Kinematical Reduction of Spatial Degrees of Freedom and Holographic Relation in Yang’s Quantized Space-Time Algebra

We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang’s quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, λ and R, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter fact, we find a certain kind of kinematical holographic relation in YSTA, which may be regarded as a primordial form of the holographic principle suggested so far in the framework of the present quantum theory that appears now in the contraction limit of YSTA, λ→0 and R→∞. S. Tanaka is an Em. Professor of Kyoto University.     

Ground State,Magnetization Process and Bipartite Quantum Entanglement of a Spin-1/2 Ising–Heisenberg Model on Planar Lattices of Interconnected Trigonal Bipyramids

The ground state, magnetization scenario and the local bipartite quantum entanglement of a mixed spin-1/2 Ising–Heisenberg model in a magnetic field on planar lattices formed by identical corner-sharing bipyramidal plaquettes is examined by combining the exact analytical concept of generalized decoration-iteration mapping transformations with Monte Carlo simulations utilizing the Metropolis algorithm. The ground-state phase diagram of the model involves six different phases, namely, the standard ferrimagnetic phase, fully saturated phase, two unique quantum ferrimagnetic phases, and two macroscopically degenerate quantum ferrimagnetic phases with two chiral degrees of freedom of the Heisenberg triangular clusters. The diversity of ground-state spin arrangement is manifested themselves in seven different magnetization scenarios with one, two or three fractional plateaus whose values are determined by the number of corner-sharing plaquettes. The low-temperature values of the concurrence demonstrate that the bipartite quantum entanglement of the Heisenberg spins in quantum ferrimagnetic phases is field independent, but twice as strong if the Heisenberg spin arrangement is unique as it is two-fold degenerate.     

现代数字物理教学连载⑦——数字化技术的表现力与技巧在教学中的应用

数字化技术是教学改革中重要的先进生产力,首先,数字化技术在表现自由度上发展了时间维、颜色维、亮度维(灰度维)、数字维和透明度维等新的展示空间;颜色的运用技巧还能表现等势线、等高线或其他等值线,特别是用来描述流体、温度、密度等;亮度或灰度在表现原子的电子云和描述微观粒子概率密度波时也有重要的作用.总之,数字化技术大大超出传统教学的表现能力.     

Logical Processing for Integer Programming

This paper reviews tools which have great potential for reducing the difficulty of solving IP (and also MIP) problems, if well implemented in solvers. Recent experiments with Branch and Bound solvers, in connection with “Short Start Features”, have shown that implementations need and can still be improved. Concepts which are likely to be specially important for (0,1) MIP are pointed out.     

Some Special Pairs of Σ2 e-Degrees

It is shown that there are incomparable Σ₂ e-degrees a, b such that every e-degree strictly less than a is also less than b .     

Buffer phenomenon in systems with one and a half degrees of freedom

The buffer phenomenon is established for some classical mechanics problems that are described by pendulum-type equations with time-periodic small additive terms. This phenomenon is as follows: the systems under consideration can have an arbitrary fixed number of stable periodic modes if the system parameters are properly chosen.     

The low<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> and low<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> r. e. degrees are not elementarily equivalent

Jockusch, Li and Yang showed that the Lown and Low1 r.e. degrees are not elementarily equivalent for n > 1. We answer a question they raise by using the results of Nies, Shore and Slaman to show that the Lown and Lowm r.e. degrees are not elementarily equivalent for n > m > 1.     

Degrees of Freedom of a Time Series

We give a formal proof that if f is a smooth dynamics on a d-dimensional smooth manifold and is an ergodic and exact dimensional measure with Hausdorff dimension dim >d–1, then the number d of degrees of freedom of the dynamics can be recovered from the observation of an orbit. We implement, with this purpose, an algorithm based on the analysis of the microstructure of . We show how a correct estimation of d permits the computation of the Liapunov spectrum with a high accuracy avoiding the issue of the spurious exponents.