The stability of the exponential equation

We generalize the well-known Baker's superstability result for exponential mappings with values in the field of complex numbers to the case of an arbitrary commutative complex semisimple Banach algebra. It was shown by Ger that the superstability phenomenon disappears if we formulate the stability question for exponential complex-valued functions in a more natural way. We improve his result by showing that the maximal possible distance of an -approximately exponential function to the set of all exponential functions tends to zero as tends to zero. In order to get this result we have to prove a stability theorem for real-valued functions additive modulo the set of all integers .

     

镀液中Ce^3＋离子对锡镀层结构缺陷和可焊性的影响

应用荧光分析法、X光电子能谱法(XPS)及正电子湮没寿命谱法(PALS)等研究了从含硫酸铈添加剂的酸性光亮锡镀液获得的锡镀层结构缺陷与可焊性的关系。结果表明,电镀时Ce与Sn不发生共沉积,Ce~(3+)的主要作用是阻化Sn~(2+)的水解和氧化使镀液稳定,因而使锡镀层纯度提高、结构致密、表层氧含量减少,有利于提高镀层的可焊性。当Ce~(3+)浓度控制在3.5g/L左右时,可使镀层结构缺陷较少,可焊性较佳,说明结构缺陷是影响锡镀层可焊性的直接原因。     

固体超强酸SO_4~(2-)/SiO_2-TiO_2催化合成异维生素C钠

在异维生素C钠(D-VcNa)的合成过程中,以SO42-/S iO2-TiO2复合固体超强酸作为酯化反应催化剂,2-酮基-D-葡萄糖酸(2-KGA)和甲醇为原料,采用精馏脱水酯化工艺,不断除去酯化过程中产生的水。催化剂的最佳焙烧温度为550℃,催化剂用量为2.5%;反应时间3~4 h,产品收率为88.6%,催化剂的重复使用性较好,催化体系优于硫酸法。     

Geometry and combinatorics of Julia sets of real quadratic maps

For real a correspondence is made between the Julia setB forz(z–)², in the hyperbolic case, and the set of-chains±(±(±..., with the aid of Cremer's theorem. It is shown how a number of features ofB can be understood in terms of-chains. The structure ofB is determined by certain equivalence classes of-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and-chains. Certain Julia sets associated with the Feigenbaum function and some theorems of Lanford are discussed.Supported by NSF grant No. MCS-8104862.Supported by NSF grant No. MCS-8203325.     

The ring opening of cyclopropylidene to allene: global features of the reaction surface

Summary The global features of the groundstate ring opening of cyclopropylidene to allene are studied by means ofab-initio FORS MCSCF calculations based on a minimal AO basis set. The energy surface is completely mapped out in terms of three reaction coordinates, namely the CCC ring-opening angle and two angles describing the rotations of the CH₂ groups. For each choice of these three variables, the twelve remaining internal coordinates are optimized by energy minimization. In the initial phase of the reaction, as the CCC angle opens, the CH₂ groups rotate in a disrotatory manner, maintainingC _s symmetry. This uphill reaction path leads to a transition region which occurs early, for a CCC angle of about 84°. In this transition region the reaction path branches into two pathways which are each others' mirror images. The system exhibits thus abifurcating transition region. Passed this region, the two pathways are overall conrotatory in character. However, these downhill reaction paths to the products are poorly defined because, from a CCC opening angle of about 90° on,the CH ₂ groups can rotate freely and isoenergetically in a synchronized, cogwheel-like manner and this disrotatory motion can mix unpredictably with the conrotatory downhill motion. There is no preference for any one of the two reaction pathways yielding the two stereoisomers of allene and the reaction is thereforenonstereospecific with respect to the numbered hydrogen atoms. The global surface is documented by means of contour maps representing slices corresponding to constant CCC angles. The bifurcating transition region is mapped in detail.Operated for the U.S. Department of Energy by Iowa State University under Contract No. 7405-ENG-82. This work was supported by the office of Basic Energy Sciences     

添加剂铜和银离子对MnO2催化燃烧CH4的影响

催化燃烧法，由于起燃温度低、去除率高、适用氧浓度范围大、无二次污染、燃烧缓和等，是国内外治理有机废气时，回收利用能量最有效的方法之一［１］．但目前用于该过程的催化剂中均含有来源有限、价格昂贵的贵金属铂或钯［２］．因此，寻找来源丰富、价格低廉、性能相当...     

