Improved Estimation of Protein Rotational Correlation Times fromN Relaxation Measurements

In the study of protein backbone dynamics by¹⁵N relaxation measurements, an initial estimation of the isotropic global correlation time, τ_m, is usually obtained from the averageT₁/T₂ratio of nuclear spins that do not exhibit slow internal motion and withT₂values not significantly shortened by chemical or conformational exchange processes. Different methods have been used for identification of the rates of internal motion. However, the number of nuclear spins included in the τ_mestimation is often larger than the number that ultimately can be fitted to a single-order parameter,S², implying that some nuclear spins involved in the initial τ_mestimation actually have an effective internal correlation time, τ_e, not as fast as assumed. As a consequence, τ_mis underestimated, since internal motion reduces theT₁/T₂ratio. This situation becomes more obvious if the molecule has a large τ_mvalue because the reduction inT₁/T₂ratio arising from internal motion is more significant than for molecules with smaller τ_mand the same degree of internal motion. This Communication describes a more reliable method for identifying nuclear spins which should be excluded from the τ_mestimation because of insufficiently rapid internal motion. This results in an improved τ_mvalue, giving a much better agreement between the number of nuclear spins fitted successfully to a single-order parameter,S², and those used in the τ_mestimation.     

受量子相位调制的两态叠加多模叠加态光场的广义非线性等阶N次方Y压缩

本文根据量子力学中的线性叠加原理,构造了由受量子相位调制的多模(即q模)虚相干态|{i^m₁Z_j}〉q及其相反态|{-i^m₂Z_j}〉q这两者的线性叠加所组成的一种新型的两态叠加多模叠加态光场|ψ_m1,m2⁽²⁾〉q.利用新近建立的多模压缩态理论,详细研究了态|ψ_m1,m2⁽²⁾〉q的广义非线性等阶N次方Y压缩特性.结果发现:1)无论态间的初始相位差(θ_m2-θm₁)、各模的初始相位φ_j、腔模总数q、压缩参量R_j以及两态叠加的几率幅r_m1和r_m2等取何值,无论压缩阶数N取奇还是取偶,只要相位调制因子m1和m2与压缩阶数N的关系满足一定的量子化条件,态|ψ_m1,m2⁽²⁾〉q就恒处于等阶N-Y最小测不准态.2)当态间的初始相位差(θ_m2-θm₁)在态间压缩区[2kθπ-π/2+ {R_j²[(m₂-m₁)π/2]},2kθπ+π/2+ {R_j²[(m₂-m₁)π/2]}]内取值时,无论压缩阶数N取奇还是取偶,只要相位调制因子m₁和m₂与N的关系式以及各模的初始相位φ_j等满足一定的量子化条件,态|ψ_m1,m2〉q就可呈现出周期性变化的,任意阶的等阶N次方Y压缩效应.3)利用相位调制因子m₁、m₂与压缩阶数N之间的解析关系式,可直接确定出|ψ_m1,m2〉q呈现等阶N次方Y压缩效应时的压缩阶数N.4)文献2、11、15关于等阶N次方Y压缩的研究结果,仅仅是本文所得普遍性结果在相位调制因子m₁和m₂取不同值时的特例.     

Fe_nO_m~+(n+m=4)团簇的构型、电子结构特征和磁性

采用二项式方案构建了FenOm+(n+m=4)团簇的大量可能初始结构.运用广义梯度近似(GGA)密度泛函理论中的PW91交换关联泛函对这些初始结构进行优化和频率分析,得到12个稳定的异构体.在此基础上计算和分析了它们的结合能、对称性、键长、磁矩,最高占据轨道与最低未占据轨道的能隙.发现Fe—O键在FenOm+(n+m=4)团簇的稳定中具有重要作用,团簇的总磁矩主要取决于铁原子的磁矩和各个原子磁矩排布情况.     

