取代基效应(SCS)与乙烯-α-烯烃共聚物的序列结构Ⅲ.定量分析

本文在分析乙烯-α-烯烃共聚物序列结构时,把代表共单体反接单元的亚甲基(CH₂)βγ和γδ分别归属给了二元组VV和三元组EEV。与此同时,CH₂-δδ和δδ⁺归属给了二元组EE。表征乙烯长序列的CH₂-δ⁺δ⁺分属二元组EE和三元组EEE,对应峰强度在EE和EEE之间的分配是处理序列分布的关键。在本文中运用序列结构的Bovey关系和Randall统计进行演算,求得了修正值△的数学表达式,严格解和近似解。在规则链条件下得到的近似解与G.J.Ray的结果完全相同。当共单体含量较少时,谱峰强度Iδ⁺δ⁺的分配接近相等。在二元组和三元组的水平上,乙烯-α-稀烃共聚物的¹³C NMR谱中共有十三个峰,属于CH₂的有十个,属于CH的有三个。利用这些谱峰的强度数据可以建立一套计算公式,由此提供共聚物序列结构的全部信息。因此这是一个研究乙烯-α-烯烃共聚物序列结构的普适方法。     

Extensivity of entropy and modern form of Gibbs paradox

The extensivity property of entropy is clarified in the light of a critical examination of the entropy formula based on quantum statistics and the relevant thermodynamic requirement. The modern form of the Gibbs paradox, related to the discontinuous jump in entropy due to identity or non-identity of particles, is critically investigated. Qualitative framework of a new resolution of this paradox, which analyses the general effect of distinction mark on the Hamiltonian of a system of identical particles, is outlined.     

From dilute to dense self-avoiding walks on hypercubic lattices

A field-theoretic representation is presented to count the number of configurations of a single self-avoiding walk on a hypercubic lattice ind dimensions with periodic boundary conditions. We evaluate the connectivity constant as a function of the fractionf of sites occupied by the polymer chain. The meanfield approximation is exact in the limit of infinite dimensions, and corrections to it in powers ofd ^–1 can be systematically evaluated. The connectivity constant and the site entropy calculated throughout second order compare well with known results in two and three dimensions. We also find that the entropy per site develops a maximum atf1–(2d)^–1. Ford=2 (d=3), this maximum occurs atf~0.80 (f~0.86) and its value is about 50% (30%) higher than the entropy per site of a Hamiltonian walk (f=1).     

Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice

This is a general and exact study of multiple Hamiltonian walks (HAW) filling the two-dimensional (2D) Manhattan lattice. We generalize the original exact solution for a single HAW by Kasteleyn to a system ofmultiple closed walks, aimed at modeling a polymer melt. In 2D, two basic nonequivalent topological situations are distinguished. (1) the Hamiltonian loops are allrooted andcontractible to a point:adjacent one to another, and, on a torus,homotopic to zero. (2) the loops can encircle one another and, on a torus, canwind around it. Forcase 1, the grand canonical partition function and multiple correlation functions are calculated exactly as those of multiple rooted spanningtrees or of a massive 2Dfree field, critical at zero mass (zero fugacity). The conformally invariant continuum limit on a Manhattantorus is studied in detail. The melt entropy is calculated exactly. We also consider the relevant effect of free boundary conditions. The number of single HAWs on Manhattan lattices with other perimeter shapes (rectangular, Kagomé, triangular, and arbitrary) is studied and related to the spectral theory of the Dirichlet Laplacian. This allows the calculation of exact shape-dependent configuration exponents y. An exact surface critical exponent is obtained. Forcase 2, nested and winding Hamiltonian circuits are allowed. An exact equivalence to thecritical Q-state Potts model exists, whereQ ^1/2 is the walk fugacity. The Hamiltonian system is then always critical (forQ<-4). The exact critical exponents, in infinite numbers, are universal and identical to those of theO(n=Q ^1/2) model in its low-temperature phase, i.e. are those of dense polymers. The exact critical partition functions on the torus are given from conformai invariance theory. These models 1 and 2 yield the two first exactly solved models of polymer melts.     

Complexity-entropy causality plane: A useful approach for distinguishing songs

Nowadays we are often faced with huge databases resulting from the rapid growth of data storage technologies. This is particularly true when dealing with music databases. In this context, it is essential to have techniques and tools able to discriminate properties from these massive sets. In this work, we report on a statistical analysis of more than ten thousand songs aiming to obtain a complexity hierarchy. Our approach is based on the estimation of the permutation entropy combined with an intensive complexity measure, building up the complexity-entropy causality plane. The results obtained indicate that this representation space is very promising to discriminate songs as well as to allow a relative quantitative comparison among songs. Additionally, we believe that the here-reported method may be applied in practical situations since it is simple, robust and has a fast numerical implementation.     

