Solution of the generalized conjugacy problem for words in pure subgroups of Artin groups of finite type

The notion of pure subgroup of an Artin group of finite type is introduced. The decidability of the generalized conjugacy problem for pure subgroups of Artin groups of finite type is proved.     

On stochastic games with additive reward and transition structure

In this paper, we introduce a new class of two-person stochastic games with nice properties. For games in this class, the payoffs as well as the transitions in each state consist of a part which depends only on the action of the first player and a part dependent only on the action of the second player.For the zero-sum games in this class, we prove that the orderfield property holds in the infinite-horizon case and that there exist optimal pure stationary strategies for the discounted as well as the undiscounted payoff criterion. For both criteria also, finite algorithms are given to solve the game. An example shows that, for nonzero sum games in this class, there are not necessarily pure stationary equilibria. But, if such a game possesses a stationary equilibrium point, then there also exists a stationary equilibrium point which uses in each state at most two pure actions for each player.     

The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games

In 1951, Dvoretzky, Wald and Wolfowitz (henceforth DWW) showed that corresponding to any mixed strategy into a finite action space, there exists a pure-strategy with an identical integral with respect to a finite set of atomless measures. DWW used their theorem for purification: the elimination of randomness in statistical decision procedures and in zero-sum two-person games. In this short essay, we apply a consequence of their theorem to a finite-action setting of finite games with incomplete and private information, as well as to that of large games. In addition to simplified proofs and conceptual clarifications, the unification of results offered here re-emphasizes the close connection between statistical decision theory and the theory of games.A first draft of this paper was completed when Khan and Rath were visiting the Institute for Mathematical Sciences at the National University of Singapore in August 2003; they thank the Institute for supporting their visit. A preliminary version was presented at the Midwest Economic Theory Conference held at Indiana University, Bloomington in October 2003; the authors are grateful to Eric Balder, Robert Becker, William Thomson and Myrna Wooders for questions and helpful suggestions.     

Directed random walks in random environments

We use holding time methods to study the asymptotic behavior of pure birth processes with random transition rates. Both the normal and slow approaches to infinity are studied. Fluctuations are shown to obey the central limit theorem for almost all sample-transition rates. Our results are stronger, and our proofs simpler, then those of recently published studies.     

Roles of Oxygen Vacancies of CeO2 and Mn-Doped CeO2 with the Same Morphology in Benzene Catalytic Oxidation

Mn-doped CeO₂ and CeO₂ with the same morphology (nanofiber and nanocube) have been synthesized through hydrothermal method. When applied to benzene oxidation, the catalytic performance of Mn-doped CeO₂ is better than that of CeO₂, due to the difference of the concentration of O vacancy. Compared to CeO₂ with the same morphology, more oxygen vacancies were generated on the surface of Mn-doped CeO₂, due to the replacement of Ce ion with Mn ion. The lattice replacement has been analyzed through XRD, Raman, electron energy loss spectroscopy and electron paramagnetic resonance technology. The formation energies of oxygen vacancy on the different exposed crystal planes such as (110) and (100) for Mn-doped CeO₂ were calculated by the density functional theory (DFT). The results show that the oxygen vacancy is easier to be formed on the (110) plane. Other factors influencing catalytic behavior have also been investigated, indicating that the surface oxygen vacancy plays a crucial role in catalytic reaction.     

Structural analysis of unstable norbixin isomers guided by pure shift nuclear magnetic resonance

We report the analysis of complex samples obtained during the microwave irradiation/heating of norbixin, which has been identified as a potential therapeutic target for age-related macular degeneration (AMD). In this context, identifying the different isomers that are obtained during its degradation is of primary importance. However, this characterization is challenging because, on the one hand, some of these isomers are unstable, and on the other hand, the ¹H spectra of these isomeric mixtures are poorly resolved. We could successfully apply 1D pure shift experiments to obtain ultrahigh-resolution ¹H nuclear magnetic resonance (NMR) spectra of the norbixin isomer samples and exploit their information content to analyze complementary 2D NMR data and describe accurately their isomeric composition.     

