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

Some formulas for determinants of tridiagonal matrices in terms of finite generalized continued fractions: Formulas for determinants of tridiagonal matrices

In the paper, by virtue of induction and properties of determinants, the authors discover explicit and recurrent formulas of evaluations for determinants of general tridiagonal matrices in terms of finite generalized continued fractions and apply these formulas to evaluations for determinants of the Sylvester matrix and two Sylvester type matrices.In the paper, by virtue of induction and properties of determinants, the authors discover explicit and recurrent formulas of evaluations for determinants of general tridiagonal matrices in terms of finite generalized continued fractions and apply these formulas to evaluations for determinants of the Sylvester matrix and two Sylvester type matrices

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

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

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

Ovarian Real-World International Consortium (ORWIC): A multicentre, real-world analysis of epithelial ovarian cancer treatment and outcomes

IntroductionMuch drug development and published analysis for epithelial ovarian cancer (EOC) focuses on early-line treatment. Full sequences of treatment from diagnosis to death and the impact of later lines of therapy are rarely studied. We describe the establishment of an international network of cancer centers configured to compare real-world treatment pathways in UK, Portugal, Germany, South Korea, France and Romania (the Ovarian Real-World International Consortium; ORWIC).Methods3344 patients diagnosed with EOC (2012-2018) were analysed using a common data model and hub and spoke programming approach applied to existing electronic medical records. Consistent definition of line of therapy between sites and an efficient approach to analysis within the limitations of local information governance was achieved.ResultsMedian age of participants was 53-67 years old and 5-29% were ECOG >1. Between 62% and 84% of patients were diagnosed with late-stage disease (FIGO III-IV). Sites treating younger and fitter patients had higher rates of debulking surgery for those diagnosed at late stage than sites with older, more frail patients. At least 21% of patients treated with systemic anti-cancer therapy (SACT) had recurrent disease following second-line therapy (2L); up to 11 lines of SACT treatment were recorded for some patients. Platinum-based SACT was consistently used across sites at 1L, but choices at 2L varied, with hormone therapies commonly used in the UK and Portugal. The use (and type) of maintenance therapy following 1L also varied. Beyond 2L, there was little consensus between sites on treatment choice: trial compounds and unspecified combinations of other agents were common.DiscussionSpecific treatment sequences are reported up to 4L and the establishment of this network facilitates future analysis of comparative outcomes per line of treatment with the aim of optimizing available options for patients with recurrent EOC. In particular, this real-world network can be used to assess the growing use of PARP inhibitors. The real-world optimization of advanced line treatment will be especially important for patients not usually eligible for involvement with clinical trials. The resources to enable this analysis to be implemented elsewhere are supplied and the network will seek to grow in coverage of further sites

Male-like sexual behavior of female mouse lacking fucose mutarotase

<p>Abstract</p> <p>Background</p> <p>Mutarotases are recently characterized family of enzymes that are involved in the anomeric conversions of monosaccharides. The mammalian fucose mutarotase (FucM) was reported in cultured cells to facilitate fucose utilization and incorporation into protein by glycosylation. However, the role of this enzyme in animal has not been elucidated.</p> <p>Results</p> <p>We generated a mutant mouse specifically lacking the fucose mutarotase (FucM) gene. The <it>FucM </it>knockout mice displayed an abnormal sexual receptivity with a drastic reduction in lordosis score, although the animals were fertile due to a rare and forced intromission by a typical male. We examined the anteroventral periventricular nucleus (AVPv) of the preoptic region in brain and found that the mutant females showed a reduction in tyrosine hydoxylase positive neurons compared to that of a normal female. Furthermore, the mutant females exhibited a masculine behavior, such as mounting to a normal female partner as well as showing a preference to female urine. We found a reduction of fucosylated serum alpha-fetoprotein (AFP) in a mutant embryo relative to that of a wild-type embryo.</p> <p>Conclusions</p> <p>The observation that <it>FucM</it>^-/-female mouse exhibits a phenotypic similarity to a wild-type male in terms of its sexual behavior appears to be due to the neurodevelopmental changes in preoptic area of mutant brain resembling a wild-type male. Since the previous studies indicate that AFP plays a role in titrating estradiol that are required to consolidate sexual preference of female mice, we speculate that the reduced level of AFP in <it>FucM</it>^-/-mouse, presumably resulting from the reduced fucosylation, is responsible for the male-like sexual behavior observed in the FucM knock-out mouse.</p