On convergence of generalized continued fractions and Ramanujan's conjecture

We consider continued fractions \frac{-a_1}{1-\frac{a_2}{1-\frac{a_3}{1-...}}} \label{fr} with real coefficients $a_i$ converging to a limit $a$. S.Ramanujan had stated the theorem (see [ABJL], p.38) saying that if $a\neq\frac14$, then the fraction converges if and only if $a<\frac14$. The statement of convergence was proved in [V] for complex $a_i$ converging to $a\in\mathbb C\setminus[\frac14,+\infty)$ (see also [P]). J.Gill [G] proved the divergence of (\ref{fr}) under the assumption that $a_i\to a>\frac14$ fast enough, more precisely, whenever \sum_i|a_i-a|<\infty.\label{gill} The Ramanujan conjecture saying that (\ref{fr}) diverges always whenever $a_i\to a>\frac14$ remained up to now an open question. In the present paper we disprove it. We show (Theorem \ref{th1}) that for any $a>\frac14$ there exists a real sequence $a_i\to a$ such that (\ref{fr}) converges. Moreover, we show (Theorem \ref{go}) that Gill's sufficient divergence condition (\ref{gill}) is the optimal condition on the speed of convergence of the $a_i$'s.Comment: Submitted to C.R.A.S. on December 23, 200

Repurposing of Meropenem and Nadifloxacin for Treatment of Burn Patients?

The escalating number of multidrug resistant pathogens has demanded the swift development of new and potent antibiotics (ref. 2). Metallo-[beta]-lactamases (MBLs) continue to evolve, rendering the latest generation of carbapenem antibiotics useless (ref. 8). SPM-1, a recently discovered MBL, was isolated from a juvenile leukemia patient residing in a hospital in San Palo, Brazil just prior to the patient succumbing to septicemia brought on by Pseudomonas aeruginosa expressing SPM-1 (ref. 8). Screening of the Johns Hopkins Compound library of 1,514 FDA or FAD approved drugs (ref. 1) identified a novel SPM-1 inhibitor that is synergistically compatible with meropenem. Using clinically achievable concentrations, meropenem coupled with nadifloxacin inhibits Pseudomonas aeruginosa expressing SPM-1. This shotgun approach to new drug discovery provided a prompt solution to the grave problem of antibiotic resistant pathogens that are thriving in hospitals today

2014 Maintenance Agenda

Asks questions about the proper reporting of premium receivable with credit balances on group contracts (gross or net reporting

Phosphomannosylation and the functional analysis of the extended Candida albicans MNN4-like gene family

We thank Luz A. López-Ramírez (Universidad de Guanajuato) for technical assistance. This work was supported by Consejo Nacional de Ciencia y Tecnología (ref. CB2011/166860; PDCPN2014-247109, and FC 2015-02-834), Universidad de Guanajuato (ref. 000025/11; 0087/13; ref. 1025/2016; Convocatoria Institucional para Fortalecer la Excelencia Académica 2015; CIFOREA 89/2016), Programa de Mejoramiento de Profesorado (ref. UGTO-PTC-261), and Red Temática Glicociencia en Salud (CONACYT-México). NG acknowledges the Wellcome Trust (086827, 075470, 101873, and 200208) and MRC Centre for Medical Mycology for funding (N006364/1). KJ was supported by a research visitor grant to Aberdeen from China Scholarship Council (CSC No. 201406055024). The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmicb.2017.02156/full#supplementary-materialPeer reviewedPublisher PD

Comment on "PT Symmetry as a Generalization of Hermiticity" [arXiv:1002.2676]

We notice that the general PT-symmetric Hamiltonian matrix(N=2) having 6-real parameters fails to reproduce one parameter PT-symmetric matrix.Comment: Title unchanged ,one ref [5] added . Abstract changed . All the previous matrices have been changed consideing the ref[5

On the isomorphism problem of concept algebras

Weakly dicomplemented lattices are bounded lattices equipped with two unary operations to encode a negation on {\it concepts}. They have been introduced to capture the equational theory of concept algebras \cite{Wi00}. They generalize Boolean algebras. Concept algebras are concept lattices, thus complete lattices, with a weak negation and a weak opposition. A special case of the representation problem for weakly dicomplemented lattices, posed in \cite{Kw04}, is whether complete {\wdl}s are isomorphic to concept algebras. In this contribution we give a negative answer to this question (Theorem \ref{T:main}). We also provide a new proof of a well known result due to M.H. Stone \cite{St36}, saying that {\em each Boolean algebra is a field of sets} (Corollary \ref{C:Stone}). Before these, we prove that the boundedness condition on the initial definition of {\wdl}s (Definition \ref{D:wdl}) is superfluous (Theorem \ref{T:wcl}, see also \cite{Kw09}).Comment: 15 page