共查询到20条相似文献,搜索用时 15 毫秒
1.
A direction–length framework is a pair (G,p) where G=(V;D,L) is a ‘mixed’ graph whose edges are labelled as ‘direction’ or ‘length’ edges and p is a map from V to ℝ
d
for some d. The label of an edge uv represents a direction or length constraint between p(u) and p(v). Let G
+ be obtained from G by adding, for each length edge e of G, a direction edge with the same end vertices as e. We show that (G,p) is bounded if and only if (G
+,p) is infinitesimally rigid. This gives a characterization of when (G,p) is bounded in terms of the rank of the rigidity matrix of (G
+,p). We use this to characterize when a mixed graph is generically bounded in ℝ
d
. As an application we deduce that if (G,p) is a globally rigid generic framework with at least two length edges and e is a length edge of G then (G∖e,p) is bounded. 相似文献
2.
In this paper we provide a complete characterization for when the Rees algebra and the associated graded ring of a perfect Gorenstein ideal of grade three are Cohen–Macaulay. We also treat the case of second analytic deviation one ideals satisfying some mild assumptions. In another set of results we give criteria for an ideal to be of linear type. Finally, we describe the equations defining the Rees algebras of certain Northcott ideals. 相似文献
3.
We establish new necessary and sufficient optimality conditions for global optimization problems. In particular, we establish tractable optimality conditions for the problems of minimizing a weakly convex or concave function subject to standard constraints, such as box constraints, binary constraints, and simplex constraints. We also derive some new necessary and sufficient optimality conditions for quadratic optimization. Our main theoretical tool for establishing these optimality conditions is abstract convexity. 相似文献
4.
AbdulRahman Al-Hussein 《Applied Mathematics and Optimization》2011,63(3):385-400
We consider a nonlinear stochastic optimal control problem associated with a stochastic evolution equation. This equation
is driven by a continuous martingale in a separable Hilbert space and an unbounded time-dependent linear operator. 相似文献
5.
In this paper we obtain a new regularity criterion for weak solutions to the 3D MHD equations. It is proved that if
div( \fracu|u|) \mathrm{div}( \frac{u}{|u|}) belongs to
L\frac21-r( 0,T;[(X)\dot]r( \mathbbR3) ) L^{\frac{2}{1-r}}( 0,T;\dot{X}_{r}( \mathbb{R}^{3}) ) with 0≤r≤1, then the weak solution actually is regular and unique. 相似文献
6.
7.
This paper obtains some equivalent conditions about the asymptotics for the density of the supremum of a random walk with
light-tailed increments in the intermediate case. To do this, the paper first corrects the proofs of some existing results
about densities of random sums. On the basis of the above results, the paper obtains some equivalent conditions about the
asymptotics for densities of ruin distributions in the intermediate case and densities of infinitely divisible distributions.
In the above studies, some differences and relations between the results on a distribution and its corresponding density can
be discovered.
相似文献
8.
Dalibor Volný 《Journal of Theoretical Probability》2010,23(3):888-903
Let (X i ) be a stationary and ergodic Markov chain with kernel Q and f an L 2 function on its state space. If Q is a normal operator and f=(I?Q)1/2 g (which is equivalent to the convergence of \(\sum_{n=1}^{\infty}\frac{\sum_{k=0}^{n-1}Q^{k}f}{n^{3/2}}\) in L 2), we have the central limit theorem [cf. (Derriennic and Lin in C.R. Acad. Sci. Paris, Sér. I 323:1053–1057, 1996; Gordin and Lif?ic in Third Vilnius conference on probability and statistics, vol. 1, pp. 147–148, 1981)]. Without assuming normality of Q, the CLT is implied by the convergence of \(\sum_{n=1}^{\infty}\frac{\|\sum_{k=0}^{n-1}Q^{k}f\|_{2}}{n^{3/2}}\), in particular by \(\|\sum_{k=0}^{n-1}Q^{k}f\|_{2}=o(\sqrt{n}/\log^{q}n)\), q>1 by Maxwell and Woodroofe (Ann. Probab. 28:713–724, 2000) and Wu and Woodroofe (Ann. Probab. 32:1674–1690, 2004), respectively. We show that if Q is not normal and f∈(I?Q)1/2 L 2, or if the conditions of Maxwell and Woodroofe or of Wu and Woodroofe are weakened to \(\sum_{n=1}^{\infty}c_{n}\frac{\|\sum_{k=0}^{n-1}Q^{k}f\|_{2}}{n^{3/2}}<\infty\) for some sequence c n ↘0, or by \(\|\sum_{k=0}^{n-1}Q^{k}f\|_{2}=O(\sqrt{n}/\log n)\), the CLT need not hold. 相似文献
9.
The question of necessary and sufficient conditions for the existence of a classical solution of inhomogeneous Cauchy–Riemann systems in a domain bounded by a piecewise smooth contour is studied. It is proved that the condition of the uniform stronger continuity of that inhomogeneity is a necessary condition, but it is also a sufficient condition if the inhomogeneity belongs to the L1 space. 相似文献
10.
