Statistical Extensions of Some Classical Tauberian Theorems for Cesàro Summability of Triple Sequences

Some growth conditions of the resolvent function of a Banach space operator are investigated using higher order Cesàro means. More precisely, Abel and Nevanlinna estimates are obtained under the condition of boundedness of some weighted Cesàro averages. Also, certains results related to the (strong or uniform) convergence of Cesàro means are mentioned.     

A note on “A LP-based heuristic for a time-constrained routing problem”

In their paper, Avella et al. (2006) investigate a time-constrained routing problem. The core of the proposed solution approach is a large-scale linear program that grows both row- and column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this linear program optimally, and an optimality condition is presented to terminate the column-and-row generation algorithm. We demonstrate by using Lagrangian duality that this optimality condition is incorrect and may lead to a suboptimal solution at termination.     

N,S-Substituted Dienes from Mono(arylthio)substituted- and S-, S,S-Substituted Dienes

Mono(thio)substituted dienes 1a-1b gave compounds 3a-c and 5d-g with piperazine and piperidine derivatives in dichloromethane. Compounds 8 , 9 , and 10 were obtained from the reactions of perchlorobutadiene ( 6 ) with 1,4-butanedithiol ( 7 ) in ethanol in the presence of sodium hydroxide. Compounds 12a-b , 13a-b were obtained from the reactions of perchlorobutadiene ( 6 ) with allylmercaptan (CH 2 =CH--CH 2 --SH) and mercaptoethanol (HO--CH 2 --CH 2 --SH).     

Einige Neue N,S-Substituierte 2-Nitrodienverbindungen Aus Reaktionen Von Mono(p-fluorarylthio)substituierten Dienen Mit Aminen

2-Nitrodiene compound 1 was stirred with p-fluorothiophenol for a long time and compound 3 was obtained. Compound 1 gave bis(thio)substituted 2-nitrodiene compound 4 and tris(thio)substituted compound 5 with 2 moles of p-fluorothiophenol in the presence of NaOH in ethanol. The compounds 9a–g have been prepared from 8a–g and 3. Compound 7 was obtained from the reaction of mono(thio)substituted 2-nitrodiene with morpholine. Compound 3 gives 11a–d in the reaction with piperidines in CH₂Cl₂ (or ether). Compound 13a–b have been obtained from the reaction of compound 3 with primary amines 12a–b. Compound 3 gives 15 and 16 in the reaction with 2,5-dimethylpiperazine in CH₂Cl₂.

     

Swelling Characterization of the Superabsorbent Copolymer in the Petroleum-Based Solvent-Water Mixtures

The crosslinked and porous copolymer grains were synthesized by inverse suspension polymerization of acrylamide. The synthesized copolymer was characterized by Fourier Transform Infrared Spectroscopy (FTIR) and Scanning Electron Microscopy (SEM). It was achieved to absorbed 418 g water by 1 g copolymer after 5 min waiting time. Moreover, it was seen that about 99% of water was absorbed by 1 g copolymer in the solvent water mixtures (300 mL solvent–200 mL distilled water) after 2.5 min waiting time. The diffusion coefficients of the copolymer in the solvent-water mixtures were found between 8.87 · 10⁴ and 10.64 · 10⁴ cm²s^?1. Furthermore, the copolymer in distilled water achieved to reach a high value of the diffusion coefficient (13.2 · 10⁴ cm²s^?1).     

Synthesis and Metal Ion Recognition Properties of a Novel Chiral Calix[4](azoxa)crown-7

A novel chiral calix[4](azoxa)crown-7 (9) has been synthesized and its metal ion recognition properties investigated. The starting reagents, chiral diamine 5 and calix[4]arene diacid chloride derivative 8, were prepared according to literature methods. ¹H and ¹³C NMR data show that 9 exists in a cone conformation. In liquid–liquid extraction experiments, 9 exhibits selectivity for Li⁺ among the other alkali metals and a good extraction ability for transition metal cations, suggesting its potential use in different fields, such as a sensor for ions as well as for chiral molecules.     

Synthesis, characterization, thermal and optical properties of styrene derivatives having pendant p-substituted benzylic ether groups

The derivatives of styrene monomer, 4-chlorophenyl-4-vinylbenzyl ether (M1), 4-methoxyphenyl-4-vinylbenzyl ether (M2), 4-ethylphenyl-4-vinylbenzyl ether (M3) and 1-naphtylphenyl-4-vinylbenzyl ether (M4) were synthesized. The normal free radical polymerization of monomers in 1,4-dioxane were performed by using 2,2′-azobisisobutyronitrile as an initiator at 65 °C. The monomers and their homopolymers were characterized by FT-IR, NMR and elemental analyses measurements. The thermal stability of polymers was investigated by thermogravimetric and differential scanning calorimetric analysis. Thermal degradation activation energies of the polymers were calculated by the Ozawa and Kissinger methods. In addition, photo-stability tests of the polymers under near-UV irradiation were performed.     

Synthesis and characterization of new 4,5-dihydropyrazol-1-yl derivatives

In this study, first, a series of chalcone compounds S1–S6 were synthesized from various acetophenone derivatives (acetophenone, p-methyl acetophenone, and p-methoxy acetophenone) and aromatic aldehyde derivatives (benzaldehyde, p-methyl benzaldehyde, and p-methoxy benzaldehyde) by the Claisen–Schmidt condensation reaction. These S1–S6 compounds were then used in the preparation of 4,5-dihydropyrazol-1-yl derivatives S7–S15. Finally, four new compounds S16–S19 were synthesized from compound (S7, S8, S9, and S12) and 2,4-dinitrophenylhydrazine. Therefore, three known and ten new heterocyclic compounds were synthesized and completely characterized using ¹H NMR, ¹³C NMR, IR, and elemental analysis.