using SBF and RBF parametric models within the MRS for evaluating and updating the elastic structure. Results for open and closed elastic structures immersed in a 2D fluid are presented, showing the efficacy of the RBF–Stokeslets method. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
42.
We define a new statistic on the even hyperoctahedral groups which is a natural analogue of the odd length statistic recently defined and studied on Coxeter groups of types and . We compute the signed (by length) generating function of this statistic over the whole group and over its maximal and some other quotients and show that it always factors nicely. We also present some conjectures. 相似文献
43.
《Mathematische Nachrichten》2017,290(17-18):2759-2774
Here we give a new approach to the Paley–Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of polar‐analytic function in the Mellin setting and Mellin–Bernstein spaces. A notion of Hardy spaces in the Mellin setting is also given along with applications to exponential sampling formulas of optical physics. 相似文献
44.
《Mathematische Nachrichten》2017,290(14-15):2259-2279
In this paper we continue the study of important Banach spaces of slice hyperholomorphic functions on the quaternionic unit ball by investigating the BMO‐ and VMO‐spaces of slice hyperholomorphic functions. We discuss in particular conformal invariance and a refined characterization of these spaces in terms of Carleson measures. Finally we show the relations with the Bloch and Dirichlet space and the duality relation with the Hardy space . The importance of these spaces in the classical theory is well known. It is therefore worthwhile to study their slice hyperholomorphic counterparts, in particular because slice hyperholomorphic functions were found to have several applications in operator theory and Schur analysis. 相似文献
45.
《Mathematische Nachrichten》2017,290(4):507-519
We show a picture of the relations among different types of summability of series in the space of integrable functions with respect to a vector measure m of relatively norm compact range. In order to do that, we study the class of the so‐called m‐1‐summing operators. We give several applications regarding the existence of copies of c 0 in , as well as on m‐1‐summing operators which are weakly compact, Asplund or weakly precompact. 相似文献
46.
《Mathematische Nachrichten》2017,290(1):19-36
Given and a Young function η, we consider the generalized fractional maximal operator defined by where the supremum is taken over every ball B contained in . In this article, we give necessary and sufficient Dini type conditions on the functions , and η such that is bounded from the Orlicz space into the Orlicz space . We also present a version of this result for open subsets of with finite measure. Both results generalize those contained in 6 and 14 when , respectively. As a consequence, we obtain a characterization of the functions involved in the boundedness of the higher order commutators of the fractional integral operator with BMO symbols. Moreover, we give sufficient conditions that guarantee the continuity in Orlicz spaces of a large class of fractional integral operators of convolution type with less regular kernels and their commutators, which are controlled by . 相似文献
47.
We present an abstract characterization of various types of Menger algebras of n-place functions allowing certain permutations of variables. 相似文献
48.
M. Ferreira M. M. Rodrigues N. Vieira 《Mathematical Methods in the Applied Sciences》2017,40(18):7033-7050
In this work, we obtain the fundamental solution (FS) of the multidimensional time‐fractional telegraph Dirac operator where the 2 time‐fractional derivatives of orders α∈]0,1] and β∈]1,2] are in the Caputo sense. Explicit integral and series representation of the FS are obtained for any dimension. We present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameters α and β. Finally, using the FS, we study some Poisson and Cauchy problems. 相似文献
49.
In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
50.