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91.
综合国力的数学建模 总被引:2,自引:0,他引:2
王树禾 《高校应用数学学报(A辑)》1997,(1):29-36
本文考虑社会文明与社会导恶现象的制约机制,建立一个综合国力的非线性数学模型,从数学上讨论了相应的二次微分系统的Hopf分叉,中心与细焦点的判定,极限环的存在唯一性等问题,并对数学结论予以合理解释,把社会相平面划成社发展区域,社会动荡区域和社会崩溃区域,研讨社会走向,确定纳入社会发展区域的途径。 相似文献
92.
Yan Ziqian 《东北数学》1995,(3)
ThreeClassesofReaction-DiffusionSystemswithNeumannBoundaryCondition¥(严子谦)YanZiqian(DepartmentofMathematics,JilinUniversity,Ch... 相似文献
93.
94.
We investigate the information theoretic properties of Kalman–Bucy filters in continuous time, developing notions of information supply, storage and dissipation. Introducing a concept of energy, we develop a physical analogy in which the unobserved signal describes a statistical mechanical system interacting with a heat bath. The abstract universe comprising the signal and the heat bath obeys a non-increase law of entropy; however, with the introduction of partial observations, this law can be violated. The Kalman–Bucy filter behaves like a Maxwellian demon in this analogy, returning signal energy to the heat bath without causing entropy increase. This is made possible by the steady supply of new information. In a second analogy the signal and filter interact, setting up a stationary non-equilibrium state, in which energy flows between the heat bath, the signal and the filter without causing any overall entropy increase. We introduce a rate of interactive entropy flow that isolates the statistical mechanics of this flow from marginal effects. Both analogies provide quantitative examples of Landauers Principle. 相似文献
95.
According to the universal entropy bound, the entropy (and hence information capacity) of a complete weakly self-gravitating
physical system can be bounded exclusively in terms of its circumscribing radius and total gravitating energy. The bound’s
correctness is supported by explicit statistical calculations of entropy, gedanken experiments involving the generalized second
law, and Bousso’s covariant holographic bound. On the other hand, it is not always obvious in a particular example how the
system avoids having too many states for given energy, and hence violating the bound. We analyze in detail several purported
counterexamples of this type, and exhibit in each case the mechanism behind the bound’s efficacy.
In memoriam Asher Peres. 相似文献
96.
George Avalos 《Journal of Mathematical Analysis and Applications》2004,294(1):34-61
We consider the null controllability problem for thermoelastic plates, defined on a two dimensional domain Ω, and subject to hinged, clamped or free boundary conditions. The uncontrolled partial differential equation system generates an analytic semigroup on the space of finite energy. Consequently, the concept of null controllability is indeed appropriate for consideration here. It is shown that all finite energy states can be driven to zero by means of just one L2((0,T)×Ω) control be it either mechanical or thermal. The singularity, as T↓0, of the associated minimal energy function is the main object studied in the paper. Singularity and blow-up rates for minimal energy function are not only of interest in their own right but are also of critical importance in Stochastic PDEs. In this paper, we establish the optimal blow-up rate for this function. It is shown that the rate of singularity is the same as for finite-dimensional truncations of the model. In view of sharp estimates available in the finite dimensional setting [Math. Control Signals Systems 9 (1997) 327], the singularity rates provided in this paper are optimal. 相似文献
97.
In this paper we study the existence and the stability of bounded solutions of the following non-linear system of parabolic equations with homogeneous Dirichlet boundary conditions:
98.
99.
For efficient progress, model properties and measurement needs can adapt to oceanic events and interactions as they occur. The combination of models and data via data assimilation can also be adaptive. These adaptive concepts are discussed and exemplified within the context of comprehensive real-time ocean observing and prediction systems. Novel adaptive modeling approaches based on simplified maximum likelihood principles are developed and applied to physical and physical–biogeochemical dynamics. In the regional examples shown, they allow the joint calibration of parameter values and model structures. Adaptable components of the Error Subspace Statistical Estimation (ESSE) system are reviewed and illustrated. Results indicate that error estimates, ensemble sizes, error subspace ranks, covariance tapering parameters and stochastic error models can be calibrated by such quantitative adaptation. New adaptive sampling approaches and schemes are outlined. Illustrations suggest that these adaptive schemes can be used in real time with the potential for most efficient sampling. 相似文献
100.
Escort distributions are a well established but (for physicists) a relatively new concept that is rapidly gaining wide acceptance in world. In this work we wish to revisit the concept within the strictures of the celebrated semiclassical Husimi distributions (HDs) and thereby investigate the possibility of extracting new semiclassical information contained, not in the HD themselves, but in their associated escort Husimi distributions. We will also establish relations, for various information measures, between their deformed versions [J. Naudts, Physica A 316 (2002) 323] and those built up with escort HDs. Bounds on the concomitant power exponents will be determined. 相似文献