Small generators of the ideal class group

Assuming the Generalized Riemann Hypothesis, Bach has shown that the ideal class group of a number field can be generated by the prime ideals of having norm smaller than . This result is essential for the computation of the class group and units of by Buchmann's algorithm, currently the fastest known. However, once has been computed, one notices that this bound could have been replaced by a much smaller value, and so much work could have been saved. We introduce here a short algorithm which allows us to reduce Bach's bound substantially, usually by a factor 20 or so. The bound produced by the algorithm is asymptotically worse than Bach's, but favorable constants make it useful in practice.

     

Steady-state diffusion regime in solid-phase microextraction kinetics

The temporal evolution of diffusion-controlled analyte accumulation in solid-phase microextraction (SPME) is critically discussed in terms of the various aspects of steady-state diffusion in the two phases under conditions of fast exchange of the analyte at the solid phase film/water interface. For partition coefficients (K_sw) much larger than unity and a sufficiently thin polymer film, the concentration gradient of the analyte in the polymer phase is largely insignificant. The growth of the accumulated amount of analyte is then adequately described by the well-known exponential expression for steady-state diffusion under non-depletive conditions, provided the initial transient stage is properly taken into account. In case of fiber-type solid phases, the cylindrical nature of the diffusion complicates the nature of the transient stage as well as the magnitude of the steady-state flux.     

Sol‐Gel‐Derived Biosensor Based on Plant Tissue: The Inhibitory Effect of Atrazine on Polyphenol Oxidase Activity for Determination of Atrazine

This work presents a sol‐gel based biosensor for atrazine determination which has been obtained by introducing the enzyme polyphenol oxidase from apple tissue in a sol‐gel matrix. Apple tissue acts as a molecular recognition element. Atrazine is an inactive compound electrochemically; redox coupling of dopamine was used for studying atrazine behavior. Atrazine was determined by monitoring the inhibition power of polyphenol oxidase activity. The measurements were performed in 0.1 M KH₂PO₄‐NaOH buffer (pH 7.5). The effect of various experimental parameters such as pH, concentration of buffer, concentration of dopamine, incubation time and matrix composition has been investigated for optimum analytical performance. The biosensor consisted of 10.3% (w/w) of apple tissue. The bioelectrode exhibits a linear response for dopamine and atrazine concentrations in the range of 5.66 × 10^?6?2.27 × 10^?3M and 1 × 10^?5 ?1 × 10^?4 M with a detection limit of 4.2 × 10^?6 and 5.5 × 10^?6 M, respectively. A correlation coefficient of 0.9945 and a relative standard deviation (R.S.D.) of 3.29% for dopamine, 0.9944 and 3.69% for a trazine were achieved.     

Cu(001)表面CO吸附单层结构和电子态的第一性原理研究

用密度泛函理论(DFT)研究了Cu(001)表面CO吸附单层的表面性质. 总能计算结果表明, 顶位结构总能最低, 相应位置的CO分子吸附能最大. 谷位吸附结构的衬底原子层间距相对于清洁表面的膨胀量约为10%, 从而导致了谷位吸附的不稳定性. 在顶位、桥位和谷位三个吸附结构中, C和Cu原子之间的距离dC-Cu分别为0.1868、0.1975和0.2231 nm, 对应的CO分子键长为0.1154、0.1165 和0.1175 nm. 计算了CO分子的态密度(DOS). 结果表明, 衬底与分子的作用主要是分子和金属轨道的杂化. 在吸附过程中, 电荷主要从碳原子的s轨道向p轨道转移. 在顶位、桥位和谷位吸附结构中, 每个碳原子内电荷的转移量分别为0.45e、0.54e 和0.55e. 衬底向吸附分子的电荷转移量不大, CO 吸附分子层为一绝缘层.     

Ab Initio and DFT Studies on CO2 Interacting with Znq+–Imidazole (q=0, 1, 2) Complexes: Prediction of Charge Transfer through σ‐ or π‐Type Models

Using first‐principles methodologies, the equilibrium structures and the relative stability of CO₂@[Zn^q+Im] (where q=0, 1, 2; Im=imidazole) complexes are studied to understand the nature of the interactions between the CO₂ and Zn^q+–imidazole entities. These complexes are considered as prototype models mimicking the interactions of CO₂ with these subunits of zeolitic imidazolate frameworks or Zn enzymes. These computations are performed using both ab initio calculations and density functional theory. Dispersion effects accounting for long‐range interactions are considered. Solvent (water) effects were also considered using a polarizable continuum model approach. Natural bond orbital, charge, frontier orbital and vibrational analyses clearly reveal the occurrence of charge transfer through covalent and noncovalent interactions. Moreover, it is found that CO₂ can adsorb through more favorable π‐type stacking as well as σ‐type hydrogen‐bonding interactions. The inter‐monomer interaction potentials show a significant anisotropy that might induce CO₂ orientation and site‐selectivity effects in porous materials and in active sites of Zn enzymes. Hence, this study provides valuable information about how CO₂ adsorption takes place at the microscopic level within zeolitic imidazolate frameworks and biomolecules. These findings might help in understanding the role of such complexes in chemistry, biology and material science for further development of new materials and industrial applications.     

