A short proof for Arnold’s Theorem on the SFT-property

Rendiconti del Circolo Matematico di Palermo Series 2 - We give a short proof for one main part of Arnold’s Theorem on the SFT-property, namely, if A is a non-SFT ring, then there exists an...     

Kinetics of acid degradation of proton pump inhibitors in the presence of a thiol

An in vitro investigation of the kinetics of the complex system of acid‐catalyzed conversions and subsequent reactions of proton pump inhibitors (PPIs; omeprazole, lansoprazole and pantoprazole) was carried out using differential pulse polarography at the static mercury drop electrode. Reactions were investigated in the presence of 2‐mercaptoethanol, in solutions buffered to pH values ranging from 2.0 to 5.0. The first‐order reaction network was proposed for all conversions. The rate of degradation of PPIs and subsequent reactions with 2‐mercaptoethanol were found to follow the following general order: lansoprazole > omeprazole > pantoprazole. The rate of conversion of PPIs into sulfenic acid was found to be directly dependent on the basicity of benzimidazole nitrogen of PPIs, which determines the electrophilic reactivity of the adjacent carbon (C2). The rate of conversion of the sulfenic acid of PPIs into the disulfide (the inhibition reaction) was found to be dependent on the electrophilicity of the sulfur atom of the sulfenic acid. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 498–506, 2009     

RP‐HPLC determination of phenylalkanoids and monoterpenoids in Rhodiola rosea and identification by LC‐ESI‐TOF

An HPLC method permitting the simultaneous determination of fourteen analytes (phenylalkanoids and monoterpenoids) from the roots of Rhodiola rosea was developed. A separation was achieved within 35 min using C₁₈ column material and a water–acetonitrile mobile phase, both containing a 0.05% phosphoric acid gradient system and a temperature of 53°C. The method was validated for linearity, repeatability, limits of detection and limits of quantification. The limits of detection and limits of quantification of 14 phenylalkanoids and monoterpenoids were found to be 0.20–1.0 and 0.5–3.5 µg/mL, respectively. The wavelengths used for quantification of phenylalkanoids and monoterpenoids with a diode array detector were 205, 220 and 251 nm. The method was used to analyze the roots of two species of Rhodiola and commercial extracts of R. rosea and provides preliminary evidence of phytochemical differences between North American and Eurasian populations of R. rosea. LC–mass spectrometry coupled with electrospray ionization (ESI) interface method is described for the identification of phenylalkanoids and monoterpenoids in various Rhodiola samples. This method involved the use of the [M + H]⁺, [M + NH₄]⁺ and [M + Na]⁺ ions in the positive ion mode with extractive ion monitoring (EIM). Copyright © 2009 John Wiley & Sons, Ltd.     

Corrigendum to “A note on the Loewenstein–Prelec theory of intertemporal choice” [Math. Social Sci. 52 (1) (2006) 99–108]

In a critique of the Loewenstein and Prelec [Loewenstein G., Prelec D., 1992. Anomalies in intertemporal choice: Evidence and an interpretation. The Quarterly Journal of Economics 107, 573–597] theory of intertemporal choice, [al-Nowaihi, A., Dhami, S., 2006. A note on the Loewenstein–Prelec theory of intertemporal choice. Mathematical Social Sciences 52, 99–108] point out four errors. One of the alleged errors was that the elasticity of the value function in prospect theory is decreasing. But it is in fact increasing. We provide a correction and a formal proof. As a corollary, we show that the elasticity of the value function is bounded between zero and one. Nevertheless, all the remaining points in [al-Nowaihi, A., Dhami, S., 2006. A note on the Loewenstein–Prelec theory of intertemporal choice. Mathematical Social Sciences 52, 99–108] remain valid     

Synthesis,spectroscopy, electrochemistry and in situ spectroelectrochemistry of partly halogenated coumarin phthalonitrile and corresponding metal-free,cobalt and zinc phthalocyanines

In this study, the preparation of novel 7-hydroxy-3-(2-chloro-4-fluorophenyl)coumarin (1), the ligand, 7-(3,4-dicyanophenoxy)-3-(2-chloro-4-fluorophenyl)coumarin (2), metal-free phthalocyanine 3 and metallophthalocyanine complexes 4 and 5 (MPcs, M = Co, Zn), β-substituted with 7-oxo-3-(2-chloro-4-fluorophenyl)coumarin functional group was achieved. By the reaction of 7-hydroxy-3-(2-chloro-4-fluorophenyl)coumarin (1) with 1,2-dicyano-4-nitrobenzen in dry DMF as the solvent in the presence of K₂CO₃ as the base, the 7-(3,4-dicyanophenoxy)-3-(2-chloro-4-fluorophenyl)coumarin (2) was synthesized. Compound 2 reacted with Co(CH₃COO)₂·4H₂O in 2-N,N-dimethylaminoethanol to furnish a novel coumarin containing cobalt(II) phthalocyanine 4. The cyclotetramerization of 2 with Zn(CH₃COO)₂·2H₂O in 2-N,N-dimethylaminoethanol gave the novel coumarin containing Zn(II)phthalocyanine 5; while tetramerization without any metal salts in 2-N,N-dimethylaminoethanol gave the metal-free phthalocyanine 3. The structures of obtained compounds were confirmed by elemental analysis, UV–Vis, IR, MALDI-TOF mass and ¹H NMR spectra. The cyclic and differential pulse voltammetry, and in situ spectroelectrochemistry of 7-oxo-3-(2-chloro-4-fuorophenyl)coumarin substituted phthalocyanines 3, 4 and 5 allowed us to identify metal- and phthalocyanine ring-based redox processes of the complexes.     

About noncommuting graphs

The noncommuting graph ?(G) of a nonabelian finite group G is defined as follows: The vertices of ?(G) are represented by the noncentral elements of G, and two distinct vertices x and y are joined by an edge if xy ≠ yx. In [1], the following was conjectured: Let G and H be two nonabelian finite groups such that ?(G) ? ?(H); then ¦G¦ = ¦H¦. Here we give some counterexamples to this conjecture.