共查询到20条相似文献,搜索用时 31 毫秒
1.
We examine existence and stability of relative equilibria of the n-vortex problem specialized to the case where N vortices have small and equal circulation and one vortex has large circulation. As the small circulation tends to zero, the
weak vortices tend to a circle centered on the strong vortex. A special potential function of this limiting problem can be
used to characterize orbits and stability. Whenever a critical point of this function is nondegenerate, we prove that the
orbit can be continued via the Implicit Function Theorem, and its linear stability is determined by the eigenvalues of the
Hessian matrix of the potential. For N≥3 there are at least three distinct families of critical points associated to the limiting problem. Assuming nondegeneracy,
one of these families continues to a linearly stable class of relative equilibria with small and large circulation of the
same sign. This class becomes unstable as the small circulation passes through zero and changes sign. Another family of critical
points which is always nondegenerate continues to a configuration with small vortices arranged in an N-gon about the strong central vortex. This class of relative equilibria is linearly unstable regardless of the sign of the
small circulation when N≥4. Numerical results suggest that the third family of critical points of the limiting problem also continues to a linearly
unstable class of solutions of the full problem independent of the sign of the small circulation. Thus there is evidence that
linearly stable relative equilibria exist when the large and small circulation strengths are of the same sign, but that no
such solutions exist when they have opposite signs. The results of this paper are in contrast to those of the analogous celestial
mechanics problem, for which the N-gon is the only relative equilibrium for N sufficiently large, and is linearly stable if and only if N≥7. 相似文献
2.
We study an N -vortex problem having J of them forming a cluster, which means the distances between the vortices in the cluster is much smaller by O (ε) than the distances, O (ℓ), to the N – J vortices outside of the cluster. With the strengths of N vortices being of the same order, the velocity and time scales for the motion of the J vortices relative to those of the N – J vortices are O (ε–1) and O (ε2) respectively. We show that this two-time and two-length scale problem can be converted to a standard two-time scale problem and then the leading order solution of the N -vortex problem can be uncoupled to two problems, one for the motion of J vortices in the cluster relative to the center of the cluster and one for the motion of the N – J vortex plus the center of the cluster. For N = 3 and J = 2, the 3-vortex problem is uncoupled to two binary vortices problems in the length scales ℓ and ℓε respectively. When perturbed in the scale ℓ, say by a fourth vortex even of finite strength, the binary problem becomes a 3-vortex problem, admitting periodic solutions. Since 3-vortex problems are solvable, the uncoupling enables us to solve 3-cluster problems having at most three vortices in each cluster. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
Bjrn Bttcher 《Mathematische Nachrichten》2005,278(11):1235-1241
We use the method proposed by H. Kumano‐go in the classical case to construct a parametrix of the equation + q (x, D )u = 0 where q (x, D ) is a pseudo‐differential operator with symbol in the class introduced by W. Hoh. In case where –q (x, D ) extends to a generator of a Feller semigroup our construction yields an approximation for the transition densities of the corresponding Markov process. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
In the reduced phase space by rotation, we prove the existence of periodic orbits of the n-vortex problem emanating from a relative equilibrium formed by n unit vortices at the vertices of a regular polygon, both in the plane and at a fixed latitude when the ideal fluid moves on the surface of a sphere. In the case of a plane we also prove the existence of such periodic orbits in the (n + 1)-vortex problem, where an additional central vortex of intensity κ is added to the ring of the polygonal configuration. 相似文献
5.
Helmut Abels 《Mathematische Nachrichten》2006,279(4):351-367
In this paper we prove unique solvability of the generalized Stokes resolvent equations in an infinite layer Ω0 = ℝn –1 × (–1, 1), n ≥ 2, in Lq ‐Sobolev spaces, 1 < q < ∞, with slip boundary condition of on the “upper boundary” ∂Ω+0 = ℝn –1 × {1} and non‐slip boundary condition on the “lower boundary” ∂Ω–0 = ℝn –1 × {–1}. The solution operator to the Stokes system will be expressed with the aid of the solution operators of the Laplace resolvent equation and a Mikhlin multiplier operator acting on the boundary. The present result is the first step to establish an Lq ‐theory for the free boundary value problem studied by Beale [9] and Sylvester [22] in L 2‐spaces. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
Let n
q
(k, d) denote the smallest value of n for which there exists a linear [n, k, d]-code over GF(q). An [n, k, d]-code whose length is equal to n
q
(k, d) is called optimal. The problem of finding n
q
(k, d)has received much attention for the case q = 2. We generalize several results to the case of an arbitrary prime power q as well as introducing new results and a detailed methodology to enable the problem to be tackled over any finite field.In particular, we study the problem with q = 3 and determine n
3(k, d) for all d when k 4, and n
3(5, d) for all but 30 values of d. 相似文献
7.
