The Core Mass Function in the Massive Protocluster G286.21+0.17 revealed by ALMA

We study the core mass function (CMF) of the massive protocluster G286.21+0.17 with the Atacama Large Millimeter/submillimeter Array via 1.3~mm continuum emission at a resolution of 1.0\arcsec\ (2500~au). We have mapped a field of 5.3\arcmin$\times$5.3\arcmin\ centered on the protocluster clump. We measure the CMF in the central region, exploring various core detection algorithms, which give source numbers ranging from 60 to 125, depending on parameter selection. We estimate completeness corrections due to imperfect flux recovery and core identification via artificial core insertion experiments. For masses $M\gtrsim1\:M_\odot$, the fiducial dendrogram-identified CMF can be fit with a power law of the form ${\rm{d}}N/{\rm{d}}{\rm{log}}M\propto{M}^{-\alpha}$ with $\alpha \simeq1.24\pm0.17$, slightly shallower than, but still consistent with, the index of the Salpeter stellar initial mass function of 1.35. Clumpfind-identified CMFs are significantly shallower with $\alpha\simeq0.64\pm0.13$. While raw CMFs show a peak near $1\:M_\odot$, completeness-corrected CMFs are consistent with a single power law extending down to $\sim 0.5\:M_\odot$, with only a tentative indication of a shallowing of the slope around $\sim1\:M_\odot$. We discuss the implications of these results for star and star cluster formation theories.Comment: 11 pages, accepted by Ap

Impact of Caesarean section on subsequent fertility: a systematic review and meta-analysis.

STUDY QUESTION: Is there an association between a Caesarean section and subsequent fertility? SUMMARY ANSWER: Most studies report that fertility is reduced after Caesarean section compared with vaginal delivery. However, studies with a more robust design show smaller effects and it is uncertain whether the association is causal. WHAT IS KNOWN ALREADY: A previous systematic review published in 1996 summarizing six studies including 85 728 women suggested that Caesarean section reduces subsequent fertility. The included studies suffer from severe methodological limitations. STUDY DESIGN, SIZE, DURATION: Systematic review and meta-analysis of cohort studies comparing subsequent reproductive outcomes of women who had a Caesarean section with those who delivered vaginally. PARTICIPANTS/MATERIALS, SETTING, METHODS: Searches of Cochrane Library, Medline, Embase, CINAHL Plus and Maternity and Infant Care databases were conducted in December 2011 to identify randomized and non-randomized studies that compared the subsequent fertility outcomes after a Caesarean section and after a vaginal delivery. Eighteen cohort studies including 591 850 women matched the inclusion criteria. Risk of bias was assessed by the Newcastle-Ottawa scale (NOS). Data extraction was done independently by two reviewers. The meta-analysis was based on a random-effects model. Subgroup analyses were performed to assess whether the estimated effect was influenced by parity, risk adjustment, maternal choice, cohort period, and study quality and size. MAIN RESULTS AND THE ROLE OF CHANCE: The impact of Caesarean section on subsequent pregnancies could be analysed in 10 studies and on subsequent births in 16 studies. A meta-analysis suggests that patients who had undergone a Caesarean section had a 9% lower subsequent pregnancy rate [risk ratio (RR) 0.91, 95% confidence interval (CI) (0.87, 0.95)] and 11% lower birth rate [RR 0.89, 95% CI (0.87, 0.92)], compared with patients who had delivered vaginally. Studies that controlled for maternal age or specifically analysed primary elective Caesarean section for breech delivery, and those that were least prone to bias according to the NOS reported smaller effects. LIMITATIONS, REASONS FOR CAUTION: There is significant variation in the design and methods of included studies. Residual bias in the adjusted results is likely as no study was able to control for a number of important maternal characteristics, such as a history of infertility or maternal obesity. WIDER IMPLICATIONS OF THE FINDINGS: Further research is needed to reduce the impact of selection bias by indication through creating more comparable patient groups and applying risk adjustment

Notes on explicit and inversion formulas for the Chebyshev polynomials of the first two kinds

Feng Qi, Da-Wei Niu, and Dongkyu Lim, Notes on explicit and inversion formulas for the Chebyshev polynomials of the first two kinds, Miskolc Mathematical Notes 20 (2019), no. 2, 1129--1137; available online at https://doi.org/10.18514/MMN.2019.2976.International audienceIn the paper, starting from the Rodrigues formulas for the Chebyshev polynomials of the first and second kinds, by virtue of the Fa\`a di Bruno formula, with the help of two identities for the Bell polynomials of the second kind, and making use of a new inversion theorem for combinatorial coefficients, the authors derive two nice explicit formulas and their corresponding inversion formulas for the Chebyshev polynomials of the first and second kinds

