Quantization of the PoissonSU(2) and its Poisson homogeneous space — The 2-sphere

We show that deformation quantizations of the Poisson structures on the Poisson Lie groupSU(2) and its homogeneous space, the 2-sphere, are compatible with Woronowicz's deformation quantization ofSU(2)'s group structure and Podles' deformation quantization of 2-sphere's homogeneous structure, respectively. So in a certain sense the multiplicativity of the Lie Poisson structure onSU(2) at the classical level is preserved under quantization.With an Appendix by Jiang-Hua Lu and Alan Weinstein Department of Mathematics, University of California, Berkely, CA 94720 USAPartially supported by NSF-Grant DMS-8505550     

The pseudopotential and certain atomic properties of the calcium lattice

The Bardeen pseudopotential is constructed for calcium to meet the requirement of a minimum binding energy per experimental volume of the elementary cell. The binding energy and compressibility are calculated as functions of the deformation caused by omnidirectional compression or extension. The equation of state is constructed. The Gruneisen parameter is calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 10, pp. 78–82, October, 1970.     

减小薄板玻璃工件研磨变形的研究

针对薄板玻璃刚度差，在研磨中易产生变形这一特点，探讨了减小其变形的不同方法。我们用传统的上盘法粘结固定工件进行加工，工件在下盘前面形精度较好，能满足要求（在２５ｍｍ×２５ｍｍ面积上的平面度为０．０５μｍ），但在下盘后产生的变形使其面形精度下降，在２５ｍｍ×２５ｍｍ面积上的平面度为０．２μｍ，已不能满足要求。采用真空吸附法国固定工件，消除了工件在粘结过程中由于温度变化产生的变形，而且在研磨过程中又设法减小对工件施加的压力，从而减小了工件在研磨过程中产生的变形，使加工后的工件面形与加工过程中的面形接近，这就保证了工件的面形精度。     

Quantization of the continuous Heisenberg ferromagnet

The quantization of the continuous anisotropic Heisenberg ferromagnet with uniaxial anisotropy is performed by means of the quantum inverse scattering method. The space of quantum states is shown to possess the positive metric only in the su(1, 1) case (the magnet on the hyperboloid). The requirement of complete integrability leads, in the anisotropic case, to a deformation of the algebra of observables. The problem of local integrals of motion is discussed. The Hamiltonian is constructed for two-particle states.     

Orthogonal Pure States in Operator Theory

We summarize and deepen existing results on systems of orthogonal pure states in the context of Jordan–Banach (JB) algebras and C* algebras. Especially, we focus on noncommutative generalizations of some principles of topology of locally compact spaces such as exposing points by continuous functions, separating sets by continuous functions, and multiplicativity of pure states.     

A Relation Between Completely Bounded Norms and Conjugate Channels

We show a relation between a quantum channel Φ and its conjugate Φ ^C , which implies that the p → p Schatten norm of the channel is the same as the 1 → p completely bounded norm of the conjugate. This relation is used to give an alternative proof of the multiplicativity of both norms.     

Sheaves on Fibered Threefolds and Quiver Sheaves

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.     

A new algorithm for analysis of ESEEM from distant matrix nuclei

A new algorithm is developed for obtaining information about the structure of the paramagnetic center’s surroundings by distant matrix deuterons, explicitly accounting for the weak quadrupole interaction of deuterium nuclei and for the multiplicativity of nuclear contributions into ESE modulation.     

Fermionic quantum stochastic flows

Existence, uniqueness and, using a higher-order Fermionic Itô formula, multiplicativity are proved for even quantum stochastic flows over ₂graded C ^*-algebras driven by Fermionic noise with bounded structure maps.Work supported by EU HCM Contract CHRX-CT93-QO94.     

High-resolution dynamic measurement using electronic speckle pattern interferometry based on multi-camera technology

The speckle interferometer based on multi-camera technologies using two cameras is applied to a dynamic measurement. The new speckle interferometer is constructed by a prism array and two cameras. A phenomenon, which a bearing-ball collides against a thin polymer film, is investigated by the proposed interferometer. Then, it is shown that the local maximum deformation of the thin film by the collision is about 1.0 μm. Such a deformation process can precisely be analyzed by this method without any troubles of optical dislocations. In the results, it is confirmed that a large deformation process can be analyzed by accumulating measured results of small deformation in every small continuous analysis. Furthermore, it is estimated that the measurement precision of this method is about 5 nm as experimental results.     

An availability requirement for fiber optic transport systems in distribution feeder applications

This paper contains a discussion of Bellcore's proposed channel availability requirement for fiber optic transport systems used in distribution feeder applications. A representative model of the distribution network is first constructed which includes a high capacity fiber optic system running to a distribution hub. An overall availability requirement, consistent with present availability requirements, is applied to this model. The allocation to the fiber system is determined by truncation of the current interoffice channel availability requirement which is prorated with distance. Further allocation of downtime to the electronic hardware reliability failures yields an objective that can be directly compared with the results of electronic hardware reliability models. This requirement is now included in Bellcore's proposed “Generic Reliability Assurance Requirements for Fiber Optic Transport Systems.”     

