Kloosterman sums with multiplicative coefficients

Let f(n)be a multiplicative function satisfying |f(n)|≤1,q(≤N~2)be a positive integer and a be an integer with(a,q)= 1.In this paper,we shall prove that ∑n≤N(n,q)=1f(n)e(an/q)■(1/2)(τ(q)/q)N loglog(6N)+ q~(1/4+ε/2)N~(2/1)(log(6N))~(1/2)+N/(1/2)(loglog(6N)),where n is the multiplicative inverse of n such that nn ≡ 1(mod q),e(x)= exp(2πix),and τ(·)is the divisor function.     

A priori estimates and blow-up behavior for solutions of −QNu = Veu in bounded domain in ℝN

Let Q_N be an N-anisotropic Laplacian operator, which contains the ordinary Laplacian operator, N-Laplacian operator and the anisotropic Laplacian operator. We firstly obtain the properties of Q_N, which contain the weak maximal principle, the comparison principle and the mean value property. Then a priori estimates and blow-up analysis for solutions of Q_Nu in bounded domain in ?^N, N ≥ 2 are established. Finally, the blow-up behavior of the only singular point is also considered.     

A new search for the atomic EDM of 129Xe at FRM-II

Permanent electric dipole moments (EDMs) arise due to the breaking of time-reversal or, equivalently, CP-symmetry. Although EDM searches have so far only set upper limits, which are many orders of magnitude larger than Standard Model (SM) predictions, the motivation for more sensitive searches is stronger than ever. A new effort at FRM-II incorporating ¹²⁹Xe and ³He as a co-magnetometer can potentially improve the current limit. The noble gas mixture of ¹²⁹Xe and ³He is simultanously polarized by spin-exchange optical pumping and then transferred into a high-performance magnetically shielded room. Inside, both species can freely precess in the presence of applied magnetic and electric fields. The precession signals are detected by LTc SQUID sensors. In EDM cells with silicon electrodes we observed spin lifetimes in excess of 2500 s without and with high-voltage applied. This meets one requirement to achieve our goal of improving the EDM limit on ¹²⁹Xe by several orders of magnitude.     

Hierarchically Structured Porous Silica Spheres by Microemulsion/Vesicle Templating for Hydrodesulfurization of Fluid Catalytic Cracking Diesel

A series of hierarchically structured porous silica sphere (HSPSS) materials are successfully fabricated by a facile, one‐step microemulsion/vesicle bimodal method in a multicomponent microemulsion system of P123/n‐butanol/1,3,5‐trimethylbenzene/KCl/H₂O (surfactant/cosurfactant/oil/salt/water). The pore structures of the obtained HSPSS products consist of mesocellular foam and mesostructured vesicles. In contrast to the traditional porous silica materials the new structures combine two separate, distinct mesophases with different‐sized mesovoids in a single porous sphere. Moreover, the proportion of every mesophase in obtained HSPSS can be easily adjusted by tuning the initially added amount of n‐butanol or KCl in this multicomponent microemulsion system. When the molar ratio of KCl/tetraethoxysilane is 2.15, the obtained HSPSS material is turned into uniform mesostructured vesicle silica spheres, which consist of many small diameter vesicle particles. The hydrodesulfurization (HDS) activity of fluid catalytic cracking diesel over the HSPSS was tested. HSPSS‐0.75‐1.43 catalyst support with multiple mesoporous structures shows the highest HDS efficiency (98.5%) among all the studied catalysts.     

Promotional effect of cobalt addition on catalytic performance of Ce<Subscript>0.5</Subscript>Zr<Subscript>0.5</Subscript>O<Subscript>2</Subscript> mixed oxide for diesel soot combustion

A series of Co-modified Ce_0.5Zr_0.5O₂ catalysts with different concentrations of Co (mass %: 0, 2, 4, 6, 8, 10) was investigated for diesel soot combustion. Ce_0.5Zr_0.5O₂ was prepared using the coprecipitation method and Co was loaded onto the oxide using the incipient wetness impregnation method. The activities of the catalysts were evaluated by thermogravimetric (TG) analysis and temperature-programmed oxidation (TPO) experiments. The results showed the soot combustion activities of the catalysts to be effectively improved by the addition of Co, 6 % Co/Ce_0.5Zr_0.5O₂ and that the 8 % Co/Ce_0.5Zr_0.5O₂ catalysts exhibited the best catalytic performance in terms of lower soot ignition temperature (T_i at 349°C) and maximal soot oxidation rate temperature (T_m at 358°C). The reasons for the improved activity were investigated by X-ray diffraction (XRD), Brunauer–Emmett–Teller (BET), H₂ temperature-programmed reduction (H₂-TPR), X-ray photoelectron spectroscopy (XPS) and transmission electron microscopy (TEM). These results revealed that the presence of Co could lower the reduction temperature due to the synergistic effect between Co and Ce, thereby improving the activity of the catalysts in soot combustion. The 6 % Co catalyst exhibited the best catalytic performance, which could be attributed to the greater amounts of Co³⁺ and surface oxygen species on the catalyst.     

