Projection of Markov Measures May Be Gibbsian

We study the induced measure obtained from a 1-step Markov measure, supported by a topological Markov chain, after the mapping of the original alphabet onto another one. We give sufficient conditions for the induced measure to be a Gibbs measure (in the sense of Bowen) when the factor system is again a topological Markov chain. This amounts to constructing, when it does exist, the induced potential and proving its Hölder continuity. This is achieved through a matrix method. We provide examples and counterexamples to illustrate our results.     

Donaldson–Friedman construction and deformations of a triple of compact complex spaces,II

In a previous paper of the same title the author gave a generalization of the constrution of Donaldson–Friedman, to prove the existence of twistor spaces of n CP ² with a special kind of divisors. In the present paper, we consider its equivariant version. When n = 3, this gives another proof of the existence of degenerate double solid with C *–action, and we show that the branch quartic surface is birational to an elliptic ruled surface. In case n ≥ 4, this yields new Moishezon twistor spaces with C *–action, which is shown to be the most degenerate ones among twistor spaces studied by Campana and Kreußler.     

An Efficient Numerical Model for Planar Spiral Inductor On-Chip

In this paper, a very useful numerical technique has been developed for analyzing the transient characteristics of a planar-spiral inductor on-chip. A locally conformal technique and an alternating-direction implicit scheme are applied to the finite-difference time-domain method. A formulation for solving three dimensional Maxwell’s equations is proposed. Using the proposed method, various parameters of the planar-spiral inductors have been analyzed and an equivalent circuit, which includes frequency-independent circuit elements, has been introduced. Highly computational efficiency is implemented. Numerical results show excellent agreement with the measured data over a wide frequency range.     

乌桕类可可脂结晶过程中表现体积变化

为了解乌桕类可可脂(CTCBE)缓冷结晶横向胀罐爆裂原因，研究CTCBE结晶过程中的膨胀特性，采用流体静力法测试了不同等温结晶条件下CTCBE结晶形成的表观密度和表观体积及其横纵向膨胀状况。结果表明，CTCBE缓冷结晶后形成外部和中部两个晶区。在5-25℃的各等温结晶范围内，当结晶温度增加时，外部结晶区域减小、表观密度变化不大；中部结晶区域增大、表观密度明显减小，CTCBE的表观体积、横向、纵向膨胀率均增大，膨胀横向大于纵向。进一步表明CTCBE在自然缓冷固化的表观体积根本上由其结晶温度决定。为有效防止横向胀罐，自然缓冷固化温度应低于10℃。     

基于改进遗传算法的布局优化子问题

本针对子问题，构造了布局子问题(关于同构布局等价类)的改进遗传算法。将该算法应用于二维布局优化子问题，数值实验表明该算法能够在很好地保持图元的邻接关系的前提下找到子问题的最优解。由于布局优化问题可分解为有限个子问题，所以利用该算法可以找到整个布局优化问题的全局最优解。     

Twistor Geometry for Hyperkähler Metrics on Complex Adjoint Orbits

We study the hyperkähler geometry of complex adjoint orbits from the point of view of twistor theory. We introduce, for complex semisimple adjoint orbits, the associated spectral curve and construct the twistor space as a union of certain regular adjoint orbits; we also exhibit the family of twistor lines. Furthermore, we show how our methods may be applied for describing hyperkähler metrics associated to more general spectral curves. In particular, we give an algebraic characterisation of the twistor lines.     

Reflection quotients in Riemannian geometry. A geometric converse to Chevalley's theorem

Chevalley's theorem and its converse, the Sheppard-Todd theorem, assert that finite reflection groups are distinguished by the fact that the ring of invariant polynomials is freely generated. We show that, in the Euclidean case, a weaker condition suffices to characterize finite reflection groups, namely, that a freely-generated polynomial subring is closed with respect to the gradient product.

     

A note on 4-dimensional locally conformally flat Walker manifolds

A 4-dimensional Walker metric on a semi Riemanian manifold M, for the canonical metric with c = 0, have been investigated by M. Chaichi, E. García—Río and Y. Matsushita. The paper generalizes these notions to the case of constant c ≠ 0. Specially the form of defining functions of this metric in locally conformally flat 4-dimensional Walker manifolds is found.     

管理人因素对风险项目期权估值的影响

本基于对风险项目及其“孪生证券”风险和收益特性的分析，认为真正的“孪生证券”实际中很难存在，进而提出利用“近似孪生证券”与无风险证券构造资产组合来复制实物期权收益特征，利用无风险套利分析确定项目实物期权价值的方法。但考虑到管理人因素造成的实物期权内部风险特征的不可复制性，本进一步提出利用“确定性等值”将内部风险价值V1具体化，从而实现对“近似孪生证券”方法进行修正。     

Decay Rates in Probability Metrics Towards Homogeneous Cooling States for the Inelastic Maxwell Model

We quantify the long-time behavior of solutions to the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell molecules by means of the contraction property of a suitable metric in the set of probability measures. Existence, uniqueness, and precise estimates of overpopulated high energy tails of the self-similar profile proved in ref. 9 are revisited and derived from this new Liapunov functional. For general initial conditions the solutions of the Boltzmann equation are then proved to converge with computable rate as t → ∞ to the self-similar solution in this distance, which metrizes the weak convergence of measures. Moreover, we can relate this Fourier distance to the Euclidean Wasserstein distance or Tanaka functional proving also its exponential convergence towards the homogeneous cooling states. The findings are relevant in the understanding of the conjecture formulated by Ernst and Brito in refs. 15, 16, and complement and improve recent studies on the same problem of Bobylev and Cercignani⁽⁹⁾ and Bobylev, Cercignani and one of the authors.⁽¹¹⁾