On Descartes’ rule for polynomials with two variations of signs

Lithuanian Mathematical Journal - For sequences of d + 1 signs + and ? beginning with a + and having exactly two variations of sign, we give some sufficient conditions for the (non)existence...     

Algebraic decay and variable speeds in wavefront solutions of a scalar reaction-diffusion equation

Wavefront solutions of scalar reaction-diffusion equations havebeen intensively studied for many years. There are two basiccases, typified by quadratic and cubic kinetics. An intermediatecase is considered in this paper, namely, u_l = u_xx + u²(1 –u). It is shown that there is a unique travelling-wave solution,with a speed 1/2, for which the decay to zero ahead of the waveis exponential with x. Moreover, numerical evidence is presentedwhich suggests that initial conditions with such exponentialdecay evolve to this travelling-wave solution, independentlyof the half-life of the initial decay. It is then shown thatfor all speeds greater than 1/2 there is also a travelling-wavesolution, but that these faster waves decay to zero algebraically,in proportion to 1/x. The numerical evidence suggests that initialconditions with such a decay rate evolve to one of these fasterwaves; the particular speed depends in a simple way on the detailsof the initial condition. Finally, initial conditions decayingalgebraically for a power law other than 1/x are considered.It is shown numerically that such initial conditions evolveeither to an algebraically decaying travelling wave, or in somecases to a wavefront whose shape and speed vary as a functionof time. This variation is monotonic and can be quite pronounced,and the speed is a function of u as well as of time. Using asimple linearization argument, an approximate formula is derivedfor the wave speed which compares extremely well with the numericalresults. Finally, the extension of the results to the more generalcase of u_l = u_xx + u^m(1 – u), with m > 1, is discussed.     

钙钛矿结构RFeO3晶体的磁化跃迁效应研究进展

钙钛矿稀土正铁氧体RFeO₃具有丰富的磁性,这主要源于4f电子层的稀土离子和3d电子层的铁离子之间复杂的相互作用。磁化跃迁作为RFeO₃体系中的重要现象,是指体系中的稀土离子磁矩和铁离子磁矩在特定的磁场和温度下发生180°旋转,宏观表现为磁热曲线中磁化强度发生断崖式变化。本文综述了不同化合物RFeO₃的两种磁化跃迁现象,第一类磁化跃迁通常具有补偿点,F_R与F_Fe的排列耦合方向不变,第二类磁化跃迁则相反,且两类磁化跃迁出现的温区受外加磁场的调控。     

无水坝抽水蓄能系统高压溶气问题研究

无水坝抽水蓄能系统利用封闭容器内的高压气体构建虚拟水坝,是兼具压缩空气储能和抽水蓄能优点的新型储能系统。但该系统的封闭容器内水和气在高压状态共存有可能造成水中溶气,从而对水轮机造成汽蚀等破坏。本文采用实际气体状态方程及分子动力学模拟方法,研究了宽广的压力、温度范围下气体在水中的溶解及扩散规律,揭示了水中气体溶解量随时间和水深的变化规律。研究结果表明释能结束后保证水-气共容舱内剩余水的高度大于0.5 m时,高压溶气不会对水轮机产生危害,该结论对系统的工程应用及推广具有指导意义。     

母乳中溴代/氯代阻燃剂及其代谢产物的分析检测方法

建立了低分辨气相色谱-负化学源质谱法(GC/NCI-LRMS)定性与定量检测母乳中的溴代/氯代阻燃剂及其代谢产物的方法。所检测的溴代/氯代阻燃剂及其代谢产物分为中性化合物和羟基化合物两部分。采用RTX-1614(30 m)作为色谱分离柱,在优化的色谱条件下对8种多溴联苯醚PBDEs(包括BDE209)及其甲氧基代谢产物MeO-PBDEs,多种其它阻燃剂及代谢物等中性化合物同时进行了分离检测;采用DB-5(30 m)作为色谱分离柱,在优化的色谱条件下分离检测了9种羟基多溴联苯醚OH-PBDEs。在母乳样本中加入代用标准或内标,经过超声提取、液液萃取、硅胶净化和浓缩定容等预处理后,分别对中性和羟基化合物进行测定。十溴联苯醚、其它多溴联苯醚、甲氧基多溴联苯醚、得克隆及脱氯产物、其它阻燃剂等中性化合物,及羟基多溴联苯醚在两个添加浓度水平的回收率分别为66.5%～75.4%,84.2%～126.4%,60.9%～115.1%,86.7%～104.9%,42.9%～113.8%和64.7%～129.5%;中性化合物的相对标准偏差均小于22%,羟基化合物的相对标准偏差均小于30%。利用本方法对我国电子垃圾拆解区人体母乳中的目标物进行了分析检测,结果可靠。     

Efficient and green syntheses of novel γ-aminophosphonate and phosphine oxide derivatives

Two synthetic protocols leading to novel γ-aminophosphonate and phosphine oxide derivatives, by reductive amination of γ-phosphonylketones, are reported. The first method involved a two-step procedure. Imine intermediates were first isolated from the p-toluenesulfonic acid-catalyzed reaction of primary amines with γ-ketophosphonates and phosphine oxides, then reduced with NaBH₄ in refluxing ethanol. The second method consists of a one-pot procedure which includes the condensation of γ-ketophosphonates and phosphine oxides with primary amines, in the presence of molecular sieves, followed by reduction with NaBH₄. These methods offer significant advantages over prior reports, such as efficiency, generality, and good yields. Furthermore, they are green protocols avoiding hazardous hydrides and solvents.     

多孔有机盐单晶的合成及各向异性质子导电性能

以cis,cis-1,3,5-三氨基环己烷·3HBr和均苯四甲酸在室温下通过离子键构筑了具有规整形貌和大尺寸的晶态多孔有机盐CPOS-10, 其具有较好的热稳定性和永久多孔性. 得益于规整形貌及大尺寸单晶, 首次实现了对多孔有机盐单晶各向异性质子导电性能的研究, 并结合晶体结构探索了各向异性质子导电的机理. 结果表明, 水分子浓度对CPOS-10质子电导率的大小具有重要作用, 骨架内水分子浓度高的晶面更易于与极性基团构成氢键网络, 促进质子传导, 利用此网络的质子传导具有更高的质子电导率. 因此, 骨架内水分子的不均匀分布是导致单晶各向异性质子导电的主要原因. 对CPOS-10单晶各向异性质子导电性能的探索可为研究多孔有机盐的质子导电机理提供重要的依据.     

Log-Polynomial Period Functions for Hecke Groups

In this article we shall determine the automorphic integrals of positive and negative integral weight associated with the full modular group and some Hecke groups. This will be done by using the Hecke Correspondence. We will also give a characterization of multiplier systems of real weight for Hecke groups.     

注入锁定铜蒸气激光器的实验研究

使用两台相同的望远镜式非稳腔铜蒸气激光器,通过一块45°玻璃平板作腔的耦合组成匹配的注入锁定系统,研究了同步、注入信号功率和光束孔径大小等因素对输出功率和方向性的影响,实验结果清楚地表明,注入信号的作用在于抑制腔内高阶横模(包括被放大的自发发射)的竞争,使高增益介质的激光器既提高效率又改善方向性。注入锁定器件功率水平在5左右的情况下,其结果与单独非稳腔振荡相比,输出功率增加30～40％,方向性改善一倍以上。