ON A PAIR OF NON-ISOMETRIC ISOSPECTRAL DOMAINS WITH FRACTAL BOUNDARIES AND THE WEYL-BERRY CONJECTURE

ＯＮＡＰＡＩＲＯＦＮＯＮＩＳＯＭＥＴＲＩＣＩＳＯＳＰＥＣＴＲＡＬＤＯＭＡＩＮＳＷＩＴＨＦＲＡＣＴＡＬＢＯＵＮＤＡＲＩＥＳＡＮＤＴＨＥＷＥＹＬＢＥＲＲＹＣＯＮＪＥＣＴＵＲＥＳＬＥＥＭＡＮ，Ｂ．Ｄ．ＣＨＥＮＨＵＡＭａｎｕｓｃｒｉｐｔｒｅｃ...     

三维光晶格中玻色凝聚气体基态波函数及干涉演化

基于Gross-Pitaevskii方程，运用有效化学势概念，研究了囚禁在组合势(由磁阱和三维光 晶格组成)中玻色凝聚气体在三维光晶格中的分布规律，并由此得到玻色凝聚气体的归 一化基态波函数.在取消组合势和仅取消光晶格而保留磁阱的两种情况下，运用传播子方 法求解出玻色凝聚气体密度分布的解析表达式.取消组合势后，理论计算所得到的玻色凝聚 气体聚随时间的演化规律与Greiner等的实验结果相一致.仅取消光晶格而保留磁阱时，研 究表明玻色凝聚气体的干涉模式呈现周期性的振荡行为.此外，在磁阱为各向异性的情况下 ， 关键词： 玻色凝聚气体 磁阱 光晶格 干涉模式     

耦合映像格子中时空混沌的状态反馈控制

利用状态反馈的方法，实现了耦合映像格子中时空混沌的稳定控制.反馈方式可以是没有延迟的，也可以是有延迟的；控制方式可以是连续的，也可以是脉冲的.数值模拟结果证明了状态反馈方法的有效性. 关键词： 耦合映像格子 时空混沌 状态反馈控制     

Differentiability of the Value Function of Nonclassical Optimal Growth Models

We consider an optimal growth (multi-sector) model with nonconvex technology. Using the Clarke results on generalized gradients, we prove that the value function has left and right derivatives with respect to the initial capital stock, without requiring supermodularity assumptions.     

Parametric and Non Homogeneous Semi-Markov Process for HIV Control

In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed. A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct times and follow-up has an impact on the evolution of patients.      

A Generalized Unpaired Electron Spin Density Equation and Organic Hyperconjugation Mechanism

A large class of stereochemcial and related interactions in organic chemistry are repulsive and others are attractive, but the relative orientation of two methyl groups and the amount of energy required to twist one relative to the other (the hindered rotation energy barriers), or the alignment of such a group with respect to a conjugated ring to which it is attached (widely attributed to a mechanism called “hyperconjugation”) are estimated to be small in compared with the total energy of the molecule. We used theories of both isotropic and anisotropic proton hyperfine interactions in the π‐electron systems developed in the early sixties. They are approximated by the magnetic dipole nteractions between each proton and an electron spin magnetization that is distributed in 2s and 2p Slater atomic orbitals center on carbon atoms. We have extended these theories to the non‐planar olefinic cation radicals, which are very important in biochemistry as well as in petroleum catalysis. A three dimensional electron spin density equation has been developed in this paper to handle some Jahn‐Teller vibronic molecules. The new electron spin density equation related the observed proton hyperfine splittings to the non‐planar structures of the open‐chain alkene cation radicals generated by radiolysis and various chemical oxidation methods. The spin densities and the conformational calculations based on valence bond theory and symmetry principles are compared with some more elaborated molecular orbital calculations in the literature. The localized valence bond approaches are better in accord with our experimental results. The anomalous line‐width effect of the four methyl groups observed in the 2,3‐dimethyl‐2‐butene cation radicals also confirmed the positive sign of the electron‐proton hyperfine constant of hyper‐conjugation mechanism. A methyl substituent attached to a conjugated molecule often behaves as if it formed part of the region of conjugation; the charge appears to flow from the methyl group into the π electron system and it may also give rise to an appreciable dipole moment. Methylation also gives rise to an appreciable dipole moment, and the resultant red shift of electronic absorption bands is of some importance in the design of dye molecules.     

Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

The Huber theorem for non-compact conformally flat manifolds

It was proved in 1957 by Huber that any complete surface with integrable Gauss curvature is conformally equivalent to a compact surface with a finite number of points removed. Counterexamples show that the curvature assumption must necessarily be strengthened in order to get an analogous conclusion in higher dimensions. We show in this paper that any non compact Riemannian manifold with finite -norm of the Ricci curvature satisfies Huber-type conclusions if either it is a conformal domain with volume growth controlled from above in a compact Riemannian manifold or if it is conformally flat of dimension 4 and a natural Sobolev inequality together with a mild scalar curvature decay assumption hold. We also get partial results in other dimensions. Received: April 14, 2000; revised version: March 20, 2001     

Boundedness and Dissipativity of Truncated Rotations on Uniform Planar Lattices

The finiteness of computer arithmetic can lead to some dramatic differences between the behaviour of a continuous dynamical system and a computer simulation. A thorough rigorous theoretical analysis of what may or what does happen is usually extremely difficult and to date little has been done even in relatively simple contexts. The comparative behaviour of a rotation mapping in the plane and on a uniform lattice in the plane is one such example. Simulations show that the rounding operator applied to a planar rotation mapping more or less preserves the qualitative behaviour of the original mapping, whereas the application of the truncation operator to a planar rotation can lead to quite different dynamical features. In this paper a theoretical justification of the properties of the planar rotation mappings under truncation to a, uniform integer lattice is provided, in particular properties of boundedness and dissipativity are investigated.     

Local-moment and itinerant antiferromagnetism in the heavy-fermion system Ce(Cu1−xNix)2Ge2

Elastic and inelastic neutron-scattering studies on the system Ce(Cu_1?xNi_x)₂Ge₂ are reported. These measurements are complemented by measurements of the magnetic susceptibility, high-field magnetization, heat capacity, thermal expansion, electrical resistivity and thermopower. The results reveal an interesting T-x phase diagram consisting of two different antiferromagnetic phases for x < 0.2 and 0.2 < x < 0.75, respectively, and a heavy-Fermi-liquid regime at higher Ni concentrations. The experimental results are interpreted in terms of an alloying-induced transition from local-moment to itinerant heavy-fermion magnetism. Fingerprints of this latter phase are a strongly reduced ordered moment and a short incommensurate ordering wave vector, in accord with theoretical predictions. A surprisingly good agreement between theory and experiment is found for x > 0.5. Further experimental evidence for different types of antiferromagnetic ordering derives from a line-shape analysis of the quasielastic neutron-scattering intensity, from magnetization and thermopower experiments.