激光剥蚀-电感耦合等离子体质谱法测定纯钌中19种杂质元素

建立了激光剥蚀-电感耦合等离子-体质谱法(LA-ICP-MS)法测定纯钌中Mg、Al、Fe、Ni、Cu、Zn、Rb、Rh、Pd、Mo、Ag、Cd、Sn、Ba、Ir、Pt、Au、Pb和Si等19种杂质元素的分析方法。优化了仪器参数：给出了激光能量为60%,剥蚀孔径为110 μm,扫描速率为50 μm/s,脉冲频率为10Hz,载气流量为0.74L/min条件下,信号强度和稳定性最佳。由于钌标准样品难以获得,本文选择用纯钌粉样品,高温高压溶解后,采用ICP-MS定值所测元素（除硅外）。根据钌粉样品的ICP-MS定值结果确定了测定元素的相对灵敏度因子（RSF）,对归一法结果进行较正,提高了方法准确度。方法的检出限为：0.001~12.81μg/g,相对标准偏差(RSD)为：10%～30%。采用本方法测定纯钌中杂质元素,结果与ICP-MS测定的结果吻合。     

Bi/TiO_2复合纳米纤维制备及可见光催化性能

以电纺TiO_2纳米纤维为基质,EDTA为鳌合剂和吸附剂,采用溶剂热法制备Bi/TiO_2复合纳米纤维光催化材料,利用X射线粉末衍射(XRD)、扫描电镜(SEM)、X射线能量色散谱(EDS)、透射电镜(TEM)、紫外-可见漫反射光谱(UV-Vis DRS)和荧光光谱(PL)等分析测试手段对样品的物相、形貌和光学性能等进行表征,以罗丹明B(Rh B)为模拟有机污染物,考察了样品的光催化性能。结果表明:EDTA在复合纳米纤维的合成过程中起到关键作用,通过改变EDTA的用量可以有效控制纤维表面构筑单质Bi纳米球的大小和覆盖密度。所制备的复合纳米纤维具有良好的可见光催化活性和稳定性,当单质Bi的负载量为65%时光催化活性最强,可见光照射180 min,RhB的降解率达到96.40%,循环使用5次降解率仍保持在91%以上。     

Influence of PtMo Structure and Composition on the Adsorption Energies, Adsorption Site and Vibrational Frequency of Carbon Monoxide

Density functional theory periodic slab calculations were carried out for CO adsorption on a series of Mo modified Pt(111) surfaces to provide an insight into the interaction between CO and doped metal surface, an important issue in CO oxidation as well as in promotion and poisoning effects of catalysis. The modification of adsorption properties with respect to those of adsorption on the pure Mo(110) and Pt(111) is described in terms of changes in the adsorption energies, adsorption sites and vibrational properties occurring upon alloying. We believe that the present DFT calculations can provide important information into optimal alloy composition for CO-tolerance, which is not easily obtained by experimental methods.     

Band‐selective excited ultrahigh resolution PSYCHE‐TOCSY: fast screening of organic molecules and complex mixtures

Precise assignments of ¹H atomic sites and establishment of their through‐bond COSY or TOCSY connectivity are crucial for molecular structural characterization by using ¹H NMR spectroscopy. However, this exercise is often hampered by signal overlap, primarily because of ¹H–¹H scalar coupling multiplets, even at typical high magnetic fields. The recent developments in homodecoupling strategies for effectively suppressing the coupling multiplets into nice singlets (pure‐shift), particularly, Morris's advanced broadband pure‐shift yielded by chirp excitation (PSYCHE) decoupling and ultrahigh resolution PSYCHE‐TOCSY schemes, have shown new possibilities for unambiguous structural elucidation of complex organic molecules. The superior broadband PSYCHE‐TOCSY exhibits enhanced performance over the earlier TOCSY methods, which however warrants prolonged experimental times due to the requirement of large number of dwell increments along the indirect dimension. Herein, we present fast and band‐selective analog of the broadband PSYCHE‐TOCSY, which is useful for analyzing complex organic molecules that exhibit characteristic yet crowded spectral regions. The simple pulse scheme relies on band‐selective excitation (BSE) followed by PSYCHE homodecoupling in the indirect dimension. The BSE‐PSYCHE‐TOCSY has been exemplified for Estradiol and a complex carbohydrate mixture comprised of six constituents of closely comparable molecular weights. The experimental times are greatly reduced viz., ~20 fold for Estradiol and ~10 fold for carbohydrate mixture, with respect to the broadband PSYCHE‐TOCSY. Furthermore, unlike the earlier homonuclear band‐selective decoupling, the BSE‐PSYCHE‐decoupling provides fully decoupled pure‐shift spectra for all the individual chemical sites within the excited band. The BSE‐PSYCHE‐TOCSY is expected to have significant potential for quick screening of complex organic molecules and mixtures at ultrahigh resolution. Copyright © 2015 John Wiley & Sons, Ltd.