A unified approach to radius of convexity problems for certain classes of univalent analytic functions

We consider functions f analytic in the unit disc and assume the power series representation of the form f(z)=z+an+1zn+1+an+2zn+2+… where an+1 is fixed throughout. We provide a unified approach to radius convexity problems for different subclasses of univalent analytic functions. Numerous earlier estimates concerning the radius of convexity such as those involving fixed second coefficient, n initial gaps, n+1 symmetric gaps, etc. are discussed. It is shown that several known results, follow as special cases of those presented in this paper

The maximum term of a power series

Let ∑n=0∞anzλn be a power series, representing an analytic function f(z) in the disc |z|<R. A characterization for the type of such functions was obtained by the authors [J. Math. Anal. Appl. 81(1981), 1-7] in terms of the maximum term and rank. It is proved in this paper by means of an example, that a similar relation does not hold in general for lower type and sufficient conditions have been obtained for the validity of the corresponding result for lower type. Alternative coefficient characterization for type and lower type have been given and a necessary and sufficient condition for the analytic function f(z) to be of perfectly regular growth has been obtained

Schroedinger equation for joint bidirectional motion in time

The conventional, time-dependent Schroedinger equation describes only unidirectional time evolution of the state of a physical system, i.e., forward or, less commonly, backward. This paper proposes a generalized quantum dynamics for the description of joint, and interactive, forward and backward time evolution within a physical system. [...] Three applications are studied: (1) a formal theory of collisions in terms of perturbation theory; (2) a relativistically invariant quantum field theory for a system that kinematically comprises the direct sum of two quantized real scalar fields, such that one field evolves forward and the other backward in time, and such that there is dynamical coupling between the subfields; (3) an argument that in the latter field theory, the dynamics predicts that in a range of values of the coupling constants, the expectation value of the vacuum energy of the universe is forced to be zero to high accuracy. [...]Comment: 30 pages, no figures. Related material is in quant-ph/0404012. Differs from published version by a few added remarks on the possibility of a large-scale-average negative energy density in spac

G12 signaling through c-jun nh 2-terminal kinase promotes breast cancer cell invasion

10.1371/journal.pone.0026085PLoS ONE611

Expert consensus statements for the management of COVID-19-related acute respiratory failure using a Delphi method.

Coronavirus disease 2019 (COVID-19) pandemic has caused unprecedented pressure on healthcare system globally. Lack of high-quality evidence on the respiratory management of COVID-19-related acute respiratory failure (C-ARF) has resulted in wide variation in clinical practice. Using a Delphi process, an international panel of 39 experts developed clinical practice statements on the respiratory management of C-ARF in areas where evidence is absent or limited. Agreement was defined as achieved when &gt; 70% experts voted for a given option on the Likert scale statement or &gt; 80% voted for a particular option in multiple-choice questions. Stability was assessed between the two concluding rounds for each statement, using the non-parametric Chi-square (χ &lt;sup&gt;2&lt;/sup&gt; ) test (p &lt; 0·05 was considered as unstable). Agreement was achieved for 27 (73%) management strategies which were then used to develop expert clinical practice statements. Experts agreed that COVID-19-related acute respiratory distress syndrome (ARDS) is clinically similar to other forms of ARDS. The Delphi process yielded strong suggestions for use of systemic corticosteroids for critical COVID-19; awake self-proning to improve oxygenation and high flow nasal oxygen to potentially reduce tracheal intubation; non-invasive ventilation for patients with mixed hypoxemic-hypercapnic respiratory failure; tracheal intubation for poor mentation, hemodynamic instability or severe hypoxemia; closed suction systems; lung protective ventilation; prone ventilation (for 16-24 h per day) to improve oxygenation; neuromuscular blocking agents for patient-ventilator dyssynchrony; avoiding delay in extubation for the risk of reintubation; and similar timing of tracheostomy as in non-COVID-19 patients. There was no agreement on positive end expiratory pressure titration or the choice of personal protective equipment. Using a Delphi method, an agreement among experts was reached for 27 statements from which 20 expert clinical practice statements were derived on the respiratory management of C-ARF, addressing important decisions for patient management in areas where evidence is either absent or limited. The study was registered with Clinical trials.gov Identifier: NCT04534569

Alternative patterns of sex chromosome differentiation in Aedes aegypti (L).

BACKGROUND: Some populations of West African Aedes aegypti, the dengue and zika vector, are reproductively incompatible; our earlier study showed that divergence and rearrangements of genes on chromosome 1, which bears the sex locus (M), may be involved. We also previously described a proposed cryptic subspecies SenAae (PK10, Senegal) that had many more high inter-sex FST genes on chromosome 1 than did Ae.aegypti aegypti (Aaa, Pai Lom, Thailand). The current work more thoroughly explores the significance of those findings. RESULTS: Intersex standardized variance (FST) of single nucleotide polymorphisms (SNPs) was characterized from genomic exome capture libraries of both sexes in representative natural populations of Aaa and SenAae. Our goal was to identify SNPs that varied in frequency between males and females, and most were expected to occur on chromosome 1. Use of the assembled AaegL4 reference alleviated the previous problem of unmapped genes. Because the M locus gene nix was not captured and not present in AaegL4, the male-determining locus, per se, was not explored. Sex-associated genes were those with FST values ≥ 0.100 and/or with increased expected heterozygosity (H exp , one-sided T-test, p < 0.05) in males. There were 85 genes common to both collections with high inter-sex FST values; all genes but one were located on chromosome 1. Aaa showed the expected cluster of high inter-sex FST genes proximal to the M locus, whereas SenAae had inter-sex FST genes along the length of chromosome 1. In addition, the Aaa M-locus proximal region showed increased H exp levels in males, whereas SenAae did not. In SenAae, chromosomal rearrangements and subsequent suppressed recombination may have accelerated X-Y differentiation. CONCLUSIONS: The evidence presented here is consistent with differential evolution of proto-Y chromosomes in Aaa and SenAae