Some Appell-type orthogonal polynomials on lattices

We investigate on some Appel-type orthogonal polynomial sequences on q-quadratic lattices and we provide some entire new characterizations of the Al-Salam Chihara polynomials (including the Rogers q-Hermite polynomials). The corresponding forms are well described. The proposed method can be applied to similar and to more general problems involving the Askey-Wilson and the Averaging operators, in order to obtain new characterization theorems for classical and semiclassical orthogonal polynomials on lattices

On First type characterizations of Askey-Wilson polynomials

In this chapter we characterize Askey-Wilson polynomials including specific and limiting cases of them by some structure relations of the first type.Comment: arXiv admin note: text overlap with arXiv:2301.0672

Epilegomena to the study of semiclassical orthogonal polynomials

In his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005 (paperback edition 2009)], Ismail conjectured that certain structure relations involving the Askey-Wilson operator characterize proper subsets of the set of all $\mathcal{D}_q$-classical orthogonal polynomials, here to be understood as the Askey-Wilson polynomials and their limit cases. In this paper we give two characterization theorems for $\mathcal{D}_q$-semiclassical (and classical) orthogonal polynomials in consonance with the pioneering works by Maroni [Ann. Mat. Pura. Appl. (1987)] and Bonan, Lubinsky, and Nevai [SIAM J. Math. Anal. 18 (1987)] for the standard derivative, re-establishing in this context the perfect "symmetry" between the standard derivative and the Askey-Wilson operator. As an application, we present a sequence of $\mathcal{D}_q$-semiclassical orthogonal polynomials of class two that disproves Ismail's conjectures. Further results are presented for Hahn's operator

On classical orthogonal polynomials on bi-lattices

In [J. Phys. A: Math. Theor. 45 (2012)], while looking for spin chains that admit perfect state transfer, Vinet and Zhedanov found an apparently new sequence of orthogonal polynomials, that they called para-Krawtchouk polynomials, defined on a bilinear lattice. In this note we present necessary and sufficient conditions for the regularity of solutions of the corresponding functional equation. Moreover, the functional Rodrigues formula and a closed formula for the recurrence coefficients are presented. As a consequence, we characterize all solutions of the functional equation, including as very particular cases the Meixner, Charlier, Krawtchouk, Hahn, and para-Krawtchouk polynomials.Comment: arXiv admin note: substantial text overlap with arXiv:2102.0003

Proof of two conjectures on Askey-Wilson polynomials

We give positive answer to two conjectures posed by M. E. H Ismail in his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, Cambridge, 2005]. These results generalize the classical problems of Sonine and Hahn

Monthly Entomological Inoculation Rate Data for Studying the Seasonality of Malaria Transmission in Africa

A comprehensive literature review was conducted to create a new database of 197 field surveys of monthly malaria Entomological Inoculation Rates (EIR), a metric of malaria transmission intensity. All field studies provide data at a monthly temporal resolution and have a duration of at least one year in order to study the seasonality of the disease. For inclusion, data collection methodologies adhered to a specific standard and the location and timing of the measurements were documented. Auxiliary information on the population and hydrological setting were also included. The database includes measurements that cover West and Central Africa and the period from 1945 to 2011, and hence facilitates analysis of interannual transmission variability over broad regions

Potent antiplasmodial extracts and fractions from Terminalia mantaly and Terminalia superba

Abstract Background The emergence and spread of malaria parasites resistant to artemisinin-based combination therapy stresses the need for novel drugs against malaria. Investigating plants used in traditional medicine to treat malaria remains a credible option for new anti-malarial drug development. This study was aimed at investigating the antiplasmodial activity and selectivity of extracts and fractions from Terminalia mantaly and Terminalia superba (Combretaceae) that are used in Cameroon to treat malaria. Methods Twelve methanolic (m) and water (w) extracts obtained by maceration of powdered dried leaves (l), stem bark (sb) and root (r) of Terminalia mantaly (Tm) and Terminalia superba (Ts) and 12 derived fractions of hexane, chloroform, ethyl acetate and 4 final residues of selected extracts were assessed for antiplasmodial potential in vitro against the chloroquine-resistant PfINDO and the chloroquine-sensitive Pf3D7 strains of Plasmodium falciparum using the SYBR green I-based fluorescence assay. The cytotoxicity of potent extracts and fractions was evaluated in vitro using the MTT assay on HEK239T cell line. Results The antiplasmodial IC50 of extracts from both plants ranged from 0.26 to > 25 µg/mL. Apart from the extracts Tmrm and Tsrw that exerted moderate antiplasmodial activities (IC50: 5–20 µg/mL) and Tmrw that was found to be non-active at the tested concentrations (IC50 > 25 µg/mL), all other tested crude extracts exhibited potent activities with IC50  158) on both resistant PfINDO and sensitive Pf3D7 strains. Four fractions upon further extraction with chloroform and ethyl acetate (TmlwChl, TmsbwChl, TmsbwEA, TsrmEA) afforded from three selected crude extracts (Tmlw, Tmsbw, Tsrm) exhibited highly potent activities against both P. falciparum strains (IC50  109). Conclusions The results achieved in this work validate the reported traditional use of Terminalia mantaly and Terminalia superba to treat malaria. Moreover, the highly potent and selective fractions warrant further investigation to characterize the active antiplasmodial principles and progress them to rodent malaria models studies if activity and selectivity are evidenced