第Ⅱ种强度不等的两态叠加多模叠加态光场的等阶N次方H压缩——2腔模总数与压缩阶数两者之积取奇数的情形

构造了由多模复共轭相干态的相反态|{-Z_j^(a)*}〉q和多模虚共轭相干态的相反态|{-Z_j^(b)*}〉q的线性叠加所组成的第Ⅱ种强度不等的非对称两态叠加多模叠加态光场|Ψ(ab)Ⅱ〉q.利用多模压缩态理论,研究了态|Ψ(ab)Ⅱ〉q的等阶N次方H压缩特性.结果发现,在腔模总数与压缩阶数这两者之积取奇数,则当各对应模的初始相位、各对应模的初始相位差,态间的初始相位差、以及光子干涉项的幅度之和等分别满足一定的量子化条件时,态|Ψ(ab)Ⅱ〉q的第一及第二正交分量可分别呈现出周期性变化的等阶N次方H压缩效应.这与现有报道的结果截然不同.     

第Ⅱ种强度不等的两态叠加多模叠加态光场的等阶N次方H压缩1腔模总数与压缩阶数两者之积取偶数的情形

利用多模压缩态理论研究了第种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)〉q的等阶N次方H压缩特性.结果发现:1)当腔模总数q与压缩阶数N的乘积取偶数,亦即qN=2p时,无论p=2m(m=1,2,3,…,…),还是p=2m+1(m=0,1,2,3,…,…),只要各模的初始相位差(φ_j^(a)-φ_j^(b))、态间的初始相位差(θ_nq^(aR)-θ_nq^(bR))及光子干涉项的幅度 1R_j^(a)R_j^(b)等分别满足一定的条件,则态|Ψ_||^(ab)〉q的第一和第二正交分量总可分别呈现出周期性变化的等阶N次方H压缩效应.2)当qN=2p且p=2m+1(m=0,1,2,3,…,…)时,若构成态|Ψ_Ⅱ^(ab)〉q的两个不同的量子光场态中各对应模的强度(即平均光子数)和初始相位相等,亦即R_j^(a)=R_j^(b)和φ_j^(a)=φ_j^(b)(j=1,2,3,…,q),则态|Ψ_Ⅱ^(ab)〉q可呈现出“等阶N次方H压缩简并”现象.     

On the stability of symmetric four-particle molecules

The stability of four-particle molecules m ₁⁺ m ₂⁺ m ₃⁻m₄⁻ with unit charges of particles is studied for different masses of the particles. It is shown that all molecules containing two like particles with masses m ₃ = m ₄ are stable against dissociation. Their stability results from the stability of symmetric molecules with m ₁ = m ₂ and m ₃ = m ₄ and from the stability of molecules with masses of particles m ₃ = m ₄ and m ₁ = ∞ containing one infinitely heavy particle.     

一种新型的两态叠加多模Schrödinger猫态光场的等阶N次方Y压缩

本文根据量子力学的线性叠加原理,构造了由多模(即q模)相干态的相反态|{-Z_j}〉q及多模虚相干态|{Z_j}〉q这两者的线性叠加所组成的一种新型的多模Schrdinger猫态光场|Ψ⁽²⁾〉q,利用新近建立的多模压缩态理论,研究了态|Ψ⁽²⁾〉q的N次方Y压缩效应。结果发现:①当压缩阶数N=2p且p=2m(m=1,2,3,…,…)时,态|Ψ⁽²⁾〉q总是恒处于N-Y最小测不准态;②当压缩阶数N=2p且p=2m+1(m=0,1,2,3,…,…)时,如果各模的初始相位φ_j,态间的初始相位差θ_pq^(I)-θ_nq^(R)以及各单模相干态光场的平均光子数之总和 等满足一定的量子化条件,则态|Ψ⁽²⁾〉q可呈现出周期性变化的、任意阶的N次方Y压缩效应;③当压缩阶数N=2p′+1时,无论p′=2m(m=0,1,2,…,…)还是p′=2m+1(m=0,1,2,3,…,…),只要各模的初始相位φ_j满足一定的量子条件,则当两态叠加几率幅满足r_pq^(I)=r_nq^(R)时,态|Ψ⁽²⁾〉q就恒处于N-Y测不准态,始终不呈现N-Y最小测不准态和N次方Y压缩;而当r_pq^(I)≠r_nq^(R)时,态|Ψ⁽²⁾〉q始终不呈现N-Y测不准态、N-Y最小测不准态和N次方Y压缩效应。     

增加光子奇偶q相干态的高阶压缩效应

通过数值计算研究了增加光子奇q相干态a_q^+m|α>_q^o和增加光子偶q相干态a_q^+m|α>_q^e的高阶压缩效应.结果表明:当q较小时,态a_q^+m|α>_q^o和a_q^+m|α>_q^e都能呈现出强烈的奇次方阶压缩效应,但无偶次方阶压缩效应,而且奇次方阶压缩随m的增大而增强.当m=0时a_q^+m|α>_q^o和a_q^+m|α>_q^e为光场振幅偶次幂的最小测不准态,但当m≠0时它们不是光场振幅偶次幂的最小测不准态.     

