On the linear Lindenbaum algebra of Basic Propositional Logic

We study the linear Lindenbaum algebra of Basic Propositional Calculus, called linear basic algebra. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stickelberger Codes

Let p be an odd prime and be a primitive p th root of unity over . The Galois group G of over is a cyclic group of order p-1. The integral group ring [G] contains the Stickelberger ideal S _p which annihilates the ideal class group of K. In this paper we investigate the parameters of cyclic codes S _p (q) obtained as reductions of S _p modulo primes q which we call Stickelberger codes. In particular, we show that the dimension of S _p (p) is related to the index of irregularity of p, i.e., the number of Bernoulli numbers B _2k , , which are divisible by p. We then develop methods to compute the generator polynomial of S _p (p). This gives rise to anew algorithm for the computation of the index of irregularity of a prime. As an application we show that 20,001,301 is regular. This significantly improves a previous record of 8,388,019 on the largest explicitly known regular prime.     

Novel Complexes of Gallium(III), Indium(III), and Thallium(III) with Pyridine‐Containing Proton Transfer Ion Pairs Obtained from Dipicolinic Acid – Synthesis,Characterization and X‐ray Crystal Structure

Three new complexes of group thirteen metals, gallium(III), indium(III), and thallium(III) with proton transfer compounds, obtained from 2,6‐pyridinedicarboxylic acid (dipicolinic acid), were synthesized and characterized using elemental analysis, IR, ¹H and ¹³C NMR spectroscopy and single crystal X‐ray diffraction. The gallium(III) and indium(III) complexes were prepared using (pydaH₂)(pydc) (pyda = 2,6‐pyridinediamine, pydcH₂ = dipicolinic acid) and thallium(III) complex was obtained from (creatH)(pydcH) (creat = creatinine). The chemical formulae and space groups of the complexes are (pydaH)[Ga(pydc)₂] · 3.25H₂O · CH₃OH, ( 1 ), [In(pydc)(pydcH)(H₂O)₂] · 5H₂O, Pna2₁ ( 2 ) and [Tl₂(pydcH)₃(pydc)(H₂O)₂], ( 3 ). Non‐covalent interactions such as ion‐pairing, hydrogen bonding and π‐π stacking are discussed. The complexation reactions of pyda, pydc, and pyda + pydc with In³⁺ and Ga³⁺ ions in aqueous solution were investigated by potentiometric pH titrations, and the equilibrium constants for all major complexes formed are described.     

p-Toluenesulfonyl Chloride (p-TsCl)-Catalyzed Trimethylsilylation of Hydroxyl Groups Using Hexamethyldisilazane and Their Regeneration Under Mild Conditions: The First Example for Catalytic Application of p-Toluenesulfonyl Chloride

The first catalytic application of p-toluenesulfonyl chloride (p-TsCl) for the efficient and selective trimethylsilylation of various types of hydroxyl groups with hexamethyldisilazane (HMDS) in dichloromethane and desilylation of these compounds in water is reported. The reactions were carried out at room temperature and were found to proceed in good to excellent yields.     

Synthesis and Characterization of Poly(Biphenyl‐2‐yl p‐Styrenesulphonate) as Profungicide in Controlled Release Technique

A new fungicide controlled release formulation was prepared by the reaction of p‐styrenesulphonyl chloride with biphenyl‐2‐ol (Dowicide A) as fungicide. The resulting monomer containing the fungicide was polymerized with benzoyl peroxide as initiator. The monomer and the polymer were identified by spectroscopic methods, and molecular weight of the polymer was determined by GPC. Also mp, Tg and Td of the polymer were identified by DSC. The release characteristic of the polymer was studied in neutral, alkaline, and acidic media. Also, the effect of the temperature on the release of bioactive agent (Dowicide A) was investigated. The hydrolysis data showed that the release rates are strongly dependent upon the pH of the medium and the temperature.     

Investigation of nanostructural,thermal and magnetic properties of yttrium iron garnet synthesized by mechanochemical method

This paper focuses on the magnetic, structural and thermal properties of mechanically alloyed Y₂O₃/α-Fe₂O₃ mixed powders and investigates the effects of the mechanical milling and heat treatment on the synthesis of yttrium iron garnet from the primary materials. The morphological and structural studies were carried out by scanning electron microscope and X-ray diffraction, respectively. The thermal activities were measured by differential thermal analysis. The magnetic properties were studied by vibrating sample magnetometer. The results showed that high-energy milling does not lead to the garnet formation and even does not decrease the temperature of the garnet formation. Furthermore, the orthoferrite phase can be achieved slightly during the milling process (up to 96 h) and completely by the heat treatment at lower temperatures (850 °C).     

Synthesis of magnetic nanoparticles Fe3O4@CQD@Si(OEt)(CH2)3@melamine@TC@Ni(NO3) with application in the synthesis of 2-amino-3-cyanopyridine and pyrano[2,3-c]pyrazole derivatives

Research on Chemical Intermediates - In the present study, magnetic nanocatalysts coated by carbon quantum dots (CQDs) and organic functional groups (Fe3O4@CQD@Si(OEt)(CH2)3@melamine@TC@Ni(NO3))...     

Electrical switching properties of nanostructured multilayer superlattice Ge–Si…Cu…Si–Ge prepared by electron beam evaporation on glass

In this study, the fabrication of nanostructured multilayer superlattice Ge–Si…Cu…Si–Ge using electron beam evaporation on glass substrates at a temperature of 200 °C has been reported. The structural, optical and electrical characteristics of such films were then studied by means of DC polarization, powder X-ray diffraction (XRD), scanning electron microscopy, atomic force microscopy (AFM), Rutherford backscattering (RBS) and UV–visible spectroscopic techniques. The XRD pattern obtained showed an amorphous state along with some reflected XRD signals from the Ge planes while there were no reflected signals from the Si and Cu layers. The average estimated grain size diameter (_Dav.)$\left(D_{av.}\right)$ is 30.13 nm as found from the XRD experiment using the Debye–Scherrer equation. The grain size as estimated from the AFM images was found to be within 28–31 nm, which is in good agreement with the XRD average value. RBS analysis confirmed the multilayer structure of the superlattice. The optical allowed indirect band gap of the superlattice obtained from the Tauc plot was found to be 1.19 eV, which is greater than that of bulk Ge semiconductor (0.66 eV). This fact indicates that the incorporation of a Cu layer instead of the Ge layer enables us to change the indirect to direct transitions in Ge/Si devices. Current density–voltage (J$J$–V$V$) characteristics of the nanodevice showed an electrical switching effect (VCNR) with the largest ON/OFF current ratio of the order of 10 ⁶ at 15 V.