Enhanced Ethanol Dehydration with Hydrostable Inorganic Pervaporation Membranes

Membranes which allow water diffusion in favour of other substances can offer increased efficiency in processes to dehydrate ethanol. Silica membranes can perform this selective diffusion, but have mostly been reported for their gas high gas separating ability. This work investigates the effectiveness of carbonised template molecular sieve (CTMSS) membrane to dehydrate ethanol/water mixtures. The silica derived top layer of the membrane was measured at 20nm thickness by XPS sputtering technique. However, the silica enters the porous structure of -alumina layer in excess of 90nm. After 200 minutes of operation, H2O/EtOH selectivity increased to 5.6 from around 1 due to gradual pore filling by adsorbed water and ethanol which contributed to inhibiting ethanol transport. The smaller water molecules were thus favoured in transporting to the permeate side. Total mass flux using a 10% ethanol feed remained constant at around 1.5 kg.m-2.hr-1. Selectivity of up to 9.5 was achieved when azeotropic feed solutions of 95% were used, displaying the potential for this technology for a wide range of ethanol dehydration applications. Pressurising the feed up to 400 kPa doubled the permeate flux, but enhanced the transport of ethanol over water

Closed formulas and identities on the Bell polynomials and falling factorials

The authors establish a pair of closed-form expressions for special values of the Bell polynomials of the second kind for the falling factorials, derive two pairs of identities involving the falling factorials, find an equivalent expression between two special values for the Bell polynomials of the second kind, and present five closed-form expressions for the (modified) spherical Bessel functions

SOME LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS AND INEQUALITIES FOR MULTINOMIAL COEFFICIENTS AND MULTIVARIATE BETA FUNCTIONS: Completely monotonic functions and inequalities

In the paper, the authors extend a function arising from the Bernoulli trials in probability and involving the gamma function to its largest ranges, find logarithmically complete monotonicity of these extended functions, and, in the light of logarithmically complete monotonicity of these extended functions, derive some inequalities for multinomial coefficients and multivariate beta functions. These results recover, extend, and generalize some known conclusions

SPECIAL VALUES OF THE BELL POLYNOMIALS OF THE SECOND KIND FOR SOME SEQUENCES AND FUNCTIONS: Special values of Bell polynomials of second kind

In the paper, the authors concisely review some closed formulas and applications of special values of the Bell polynomials of the second kind for some special sequences and elementary functions, explicitly present closed formulas for those sequences investigated in [F. T. Howard, A special class of Bell polynomials, Math. Comp. 35 (1980), no. 151, 977–989; Available online at https://doi.org/10.2307/2006208], and newly establish some closed formulas for some special values of the Bell polynomials of the second kind

High selectivity microporous silica membranes for lactic acid dehydration

Lactic acid (LA) has significant market potential for many industries including food, cosmetics, pharmaceuticals, medical and biodegradable materials. Production of LA usually begins with the fermentation of glucose but subsequent stages for the enrichment of lactic acid are complex and energy intensive and could be minimised using water selective membrane technology. In this work, we trialled a highly selective hydrostable carbonised template molecular sieve silica (CTMSS) membrane for the dehydration of a 15 vol% aqueous lactic acid solution with 0.1 vol% glucose. CTMSS membrane films were developed by dip-coating ceramic substrates with silica sols made using the acid catalysed sol-gel process. Permeation was performed by feeding LA/glucose solution to the membrane cell at 18°C in a standard pervaporation setup. The membrane showed selective transport of water from the aqueous feed to the permeate while glucose was not detected. CTMSS membrane permeate flux stabilised at 0.2 kg.m-2.hr-1 in 3.9 hours, and reduced LA to lower than 0.2 vol%. Flux through the CTMSS micropores was activated, displaying increased initial flux to 1.58 kg.m-2.hr-1 at 60°C. To enrich a 1 l.min-1 stream to 85% LA in a single stage, a minimum membrane area of 324 m2 would be required at 18°C. Increased operating temperature to 80°C significantly reduced this area to 24 m2 but LA levels in the permeate stream increased to 0.5 vol%. The highly selective CTMSS membrane technology is an ideal candidate for LA purification. CTMSS membrane systems operate stably in aqueous systems leading to potential cost reductions in LA processing for future markets