Preparation of poly(methyl methacrylate) and copolymers having enhanced thermal stabilities using sucrose-based comonomers and additives

A series of methyl methacrylate polymers have been prepared containing sucrose-based crosslinkers and additives. Thermogravimetry and long-term aging studies at 200°C show that sucrose-based alkyl and allyl ethers provide unprecedented thermal stability to linear, as well as crosslinked, poly (methyl methacrylate) or PMMA. Linear PMMA and PMMA crosslinked with trimethylolpropane trimethacrylate (TMPTMA) both degrade at 284°C. PMMA containing octa-O-crotylsucrose (1 mol %) degraded at 322°C. Depending on concentration, PMMA containing octa-O-allylsucrose (0.1-1.0 mol % and higher) degraded between 334 and 354°C, and PMMA containing 1′,6,6′-trimethacryloyl-2,3,3′,4,4′-penta-O-methylsucrose (0.1-1.0 mol %) degraded between 309 and 320°C. PMMA containing (1 mol % each) sucrose-based esters, ester-ether derivatives, all degraded at or below the degradation temperature of pure PMMA. Long-term air aging studies revealed that PMMA containing penta-O-methylsucrose trimethacrylate, octa-O-allylsucrose, and octa-O-crotylsucrose did not flow or sag after heating for 24 h at 200°C, but the polymers did show yellowing. While linear and crosslinked samples of PMMA containing compounds other than sucrose ethers lost more than 50% of their original weight within 15 h at 200°C, PMMA containing sucrose-based ethers lost about 8 and 20% of their original weight after 1 and 8.5 days, respectively. Herein we propose a unique mechanism by which saccharide ethers may be imparting this unprecedented thermal stabilization to PMMA. While tertiary hydrogens alpha to oxygens in saccharide ethers are stable to chain transfer during normal polymerization temperatures, they readily chain transfer at 200°C where PMMA is unstable. Chain transfer of these hydrogens is followed by fragmentation to produce alkyl, allyl or crotyl radicals, which combine with the macroradicals and terminate depropagation. © 1995 John Wiley & Sons, Inc.     

核磁共振研究MoDTP及其与ZnDTP的相互作用和机理

利用31P核磁共振谱研究了MoDTP及其与ZnDTP的相互作用，并用Timken实验机、SEM、DSC法分别考察了MoDTP与ZnDTP复合对润滑油板压、抗磨损及抗氧化性能的影响。结果表明：MoDTP与ZnDTP分子间有烷基和／或烷氧基的相互转换；二者并用在综合性能上有较好的协同增效作用。在此基础上，提出了MoDTP与ZnDTP协同增效作用的机理。     

Additives for the reduction of sulfur in FCC gasoline

Sulfur reduction ability of alumina supported zinc, gallium and zinc-gallium additives for fluid catalytic cracking catalysts was evaluated in a micro-activity test unit (MAT). Gallium/alumina showed the highest sulfur reduction of 31%, but the cracking activity of the catalyst was decreased. Zinc-gallium/alumina reduced sulfur in 24 wt.% without decreasing the base catalyst activity.     

Ionization thresholds and positions of avoided crossing of potassium Stark Rydberg states: a Stark-adapted quantum defect orbital treatment

We have calculated the positions of the avoided level crossings between (n+2)s, np states and nd, k Stark states in the Rydberg Stark states of the potassium atom with principal quantum number n comprised between 12 and 17. We have also studied the adiabatic electric field ionization thresholds for the above Rydberg states. Both the ionization thresholds and the positions of avoided crossings have been calculated using the recently developed Stark-adapted quantum defect orbital (SQDO) formalism. The presently reported values appear to be in very good agreement with the available theoretical and experimental data.