共查询到20条相似文献,搜索用时 31 毫秒
1.
《Journal of Differential Equations》2014,257(8):2950-2983
We present a rigorous numerical proof based on interval arithmetic computations categorizing the linearized and nonlinear stability of periodic viscous roll waves of the KdV–KS equation modeling weakly unstable flow of a thin fluid film on an incline in the small-amplitude KdV limit. The argument proceeds by verification of a stability condition derived by Bar–Nepomnyashchy and Johnson–Noble–Rodrigues–Zumbrun involving inner products of various elliptic functions arising through the KdV equation. One key point in the analysis is a bootstrap argument balancing the extremely poor sup norm bounds for these functions against the extremely good convergence properties for analytic interpolation in order to obtain a feasible computation time. Another is the way of handling analytic interpolation in several variables by a two-step process carving up the parameter space into manageable pieces for rigorous evaluation. These and other general aspects of the analysis should serve as blueprints for more general analyses of spectral stability. 相似文献
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We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations). Given two curves, the distance between them is defined as the infimum of an energy functional which, roughly speaking, measures the extent to which the jet field of the first curve needs to be rotated to match up with the jet field of the second curve. We show that this energy functional attains a global minimum on the appropriate function space, and we derive a set of first-order ODEs for the minimizer. 相似文献
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《Applied Mathematical Modelling》2014,38(21-22):5347-5355
This paper investigates the multi-mode resource availability cost problem with recruitment and release dates for resources. This problem is a more realistic model and extended case of the resource availability cost problem. The project contains activities interrelated by finish–start precedence relations with zero time lags, which require a set of renewable resources. First, a mixed integer programming formulation is proposed for the problem. Then, simulated annealing (SA) algorithm is proposed to obtain a satisfying solution for this NP-hard problem. The effectiveness of the proposed algorithm is demonstrated through comprehensive experimentation based on 300 test problems. The results are analyzed and discussed. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(8):2905-2917
We study the structure of the periodic steady-state solutions of forced and damped strongly nonlinear coupled oscillators in the frequency–energy domain by constructing forced and damped frequency – energy plots (FEPs). Specifically, we analyze the steady periodic responses of a two degree-of-freedom system consisting of a grounded forced linear damped oscillator weakly coupled to a strongly nonlinear attachment under condition of 1:1 resonance. By performing complexification/averaging analysis we develop analytical approximations for strongly nonlinear steady-state responses. As an application, we examine vibration isolation of a harmonically forced linear oscillator by transferring and confining the steady-state vibration energy to the weakly coupled strongly nonlinear attachment, thereby drastically reducing its steady-state response. By comparing the nonlinear steady-state response of the linear oscillator to its corresponding frequency response function in the absence of a nonlinear attachment we demonstrate the efficacy of drastic vibration reduction through steady-state nonlinear targeted energy transfer. Hence, our study has practical implications for the effective passive vibration isolation of forced oscillators. 相似文献
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In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative formulas extend to arbitrary continuous and translation invariant valuations. Then, we discuss applications to Poisson particle processes and Boolean models which contain, as a special case, some new results for flag measures. 相似文献
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When faced with a false generalization and a counterexample, what types of claims do prospective K-8 teachers make, and what factors influence the type and prudence of their claims relative to the data, observations, and arguments reported? This article addresses that question. Responses to refutation tasks and cognitive interviews were used to explore claiming. It was found that prospective K-8 teachers’ claiming can be influenced by knowledge of argumentation; knowledge and use of the mathematical practice of exception barring; perceptions of the task; use of natural language; knowledge of, use of, and skill with the mathematics register; and abilities to technically handle data or conceptual insights. A distinction between technical handlings for developing claims and technical handlings for supporting claims was made. It was found that prudent claims can arise from arguer-developed representations that afford conceptual insights, even when searching for support for a different claim. 相似文献
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Liping Feng Xiaofeng Liao Qi Han Huaqing Li 《Applied Mathematical Modelling》2013,37(16-17):8225-8236
A variable infection rate is more realistic to forecast dynamical behaviors of malware (malicious software) propagation. In this paper, we propose a time-delayed SIRS model by introducing temporal immunity and the variable infection rate. The basic reproductive number R0 which determines whether malware dies out is obtained. Furthermore, using time delay as a bifurcation parameter, some necessary and sufficient conditions ensuring Hopf bifurcation to occur for this model are derived. Finally, numerical simulations verify the correctness of theoretical results. Most important of all, we investigate the effect of the variable infection rate on the scale of malware prevalence and compare our model with stationary analytical model by simulation. According to simulating results, some strategies that control malware rampant are given, which may be incorporated into cost-effective antivirus policies for organizations to work quite well in practice. 相似文献
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We discuss some recent results of us regarding a class of polar spaces which includes the nonembeddable polar spaces introduced by Tits [Tits, J., “Buildings of spherical type and finite BN-pairs,” Lecture Notes in Mathematics 386, Springer-Verlag, Berlin-New York, 1974]. These results include an elementary construction of the polar space, a construction of a polarized embedding of the corresponding dual polar space and the determination whether this projective embedding is universal and unique (as a polarized embedding). 相似文献
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Guangcun Lu 《Israel Journal of Mathematics》2006,156(1):1-63
We introduce the concept of pseudo symplectic capacities which is a mild generalization of that of symplectic capacities.