一种新型的两态叠加多模叠加态光场的广义非线性等阶N次方H压缩

本文根据量子力学中的线性叠加原理,构造了由多模(即 q模)相干态的相反态 | {-Z_j}〉_q及多模虚相干态的相反态 | {-iZ_j}〉_q 这两者的线性叠加所组成的一种新型的两态叠加多模叠加态光场 | ψ_msc⁽²⁾〉_q 利用新近建立的多模压缩态理论,详细研究了态 | ψ_msc⁽²⁾〉_q 的广义非线性等阶N次方H压缩特性 结果发现:1)当压缩阶数N与腔模总数q这两者之积为偶数,亦即当q·N =2p且p =2m(m =1,2,3,…,…)时,态 | ψ_msc⁽²⁾〉_q恒处于等阶N-H最小测不准态;2)当q·N =2p且 p =2m′+ 1(m′ =0,1,2,3,…,…)时,如果各模的初始相位之和 、态间的初始相位差(θ_nq^(I)-θ_nq^(R))、各多模相干态光场的总的平均光子数 以及 [(θ_nq^(I)-θ_nq^(R))+ ]等满足一定的量子化条件时,态 | ψ_msc⁽²⁾〉_q 总可呈现出周期性变化的、任意阶的等阶N次方H压缩效应;3)当压缩阶数N与腔模总数 q这两者之积为奇数时,亦即当 q·N =2p + 1时,无论 p =2m(m =0,1,2,3,…,…)还是 p =2m′ + 1(m′ =0,1,2,3,…,…),只要各模初始相位之和 满足一定的量子化条件,则当两态叠加几率幅满足r_nq^(R) =r_nq^(I) 时,态 | ψ_msc⁽²⁾〉_q 就恒处于N-H测不准态     

第Ⅱ类三态叠加多模叠加态光场等幂次2m+1次方Y压缩

构造了由多模虚相干态|{iZ_j}>_q、多模虚相干态的相反态|{-iZ_j}>_q和多模真空态|{O_j}>_q这三种不同的量子光场态的线性叠加所组成的第Ⅱ类三态叠加多模叠加态光场|ψ₂⁽³⁾>_q.利用多模压缩态理论,研究了态|ψ₂⁽³⁾>_q的广义非线性等幂次2m+1次方Y压缩特性.结果发现:在压缩次数N=2m+1(m=0,1,2,3,…,…)的条件下,只要各模的初始相位和态间的初始相位差分别满足一定的取值条件,态|ψ₂⁽³⁾>_q就可呈现出周期性变化的、任意奇数次的广义非线性等幂次N次方Y压缩效应.     

Electron irradiation effects in doped high temperature superconductors YBa2Cu3? x M x O y (M = Fe, Ni; x=0; x =0:01)

The influence of irradiation by electrons with an energy of 8 MeV, at dose intervals between 10¹³ and 2×10¹⁸el/cm², on the properties of impurity doped, high-temperature superconductor YBa₂Cu_3−x M _x O _y (M = Fe, Ni; x=0; x=0:01) ceramics has been studied. It has been established that, as the irradiation dose is increased, the onset temperature of the transition to the superconducting state (T _c ^on ), and the intergranular weak link coupling temperature between granules (T _m ^J ), exhibit an oscillation around their initial values of approximately about 1–1.5 K. This oscillation indicates that the process of radiation defect formation in HTSC occurs in multiple stages. It was also found that the critical current (J _c )decreases with an increase of the irradiation dose, and exhibits a local minimum at a dose of 8×10¹⁶el/cm²coinciding with minima for T _c ^on and T _m ^J at this dose. It was found that the introduction of Fe atoms to the ceramic decreases T _m ^J , while introducing Ni atoms decreases both T _c ^on and T _m ^J ; it is suggested that this is a result of Ni substitution of Cu both in Cu2 plane sites and Cu1 chain sites. The introduction of Ni causes a large change in the intergranular critical current density, J _c . A critical irradiation dose is obtained (2×10¹⁸)after which all HTSC parameters strongly decrease, i. e. the superconductivity of HTSC is destroyed.      

