The Chemistry of Some Isopolar Analogues of Phosphoric and Pyrophosphoric Acids

Abstract

We have previously established that the α-fluorination of alkanephosphonates provides analogues of phosphate esters which have improved ‘isopolarity’ relative to simple alkanephosphonates.¹ This property is manifest, inter alia, in enhanced acidity and in the upfield shift for the ³¹P n.m.r. resonance. Indeed, for a range of halomethanephosphonic acids we have found the relationship “δ_P=9.61 (pK_a2 - 4.59) ppm” gives an excellent correlation between these parameters. In this context, the properties of CF₂CIPO(OR)₂ species, derived from the Michaelis-Becker reaction of dialkyl phosphonates with Freon 22, CF₂Cl₂, will be described.     

Metamaterial absorber integrated microfluidic terahertz sensors

Spatial overlap between the electromagnetic fields and the analytes is a key factor for strong light‐matter interaction leading to high sensitivity for label‐free refractive index sensing. Usually, the overlap and therefore the sensitivity are limited by either the localized near field of plasmonic antennas or the decayed resonant mode outside the cavity applied to monitor the refractive index variation. In this paper, by constructing a metal microstructure array‐dielectric‐metal (MDM) structure, a novel metamaterial absorber integrated microfluidic (MAIM) sensor is proposed and demonstrated in terahertz (THz) range, where the dielectric layer of the MDM structure is hollow and acts as the microfluidic channel. Tuning the electromagnetic parameters of metamaterial absorber, greatly confined electromagnetic fields can be obtained in the channel resulting in significantly enhanced interaction between the analytes and the THz wave. A high sensitivity of 3.5 THz/RIU is predicted. The experimental results of devices working around 1 THz agree with the simulation ones well. The proposed idea to integrate metamaterial and microfluid with a large light‐matter interaction can be extended to other frequency regions and has promising applications in matter detection and biosensing.

     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

库仑加线性位基态解析解

应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统.