CPT violation does not lead to violation of Lorentz invariance and vice versa

We present a class of interacting nonlocal quantum field theories, in which the CPT invariance is violated while the Lorentz invariance is present. This result rules out a previous claim in the literature that the CPT violation implies the violation of Lorentz invariance. Furthermore, there exists the reciprocal of this theorem, namely that the violation of Lorentz invariance does not lead to the CPT violation, provided that the residual symmetry of Lorentz invariance admits the proper representation theory for the particles. The latter occurs in the case of quantum field theories on a noncommutative space–time, which in place of the broken Lorentz symmetry possesses the twisted Poincaré invariance. With such a CPT-violating interaction and the addition of a C-violating (e.g., electroweak) interaction, the quantum corrections due to the combined interactions could lead to different properties for the particle and antiparticle, including their masses.     

Corrigendum to “Convexity and concavity constants in Lorentz and Marcinkiewicz spaces” [J. Math. Anal. Appl. 343 (2008) 337-351]

In this note we state the accurate formulas of convexity and concavity constants in Lorentz spaces, correcting the formulas from Kamińska and Parrish (2008) [2].     

Morphology,structure, and photoactivity of two types of graphene oxide-TiO<Subscript>2</Subscript> composites

Two types of graphene oxide-TiO₂ composites were prepared: one by including graphene oxide flakes in the TiO₂ sol, followed by thermal treatment (GI composite) at 300°C, and the second by including graphene oxide flakes in the calcined (at 500°C) TiO₂ xerogel (GII composite). The composites were characterized by SEM, TEM-EDS, TEM-SADP, STEM-HAADF, HRTEM coupled with FT, XRD, and XPS. Photocatalysis results were fitted to different kinetic models (pseudo-first and pseudo-second kinetics, intraparticle Weber-Morris diffusion, film diffusion, and external mass transfer). The results showed that by introducing graphene oxide flakes in the TiO₂ sol, followed by thermal treatment at 300°C (GI composite), an efficient graphene oxide-TiO₂ catalyst with high specific surface area, heterogeneity, and many graphitized areas can be obtained. Complete crystallization of the composite is not the key issue for the best photoactivity achievement. The rate limiting step in the photocatalytic process is the photooxidation of SA molecules on the TiO₂ surface.     

Synthesis and Antimicrobial Activity of Some New N‐substituted‐5‐arylidene‐thiazolidine‐2,4‐diones

A total of 17 new N‐substituted derivatives ( 2b , 2c , 2d , 2e , 2f , 2g , 2h , 2i , 2j , 2k and 3b , 3c , 3d , 3e , 3f , 3g , 3h ) of 5‐((2‐phenylthiazol‐4‐yl)methylene) thiazolidine‐2,4‐dione ( 2a ) and 5‐(2,6‐dichloro‐ benzylidene)thiazolidine‐2,4‐dione ( 3a ) were synthesized. The structural elucidation of the newly synthesized compounds was based on elemental analysis and spectroscopic data (MS, ¹H NMR, ¹³C NMR), and their antimicrobial activities were assessed in vitro against several strains of Gram‐positive and Gram‐negative bacteria and one fungal strain (Candida albicans) as growth inhibition diameter. Some of them showed modest to good antibacterial activity against Gram‐negative Escherichia coli and Salmonella typhimurium and Gram‐positive Staphylococcus aureus, Bacillus cereus, and Enterococcus fecalis bacterial strains, whereas almost all the compounds were inactive against Listeria monocytogenes. All of the synthesized compounds showed moderate to very good activity against C. albicans.     