Direct numerical simulation of transition and turbulence in compressible mixing layer 总被引:2,自引:0,他引:2
The three-dimensional compressible Navier-Stokes equations are approximated by a fifth order upwind compact and a sixth order
symmetrical compact difference relations combined with three-stage Ronge-Kutta method. The computed results are presented
for convective Mach numberMc = 0.8 andRe = 200 with initial data which have equal and opposite oblique waves. From the computed results we can see the variation of
coherent structures with time integration and full process of instability, formation of A -vortices, double horseshoe vortices
and mushroom structures. The large structures break into small and smaller vortex structures. Finally, the movement of small
structure becomes dominant, and flow field turns into turbulence. It is noted that production of small vortex structures is
combined with turning of symmetrical structures to unsymmetrical ones. It is shown in the present computation that the flow
field turns into turbulence directly from initial instability and there is not vortex pairing in process of transition. It
means that for large convective Mach number the transition mechanism for compressible mixing layer differs from that in incompressible
mixing layer. 相似文献
8.
In this paper we study the dynamics of properly discontinuous and crystallographic affine groups leaving a quadratic from
of signature (p, q) invariant. The main results are: (I) If p − q ≥ 2, then the linear part of the group is not Zariski dense in the corresponding orthogonal group. (II) If q = 2 and the group is crystallographic, then the group is virtually solvable. This proves the Auslander conjecture for this
case. 相似文献
9.
Doug Hensley 《Mathematische Nachrichten》1997,184(1):177-190
Given a finite field Fq of order q, a fixed polynomial g in –Fq[X] of positive degree, and two elements u and v in the ring of polynomials in R = Fq [X]/gFq[X], the question arises: How many pairs (a, 6) are there in R × R so that ab ? 1 mod g and so that a is close to u while b is close to v ? The answer is, about as many as one would expect. That is, there are no favored regions in R × R where inverse pairs cluster. The error term is quite sharp in most cases, being comparable to what would happen with random distribution of pairs. The proof uses Kloosterman sums and counting arguments. The exceptional cases involve fields of characteristic 2 and composite values of g. Even then the error term obtained is nontrivial. There is no computational evidence that inverses are in fact less evenly distributed in this case, however. 相似文献
10.
The best constant in a generalized complex Clarkson inequality is Cp,q (?) = max {21–1/p , 21/q , 21/q –1/p +1/2} which differs moderately from the best constant in the real case Cp,q (?) = max {21–1/p , 21/q ,Bp,q }, where . For 1 < q < 2 < p < ∞ the constant Cp,q (?) is equal to Bp,q and these numbers are difficult to calculate in general. As applications of the generalized Clarkson inequalities the (p, q)‐Clarkson inequalities in Lebesgue spaces, in mixed norm spaces and in normed spaces are presented. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
We study the bifurcation diagrams of (classical) positive solutions u with |u |∞ ∈ (0, ∞) of the p -Laplacian Dirichlet problem (φp (u ′(x)))′ + λfq (u (x))) = 0, –1 ≤ x ≤ 1, u (–1) = 0 = u (1), where p > 1, φp (y) = |y |p –2 y, (φp (u ′))′ is the one-dimensional p -Laplacian, λ > 0 is a bifurcation parameter, and the nonlinearity fq (u) = |1 – u |q is defined on [0, ∞) with constant q > 0. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
12.
A linear (qd, q, t)‐perfect hash family of size s consists of a vector space V of order qd over a field F of order q and a sequence ?1,…,?s of linear functions from V to F with the following property: for all t subsets X ? V, there exists i ∈ {1,·,s} such that ?i is injective when restricted to F. A linear (qd, q, t)‐perfect hash family of minimal size d( – 1) is said to be optimal. In this paper, we prove that optimal linear (q2, q, 4)‐perfect hash families exist only for q = 11 and for all prime powers q > 13 and we give constructions for these values of q. © 2004 Wiley Periodicals, Inc. J Comb Designs 12: 311–324, 2004 相似文献
13.
Shiro Iwasaki 《组合设计杂志》1997,5(2):95-110
Let p be an odd prime number such that p − 1 = 2em for some odd m and e ≥ 2. In this article, by using the special linear fractional group PSL(2, p), for each i, 1 ≤ i ≤ e, except particular cases, we construct a 2-design with parameters v = p + 1, k = (p − 1)/2i + 1 and λ = ((p − 1)/2i+1)(p − 1)/2 = k(p − 1)/2, and in the case i = e we show that some of these 2-designs are 3-designs. Likewise, by using the linear fractional group PGL(2,p) we construct an infinite family of 3-designs with the same v k and λ = k(k − 2). These supplement a part of [4], in which we gave an infinite family of 3-designs with parameters v = q + 1, k = (q + 1)/2 = (q − 1)/2 + 1 and λ = (q + 1)(q − 3)/8 = k(k − 2)/2, where q is a prime power such that q − 1 = 2m for some odd m and q > 7. Some of the designs given in this article and in [4] fill in a few blanks in the table of Chee, Colbourn, and Kreher [2]. © 1997 John Wiley & Sons, Inc. 相似文献
14.