Structural,magnetic and magnetocaloric properties of AMn1−xGaxO3 compounds with 0≤x≤0.2

Structural, magnetic and magnetocaloric properties of manganites series with the AMn_1−xGa_xO₃ (A=La_0.75Ca_0.08Sr_0.17 and x=0, 0.05, 0.1 and 0.2) composition have been investigated to shed light on Ga-doping influence. Solid-state reaction method was used for preparation. From XRD study, all samples are found single phase and crystallize in the orthorhombic structure with the Pnma space group. The variation of the magnetization M vs. temperature T, under an applied magnetic field of 0.05 T, reveals a ferromagnetic–paramagnetic transition for all samples. The experimental results indicate that T_C decreases from 336 to 135 K with increasing Ga substitution. Magnetocaloric effect (MCE) was estimated, in terms of isothermal magnetic entropy change (−ΔS_M), using the M(T, μ₀H) data and employing the thermodynamic Maxwell equation. The maximum entropy change and Relative Cooling Power (RCP) show non-monotonic behaviors with increasing the concentration of Gallium. In fact, the maximum value of ΔS_Mmaxof AMn_1−xGa_xO₃ for x=0.00 and 0.2 samples is found to be, respectively, 2.87 and 1.17 J/kg/K under an applied magnetic field change of 2 T. For the same applied magnetic field (μ₀H=2 T), the RCP values are found to vary between 97.58 and 89 J/kg.     

Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.     

Information Theories with Adversaries,Intrinsic Information,and Entanglement

There are aspects of privacy theory that are analogous to quantum theory. In particular one can define distillable key and key cost in parallel to distillable entanglement and entanglement cost. We present here classical privacy theory as a particular case of information theory with adversaries, where similar general laws hold as in entanglement theory. We place the result of Renner and Wolf—that intrinsic information is lower bound for key cost—into this general formalism. Then we show that the question of whether intrinsic information is equal to key cost is equivalent to the question of whether Alice and Bob can create a distribution product with Eve using I_M bits of secret key. We also propose a natural analogue of relative entropy of entanglement in privacy theory and show that it is equal to the intrinsic information. We also provide a formula analogous to the entanglement of formation for classical distributions. It is our pleasure to dedicate this paper to Asher Peres on the occasion of his seventieth birthday.     

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

In this paper, we introduce optimal control algorithm for the design of pulse sequences in NMR spectroscopy. This methodology is used for designing pulse sequences that maximize the coherence transfer between coupled spins in a given specified time, minimize the relaxation effects in a given coherence transfer step or minimize the time required to produce a given unitary propagator, as desired. The application of these pulse engineering methods to design pulse sequences that are robust to experimentally important parameter variations, such as chemical shift dispersion or radiofrequency (rf) variations due to imperfections such as rf inhomogeneity is also explained.     

A half-moment model for radiative transfer in a 3D gray medium and its reduction to a moment model for hot, opaque sources

We present in this paper a new 3D half-moment model for radiative transfer in a gray medium, called the model, which uses maximum entropy closure. This model is a generalization to 3D of the 1D version recently proposed in (J. Comp. Phys. 180 (2002) 584). The direction space Ω is divided into two pieces, Ω⁺ and Ω^-, in a dynamical way by the plane perpendicular to the total radiative flux, and the half moments are defined from these subspaces. The model closure and the integrations of the radiative transfer equation performed on the moving Ω^± spaces are detailed. 1D planar results, which have motivated the extension of the model of (J. Comp. Phys. 180 (2002) 584) to multi-dimensions, are shown. These results are very good. The model is thereafter derived for 3D spherically symmetric geometry, where the correctness of the non-trivial border terms can be checked. Two 3D spherically symmetric problems are numerically solved in order to show the accuracy of the closure and the role of the border terms. Once again, compared to the solution obtained with a ray tracing solver, results are very good. From the 3D half-moment model, a new moment model, called , is derived for the particular case of a 3D hot and opaque source radiating into a cold medium, for applications such as simulations of stellar atmospheres and fires. Two-dimensional numerical results are presented and compared to those obtained solving the RTE and with other moment models. They demonstrate the very good accuracy of the model, its good convergence properties, and better prediction compared to all other existing moment models in its domain of applicability.