Quasinilpotency of the operators in picard-lindelöf iteration

The superlinear convergence of Picard-Lindelöf iteration on finite time intervals is studied by considering the resolvent operator as an operator-valued entire function. The main conclusions of this paper are related to the following fact: the convergence properties of the iteration when applied to a large and sparse system are largely determined by the graph properties of the decomposition and are partly insensitive in terms of the values of the elements of the matrices.     

Kinetics and modeling of (R,S)‐1‐phenylethanol acylation over lipase

The kinetics of the acylation of (R,S)‐1‐phenylethanol was investigated using lipase as a catalyst. The main parameters were temperature, reaction atmosphere, different acyl donors, and different amounts of acyl donor as well as the presence of some additives in the reaction mixture. The initial reaction rate increased with increasing temperature and with a decreasing amount of an acyl donor. The activated esters, such as isopropenyl‐ and vinyl acetate, exhibited very high acylation rates for R‐1‐phenylethanol, whereas low rates were obtained with ethyl acetate and 2‐methoxyethyl acetate. The addition of water and acetophenone decreased the acylation rate. A kinetic model was developed based on a sequential step mechanism, in which enzyme was reacting in the first step with an acyl donor followed by the reaction of a modified enzyme complex with the reactant, R‐1‐phenylethanol. Comparison with experimental data obtained at different temperatures allowed simplification of this model, leading to a kinetic equation with just one apparent parameter. The influence of the amount of acyl donor, ethyl acetate, could be quantitatively described by taking into account the competitive inhibition of the ethanol produced. The rate constants and apparent activation energy for experiments performed under different temperatures and the amounts of acylation agent were determined. The apparent activation energy was 24.5 kJ/mol. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 629–639, 2010     

Ultrasonic Irradiation in Enantioselective Hydrogenation of 1-Phenyl-1,2-Propanedione

In the presence of ultrasound both the initial hydrogenation rate of 1-phenyl-1,2- propanedione and the enantiomeric excess of the main product, i.e. (R)-1-hydroxy- 1-phenylpropanone, increased by 75 % and 52 % in toluene, respectively, as compared to the silent hydrogenation.     

Accelerated beam tracing algorithm

Determining early specular reflection paths is essential for room acoustics modeling. Beam tracing algorithms have been used to calculate these paths efficiently, thus allowing modeling of acoustics in real-time with a moving listener in simple, or complex but densely occluded, environments with a stationary sound source. In this paper, it is shown that beam tracing algorithms can still be optimized by utilizing the spatial coherence in path validation with a moving listener. Since the precalculations required for the presented technique are relatively fast, the acoustic reflection paths can be calculated even for a moving source in simple cases. Simulations were performed to show how the accelerated algorithm compares with the basic algorithm with varying scene complexity and occlusion. Up to two-orders of magnitude speed-up was achieved.     

碳点的高性能化和功能化改性:方法、特性与展望

碳点作为一种新型碳纳米材料,由于其出色的光学性能、低毒性、良好的生物相容性和易修饰性而被广泛应用于各个领域。为了满足不同领域的需求,几种用以调控碳点光学性能的方法已被提出,例如杂原子掺杂、半导体量子点掺杂、聚合物钝化和改性以及主-客体构建。其中,杂原子掺杂是通过单原子或多原子引入电子给体或受体改变其相邻碳原子的电子密度来增加荧光强度;半导体量子点也可与碳点进行复合提升电子分离效率而起到荧光增强的效果;就聚合物改性而言,聚合物不仅可以对碳点表面实施钝化和功能化,而且其固态(或固化)薄膜可以提供紧密的空间促进碳点表面的辐射跃迁起到荧光增强的效果。此外,由碳点-染料和多孔材料-碳点构成的两种主要的主-客体结构中,前者不仅对碳点的荧光发射强度有着促进的作用,更使得碳点具备了显著的红/近红外荧光发射性能,后者对固态发光碳点不仅提供了可能性和设计的灵活性,且为打开碳点新的应用领域提供了机会。本文将围绕四种碳点功能化的方法逐步展开讨论,并介绍相应碳点的光学性能、发光机理和潜在应用;论述功能化碳点的研究现状,并展望功能化碳点的研究方向。     

Polymer escape from a metastable Kramers potential: path integral hyperdynamics study

We study the dynamics of flexible, semiflexible, and self-avoiding polymer chains moving under a Kramers metastable potential. Due to thermal noise, the polymers, initially placed in the metastable well, can cross the potential barrier, but these events are extremely rare if the barrier is much larger than thermal energy. To speed up the slow rate processes in computer simulations, we extend the recently proposed path integral hyperdynamics method to the cases of polymers. We consider the cases where the polymers' radii of gyration are comparable to the distance between the well bottom and the barrier top. We find that, for a flexible polymers, the crossing rate (R) monotonically decreases with chain contour length (L), but with the magnitude much larger than the Kramers rate in the globular limit. For a semiflexible polymer, the crossing rate decreases with L but becomes nearly constant for large L. For a fixed L, the crossing rate becomes maximum at an intermediate bending stiffness. For the self-avoiding chain, the rate is a nonmonotonic function of L, first decreasing with L, and then, above a certain length, increasing with L. These findings can be instrumental for efficient separation of biopolymers.     

