行为ρ*混合阵列加权和的矩完全收敛性

研究行为ρ*混合阵列加权和的矩完全收敛性,完善了Ahmed et al.[Statist.Probab.Lett.,2002,58:185-194],Peligrad et al.[J.Theoret.Probab.,1999,12:87-104]以及Baeket al.[J.Korean Stat.Soc.,2008,37:73-80]的结果.同时,给出一个应用,得到基于ρ*混合序列的平滑移动过程的矩完全收敛性,扩充了Kim et al.[Statist.Probab.Lett.,2008,78:839-846]的结果.     

Exchange-mediated contrast in CEST and spin-lock imaging

Purpose

Magnetic resonance images of biological media based on chemical exchange saturation transfer (CEST) show contrast that depends on chemical exchange between water and other protons. In addition, spin–lattice relaxation rates in the rotating frame (R_1ρ) are also affected by exchange, especially at high fields, and can be exploited to provide novel, exchange-dependent contrast. Here, we evaluate and compare the factors that modulate the exchange contrast for these methods using simulations and experiments on simple, biologically relevant samples.

Methods

Simulations and experimental measurements at 9.4 T of rotating frame relaxation rate dispersion and CEST contrast were performed on solutions of macromolecules containing amide and hydroxyl exchanging protons.

Results

The simulations and experimental measurements confirm that both CEST and R_1ρ measurements depend on similar exchange parameters, but they manifest themselves differently in their effects on contrast. CEST contrast may be larger in the slow and intermediate exchange regimes for protons with large resonant frequency offsets (e.g. > 2 ppm). Spin-locking techniques can produce larger contrast enhancement when resonant frequency offsets are small (< 2 ppm) and exchange is in the intermediate-to-fast regime. The image contrasts scale differently with field strength, exchange rate and concentration.

Conclusion

CEST and R_1ρ measurements provide different and somewhat complementary information about exchange in tissues. Whereas CEST can depict exchange of protons with specific chemical shifts, appropriate R_1ρ-dependent acquisitions can be employed to selectively portray protons of specific exchange rates.     

Extensions of n-Hom Lie algebras

n-Hom Lie algebras are twisted by n-Lie algebras by means of twisting maps. n-Hom Lie algebras have close relationships with statistical mechanics and mathematical physics. The paper main concerns structures and representations of n-Hom Lie algebras. The concept of n_ρ-cocycle for an n-Hom Lie algebra (G, [,… , ], α) related to a G-module (V, ρ, β) is proposed, and a sufficient condition for the existence of the dual representation of an n-Hom Lie algebra is provided. From a G-module (V, ρ, β) and an n_ρ-cocycle θ, an n-Hom Lie algebra (T_θ(V ), [, … , ]θ, γ) is constructed on the vector space T_θ(V ) = G⊕V, which is called the T_θ-extension of an n-Hom Lie algebra (G, [, … , ], α) by the G-module (V, ρ, β).     

A Class of ∗-Simple Type $A$ $ω^2$ -Semigroups (I)

In this paper, we study ∗-simple type $A$ $ω^2$-semigroups in which$\mathcal{D}^∗ =\widetilde{D}$and $\mathcal{D}^∗|_{E_S} = \mathcal{M}_d$ by the generalized Bruck-Reilly extension and obtain its structure theorem. We also obtain a criterion for isomorphisms of two such semigroups.     

Unified treatment of nonrelativistic and quasirelativistic atomic integrals over complete orthonormal sets of $${\Psi^{\alpha}}$$ -exponential type orbitals

The new one- and two-electron nonrelativistic and quasirelativistic basic functions are introduced. The general analytical relations in terms of basic functions suggested are derived for the non- and quasi-relativistic atomic integrals over complete orthonormal sets of -exponential type orbitals introduced by the author, where α  = 1,0, − 1, − 2, . . . The relationships obtained are valid for the arbitrary values of quantum numbers and screening constants of orbitals.     

非光滑(F,ρ,)θ-d一致不变凸广义分式规划的对偶性

结合F-凸,η-不变凸及d一致不变凸的概念给出了非光滑广义(F,ρ,θ)-d一致不变凸函数;就一类在凸集C上目标函数为Lipschitz连续的带有可微不等式约束的广义分式规划,提出一个对偶,并利用在广义Kuhn-Tucker约束品性或广义Arrow-Hurwicz-Uzawa约束品性的条件下得到的最优性必要条件,证明相应的弱对偶定理、强对偶定理及严格逆对偶定理.     

Riemann流形上ρ-(η,d)-B不变凸的向量变分不等式及向量优化问题

该文研究了Riemann流形上的优化问题.首先,利用广义方向导数在Riemann流形上引入ρ-(η,d)-B不变凸函数、ρ-(η,d)-B伪不变凸函数和ρ-(η,d)-B拟不变凸函数.其次,讨论了变分不等式的解与Riemann流形上向量优化问题解之间的关系.最后,建立了优化问题的Kuhn-Tucker充分条件.     

氦原子2 3P态自旋-其他轨道相互作用的理论计算

借助不可约张量理论,导出了氦原子2^3P态自旋-其他轨道相互作用能的理论计算式,在推导过程中完成了所有角向积分和自旋求和计算．     

从$\alpha$-Bloch空间到$Q_K$型空间的复合算子

Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator Cφ： Cφf = f °φ, for all f ∈ X. In this paper, the boundedness and compactness of the composition operators from α-Bloch spaces into QK（p,q） and QK,0（p,q） spaces are discussed, where 0 〈 α 〈 ∞.     

The Cubic-Two-State Equation of State: Cross-associating mixtures and Monte Carlo study of self-associating prototypes

A new equation of state for associating fluids has recently been presented by Medeiros and Tellez-Arredondo, the Cubic-Two-State Equation of State (CTS EoS) [Ind. Eng. Chem. Res. 47 (2008) 5723]. This equation arises from the coupling of the Soave–Redlich–Kwong EoS (SRK) with an association term from a two-state association model. The CTS EoS is polynomial in volume and it is able to describe vapor pressures and molar volume of associating fluids such as water, alcohol and phenol, among others. The equation is also able to describe the liquid–vapor equilibria of their mixtures with alkanes. In this paper, the physical and thermodynamic foundations of the CTS EoS are further investigated. In order to verify its applicability for cross-associating systems, the equation was employed in the prediction of phase equilibria behavior of binary alcohol–alcohol and water–alcohol mixtures. Very good agreement between predictions and experimental phase equilibria data was obtained with very simple combining rules and only one adjustable binary parameter. No additional parameters were necessary to describe ternary systems. With the purpose of checking the model's hypothesis and limitations, the two-state association term was coupled with the hard sphere Carnahan–Starling EoS, forming the CS-TS equation and the association characteristic parameters were determined theoretically for prototype association fluids. Monte Carlo NPT simulations of such fluids were performed and the results were compared with the equation's predictions. The CS-TS was able to describe qualitatively the pvT$pvT$ behavior of the prototype; nevertheless, it is not as accurate as those predictions obtained from the combination CS with Wertheim's association term. It seems that, when adjusting parameters of the CTS EoS to real substances, the discrepancies between the predicted and the real association contribution are dissipated among other adjustable parameters, specially on the dispersive term of the SRK equation. Finally, it is shown that CTS EoS isotherms can only have one or three real bigger roots than the co-volume for positive pressures, similar to cubic equations of state, and then it has the desirable form to describe vapor–liquid phase equilibria of associating compounds mixtures.