Normal subgroup based power graph of finite groups

Ricerche di Matematica - Let G be a finite group and $$N \unlhd G$$ . The normal subgroup based power graph of G, $$\Gamma _N(G)$$ , is an undirected graph with vertex set $$(G{\setminus }N) \cup...     

Vieta–Fibonacci wavelets: Application in solving fractional pantograph equations

In this paper, the Vieta–Fibonacci wavelets as a new family of orthonormal wavelets are generated. An operational matrix concerning fractional integration of these wavelets is extracted. A numerical scheme is established based on these wavelets and their fractional integral matrix together with the collocation technique to solve fractional pantograph equations. The presented method reduces solving the problem under study into solving a system of algebraic equations. Several examples are provided to show the accuracy of the method.     

New Developments on Operator Reverse AM-GM Inequality for Positive Linear Maps

Acta Mathematica Sinica, English Series - In this research article, we shall give some reverse Arithmetic-Geometric mean inequalities for unital positive linear maps on Hilbert space operators...     

Reactions of [(Cp)2Ti(NCS)2] as a potential metalloligand; synthesis and physico-chemical investigations of novel heterobimetallic complexes

Summary Bis(cyclopentadienyl)titanium(IV) diisothiocyanate [(Cp)₂-Ti(NCS)₂] reacts with MCl₂ (M = Cu, Pd or Pt), [CuCl(PPh₃)₃], [RuCl₂(PPh₃)₃] and [RuCl₂(DMSO)₄] (DMSO = dimethylsulphoxide) giving solid compounds of stochiometry [(Cp)₂Ti(-NCS)₂MCl₂] (M = Cu, Pd or Pt), [(Cp)₂Ti(-NCS)₂CuCl(PPh₃)], [(Cp)₂Ti(-NCS)₂-RuCl(PPh₃)₂]Cl and [(Cp)₂Ti(-NCS)₂RuCl₂(DMSO)2]. These products have been characterized by physicochemical and spectroscopic methods.     

Highly Efficient and Practical Syntheses of Lavendamycin Methyl Ester and Related Novel Quinolindiones

The novel 7-(N-formyl-, 7-(N-acetyl-, and 7-(N-isobutyrylamino)-2-methylquinoline-5,8-diones were synthesized in excellent overall yields in three steps via the nitration of the commercially available 8-hydroxy-2-methylquinoline followed by a reduction-acylation step and then oxidation. Acid hydrolysis of 7-(N-acetylamino)-2-methylquinoline-5,8-dione (14a) afforded the novel 7-aminoquinoline-5,8-dione 7 in excellent yields. Due to our efficient preparation of dione 14a, we now report a short and practical method for the total synthesis of the potent antitumor agent lavendamycin methyl ester (1b) with an excellent overall yield.     

Dynamics of polymer packaging

We use the stochastic rotation dynamics algorithm to investigate the packaging of flexible and semiflexible polymers into a capsid that is permeable to solvent molecules. The model takes into account hydrodynamic interactions arising due to local flow. The flexible chain maintains a random configuration as it is being fed into the capsid, in contrast to the semiflexible chain, whose configuration is initially spool-like, becoming more random at high packing. We measure the packing rate, which is found to decrease with the percentage of the chain packed and highlight the difference between the flexible and semiflexible chains. Reflecting experiments, we find pauses in the packing process for individual chains as the motor loses grip of the fluctuating beads. We also find that hydrodynamics is important, in that the packaging rate is faster when flow is included.     

Imidomethylation of C-nucleophiles using O-phthalimidomethyl trichloroacetimidate and catalytic amounts of TMSOTf

The O-phthalimidomethyl trichloroacetimidate (1), as a latent aminomethylating agent, exhibits high electrophilicity towards a variety of C-nucleophiles in the presence of catalytic amounts of TMSOTf and mild reaction conditions. The nucleophiles include aromatics, alkenes and active methylene compounds 2-11 whereby a phthalimidomethyl group could be introduced to give compounds 12-22. Removal of the phthaloyl group gave the respective amines, β-amino ketones, and β-amino acids. The O-(trichloroacetamido)methyl trichloroacetimidate (35) was also found to be a good amidomethylating agent.     

Copolymers and two-layered composites of poly(<Emphasis Type="Italic">o</Emphasis>-aminophenol) and polyaniline

Electroactive conducting copolymers of aniline (ANI) and o-aminophenol (OAP) and two-layered poly(o-aminophenol) (POAP)/polyaniline (PANI) composites were prepared in aqueous acidic solution by electrode potential cycling. Copolymerization was carried out at different feed concentrations of OAP and ANI on a gold electrode. A strong inhibition of electropolymerization was found at a high molar fraction of OAP in the feed. The copolymers showed good adherence on the electrode surface and gave a redox response up to pH=10.0. Two transitions were observed in the in situ conductivities of the copolymers (as with PANI), but the conductivities were lower by 2.5–3 orders of magnitude as compared to PANI. Electrosynthesis of PANI on POAP modified electrodes showed copolymer formation after reaction initiation and finally formation of a PANI layer at the copolymer/solution interface. The ‘memory effect’ of the bilayer structures of both polymers was discussed in terms of protonation/deprotonation and anion consumption taking place during redox processes of both polymers.     

Röntgenstrukturanalysen von Cyclododekaschwefel (S12) und Cyclododekaschwefel-1-Kohlendisulfid (S12 · CS2) [1]

X-Ray Structural Analyses of Cyclododecasulfur (S₁₂) and Cyclododecasulfur-1-Carbon-disulfide (S₁₂ · CS₂) S₁₂ · CS₂ crystallizes in space group R&3macr;m–D with hexagonal lattice constants a = 1066.8(3), c = 1155.1(4) pm, Z = 3, d_calc. = 2.04 g · cm^?3. The S₁₂ molecules occupy sites of D_3d symmetry with bond distance (d_ss) of 205.4(1) pm, bond angles (α) of 105.80(5) and 106.65(6)º and torsional angle (τ) of 87.20(7)º. The CS₂ molecule interacts only very weakly with the S₁₂ units. S₁₂ crystallizes in space group Pnnm–D with lattice constants a = 472.5(2), b = 910.4(3), c = 1453.2(3) pm, Z = 2, d_calc = 2.045 g · cm^?3. The molecules with mean parameters d = 205.2 pm, α 106.6º, τ 88.0º occupy sites of C_2h symmetry.