The self-similarity of wall-bounded temporally accelerating turbulent flows

From the study of viscous flow it is known that certain time-dependent laminar problems, such as the impulsively started flat plate and the diffusion of a vortex sheet, possess self-similar solutions. Previous studies of turbulent channel and pipe flows accelerating between two steady states have shown that the flow field evolves in three distinct stages. Furthermore, recent direct numerical simulations have shown that the perturbation velocity, i.e. the surplus velocity from the initial value, in an impulsively accelerating turbulent channel and pipe flow also possesses a self-similar distribution during the initial stage. In here, these results are developed analytically and it is shown that accelerating flows in which the centreline velocity develops as U^∧_c(t) = U₀(t/t₀)^m will possess a self-similar velocity distribution during the initial stage. The displacement thickness of the perturbation velocity is shown to be dependent only on the type of acceleration, and not on the initial Reynolds number, the acceleration rate or the change in Reynolds number. The derived formulas are verified with good agreement against measurements performed in a linearly accelerating turbulent pipe flow and with data from channel flow simulations.     

Radiative neutrino decays in very strong magnetic fields

The radiative decay ν_H → ν_L + γ of massive neutrinos is analyzed in the framework of the standard model with lepton mixing for very strong magnetic fields B B_cr = m²_e/e 4.14 × 10¹³ G. The analysis is based on the approximate decay amplitude obtained by Gvozdev et al. Numerical results as well as analytical approximations for the decay rate are obtained for energies of the initial neutrino below and above the electron-positron pair creation threshold 2m_e.     

Spin-polarized Dirac-Slater calculations on the energies of hollow argon atom

In this work, the multiplet splitting in terms of a spin-dependent model is analyzed. The spin-polarized and unpolarized single configuration Dirac-Fock-Slater wavefunctions have been used in the evaluation of the total energies of highly ionized argon with different L shell population The transition energies of hollow argon atom with initial configurations 1s ⁰ _1/22s ^m _1/22p ⁿ _1/22p ^l _3/2 with m = 0 to 2 and n + l varying from 6 to 1 are reported in this work. The calculations have been carried out by taking into account a relativistic exchange potential in the Dirac-Slater potential. To account for the correlation effects, a correction term has also been considered perturbatively. The present calculations show that the spin-polarized technique which is mainly applied to the ground states of atoms may also be applied to atoms ionized in the inner shells with a good degree of accuracy. Received 5 December 2000 and Received in final form 9 April 2001     

Mass Scales and the Cosmological Coincidences

Theories involving the parameters h, c, G, H (in a usual notation) are considered. A huge ratio of 10¹²⁰ of the mass of the universe (m_u) to the smallest determinable mass m₀ in the period since the big bang occurs in such theories. Five masses are here identified and interpreted between these two limits so that one has in all seven analytical expressions for masses. They form a geometrical progression m₀, m₀R, …, m₀R⁶ = m_u with R ≈ 10²⁰. It is shown that this formulation is easily adapted to explain existing cosmological coincidences and to generate new ones.     

第Ⅶ类两态叠加多模叠加态光场的偶数阶等阶N次方Y压缩

本文构造了由多模相干态|{Z_j}>_q与多模虚相干态的相反态|{-iZ_j}>_q这两者的线性叠加所组成的第Ⅶ类两态叠加多模叠加态光场|ψ₇⁽²⁾>_q.利用多模压缩态理论,研究了态|ψ₇⁽²⁾>_q的偶数阶等阶N次方Y压缩特性.结果发现:在压缩阶数N=2p、并且P=2m+1(m=0,1,2,3,…,…)的条件下,如果各模的初始相位φj(j=1,2,3,…,q)、态间的初始相位差与各单模相干态光场的平均光子数之和 等分别满足一定的取值条件,则在这种情况下态|ψ₇⁽²⁾>_q可呈现出周期性变化的偶数阶等阶N次方Y压缩效应.     