Theory of polymorphic transformations in ammonium halides with allowance for three-particle interactions

In the approximation of multiplicativity of the binary and ternary distribution functions, Bogolyubov's method is used to calculate the chemical potentials of the cubic modifications of ammonium halides with allowance for three-particle interactions between the ions. The temperatures of polymorphic transitions are determined for different pressures together with the discontinuities of the volume and the heats of transition. The results are compared with the experimental data.     

Complementary energy principle for large elastic deformation

Using the “base forces” as the fundamental unknowns to determine the state of an elastic system, the complementary energy principle for large elastic deformation is constructed for the conjugate quantities being displacement gradients, which possesses exactly the same form as that of classical linear elasticity. It is revealed that the complementary energy contains deformation part and rotation part.     

An availability requirement for fiber optic transport systems in distribution feeder applications

This paper contains a discussion of Bellcore's proposed channel availability requirement for fiber optic transport systems used in distribution feeder applications. A representative model of the distribution network is first constructed which includes a high capacity fiber optic system running to a distribution hub. An overall availability requirement, consistent with present availability requirements, is applied to this model. The allocation to the fiber system is determined by truncation of the current interoffice channel availability requirement which is prorated with distance. Further allocation of downtime to the electronic hardware reliability failures yields an objective that can be directly compared with the results of electronic hardware reliability models. This requirement is now included in Bellcore's proposed “Generic Reliability Assurance Requirements for Fiber Optic Transport Systems.”     

基于Wigner分布函数的光学元件评价方法

为了有效地表征和评价光学元件局部小尺度波前畸变,提出了能同时反映空间频率和空间位置的Wigner分布函数评价方法。通过理论分析Wigner分布函数与功率谱密度之间的关系,得到了局部波前畸变的评价方法和指标。模拟计算和实验结果验证了该方法的有效性,并表明:该方法不但能判断光学元件的中频误差是否满足惯性约束聚变系统要求,而且还能确定不满足要求的特定区域,从而有效地指导光学元件的返修。     

Group theory of the massless spin 2 field and gravitation

The simplest manifestly covariant unitary representation of the Poincaré group for zero mass and spin 2 is constructed. This representation is carried by fourth rank tensors which satisfy the equations of the Riemann curvature tensor in the linearized theory of gravitation in vacuo. In particular, the requirement of unitarity implies the Bianchi identities.     

基于无网格点插值法的旋转悬臂梁的动力学分析

将基于多项式点插值的无网格方法用于旋转悬臂梁的动力学分析. 利用无网格点插值方法对柔性梁的变形场进行离散, 考虑梁的纵向拉伸变形和横向弯曲变形, 并计入横向弯曲变形引起的纵向缩短, 即非线性耦合项, 运用第二类Lagrange方程推导得到系统刚柔耦合动力学方程. 与有限元法相比, 该方法只需节点信息, 无需定义单元, 具有前处理简单的优势; 构造的形函数采用更多的节点插值, 具有高阶连续性. 将无网格点插值方法的仿真结果与有限元和假设模态法进行比较分析, 验证了该方法的正确性, 并表明其作为一种柔性体离散方法在刚柔耦合多体系统动力学的研究中具有可推广性.     

Integrated analysis of strap mount for a circular mirror

In order to solve the nonlinear contact problem with the friction action in the mirror assembly, the modeling analysis is carried out by the MPC method of shell-to-solid coupling. Considering the friction factor existing in the contact region, the deformation and stress of the strap obviously changes from fixed region, transition region to contact region, which further produces a serious edge effect around the mirror and leads to the uneven stress distribution. The results show the maximal deformation of the assembly is 9.98 μm and the maximal stress is 10.5 MPa, which has much tolerance to the precision requirement of structure and the admissible stress of material; the influence of heat effect on the surface deformations of mirror is proved to be far greater than that of only gravity load. The advantages of the contact model built by the MPC method are more close to the actual working conditions and more accurate analysis results can be obtained.     

Accumulation of dislocations and thermal strengthening of alloys having an L12 superstructure

This paper discusses the dislocation-accumulation mechanism in alloys having an L1₂ superstructure, which is associated with the formation of Kira-Wilsdorf barriers and the retardation of superdislocations during plastic deformation. A model of the dislocation-accumulation kinetics during plastic deformation is constructed, on the basis of which a mathematical model is formulated for the thermal and deformation strengthening of single crystals of alloys having the L1₂ superstructure. The results of numerical calculations based on the model are compared with the experimentally observed regularities of the deformation and thermal strengthening of single crystals of Ni₃Ge. Fiz. Tverd. Tela (St. Petersburg) 41, 454–460 (March 1999)     

Iso-spectral deformations of general matrix and their reductions on Lie algebras

We study an iso-spectral deformation of the general matrix which is a natural generalization of the nonperiodic Toda lattice equation. This deformation is equivalent to the Cholesky flow, a continuous version of the Cholesky algorithm, introduced by Watkins. We prove the integrability of the deformation and give an explicit formula for the solution to the initial value problem. The formula is obtained by generalizing the orthogonalization procedure of Szegö. Using the formula, the solution to the LU matrix factorization can the constructed explicitly. Based on the root spaces for simple Lie algebras, we consider several reductions of the equation. This leads to generalized Toda equations related to other classical semi-simple Lie algebras which include the integrable systems studied by Bogoyavlensky and Kostant. We show these systems can be solved explicitly in a unified way. The behaviors of the solutions are also studied. Generically, there are two types of solutions, having either sorting property or blowing up to infinity in finite time.