New Equation for Predicting Pipe Friction Coefficients Using the Statistical Based Entropy Concepts

In general, this new equation is significant for designing and operating a pipeline to predict flow discharge. In order to predict the flow discharge, accurate determination of the flow loss due to pipe friction is very important. However, existing pipe friction coefficient equations have difficulties in obtaining key variables or those only applicable to pipes with specific conditions. Thus, this study develops a new equation for predicting pipe friction coefficients using statistically based entropy concepts, which are currently being used in various fields. The parameters in the proposed equation can be easily obtained and are easy to estimate. Existing formulas for calculating pipe friction coefficient requires the friction head loss and Reynolds number. Unlike existing formulas, the proposed equation only requires pipe specifications, entropy value and average velocity. The developed equation can predict the friction coefficient by using the well-known entropy, the mean velocity and the pipe specifications. The comparison results with the Nikuradse’s experimental data show that the R2 and RMSE values were 0.998 and 0.000366 in smooth pipe, and 0.979 to 0.994 or 0.000399 to 0.000436 in rough pipe, and the discrepancy ratio analysis results show that the accuracy of both results in smooth and rough pipes is very close to zero. The proposed equation will enable the easier estimation of flow rates.     

Synergistic cascade catalysis by metal nanoparticles and Lewis acids in hydrogen autotransfer

Of the many types of catalysis involving two or more catalysts, synergistic catalysis is of great interest because novel reactions or reaction pathways may be discovered when there is synergy between the catalysts. Herein, we describe a synergistic cascade catalysis, in which immobilized Au/Pd bimetallic nanoparticles and Lewis acids work in tandem to achieve the N-alkylation of primary amides to secondary amides with alcohols via hydrogen autotransfer. When Au/Pd nanoparticles were used with metal triflates, a significant rate acceleration was observed, and the desired secondary amides were obtained in excellent yields. The metal triflate is thought to not only facilitate the addition of primary amides to aldehydes generated in situ, but also enhance the returning of hydrogen from nanoparticles to hydrogen-accepting intermediates. This resulted in a more rapid turnover of the nanoparticle catalyst, and ultimately translated into an increase in the overall rate of the reaction. The two catalysts in this co-catalytic system work in a synergistic and cascade fashion, resulting in an efficient hydrogen autotransfer process.     

Super-hydrophobic transparent surface by femtosecond laser micro-patterned catalyst thin film for carbon nanotube cluster growth

In this work, super-hydrophobic surfaces were fabricated by femtosecond laser micro-machining and chemical vapor deposition to constitute hybrid scale micro/nano-structures formed by carbon nanotube (CNT) clusters. Nickel thin-film microstructures, functioning as CNT growth catalyst, precisely control the distribution of the CNT clusters. To obtain minimal heat-affected zones, femtosecond laser was used to trim the nickel thin-film coating. Plasma treatment was subsequently carried out to enhance the lotus-leaf effect. The wetting property of the CNT surface is improved from hydrophilicity to super-hydrophobicity at an advancing contact angle of 161 degrees. The dynamic water drop impacting test further confirms its enhanced water-repellent property. Meanwhile, this super-hydrophobic surface exhibits excellent transparency with quartz as the substrate. This hybrid fabrication technique can achieve super-hydrophobic surfaces over a large area, which has potential applications as self-cleaning windows for vehicles, solar cells and high-rise buildings.     

Loss reserving using loss aversion functions

This article discusses the determination of risk capital based on “aversion” functions. Aversion functions weigh different outcomes according to perceived severity. Many practical and popular risk measures are usefully viewed in terms of aversion functions including those arising from distortion operators and risk margin loadings. The approach of this paper builds on, unifies, and extends existing disparate approaches discussed in the literature. Analytical and computer generated illustrations are given as well as suggestions for the practical determination of aversion functions.     

Fluorescence and ultraviolet absorption spectra and structure of coumaran and its ring-puckering potential energy function in the S1(pi,pi*) excited state

The fluorescence excitation (jet cooled), single vibrational level fluorescence, and the ultraviolet absorption spectra of coumaran associated with its S1(pi,pi*) electronic excited state have been recorded and analyzed. The assignment of more than 70 transitions has allowed a detailed energy map of both the S0 and S1 states of the ring-puckering (nu45) vibration to be determined in the excited states of nine other vibrations, including the ring-flapping (nu43) and ring-twisting (nu44) vibrations. Despite some interaction with nu43 and nu44, a one-dimensional potential energy function for the ring puckering very nicely predicts the experimentally determined energy level spacings. In the S1(pi,pi*) state coumaran is quasiplanar with a barrier to planarity of 34 cm(-1) and with energy minima at puckering angles of +/-14 degrees. The corresponding ground state (S0) values are 154 cm(-1) and +/-25 degrees . As is the case with the related molecules indan, phthalan, and 1,3-benzodioxole, the angle strain in the five-membered ring increases upon the pi-->pi* transition within the benzene ring and this increases the rigidity of the attached ring. Theoretical calculations predict the expected increases of the carbon-carbon bond lengths of the benzene ring in S1, and they predict a barrier of 21 cm(-1) for this state. The bond length increases at the bridgehead carbon-carbon bond upon electron excitation to the S1(pi,pi*) state give rise to angle changes which result in greater angle strain and a nearly planar molecule.     

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.