Statistical Limit Superior and Limit Inferior

Following the concept of statistical convergence and statistical cluster points of a sequence , we give a definition of statistical limit superior and inferior which yields natural relationships among these ideas: e.g., is statistically convergent if and only if . The statistical core of is also introduced, for which an analogue of Knopp's Core Theorem is proved. Also, it is proved that a bounded sequence that is -summable to its statistical limit superior is statistically convergent.

     

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.     

Bis{[μ‐N,N′‐bis­(salicyl­idene)‐1,4‐butane­di­amine‐N,N′,O,O′‐copper(II)]‐μ‐chloro‐chloromercury(II)}

A new tetranuclear Cu^II–Hg^II–Hg^II–Cu^II complex, [Cu₂Hg₂Cl₄(C₁₈H₁₈N₂O₂)₂], has been prepared by means of a copper complex found in the literature. The molecular structure of this complex was determined by X‐ray diffraction and the Cu–Hg–Hg–Cu chain was seen to be non‐linear. The change in magnetic susceptibility with temperature was recorded for this complex and observed to abide by the Curie–Weiss law. The coordination around the Hg^II ions is square pyramidal. The Cu?Hg bridging distance is 3.5269 (7) Å.     

Determination of bismuth and lead in geological samples by electrothermal AAS Part 1. Comparative study of tungsten containing chemical modifiers

A comparative study on the efficiency of some tungsten containing chemical modifiers such as W, W+Pd, W+Rh, W+Pt and W+Ru for thermal stabilization of Bi, In, Pb and Sb has been performed systematically by a Zeeman electrothermal atomization atomic absorption spectrometer (ETAAS). The addition of tartaric acid (TA) as a reducing agent additionally to the mixed modifiers was studied. A mixture of W+Pd+TA was found to be a powerful mixed modifier for the determination of Bi, In, Pb and Sb. Pretreatment temperatures could be increased up to 1250–1500° C using this mixed modifier. The use of the mixed modifier results in an enhanced accuracy and precision of the method and recovery rates above 97% for all samples. The W+Pd+TA mixed modifier was applied to the determination of Bi and Pb in dissolved geological reference samples. Received: 14 March 1996 / Revised: 3 June 1996 / Accepted: 30 June 1996     

4‐Amino‐3,5‐diethyl‐4H‐1,2,4‐triazole at 100 K: chains of edge‐fused R44(10) and R44(20) rings

The title compound, C₆H₁₂N₄, has four crystallographically independent molecules in the asymmetric unit. Intermolecular N—H...N hydrogen bonds involving amino groups and triazole N atoms form a three‐dimensional framework involving R₄⁴(10) and R₄⁴(20) rings. The hydrogen bonding is supported by weak C—H...π interactions.     

Determination of bismuth and lead in geological samples by electrothermal AAS Part 1. Comparative study of tungsten containing chemical modifiers

A comparative study on the efficiency of some tungsten containing chemical modifiers such as W, W+Pd, W+Rh, W+Pt and W+Ru for thermal stabilization of Bi, In, Pb and Sb has been performed systematically by a Zeeman electrothermal atomization atomic absorption spectrometer (ETAAS). The addition of tartaric acid (TA) as a reducing agent additionally to the mixed modifiers was studied. A mixture of W+Pd+TA was found to be a powerful mixed modifier for the determination of Bi, In, Pb and Sb. Pretreatment temperatures could be increased up to 1250–1500° C using this mixed modifier. The use of the mixed modifier results in an enhanced accuracy and precision of the method and recovery rates above 97% for all samples. The W+Pd+TA mixed modifier was applied to the determination of Bi and Pb in dissolved geological reference samples. Received: 14 March 1996 / Revised: 3 June 1996 / Accepted: 30 June 1996     

[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.     

Diaquabis(5-methoxyindole-2-carboxylato)bis(3-picoline)nickel(II) Complex: Synthesis,Characterization, XRD,TGA, DFT and HSA

A new complex of diaquabis(5-methoxyindole-2-carboxylato)bis(3-picoline)nickel(II) (Ni(5-MeOI2CA)₂(3-pic)₂(H₂O)₂), was synthesized for the first time and characterized by elemental analysis, FT-IR and electronic spectroscopy (UV-Vis) and single-crystal X-ray diffraction (XRD) techniques. The thermal degradation of the Ni(II) complex was investigated using thermogravimetric and differential thermal analyses techniques in oxygen atmosphere. The molecular structure of the complex was determined by single crystal X-ray diffraction technique. Hirshfeld surface analysis (HSA) investigated the packing modes and intermolecular interactions in molecular crystals, as they provide a visual picture of intermolecular interactions. In addition, all computational studies at B3LYP/6-311++G(d,p) were carried out for theoretical characterization of Ni(II) complex. The optimized geometry results, which were well represented the X-ray data, were shown that the chosen of DFT/B3LYP/6-311++G(d,p) was a successful choice for title compound. After a successful optimization, FMOs, chemical activity, non-linear optical properties (NLO), molecular electrostatic potential (MEP), Mulliken population (MPA), natural population analyses (NPA), Fukui function analysis (FFA) and natural bond orbital analysis (NBO), which could not obtained by experimental ways, were calculated and investigated. The computed of net charges and chemical activity studies which helped to identifying the electrophilic/nucleophilic nature.     

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.