Hidden structure in the randomness of the prime number sequence?

We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes, that would eventually appear in applications. Finally, our theory allows us to link with three different but important topics: the Hardy–Littlewood conjecture, the statistical mechanics of spin systems, and the celebrated Sierpinski fractal.     

Dispersion relations and the spin polarizabilities of the nucleon

A forward dispersion calculation is implemented for the spin polarizabilities γ₁,,γ₄ of the proton and the neutron. These polarizabilities are related to the spin structure of the nucleon at low energies and are structure-constants of the Compton scattering amplitude at . In the absence of a direct experimental measurement of these quantities, a dispersion calculation serves the purpose of constraining the model building, and of comparing with recent calculations in heavy baryon chiral perturbation theory.     

低密度聚乙烯光引发交联机理——Ⅱ.BNB自旋捕捉ESR研究

在光引发剂二苯甲酮(BP)存在下,紫外光辐照低密度聚乙烯(LDPE)所形成的自由基中间体已被自旋捕捉剂2,4,6-三特丁基亚硝基苯(BNB)所捕捉,其自旋加合物自由基已为电子自旋共振(ESR)所特征。现已检测和鉴定到二种自旋加合物:一种是叔碳自由基;另一种是仲碳自由基。它们分别是由BP的激发三重态从LDPE链的支化点和亚甲基团上夺氢所形成的自由基中间体同自旋捕捉剂BNB反应生成的。上述的证据表明:LDPE的光引发交联点主要发生在叔碳和仲碳原子上,且H-型交联点占主导地位。     

低场脉冲核磁共振测定二醋酸纤维素丝束中油剂

研究了采用低场脉冲核磁共振(NMR)测定二醋酸纤维素丝束油剂的新方法，给出NMR法测定二醋酸纤维素丝束油荆含量的标准曲线。同时对NMR法测量二醋酸纤维素丝束油荆不确定度进行了评估。结果表明，NMR法具有分析速度快、无污染、无损伤和准确度高的优点，适合于二醋酸纤维素丝束油荆的分析。     

Ground state of a spin-phonon system. I. Variational estimates

A study is made of the ground-state energy of a spin-one-half particle in a fieldB and interacting with a phonon bath. The infrared-sensitive case of acoustic phonons with point coupling in three dimensions is characterized by two parameters, a coupling constant andB. Units are used where the high-momentum phonon cutoff is unity. There is a curve (B) separating a symmetry-breaking region with a long-range phonon field from a normal region. Two simple, well-known, approximations are compared. The source theory yields discontinuities in the first derivatives of the energy with respect toB and whenB>e ^–1 and an infinite-order transition whenB<e ^–1, but is trivial in the large- region. The classical theory yields discontinuities in the second derivatives but is trivial in the small- region. An improved variationally fixed ground-state wave function is analyzed. It gives a new (B) curve with an infinite-order transition with continuous energy derivatives whenB<e/(e ²–1/4) and with discontinuous derivatives whenB is larger than this value. It is nontrivial in the entire (B) plane. The crossover to classical behavior occurs near =1/2 forB1. But the wave function does not describe quantum fluctuations in the large- phase. A second way of combining source and classical effects is described. It yields a second-order transition (near =1/2 forB1) everywhere. These theories are special cases of a symmetry-breaking transformation together with a one-mode treatment of quantum fluctuations. The transition is viewed in terms of a single mode with a variable length, coupled dynamically to the spin.     

自旋交叉配合现象与分子电子器件

自旋交叉配合物在热、压力或光诱导自旋交叉现象的同时会伴随着其它一些协同效应，比如配合物颜色的改革、存在着大的热滞后效应等，这些协同效应是单个分子或分子集合体作为热开关、光开关和信息存储元件材料的基础。因此，自旋交叉配合物是开发新型的热开关、光开关和信息存储元件材料的理想分子体系。本文概述了自旋交叉现象的研究历史、现状和未来的发展趋势。讨论了影响配合物自旋交叉性质的各种内在的和外部的因素，总结了目前用于研究自旋交叉现象的各种现代测试技术。最后，展望了自旋交叉配合物在分子电子器件方面的应用前景。     

Comparison of localization and delocalization indices obtained with Hartree-Fock and conventional correlated methods: effect of Coulomb correlation

Atomic populations and localization [lambda(A)] and delocalization [delta(A,B)] indices (LIs and DIs) are calculated for a large set of molecules at the Hartree-Fock (HF), MP2, MP4(SDQ), CISD, and QCISD levels with the 6-311++G(2d,2p) basis set. The HF method and the conventional correlation methods [MP2, MP4(SDQ), CISD, and QCISD] yield distinct sets of LIs and DIs. Yet, within the four conventional correlation methods the differences in atomic populations and LIs and DIs are small. Relative to HF, the conventional correlation methods [MP2, MP4(SDQ), CISD, QCISD] yield virtually the same LIs and DIs for molecules with large charge separations while LIs and DIs that differ significantly from the HF values--the LIs are increased and DIs decreased--are obtained for bonds with no or small charge separations. Such is the case in the archetypal homopolar molecules HC(triple bond)CH, H2C=CH2, CH3-CH3, and "protonated cyclopropane" C(3)H(7) (+), in which case the bonding may be atypical. Relative to HF, the typical effect of the conventional correlation methods is to decrease the DI between atoms.     

Spin Density Distribution in 2,4,6-Triphenylphenoxyl

The distribution of the unpaired electron over the oxygen and the 24 carbon atoms in the free 2,4,6-triphenylphenoxy radical was determined by electron spin resonance spectroscopy and quantum-mechanical approximation methods. The hyperfine splitting was evaluated with the aid of the spectra of triphenylphenoxyls deuterated in some or all of the substituent phenyl groups. The results of the quantum-mechanical approximations were checked by recording the ESR spectra of triphenylphenoxyls labeled with ¹³C in positions 1,2,3, or 4 of the central ring. The spin density distribution permits a first discussion of the ¹⁷O-coupling constants of correspondingly labeled triphenylphenoxyl and other organic free radicals.     

Identification of radicals spin-trapped in autoxidized linoleic acids: A high performance liquid chromatography and electron spin resonance study

Radicals generated in linoleic acid and deuterated linoleic acid have been trapped by the spin trap 2-methyl-2-nitroso-propane (MNP) and identified by electron spin resonance (ESR) and ENDOR spectroscopy. The formation of two distinct secondary alkyl radical adducts (one conjugated, the other non-conjugated, as shown by their UV absorption spectra) was demonstrated by 11, 11-dideuterio-9-cis-12-cis-linoleic acid using HPLC and ESR spectroscopy.