态|Ψ(3)〉q中广义电场分量的不等幂次Nj次方Y压缩

利用多模压缩态理论,研究了由多模复共轭虚相干态|{iZ_j^*}〉q、多模复共轭虚相干态的相反态|{-iZ_j^*}〉q和多模复共轭相干态|{Z_j^*}〉q的线性叠加所组成的新型三态叠加多模叠加态光场|Ψ⁽³⁾〉_q中广义电场分量的偶数次不等幂次Nj次方Y压缩特性.结果发现:在各模的压缩次数N_j=2pj且pj=2m′j+1(m′j=0,1,2,3,…,…)和Nj′=2pj′且pj′=2m′j′+1(m′j′=0,1,2,3,…,…)的条件下,当各模的初始相位φ_j与φ_j′、态间的初始相位差(θ₁-θ₃)与(θ₂-θ₃),以及各单模相干态光场总的平均光子数之和qj=1R2j等分别满足一定的取值条件时,态|Ψ⁽³⁾〉_q的广义电场分量(即第二正交相位分量)总可呈现出周期性变化的、偶数次的广义非线性不等幂次N_j次方Y压缩效应.     

Convexity relation for energy in quantum mechanics

The dependence of the ground-state energy E of a quantum-mechanical system on the parameter λ appearing linearly in the Hamiltonian is studied. A variation of the scale makes it possible to supplement the convexity-concavity relation for energy as a function of this parameter with a refined relation between the energies of systems that go over to one another upon a change in the particle charges or masses. This relation follows from the fundamentals of quantum mechanics and is valid for exact energies of the systems being considered. Its application does not require calculating wave functions and makes it possible to determine the boundaries of the ground-state energy level and the boundaries of the region of obvious stability of various systems. The results of applying the theory to m ₁⁺ m ₂⁺ m ₃⁻ and m ₁⁺ m ₂⁺ m ₄⁻ three- and four-particle mesic atoms and molecules featuring particles of various mass are presented.     

Recrystallization of pure and strontium-doped KCl crystals

The kinetics of microstructure transformations are studied during annealing of deformed single crystals of KCl and KCl:0.05wt %Sr²⁺ at temperatures of (0.35–0.55)T _m (where T _m is the melting temperature) and during storage at room temperature. The effect of deformation rates ranging from 0.01 mm/min to 0.1 mm/min at a deformation temperature T _d=0.5T _m on the crystal structure and on the recrystallization kinetics is noted. It is found experimentally that the incubation period for static recrystallization in single-crystal KCl:0.05wt%Sr²⁺ is shortened and recrystallization takes place at room temperature after deformation in this temperature range. Here, during the new recrystallization grains have a twinned orientation with respect to the initial single crystal during the first stage and to the subgrains of the deformed crystal. As the annealing temperature is raised, the stage in which twins grow in KCl:0.05wt%Sr²⁺ crystals is shortened and it is displaced by recrystallization through migration of high-angle grain boundaries of the common type. Deformation conditions which ensure prolonged (at least three months) stability of the post-deformation hardening of single crystals are found experimentally for Sr²⁺-doped deformed single crystals. Fiz. Tverd. Tela (St. Petersburg) 41, 259–264 (February 1999)     

Stability of Three-Body Coulomb Systems with J = 1 in the Oscillator Representation

The oscillator representation is applied to calculate the energy spectrum of three-body Coulomb systems with total angular momentum ^J. For three-body Coulomb systems with J = 1 and arbitrary masses the region of stability is determined. For the systems (A ⁺ A ⁻ e ⁻), (pe ⁻ C ⁺), (pB ⁻ e ⁻), and (D ⁺ e ⁻ e ⁺), the values of the critical masses of the particles A, B, C, and D are obtained as m _A = 2.22m _e , m _B = 1.49m _e , m _C = 2.11m _e and m _D = 4.15m _e . Received November 6, 1995; received December 4, 1995; accepted for publication January 22, 1996