Measurement of diffusion coefficients using a quick echo split NMR imaging technique

A new method for the ultrafast generation of diffusion-weighted images is reported. The technique combines a quick echo split NMR imaging sequence with the principle of Stejskal and Tanner. It allows to determine the diffusion constant with nearly the same accuracy as the conventional spin-echo technique, requiring only a fraction of the time. The determined values for water doped with 1 g Cu(NO₃)₂ per liter of H₂O and pure acetone were D_water = (1.95 ± 0.02) × 10⁻⁹ m²/s and D_acetone = (4.05 ± 0.02) × 10⁻⁹ m²/s at 18.5°C. They are in good agreement both with literature and our own reference measurements using a diffusion-weighted spin-echo sequence. In addition, the temperature dependence of D_water was measured in the range of 18.5–45.9°C and a good correspondence with reported data was found.     

用偶幂级数处理Abel变换问题

本文提出了用偶幂级数代替对称分布函数,使其线积分成为递推可积,从而简化了Abel逆变换。引进权函数使本方法简单地过渡到非对称问题。对一组假想相移信号进行变换,获得了可靠的密度分布结果,并对影响变换精度的各种因素作了讨论。     

标准加入ICP-AES法测定铬酸钠中杂质元素

采用ICP-AES法同时测定工业铬酸钠溶液中微量Al,Ca,Fe,Mg,Si杂质元素。针对测定过程中存在的基体干扰、谱线干扰等问题,通过实验确定了铬酸钠中微量的Al,Ca,Fe,Mg,Si的分析测试谱线:Al 167.079nm,Ca 393.366nm,Fe 259.940nm,Mg 279.533nm,Si 251.61nm。实验用优级纯HCl将待测溶液调为酸性,消除工业铬酸钠溶液酸度不稳定引起的测定误差,采用标准加入法消除基体干扰,探讨了Al,Ca,Fe,Mg,Si等五种微量组分检测方法标准曲线线性相关性、检出限、精密度以及回收率等分析指标,详细研究了在选定分析谱线下,标准加入法对铬酸钠溶液中Al,Ca,Fe,Mg,Si等微量杂质含量测定结果的准确性的影响。结果表明标准曲线呈线性关系(R2=0.998 8~0.999 6之间),五种元素检出限在(0.013 4~0.028 0)mg·L-1之间,11次测量标准偏差小于5.86%,回收率在97.30%~107.50%之间。实验建立的分析方法的检出限、精密度、准确度均能满足分析测试要求;方法实用性强,已经成功用于离子膜电解法中铬酸钠原料液微量离子检测;利用铬酸钠、重铬酸钠和重铬酸酐与溶液酸度的关系,实验建立的分析方法还可拓展于重铬酸钠及铬酐甚至其他六价铬产品中Al,Ca,Fe,Mg,Si杂质离子的检测,同时也可以扩展到上述样品中其他杂质元素的测定。     

催化分光光度法中的二标样计算法

本方导出了一种催化分光光度法计算公式，即二标样计算法，并进行了实验验证，结果良好。     

Analysis of unsteady gas–liquid flows in a rectangular tank: Comparison of Euler–Eulerian and Euler–Lagrangian simulations

We study the dynamics of gas–liquid flows experimentally and computationally in a rectangular bubble column where the gas source is introduced at the corner. The flow in this reactor is complex and inherently unsteady in nature. The two-dimensional liquid phase velocity field is calculated by an Eulerian approach solving the unsteady Reynolds Averaged Navier Stokes equations. The conservation equations are closed using a two parameter turbulence model. The two-way coupling was accounted for by adding source terms in the conservation equations of the continuous phase to take into account the interaction with the dispersed phase. Bubble tracking is achieved through a Lagrangian approach. Here the equations of motion are solved taking into account the drag, pressure, buoyancy and gravity forces. The time-averaged flows along with the variables which characterize turbulence are analyzed for a wide range of gas flow-rates using Euler–Lagrangian simulations. These simulation predictions are validated with Euler–Eulerian simulations where the gas-phase distribution is captured as a void fraction and PIV experiments. The motion of bubbles induces turbulence in the flow. The applicability of two parameter models for turbulence like the standard k–ε model on time-averaged flow properties is addressed. From the results of the time averaged velocity field, turbulence intensity, turbulent viscosity and gas hold-up profiles, it is concluded that the Euler–Lagrangian model is applicable at lower gas flow-rates. The Euler–Eulerian approach was found to be valid at lower as well as higher gas flow-rates.     

Generic initial ideals of Artinian ideals having Lefschetz properties or the strong Stanley property

For a standard Artinian k-algebra A=R/I, we give equivalent conditions for A to have the weak (or strong) Lefschetz property or the strong Stanley property in terms of the minimal system of generators of gin(I). Using the equivalent condition for the weak Lefschetz property, we show that some graded Betti numbers of gin(I) are determined just by the Hilbert function of I if A has the weak Lefschetz property. Furthermore, for the case that A is a standard Artinian k-algebra of codimension 3, we show that every graded Betti number of gin(I) is determined by the graded Betti numbers of I if A has the weak Lefschetz property. And if A has the strong Lefschetz (respectively Stanley) property, then we show that the minimal system of generators of gin(I) is determined by the graded Betti numbers (respectively by the Hilbert function) of I.     

保持算子乘积谱函数的映射

设A和B为无限维复Banach空间上的标准算子代数,记Δ~R(·)为下列谱函数之一:σ~R(·),σ_l~R(·),σ_r~R(·),σ_l~R(·)∩σ_r~R(·),(?)σ~R(·),(?)σ~R(·),σ_p~R(·),σ_c~R(·),σ_(ap)~R(·),σ_s~R(·),σ_(ap)~R(·)∩σ_s~R(·),σ_p~R(·)∩σ_c~R(·),σ_p~R(·)∪σ_c~R(·),其中R=A或B.证明了A和B之间的每个保持算子Jordan三乘积(算子乘积)之谱函数△~R(·)的满射Φ必有形式Φ=(?)π,其中(?)是1的立方根(1的平方根)而π或者是A和B之间的代数同构,或者是代数反同构.也获得不定度规空间上的标准算子代数之间保持算子斜乘积之谱函数的映射的完全刻画.     

Common properties of table algebras and association schemes

The concept of table algebra in the title is a real nonsingular generalized table algebra in the sense of [Z. Arad, E. Fisman, M. Muzychuk, Generalized table algebras, Israel J. Math. 114 (1999) 29–60]. In this paper we first give some definitions and facts about table algebras. It is well known that every association scheme gives a Hecke-algebra which is a table algebra too. This leads to the natural question which properties of association schemes stay valid for table algebras. For instance, we prove the Second Isomorphism Theorem and the Jordan–Holder's theorem for standard table algebras.     

Sur la systole de la sphère au voisinage de la métrique standard

We study the systolic area (defined as the ratio of the area over the square of the systole) of the 2-sphere endowed with a smooth Riemannian metric as a function of this metric. This function, bounded from below by a positive constant over the space of metrics, admits the standard metric g ₀ as a critical point, although it does not achieve the conjectured global minimum: we show that for each tangent direction to the space of metrics at g ₀, there exists a variation by metrics corresponding to this direction along which the systolic area can only increase.