We are concerned with the global weak rigidity of the Gauss–Codazzi–Ricci (GCR) equations on Riemannian manifolds and the corresponding isometric immersions of Riemannian manifolds into the Euclidean spaces. We develop a unified intrinsic approach to establish the global weak rigidity of both the GCR equations and isometric immersions of the Riemannian manifolds, independent of the local coordinates, and provide further insights of the previous local results and arguments. The critical case has also been analyzed. To achieve this, we first reformulate the GCR equations with div-curl structure intrinsically on Riemannian manifolds and develop a global, intrinsic version of the div-curl lemma and other nonlinear techniques to tackle the global weak rigidity on manifolds. In particular, a general functional-analytic compensated compactness theorem on Banach spaces has been established, which includes the intrinsic div-curl lemma on Riemannian manifolds as a special case. The equivalence of global isometric immersions, the Cartan formalism, and the GCR equations on the Riemannian manifolds with lower regularity is established. We also prove a new weak rigidity result along the way, pertaining to the Cartan formalism, for Riemannian manifolds with lower regularity, and extend the weak rigidity results for Riemannian manifolds with corresponding different metrics. 相似文献
11.
Konstantin E. Starkov Luis N. Coria 《Nonlinear Analysis: Real World Applications》2013,14(3):1425-1433
In this paper we examine the global dynamics of the Kirschner–Panetta model describing the tumor immunotherapy. We give upper and lower ultimate bounds for densities of cell populations involved in this model. We demonstrate for this dynamics that there is a positively invariant polytope in the positive orthant. We present sufficient conditions on model parameters and treatment parameters under which all trajectories in the positive orthant tend to the tumor-free equilibrium point. We compare our results with Kirschner–Tsygvintsev results and concern biological implications of our assertions. 相似文献
12.
NecessaryandSufficientConditionsfortheStrongConsistencyofMnltipleRegressionCoefficientsUnderaRestrictiveConditionJinMingzhong... 相似文献
13.
A particular theorem for linear separation between two sets is applied in the image space associated with a constrained extremum
problem. In this space, the two sets are a convex cone, depending on the constraints (equalities and inequalities) of the
given problem and the homogenization of its image. It is proved that the particular linear separation is equivalent to the
existence of Lagrangian multipliers with a positive multiplier associated with the objective function (i.e., a necessary optimality
condition). A comparison with the constraint qualifications and the regularity conditions existing in the literature is performed. 相似文献
14.
《Optimization》2012,61(9):1099-1117
In this article, we study a multiobjective optimization problem involving inequality and equality cone constraints and a set constraint in which the functions are either locally Lipschitz or Fréchet differentiable (not necessarily C 1-functions). Under various constraint qualifications, Kuhn–Tucker necessary conditions for efficiency in terms of the Michel–Penot subdifferentials are established. 相似文献
15.
We propose an algorithm for the global optimization of continuous minimax problems involving polynomials. The method can be
described as a discretization approach to the well known semi-infinite formulation of the problem. We proceed by approximating
the infinite number of constraints using tools and techniques from semidefinite programming. We then show that, under appropriate
conditions, the SDP approximation converges to the globally optimal solution of the problem. We also discuss the numerical
performance of the method on some test problems.
Financial support of EPSRC Grant GR/T02560/01 gratefully acknowledged. 相似文献
16.
T. Tachim Medjo 《Applied Mathematics and Optimization》2011,63(1):75-106
We investigate in this article the Pontryagin’s maximum principle for control problem associated with the primitive equations (PEs) of the ocean with periodic inputs. We also derive a second-order sufficient condition for optimality. This work is closely related to Wang (SIAM J. Control Optim. 41(2):583–606, 2002) and He (Acta Math. Sci. Ser. B Engl. Ed. 26(4):729–734, 2006), in which the authors proved similar results for the three-dimensional Navier-Stokes (NS) systems. 相似文献
17.
In this paper,we estimate the dimension of the global attractor for nonlinear dissipative Kirchhoff equation in Hilbert spaces
H
01×L
2(Ω) and D(A)×H
01(Ω). Using rescaling technology and linear variation method, we obtain the upper bound for its Hausdorff and fractal dimensions. 相似文献
18.
19.
Hans Martin Reimann 《Mathematische Zeitschrift》2001,237(4):697-725
On H–type groups N the left invariant horizontal vector fields span a subbundle of the tangent bundle, called the horizontal bundle HN. Generalized contact mappings f on N are smooth mappings which preserve HN. The question is: how many such mappings exist? In the case of the Heisenberg group these are the contact mappings in the
classical sense and they exist in abundance. In this paper it is shown that if the dimension of the center of N is at least three, then the generalized contact mappings are in the automorphism group of a finite dimensional Lie algebra
g. The elements in are the infinitesimal generators of local one parameter subgroups of generalized contact transformations. Rigidity is defined
as the property that is finite dimensional. For the case of the complexified Heisenberg group, i.e. the case when the dimension of the center
of N is two, it has been shown [RR] that g is infinite dimensional.
Received January 4, 2000; in final form March 20, 2000 / Published online April 12, 2001 相似文献
20.
In this paper, we investigate a global complexity bound of the Levenberg-Marquardt method (LMM) for the nonlinear least squares problem. The global complexity bound for an iterative method solving unconstrained minimization of φ is an upper bound to the number of iterations required to get an approximate solution, such that ‖∇φ(x)‖≤ε. We show that the global complexity bound of the LMM is O(ε −2). 相似文献