As a generalization of the Hofer-Zehnder capacity we construct a Hofer-Zehnder type pseudo symplectic capacity and estimate
it in terms of Gromov-Witten invariants. The (pseudo) symplectic capacities of Grassmannians and some product symplectic manifolds
are computed. As applications we first derive some general nonsqueezing theorems that generalize and unite many previous versions
then prove the Weinstein conjecture for cotangent bundles over a large class of symplectic uniruled manifolds (including the
uniruled manifolds in algebraic geometry) and also show that any closed symplectic submanifold of codimension two in any symplectic
manifold has a small neighborhood whose Hofer-Zehnder capacity is less than a given positive number. Finally, we give two
results on symplectic packings in Grassmannians and on Seshadri constants.
Partially supported by the NNSF 10371007 of China and the Program for New Century Excellent Talents of the Education Ministry
of China. 相似文献
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We study certain algebraic properties of the small quantum homology algebra for the class of symplectic toric Fano manifolds.
In particular, we examine the semisimplicity of this algebra, and the more general property of containing a field as a direct
summand. Our main result provides an easily verifiable sufficient condition for these properties which is independent of the
symplectic form. Moreover, we answer two questions of Entov and Polterovich negatively by providing examples of toric Fano
manifolds with non-semisimple quantum homology, and others in which the Calabi quasi-morphism is not unique.
相似文献
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N. A. Tyurin 《Theoretical and Mathematical Physics》2010,162(3):255-275
We introduce the notion of a pseudotoric structure on a symplectic manifold, generalizing the notion of a toric structure.
We show that such a pseudotoric structure can exist on toric and nontoric symplectic manifolds. For the toric manifolds, it
describes deformations of the standard toric Lagrangian fibrations; for the nontoric ones, it gives Lagrangian fibrations
with singularities that are very close to the toric fibrations. We present examples of toric manifolds with different pseudotoric
structures and prove that certain nontoric manifolds (smooth complex quadrics) have such structures. In the future, introducing
this new structure can be useful for generalizing the geometric quantization and mirror symmetry methods that work well in
the toric case to a broader class of Fano varieties. 相似文献
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Ion Alexandru Mihai 《Transformation Groups》2007,12(3):573-599
We define the odd symplectic Grassmannians and flag manifolds, which are smooth projective varieties equipped with an action
of the odd symplectic group, analogous to the usual symplectic Grassmannians and flag manifolds. Contrary to the latter, which
are the flag manifolds of the symplectic group, the varieties we introduce are not homogeneous. We argue nevertheless that
in many respects the odd symplectic Grassmannians and flag manifolds behave like homogeneous varieties; in support of this
claim, we compute the automorphism group of the odd symplectic Grassmannians and we prove a Borel-Weil-type theorem for the
odd symplectic group. 相似文献
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Matthias Schwarz 《Inventiones Mathematicae》1998,133(2):353-397
A new lower bound for the number of fixed points of Hamiltonian automorphisms of closed symplectic manifolds (M,ω) is established. The new estimate extends the previously known estimates to the class of weakly monotone symplectic manifolds.
We prove for arbitrary closed symplectic manifolds with rational symplectic class that the cup-length estimate holds true
if the Hofer energy of the Hamiltonian automorphism is sufficiently small. For arbitrary energy and on weakly monotone symplectic
manifolds we define an analogon to the cup-length based on the quantum cohomology ring of (M,ω) providing a quantum cup-length estimate.
Oblatum 12-IX-1997 相似文献
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We construct smooth circle actions on symplectic manifolds with non-symplectic fixed point sets or cyclic isotropy sets. All
such actions are not compatible with any symplectic form on the manifold in question. In order to cover the case of non-symplectic
fixed point sets, we use two smooth 4-manifolds (one symplectic and one non-symplectic) which become diffeomorphic after taking
the products with the 2-sphere. The second type of actions is obtained by constructing smooth circle actions on spheres with
non-symplectic cyclic isotropy sets, which (by the equivariant connected sum construction) we carry over from the spheres
on products of 2-spheres. Moreover, by using the mapping torus construction, we show that periodic diffeomorphisms (isotopic
to symplectomorphisms) of symplectic manifolds can provide examples of smooth fixed point free circle actions on symplectic
manifolds with non-symplectic cyclic isotropy sets. 相似文献