Determination of the modes of action and synergies of xylanases by analysis of xylooligosaccharide profiles over time using fluorescence‐assisted carbohydrate electrophoresis

The structure of xylan, which has a 1,4‐linked β‐xylose backbone with various substituents, is much more heterogeneous and complex than that of cellulose. Because of this, complete degradation of xylan needs a large number of enzymes that includes GH10, GH11, and GH3 family xylanases together with auxiliary enzymes. Fluorescence‐assisted carbohydrate electrophoresis (FACE) is able to accurately differentiate unsubstituted and substituted xylooligosaccharides (XOS) in the heterogeneous products generated by different xylanases and allows changes in concentrations of specific XOS to be analyzed quantitatively. Based on a quantitative analysis of XOS profiles over time using FACE, we have demonstrated that GH10 and GH11 family xylanases immediately degrade xylan into sizeable XOS, which are converted into smaller XOS in a much lower speed. The shortest substituted XOS produced by hydrolysis of the substituted xylan backbone by GH10 and GH11 family xylanases were MeGlcA²Xyl₃ and MeGlcA²Xyl₄, respectively. The unsubstituted xylan backbone was degraded into xylose, xylobiose, and xylotriose by both GH10 and GH11 family xylanases; the product profiles are not family‐specific but, instead, depend on different subsite binding affinities in the active sites of individual enzymes. Synergystic action between xylanases and β‐xylosidase degraded MeGlcA²Xyl₄ into xylose and MeGlcA²Xyl₃ but further degradation of MeGlcA²Xyl₃ required additional enzymes. Synergy between xylanases and β‐xylosidase was also found to significantly accelerate the conversion of XOS into xylose.     

Progress of pyrene-based organic semiconductor in organic field effect transistors

Thanks to the pure blue emitting, high planarity, electron rich and ease of chemical modification, pyrene has been thoroughly investigated for applications in organic electronics such as organic light emitting diodes (OLEDs), organic field effect transistors (OFETs), and organic solar cells (OSCs). Especially, great progresses have been made of pyrene-based organic semiconductors for OFETs in past decades. Due to the difference of molecular structure, pyrene-based organic semiconductors are divided into three categories, pyrene as terminal group, pyrene as center core and fused pyrene derivatives. This minireview gives a brief introduction of the structure-property relationship and application in OFETs about most of pyrene-based semiconducting materials since 2006, illustrating that pyrene is a good building block to construct semiconductors with superior transport property for OFETs. Finally, we provide a summary concerning the methodology to improve the transport property of the pyrene-based semiconducting materials as well as an outlook.     

Facile Assembly of Benzo[b]naphtho[2,3‐d]azocin‐6(5 H)‐ones by a Palladium‐Catalyzed Double Carbometalation

The palladium‐catalyzed reaction of 2‐alkynylanilines with 2‐(2‐bromobenzylidene)cyclobutanone as an efficient route to 7,8‐dihydrobenzo[b]naphtho[2,3‐d]azocin‐6(5 H)‐ones was developed. The fused eight‐membered ring was constructed conveniently. During the reaction process, double carbometalation was involved, which resulted in excellent selectivity with the formation of three new bonds. This transformation is highly efficient and leads to fused polycycles in good to excellent yields with good functional group tolerance.     

Molecular Orbital Controlling Donor Moiety for High‐Efficiency Thermally Activated Delayed Fluorescent Emitters

A new donor moiety, 7,7,13,13‐tetramethyl‐7,13‐dihydro‐5H‐indeno[1,2‐b]acridine (IAc), was developed to control the highest occupied molecular orbital (HOMO) dispersion of thermally activated delayed fluorescent (TADF) emitters. The IAc unit expanded the HOMO dispersion of the emitters and increased the quantum efficiency of the TADF devices up to 20.9 %.