Organomercury(II) and tellurium(II) compounds with the "pincer" ligand 2,6-[O(CH2CH2)2NCH2]2C6H3--stabilization of an unusual organotellurium(II) cationic species

The reaction of RH (1) with Hg(OAc)(2), in EtOH, gave the acetate RHgOAc (2) [R = 2,6-[O(CH(2)CH(2))(2)NCH(2)](2)C(6)H(3)]. The corresponding RHgCl (3) was obtained from 2 and LiCl. The reaction of 3 with TeCl(4) (1:1 molar ratio), in anhydrous 1,4-dioxane, resulted in the transfer of the organic ligand from mercury to tellurium and the isolation of the unexpected ionic compounds [RTe](2)[Hg(2)Cl(6)] (4) and [RH(3)][HgCl(4)] (5). The molecular structures of 1-4 and 5·H(2)O were established by single-crystal X-ray diffraction. The acetate 2 and the chloride 3 are monomeric in solid state. In both mercury and tellurium organometallic compounds the organic group acts as an (N,C,N) "pincer" ligand. This coordination pattern provided stability for the rare [RTe](+) cation. Weak cation-anion interactions [Te···Cl 3.869(3) ?] are present between [RTe](+) and the dinuclear anion [Hg(2)Cl(6)](2-) in the crystal of 4. Theoretical calculations with DFT methods were performed for models of 3 and 4. The results show that in the cation of 4 the coordination of the nitrogen atoms play an important role for the stabilization of the structure found in the crystal whereas in 3 the coordination of the nitrogen atoms to the metal centre stabilizes to a less extent the structure found in solid state.     

Chemical, antioxidant and antimicrobial investigations of Pinus cembra L. bark and needles

The chemical constituents and biological activity of Pinus cembra L. (Pinaceae), native to the Central European Alps and the Carpathian Mountains, are not well known. The aim of the present work was to examine the phenolic content, antioxidant and antimicrobial effects of hydromethanolic extracts of Pinus cembra L. bark and needles. Bark extract had higher concentrations of total phenolics (299.3 vs. 78.22 mg gallic acid equivalents/g extract), flavonoids (125.3 vs. 19.84 mg catechin equivalents/g extract) and proanthocyanidins (74.3 vs. 12.7 mg cyanidin equivalents/g extract) than needle extract and was more active as a free radical scavenger, reducing agent and antimicrobial agent. The EC?? values in the 2,2-diphenyl-1-picrylhydrazyl (DPPH), 2,2'-azino-bis(3-ethylbenzo-thiazoline-6-sulfonic acid) diammonium salt (ABTS) and reducing power assays were 71.1, 6.3 and 26 mg/mL for bark extract and 186.1, 24 and 104 mg/mL for needle extract, respectively. In addition, needle extract showed ferrous ions chelating effects (EC?? = 1,755 μg/mL). The antimicrobial effects against Staphylococcus aureus, Sarcina lutea, Bacillus cereus, Escherichia coli, Pseudomonas aeruginosa and Candida albicans were assessed by the agar diffusion method. Both extracts (4 mg/well) were active against all the microorganisms tested; bark extract showed higher inhibition on all strains. These results indicate that Pinus cembra L. bark and needles are good sources of phytochemicals with antioxidant and antimicrobial activities.     

Irreducibility Results for Compositions of Polynomials with Integer Coefficients

We obtain explicit upper bounds for the number of irreducible factors for a class of polynomials of the form f ○ g, where f,g are polynomials with integer coefficients, in terms of the prime factorization of the leading coefficients of f and g, the degrees of f and g, and the size of coefficients of f. In particular, some irreducibility results are given for this class of compositions of polynomials.     

Die Bildung cyclischer Amidiniumiodide und -polyiodide aus 1,3,5-Trimethyl-hexahydro-1,3,5-triazin und Iod

Formation of cyclic Amidiniumiodides and -polyiodides from 1,3,5-Trimethyl-hexahydro-1,3,5-triazine and Iodine The reaction of 1,3,5-trimethyl-hexahydro-1,3,5-triazine (CH₃NCH₂)₃ with iodine in the molar ratio (CH₃NCH₂)₃:I₂ = 2:1 gives the new compound 1,3,5-trimethyl-tetrahydro-1,3,5-triazinium-iodide C₆H₁₄N₃I. This iodide adds one mole I₂ and forms 1,3,5-trimethyl-tetrahydro-1,3,5-triazinium-triiodide C₆H₁₄N₃I₃. The crystal structure analysis shows a cation, in which two methyl groups and five ring atoms are planar arranged. The third methyl group stands axial to the ring. 1,3,5-Trimethyl-tetrahydro-1,3,5-triazinium-pentaiodide is formed by adding a further mole I₂.