The trigonometric tables of al-Kāshī in his Zīj-i Khāqānī

The trigonometric tables of al-Kāshī in his Zīj-i Khāqānī are described and the degree of their accuracy is investigated. Also, his account of the particular interpolation schemes based on the numerical material of the tables is translated into English and given with a commentary.     

Molecular Imaging of Biological Samples on Nanophotonic Laser Desorption Ionization Platforms

Mass spectrometry imaging (MSI) is a comprehensive tool for the analysis of a wide range of biomolecules. The mainstream method for molecular MSI is matrix‐assisted laser desorption ionization, however, the presence of a matrix results in spectral interferences and the suppression of some analyte ions. Herein we demonstrate a new matrix‐free MSI technique using nanophotonic ionization based on laser desorption ionization (LDI) from a highly uniform silicon nanopost array (NAPA). In mouse brain and kidney tissue sections, the distributions of over 80 putatively annotated molecular species are determined with 40 μm spatial resolution. Furthermore, NAPA‐LDI‐MS is used to selectively analyze metabolites and lipids from sparsely distributed algal cells and the lamellipodia of human hepatocytes. Our results open the door for matrix‐free MSI of tissue sections and small cell populations by nanophotonic ionization.     

Split Common Fixed Point Problem of Nonexpansive Semigroup

In this paper, we first introduce a new algorithm with a viscosity iteration method for solving the split common fixed point problem (SCFP) for a finite family of nonexpansive semigroups. We also present a new algorithm for solving the SCFP for an infinite family of quasi-nonexpansive mappings. We establish strong convergence of these algorithms in an infinite-dimensional Hilbert spaces. As application, we obtain strong convergence theorems for split variational inequality problems and split common null point problems. Our results improve and extend the related results in the literature.     

New orthopalladated complexes of phosphorus ylides: Crystal structure of [Pd{CH{P(C7H6)(p-tolyl)2}COCH3}Cl{P(p-tolyl)3}]

This work reports on the preparation of the complexes [PdCl₂(Y¹)₂], [PdCl₂(Y²)₂] (Y¹ = (p-tolyl)₃PCHCOCH₃ (1a); Y² = Ph₃PCHCO₂CH₂Ph (1b)), [Pd{CHP(C₇H₆)(p-tolyl)₂COCH₃}(μ-Cl)]₂ (2a), [Pd{CHP(C₆H₄)Ph₂CO₂CH₂Ph}(μ-Cl)]₂ (2b), [Pd{CH{P(C₇H₆)(p-tolyl)₂}COCH₃}Cl(L)] (L = PPh₃ (3a), P(p-tolyl)₃ (4a)) and [Pd{CH{P(C₆H₄)Ph₂}CO₂CH₂Ph}Cl(L)] (L = PPh₃ (3b), P(p-tolyl)₃ (4b)). Orthometallation and ylide C-coordination in complexes 2a–4b are demonstrated by an X-ray diffraction study of 4a.     

Synthesis and NMR Study of α‐Keto Stabilized Ylides of the Type RCOCH=PAr3, (R=MeO‐C6H4, Cl‐C6H4, NO2‐C6H4, α‐Thiophenyl and Naphthyl; Ar = p‐Tolyl or Phenyl)

Synthesis and characterization of five new phosphonium salts and related phosphorus ylides of the type R‐COCH=PAr₃ are reported. The reaction of bromo 4′‐methoxo/chloro/nitro acetophenone, α‐thiophenyl and naphthoyl acetophenone with triphenylphosphine or triparatolylphosphine in acetone gives phosphonium salts. Dehydrogenation of these salts in aqueous sodium hydroxide solution form ylides. Characterization of obtained compounds was performed by IR, ¹H, ¹³C, ³¹PNMR and elemental analysis.     

Fourier Series in Weighted Lorentz Spaces

The Fourier coefficient map is considered as an operator from a weighted Lorentz space on the circle to a weighted Lorentz sequence space. For a large range of Lorentz indices, necessary and sufficient conditions on the weights are given for the map to be bounded. In addition, new direct analogues are given for known weighted Lorentz space inequalities for the Fourier transform. Applications are given that involve Fourier coefficients of functions in LogL and more general Lorentz–Zygmund spaces.     

Competition between chalcogen bond and halogen bond interactions in YOX<Subscript>4</Subscript>:NH<Subscript>3</Subscript> (Y = S,Se; X = F,Cl, Br) complexes: An ab initio investigation

Using ab initio calculations, the geometries, interaction energies and bonding properties of chalcogen bond and halogen bond interactions between YOX₄ (Y = S, Se; X = F, Cl, Br) and NH₃ molecules are studied. These binary complexes are formed through the interaction of a positive electrostatic potential region (σ-hole) on the YOX₄ with the negative region in the NH₃. The ab initio calculations are carried out at the MP2/aug-cc-pVTZ level, through analysis of molecular electrostatic potentials, quantum theory of atoms in molecules and natural bond orbital methods. Our results indicate that even though the chalcogen and halogen bonds are mainly dominated by electrostatic effects, but the polarization and dispersion effects also make important contributions to the total interaction energy of these complexes. The examination of interaction energies suggests that the chalcogen bond is always favored over the halogen bond for all of the binary YOX₄:NH₃ complexes.     

Preconcentration of cobalt ions by a melamine-modified cellulose@MWCNT nanohybrid

Melamine functionalized cellulose@carbon nanotubes were prepared by the following method: (a) Cellulose was dissolved in a mixture of urea and NaOH solutions and then mixed with multiwall carbon nanotubes; (b) the MWCT-modified cellulose was precipitated by addition of water; (c) the MWCNTs were activated with thionyl chloride, and finally reacted with melamine. The resulting sorbent was used in preconcentration of Co(II) ions prior to their determination by flame atomic absorption spectroscopy. The sorbent was characterized by FTIR and field emission scanning electron microscopy. The effects of the pH value of the medium, contact time, and elution conditions were optimized. The calibration plot is linear in the 3 to 200 μg·L￣¹ Co(II) concentration range, the limit of detection is 0.8 μg·L￣¹, and the relative standard deviation (at a concentration of 100 μg·L￣¹) is 3.5 %. The maximum sorption capacity is 167 mg·g￣¹. The method was applied to the preconcentration of cobalt ions from (spiked) food and water samples and gave recoveries between 96 and 102 %.

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Graphical abstract A composite of the type melamine - cellulose/MWCNT was used for fast preconcentration of cobalt ions.

     

Nano‐TiO2 as an Efficient Catalyst for Tandem Knoevenagel–Michael‐Cyclocondensation Reaction of Dimedone with Aromatic Aldehydes and Ammonium Acetate or Aromatic Amines under Solvent‐free Conditions

TiO₂ nanoparticles in anatase and rutile forms was characterized and studied by several techniques including X‐ray diffraction (XRD), scanning electron microscope (SEM), transmission electron microscopy (TEM) and successfully applied as an efficient and heterogeneous catalyst in the synthesis of 1,8‐dioxo‐decahydroacridines via the one‐pot multi‐component condensation reaction of dimedone with aromatic aldehydes and ammonium acetate or aromatic amines under mild and solvent‐free conditions.