Dipotassium maleate with boric acid

In the title compound, poly[(μ₃‐boric acid)‐μ₄‐maleato‐dipotassium], [K₂(C₄H₂O₄){B(OH)₃}]_n, there are two independent K⁺ cations, one bonded to seven O atoms (three from boric acid and four from maleate), and the other eight‐coordinate via three boric acid and four maleate O atoms and a weak η¹‐type coordination to the C=C bond of the maleate central C atoms. Hydrogen bonding links the boric acid ligands and maleate dianions, completing the packing structure.     

Electrical transport mechanism in boron nitride thin film

Both dc and ac transport characteristics of plasma enhanced chemical vapor deposited (PECVD) boron nitride (BN) thin film was investigated by dc current vs. dc voltage measurement at different temperatures and admittance vs. gate voltage at various frequencies/temperatures, respectively. MIM ≡ metal (Al)-insulator (BN)-metal (Al) or MIS ≡ metal (Al)-BN-semiconductor (p-Silicon) test devices were conventionally produced. Both conductivity anisotropy and dc/ac detailed transport mechanism were analyzed within the frame of a turbostratic structure (t-BN), interfacing the substrate by a thin amorphous layer (a-BN). This defective BN film has been justified by both infrared (IR) analysis and indirectly by the resulting electrical transport behavior. Transport and its variations as a function of temperature/frequency are in agreement with a hopping mechanism across Gauss-like energy distributed localized deep traps.     

[N‐(2‐Hydroxy­ethyl)ethyl­enediamine‐κ3N,N′,O]‐cis‐bis(isothio­cyanato‐κN)copper(II)

In the novel transition metal isothio­cyanate complex of N‐(2‐hydroxy­ethyl)ethyl­enediamine (hydet‐en) with copper, [Cu(NCS)₂(C₄H₁₂N₂O)], the Cu atom lies in a distorted square‐pyramidal environment, coordinated by four N atoms in the basal plane and an apical O atom. The hydet‐en ligand is N,N,O‐tridentate, in contrast to the disposition in previously studied complexes, while the isothio­cyanate ions act as N‐atom donor ligands. The monomeric units are linked to one another by hydrogen bonds.     

(2,9‐Dimethyl‐1,10‐phenanthroline‐κ2N,N′)(pyridine‐2,6‐dicarboxylato‐κ3O2,N,O6)copper(II) trihydrate

The copper(II) centre in the mononuclear title complex, [Cu(C₇H₃NO₄)(C₁₄H₁₂N₂)]·3H₂O, is surrounded by one bidentate 2,9‐dimethyl‐1,10‐phenanthroline (dmphen) ligand and one tridentate pyridine‐2,6‐dicarboxylate ligand, and exhibits a distorted square‐pyramidal geometry. The crystal packing involves both hydrogen‐bonding and π–π inter­actions. The solvent water mol­ecules link monomers to one another through hydrogen‐bonding inter­actions, forming ladder‐like chains in the bc plane. Face‐to‐face and slipped π–π inter­actions also occur between dmphen rings of neighboring mol­ecules and are responsible for inter­chain packing.     

Aqua­di­chloro­(di‐2‐pyridyl­di­azene)copper(II) monohydrate

The crystal structure of the mononuclear title complex, [CuCl₂(C₁₀H₈N₄)(H₂O)]·H₂O, shows an s‐cis/E/s‐trans‐configured di‐2‐pyridyl­diazene ligand, with the square‐pyramidal Cu^II ion coordinated to one pyridyl and one diazene N atom together with two Cl atoms and one aqua ligand. The crystal packing involves both hydrogen‐bonding and π–π interactions. The solvent water mol­ecule links three monomers to one another through hydrogen‐bonding interactions in which two monomers are linked via chloro ligands and the third via the aqua ligand. Face‐to‐face and weak slipped π–π interactions also occur between di‐2‐pyridyl­diazene moieties, and these interactions are responsible for the interchain packing.     

$$K_{a}$$-convergence and Korovkin type approximation

In the present paper, we study a Korovkin type approximation theorem in the setting of \(K_{a}\)-convergence that contains the classical result. We also study the rate of \(K_{a}\)-convergence and afterwards, we give some concluding remarks.     

[1,3‐Bis(2‐ethoxy­phenyl)imidazolidin‐2‐yl­idene]bromo­(cyclo­octa‐1,5‐diene)­rhodium(I)

The title complex, [RhBr(C₈H₁₂)(C₁₉H₂₂N₂O₂)], has a distorted square‐planar geometry. There are two mol­ecules, A and B, in the asymmetric unit. The Rh—C bond distance between the N‐heterocyclic ligand and the metal atom is 2.039 (2) Å in mol­ecule A and 2.042 (2) Å in mol­ecule B. The angle between the carbene heterocycle and the coordination plane is 87.56 (12)° in mol­ecule A and 87.03 (11)° in mol­ecule B. It is shown that the average Rh—C(COD) (COD is cyclo­octa­diene) distance is linearly dependent on the Rh—C(imidazolidine) distance in this type of compound. This can be ascribed to the steric hindrance produced by the packing. The crystal structure contains intra­molecular C—H⋯O and inter­molecular C—H⋯Br inter­actions.     

Some variations of the Bohman–Korovkin theorem

In this paper we develop the main aspects of the Bohman–Korovkin theorem on approximation of continuous functions with the use of A-statistical convergence and matrix summability method which includes both convergence and almost convergence. Since statistical convergence and almost convergence methods are incompatible we conclude that these methods can be used alternatively to get some approximation results.