Synthesis and characterization of substituted garnet and perovskite-based lithium-ion conducting solid electrolytes

Titanium, tantalum-substituted Li₇La₃Zr_2-xA_xO₁₂ (LLZO, A?=?Ta, Ti) garnets, and chromium-substituted La_(2/3)-xLi_3xTi_1-yCr_yO₃ (LLTO) perovskites were prepared by a conventional solid-state reaction and the Pechini processes. The desired crystal phases were obtained by varying the calcination temperature and time, as well as the substitution concentration. All samples indicated decomposition of the precursors when heated above 750 °C and formation of the desired phase after heat treatment at higher temperatures. Neutron diffraction data shows the formation of a predominant cubic phase in the case of Ta-LLZO, and monoclinic phase with minor impurity phases for Cr-LLTO. Ionic conductivity for Ti-LLZO (Li₇La₃Zr_1.4Ti_0.6O₁₂), Ta-LLZO (Li_6.03La₃Zr_1.533Ta_0.46O₁₂), and Cr-LLTO (La_(2/3)-xLi_3xTi_0.9Cr_0.1O₃) at room temperature were found to be 5.21?×?10^?6, 1.01?×?10^?6, and 1.2?×?10^?4 S cm^?1, respectively. The activation energies of the compounds were determined from the Arrhenius plot and were 0.44 eV (Ti_0.6-LLZO), 0.54 eV (Ta_0.5-LLZO), and 0.20 eV (Cr_0.1-LLTO).     

Constructive Approximation in de Branges–Rovnyak Spaces

In most classical holomorphic function spaces on the unit disk in which the polynomials are dense, a function f can be approximated in norm by its dilates \(f_r(z):=f(rz)~(r<1)\). We show that this is not the case for the de Branges–Rovnyak spaces \(\mathcal{H}(b)\). More precisely, we exhibit a space \(\mathcal{H}(b)\) in which the polynomials are dense and a function \(f\in \mathcal{H}(b)\) such that \(\lim _{r\rightarrow 1^-}\Vert f_r\Vert _{\mathcal{H}(b)}=\infty \). On the positive side, we prove the following approximation theorem for Toeplitz operators on general de Branges–Rovnyak spaces \(\mathcal{H}(b)\). If \((h_n)\) is a sequence in \(H^\infty \) such that \(\Vert h_n\Vert _{H^\infty }\le 1\) and \(h_n(0)\rightarrow 1\), then \(\Vert T_{\overline{h}_n}f-f\Vert _{\mathcal{H}(b)}\rightarrow 0\) for all \(f\in \mathcal{H}(b)\). Using this result, we give the first constructive proof that, if b is a nonextreme point of the unit ball of \(H^\infty \), then the polynomials are dense in \(\mathcal{H}(b)\).     

Relative Stanley–Reisner theory and Upper Bound Theorems for Minkowski sums

In this paper we settle two long-standing questions regarding the combinatorial complexity of Minkowski sums of polytopes: We give a tight upper bound for the number of faces of a Minkowski sum, including a characterization of the case of equality. We similarly give a (tight) upper bound theorem for mixed facets of Minkowski sums. This has a wide range of applications and generalizes the classical Upper Bound Theorems of McMullen and Stanley.Our main observation is that within (relative) Stanley–Reisner theory, it is possible to encode topological as well as combinatorial/geometric restrictions in an algebraic setup. We illustrate the technology by providing several simplicial isoperimetric and reverse isoperimetric inequalities in addition to our treatment of Minkowski sums.     

高纯锗探测器的广泛应用和自主研制进展

以目前国际上极为活跃开展的暗物质探测、无中微子双 衰变研究为例,评述了高纯锗探测器的重要性及其广泛的应用前景。介绍了己开展的高纯锗单晶、探测器制备的关键技术研究进展:合作单位已研制出了用于高纯锗单晶材料制备的区熔炉、单晶炉;并制备出直径为20  50 cm、纯度为12N(< 41011  atoms/cm3)、位错< 5000 atoms/cm2 的锗单晶;掌握了高纯锗探测器(平面型、同轴型)制备的关键技术,用进口高纯锗单晶材料制备出的同轴型高纯锗探测器对射线的能量分辨率及探测效率均达到进口产品指标,使用自制的12N 高纯锗单晶材料己制备出平面型高纯锗探测器。呼吁加速高纯锗研制的自主创新步伐,尽早实现其国产化目标。The article reviews importance and wide applications of HPGe detector, especially the application on the dark matter search experiment and double beta decay experiment. The research progress on the Highpurity germanium single crystal and HPGe detector in China has been introduced. The cooperation partner developed new type zone-refining furnace and single crystal furnace. The ultra-purity germanium single crystal with 20~50 cm, purity up to 12N(net impurity concentration is less than 41011 atoms/cm3), and dislocation less than 5 000 /cm3 was prepared. The key technologies for preparing planar and coaxial HPGe detector were mastered. The coaxial detector, which has been made of imported ultra-purity germanium single crystal has excellent energy resolution and efficiency as the imported commercial detector. The planar detector using selfmade germanium single crystal was also successfully manufactured. The research group appeals for speeding up the pace of independent innovation on the high-purity germanium, and achieving the high-purity germanium localization as soon as possible.     

Comparison of the adsorption orientation for 2-mercaptobenzothiazole and 2-mercaptobenzoxazole by SERS spectroscopy

In this study, the adsorption orientation for 2-mercaptobenzothiazole (MBT) and 2-mercaptobenzoxazole (MBO) on to silver mirror and silver sol substrates have been studied by surface enhanced Raman scattering (SERS). The MBT and MBO were chemisorbed on both silver mirror and silver sol after deprotonation with a tilted orientation to the silver surfaces. The surface enhanced properties of MBT and MBO showed that the substrate of silver mirror was superior to the sliver sol. The SERS spectra of MBT and MBO revealed that both of the MBT and MBO were adsorbed on silver surfaces strongly by a common sulfur molecule and a sulfur atom from MBT and an oxygen atom from MBO. Therefore, the adsorption orientation of MBT and MBO was little tilted perpendicularly to the silver surfaces. The adsorption geometry did not undergo any significant changes in acidic and basic solutions. It showed that the adsorption orientation for MBT and MBO were stable in the both solutions.