The axisymmetric and stationary basic flow due to the unstable stratification in the lower region of a spherical annulus cooled from inside has already been investigated in some detail ([5], [4]). The same applies to the columnar cell flow regime of high Taylor numbers dominated by the force component perpendicular to the rotation axis ([2] and [3]). Yet the question of the initial mechanism of symmetry breaking at medium Taylor numbers has still not been investigated. Therefore the present paper investigates the onset of natural convection in a differentially heated wide spherical gap. The stability curves for radius ratio η = 0.4 and a silicon oil fluid with Pr = 39 are determined by varying Rayleigh and Taylor number. The m = 2 vortex is investigated in detail using quasi 3D Particle Image Velocimetry (PIV). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
Edward Spence 《组合设计杂志》1993,1(3):193-211
If a symmetric (41,16,6)-design has an automorphism σ of odd prime order q then q = 3 or 5. In the case q = 5 we determine all such designs and find a total of 419 nonisomorphic ones, of which 15 are self-dual. When q = 3 a combinatorial explosion occurs and the complete classification becomes impracticable. However, we give a characterization in the particular case when σ has order 3 and fixes 11 points, and find that there are 3,076 nonisomorphic designs with this property, all of them being non self-dual. The other remaining possibility is that σ, of order 3, fixes 5 points. In this case there are 960 orbit matrices (up to isomorphism and duality) and all but one of them yield designs. Here an incomplete investigation shows that in total there are at least 112,000 nonisomorphic designs. © 1993 John Wiley & Sons, Inc. 相似文献
16.
Meirong Zhang 《Mathematische Nachrichten》2005,278(15):1823-1836
Given a positive integer n and an exponent 1 ≤ α ≤ ∞. We will find explicitly the optimal bound rn such that if the Lα norm of a potential q (t ) satisfies ‖q ‖equation/tex2gif-inf-2.gif < rn then the n th Dirichlet eigenvalue of the onedimensional p ‐Laplacian with the potential q (t ): (|u ′|p –2 u ′)′ + (λ + q (t )) |u |p –2u = 0 (1 < p < ∞) will be positive. Using these bounds, we will construct, for the Dirichlet, the Neumann, the periodic or the antiperiodic boundary conditions, certain classes of potentials q (t ) so that the p ‐Laplacian with the potential q (t ) is non‐degenerate, which means that the above equation with λ = 0 has only the trivial solution verifying the corresponding boundary condition. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
Zhi Yuan HUANG Pei Yan LI Ying WU 《数学学报(英文版)》2008,24(2):201-214
The classical Levy-Meixner polynomials are distinguished through the special forms of their generating functions. In fact, they are completely determined by 4 parameters: c1, c2,γ and β. In this paper, for-1 〈q〈 1, we obtain a unified explicit form of q-deformed Levy-Meixner polynomials and their generating functions in term of c1, c2, γand β, which is shown to be a reasonable interpolation between classical case (q=1) and fermionic case (q=-1).In particular, when q=0 it's also compatible with the free case. 相似文献
18.
Masao Iri 《Mathematical Programming》1991,52(1-3):511-525
In the feasible region of a linear programming problem, a number of desirably good directions have been defined in connexion with various interior point methods. Each of them determines a contravariant vector field in the region whose only stable critical point is the optimum point. Some interior point methods incorporate a two- or higher-dimensional search, which naturally leads us to the introduction of the corresponding contravariant multivector field. We investigate the integrability of those multivector fields, i.e., whether a contravariantp-vector field isX
p
-forming, is enveloped by a family ofX
q
's (q > p) or envelops a family ofX
q
's (q < p) (in J.A. Schouten's terminology), whereX
q
is aq-dimensional manifold.Immediate consequences of known facts are: (1) The directions hitherto proposed areX
1-forming with the optimum point of the linear programming problem as the stable accumulation point, and (2) there is anX
2-forming contravariant bivector field for which the center path is the critical submanifold. Most of the meaningfulp-vector fields withp 3 are notX
p
-forming in general, though they envelop that bivector field. This observation will add another circumstantial evidence that the bivector field has a kind of invariant significance in the geometry of interior point methods for linear programming.For a kind of appendix, it is noted that, if we have several objectives, i.e., in the case of multiobjective linear programs, extension to higher dimensions is easily obtained. 相似文献
19.
S. A. Malyugin 《Journal of Applied and Industrial Mathematics》2010,4(2):218-230
The nonsystematic perfect q-ary codes over finite field F
q
of length n = (q
m
− 1)/(q − 1) are constructed in the case when m ≥ 4 and q ≥ 2 and also when m = 3 and q is not prime. For q ≠ 3, 5, these codes can be constructed by switching seven disjoint components of the Hamming code H
q
n
; and, for q = 3, 5, eight disjoint components. 相似文献
20.
Sofiya Ostrovska 《Czechoslovak Mathematical Journal》2008,58(4):1195-1206
Due to the fact that in the case q > 1 the q-Bernstein polynomials are no longer positive linear operators on C[0, 1], the study of their convergence properties turns out to be essentially more difficult than that for q < 1. In this paper, new saturation theorems related to the convergence of q-Bernstein polynomials in the case q > 1 are proved. 相似文献