Separation of different ion structures in atmospheric pressure photoionization-ion mobility spectrometry-mass spectrometry (APPI-IMS-MS)

This study demonstrates how positive ion atmospheric pressure photoionization-ion mobility spectrometry-mass spectrometry (APPI-IMS-MS) can be used to produce different ionic forms of an analy te and how these can be separated. When hexane:toluene (9:1) is used as a solvent, 2,6-di-tert-butylpyridine (2,6-DtBPyr) and 2,6-di-tert-4-methylpyridine (2,6-DtB-4-MPyr) efficiently produce radical cations [M]⁺ and protonated [M + H]⁺ molecules, whereas, when the sample solvent is hexane, protonated molecules are mainly formed. Interestingly, radical cations drift slower in the drift tube than the protonated molecules. It was observed that an oxygen adduct ion, [M + O₂]⁺, which was clearly seen in the mass spectra for hexane:toluene (9:1) solutions, shares the same mobility with radical cations, [M]⁺. Therefore, the observed mobility order is most likely explained by oxygen adduct formation, i.e., the radical cation forrning a heavier adduct. For pyridine and 2-tert-butylpyridine, only protonated molecules could be efficiently formed in the conditions used. For 1- and 2-naphthol it was observed that in hexane the protonated molecule typically had a higher intensity than the radical cation, whereas in hexane:toluene (9:1) the radical cation [M]⁺ typically had a higher intensity than the protonated molecule [M + H]⁺. Interestingly, the latter drifts slower than the radical cation [M]⁺, which is the opposite of the drift pattern seen for 2,6-DtBPyr and 2,6-DtB-4-MPyr.     

Direct electrochemistry and spectroelectrochemistry of osmium substituted horseradish peroxidase

In this contribution the substitution of the central protoporphyrin IX iron complex of horseradish peroxidase by the respective osmium porphyrin complex is described. The direct electrochemical reduction of the Os containing horseradish peroxidase (OsHRP) was achieved at ITO and modified glassy carbon electrodes and in combination with spectroscopy revealed the three redox couples Os^IIIHRP/Os^IVHRP, Os^IVHRP/Os^VHRP and Os^VHRP/Os^VIHRP. The midpoint potentials differ dependent on the electrode material used with E_1/2 (Os^III/IV) of − 0.4 V (ITO) and − 0.25 V (GC), E_1/2 (Os^IV/^V) of − 0.16 V (ITO) and + 0.10 V (GC), and E_1/2 (Os^V/VI)of + 0.18 V (ITO), respectively. Moreover, with immobilised OsHRP the direct electrocatalytic reduction of hydrogen peroxide and tert-butyl hydroperoxide was observed. In comparison to electrodes modified with native HRP the sensitivity of the OsHRP-electrode for tert-butyl hydroperoxide is higher.     

Comparison of chromatographic ion-exchange resins V. Strong and weak cation-exchange resins

Strong and weak cation-exchangers were compared for a number of chromatographic parameters, i.e. pH dependence, efficiency, binding strength, particle size distribution, static and dynamic capacity, and scanning electron microscopy (SEM) pictures. Chromatographic resins investigated were Fractogel EMD SO3- (M), Fractogel EMD SE Hicap (M), Fractogel EMD COO- (M), MacroPrep 25S, MacroPrep High S, MacroPrep CM, CM HyperZ, and Matrex Cellufine C-500. Testing was done with three proteins: Anti-FVII Mab (IgG), aprotinin, and lysozyme. For lysozyme and aprotinin with pI above experimental pH, dependence of pH on retention was generally low, though some pronounced decrease of retention with increasing pH was observed for CM HyperZ. For Anti-FVII Mab with pI<7.5, binding was observed on several resins at pH 7.5. Efficiency results present the expected trend of increasing dependence of plate height as a function of increasing flow rate, and the highest flow dependence was observed for Fractogel EMD COO-. Particle size distribution was determined by two independent methods, coulter counting and SEM pictures, with fair agreement. Binding strength data of cation-exchange resins as a function of ionic strength depends on the protein, but binding and elution at high salt concentration may in general be performed with MacroPrep resins. Comparison of dynamic capacity data at 10% break-through and static capacity measurements shows that a very diverse utilization of approximately 25-90% of the total available capacity is employed during chromatographic operation. The effect of competitive binding from yeast fermentation components on dynamic binding capacity of aprotinin was studied showing a significant decrease in binding capacity. Sepharose FF, Toyopearl 650 M, and Ceramic HyperD F strong and weak cation-exchange resins were included in this study. Resins with good pure aprotinin capacity also performed well for aprotinin in fermentation broth, but the highest relative capacity was obtained with MacroPrep High S having a fairly low pure component dynamic capacity. Results of this paper may be used in the selection of resins for further testing in biopharmaceutical protein purification process development.