共查询到20条相似文献,搜索用时 15 毫秒
1.
Ekiel-Jezewska ML; Wajnryb E 《The Quarterly Journal of Mechanics and Applied Mathematics》2006,59(4):563-585
An example system is studied to discuss precision of the multipoleexpansion, applied to determine forces exerted on particlesby a viscous low-Reynolds-number fluid flow. A single spherein an ambient flow (pure shear, quadratic, and modulated shear)parallel to a close plane wall is considered. Forces and torquesexerted by the ambient flow on a motionless sphere are evaluated.Their precision is determined and related to a multipole orderof the truncation. Similar analysis is performed for a movingsphere with no ambient flow and for a freely moving sphere.Relative motion of the sphere with respect to the wall givesrise to strong lubrication interactions. It is analysed howthese interactions affect accuracy of the pure multipole expansion,and what are the smallest distances where it becomes insufficient.An alternative precise method is applied, in which lubricationexpressions are subtracted from the hydrodynamic forces andtorques, and the residue is evaluated as a fast-convergent seriesof inverse powers of the distance between the sphere centreand the wall. The accuracy of this procedure is carefully analysed. 相似文献
2.
《Operations Research Letters》2023,51(1):67-71
Let us consider a network flow respecting arc capacities and flow conservation constraints. The flow degree of a node is sum of the flow entering and leaving it. We study the problem of determining a flow that minimizes the maximum flow degree of a node. We show how to solve it in strongly polynomial time with linear programming. 相似文献
3.
Wolfgang A. Halang 《Numerical Functional Analysis & Optimization》2013,34(7-8):725-742
The existence of minimum norm properties for even degree polynomial splines, analogous to the. ones known for odd degree splines, is investigated within the framework of the theory of topological spline systems. It is shown that such properties cannot exist for even degree splines interpolating functions halfway between the partition points. For another class of even degree spline functions, however, which hterpolate the local integrals of given functions with respect to the partitions, the seeked minimum norm properties can be proved. This is carried out by first investigating a generalized problem within the theory of spline systems and then deriving corresponding conclusions. As a corollary the existence of spline systems with respect to differential operators of fractional degree is obtained. 相似文献
4.
5.
A global recursive bisection algorithm is described for computing the complex zeros of a polynomial. It has complexityO(n
3
p) wheren is the degree of the polynomial andp the bit precision requirement. Ifn processors are available, it can be realized in parallel with complexityO(n
2
p); also it can be implemented using exact arithmetic. A combined Wilf-Hansen algorithm is suggested for reduction in complexity. 相似文献
6.
Hong-Wei Xu 《Archiv der Mathematik》1993,61(5):489-496
7.
Stéphane Vénéreau 《Mathematische Annalen》2011,349(3):589-597
We give a simpler proof as well as a generalization of the main result of an article of Shestakov and Umirbaev. This latter article being the first of two that solve a long-standing conjecture about the non-tameness, or “wildness”, of Nagata’s automorphism. As corollaries we get interesting informations about the leading terms of polynomials forming an automorphism of K[x 1, . . . , x n ] and reprove the tameness of automorphisms of K[x 1, x 2]. 相似文献
8.
9.
We study the unsteady rotary motion of a sphere immersed in a Stokes fluid. The equation of motion for the sphere leads to
an integro-differential equation, and we are interested in the asymptotic behavior in time of the solution. Preparing initially
the system (sphere + fluid) as a stationary state, we prove that the angular velocity of the sphere slows down with a law
t
−3/2 if no other forces than the one exerted by the fluid act on the sphere, while if the sphere is subject also to an elastic
torque the asymptotic behavior of the angular position of the sphere is t
−γ
, with γ = 5/2 if the initial angular velocity is zero, γ = 3/2 otherwise. This behavior is due to the memory effect of the surrounding fluid. We discuss briefly other initial preparations
of the system. 相似文献
10.
We study two instances of polynomial optimization problem over a single sphere. The first problem is to compute the best rank-1 tensor approximation. We show the equivalence between two recent semidefinite relaxations methods. The other one arises from Bose-Einstein condensates (BEC), whose objective function is a summation of a probably nonconvex quadratic function and a quartic term. These two polynomial optimization problems are closely connected since the BEC problem can be viewed as a structured fourth-order best rank-1 tensor approximation. We show that the BEC problem is NP-hard and propose a semidefinite relaxation with both deterministic and randomized rounding procedures. Explicit approximation ratios for these rounding procedures are presented. The performance of these semidefinite relaxations are illustrated on a few preliminary numerical experiments. 相似文献
11.
《中国科学 数学(英文版)》2021,(6)
We define the second discriminant D_2 of a univariate polynomial f of degree greater than 2 as the product of the linear forms 2r_k-r_i-r_j for all triples of roots r_i, r_k, r_j of f with ij and j≠k, k≠i.D_2 vanishes if and only if f has at least one root which is equal to the average of two other roots. We show that D_2 can be expressed as the resultant of f and a determinant formed with the derivatives of f, establishing a new relation between the roots and the coefficients of f. We prove several notable properties and present an application of D_2. 相似文献
12.
Girishwar Nath 《Proceedings Mathematical Sciences》1964,60(6):396-415
The effects of dissociation or ionization of air on the analytical solution for hypersonic flow past a sphere are considered here, under certain assumptions. It has been assumed that the shock wave is in the shape of a sphere, that the density ratio across the shock is constant, that the flow behind the shock is at constant density and that dissociation or ionization only occurs behind the shock wave. Thus the effects of the compressibility of the air, variation of density ratio along the shock, and the department of the shock shape from being circular are not taken into account. Here the velocity, pressure, temperature, pressure coefficient and vorticity, etc., at any point between the shock and the surface of the sphere in the presence of dissociation or ionization are obtained. In addition, shock detachment distance, drag coefficient, stagnation point velocity gradient and sonic points on the shock and the surface have also been obtained. The results have been compared with the corresponding results obtained in the case when dissociation or ionization does not occur behind the shock. 相似文献
13.
We show that every sufficiently high dimensional Euclidean sphere admits an odd dimensional Riemannian submanifold M having the properties: (1) M is a homogeneous submanifold with nonzero parallel mean curvature vector in the ambient sphere; (2) M is a Berger sphere; (3) M is a Sasakian space form of constant ${\phi}$ -sectional curvature. Note that our manifold M is diffeomorphic but not isometric to a Euclidean sphere. 相似文献
14.
P. Maroni 《Advances in Computational Mathematics》1995,3(1-2):59-88
We are dealing with orthogonal sequences with respect to forms verifying a second degreee equation, i.e. that its formal Stieltjes functionS(u)(z) satisfies a quadratic equation of the formB(z)S 2(u)(z)+C(z)S(u)(z)+D(z)=0, whereB, C, D are polynomials. Various algebraic properties are given, especially those concerning the quasi-orthogonality of associated sequences. A classification is outlined. Some examples are quoted. In particular, we give the representation of Tchebychev co-recursive forms for any complex value of the parameter. 相似文献
15.
P. Maroni 《Advances in Computational Mathematics》1995,3(1):59-88
We are dealing with orthogonal sequences with respect to forms verifying a second degreee equation, i.e. that its formal Stieltjes
functionS(u)(z) satisfies a quadratic equation of the formB(z)S
2(u)(z)+C(z)S(u)(z)+D(z)=0, whereB, C, D are polynomials. Various algebraic properties are given, especially those concerning the quasi-orthogonality of associated
sequences.
A classification is outlined. Some examples are quoted. In particular, we give the representation of Tchebychev co-recursive
forms for any complex value of the parameter. 相似文献
16.
17.
J. Monterde 《Advances in Computational Mathematics》2009,30(1):61-78
We give a full characterization of helical polynomial curves of any degree and a simple way to construct them. Existing results
about Hermite interpolation are revisited. A simple method to select the best quintic interpolant among all possible solutions
is suggested.
相似文献
18.
Heidi Haynal 《Journal of Algebra》2008,319(10):4199-4221
19.
M. Emin Erdogan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1970,21(3):485-490
Résumé Dans le présent travail on étudie les mouvements stationnaires lents d'un fluide visqueux en présence d'une sphère poreuse. Les mouvements considérés sont l'écoulement en présence d'une sphère poreuse dans une translation uniforme, dans une rotation uniforme, et dans un mouvement de déformation pure. On donne aussi une expression pour la viscosité de suspension des sphères poreuses. Elle montre que la viscosité de suspension des sphères poreuses est plus petite que celle des sphères rigides. 相似文献
20.
Let M n be an n-dimensional closed submanifold of a sphere with parallel normalized mean curvature vector. Denote by S and H the squared norm of the second fundamental form and the mean curvature of M n , respectively. Assume that the fundamental group \({\pi_{1}(M^{n})}\) of M n is infinite and \({S\, \leqslant\, S(H)=n+\frac{n^{3}H^{2}}{2(n-1)}-\frac{n(n-2)H}{2(n-1)}\sqrt{n^{2}H^{2}+4(n-1)}}\), then S is constant, S = S(H), and M n is isometric to a Clifford torus \({S^{1}(\sqrt{1-r^{2}})\times S^{n-1}(r)}\) with \({r^{2}\leqslant \frac{n-1}{n}}\). 相似文献