Conformationally controlled intramolecular heterocyclization of 2,4-diaminoperfluoro-4-methyl-2-pentenethiocyanate-3

Perfluoro-2-methyl-2-pentene-thiocyanate-3 reacts with ammonia to give 2,4-diaminoperfluoro-4-methyl-2-pentenethiocyanate-3 ( 4 ) and 2-aminoperfluoro-4, 4-dimethyl-4,5-dihydro-5-ethylidene-1,3-thiazole ( 5 ). Compound 4 is kinetically stable and at 150°C under-goes rotational isomerization to afford the cyclic isomer 2-amino-4,4-bis(trifluoromethyl)-4,5-dihydro-5-(1-aminoperfluoroethylidene) -1,3-thiazole ( 6 ). Intramolecular cyclizations, resulting in the thiazolines 5 and 6 , proceed likewise via the Thorpe reaction. For compounds 4–6 , X-ray diffraction analyses were undertaken and IR spectra in solution and in solid state were investigated. It is supposed that a high kinetic preference for formation of 4 and the fact that it does not undergo spontaneous cyclization in ammonolysis stem from the NH …︁ N intramolecular hydrogen bonding between two amino groups.     

Selective Synthesis of 2,5‐Diformylfuran by Sustainable 4‐acetamido‐TEMPO/Halogen‐Mediated Electrooxidation of 5‐Hydroxymethylfurfural

A new method was developed for the selective gram‐scale synthesis of 2,5‐diformylfuran (DFF), which is an important chemical with a high application potential, via oxidation of biomass‐derived 5‐hydroxylmethylfurfural (HMF) catalyzed by 4‐acetylamino‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl (4‐AcNH‐TEMPO) in a two‐phase system consisting of a methylene chloride and aqueous solution containing sodium hydrogen carbonate and potassium iodide. The key feature of this method is the generation of the I₂ (co‐)oxidant by anodic oxidation of iodide anions during pulse electrolysis. In addition, the electrolyte can be successfully recycled five times while maintaining a 62–65 % yield of DFF. This novel method provides a sustainable pathway for waste‐free production of DFF without the use of metal catalysts and expensive oxidants. An advantage of electrooxidation is utilized in the preparation of demanding chemical.     

Compactness of support of solutions to nonlinear second-order elliptic and parabolic equations in a half-cylinder

We study equations of the form $$\begin{gathered} u_{tt} + Lu + b(x,t)u_t = a(x,t)\left| u \right|^{\sigma - 1} u, \hfill \\ - u_t + Lu = a(x,t)\left| u \right|^{\sigma - 1} u \hfill \\ \end{gathered}$$ , whereL is a uniformly elliptic operator and 0<σ<1. In the half-cylinder II_0,∞={(x, t):x= (x ₁,...,x _n )∈ ω,t>0}, where ? ? ? _n is a bounded domain, we consider solutions satisfying the homogeneous Neumann condition forx∈?ω andt>0. We find conditions under which these solutions have compact support and prove statements of the following type: ifu(x, t)=o(t ^γ) ast→∞, then there exists aT such thatu(x, t)≡0 fort>T. In this case γ depends on the coefficients of the equation and on the exponent σ.     

Hippocampal activity during the transverse patterning task declines with cognitive competence but not with age

Background  

The hippocampus is a brain region that is particularly affected by age-related morphological changes. It is generally assumed that a loss in hippocampal volume results in functional deficits that contribute to age-related cognitive decline. In a combined cross-sectional behavioural and magnetoencephalography (MEG) study we investigated whether hippocampal-associated neural current flow during a transverse patterning task - which requires learning relational associations between stimuli - correlates with age and whether it is modulated by cognitive competence.     

Classification of finite groups according to the number of conjugacy classes II

In the following,G denotes a finite group,r(G) the number of conjugacy classes ofG, β(G) the number of minimal normal subgroups ofG andα(G) the number of conjugate classes ofG not contained in the socleS(G). Let Φ _j = {G|β(G) =r(G) −j}. In this paper, the family Φ₁₁ is classified. In addition, from a simple inspection of the groups withr(G) =b conjugate classes that appear in ϒ _j ^=1/11 Φ _j , we obtain all finite groups satisfying one of the following conditions: (1)r(G) = 12; (2)r(G) = 13 andβ(G) > 1; …; (9)r(G) = 20 andβ(G) > 8; (10)r(G) =n andβ(G) =n −a with 1 ≦a ≦ 11, for each integern ≧ 21. Also, we obtain all finite groupsG with 13 ≦r(G) ≦ 20,β(G) ≦r(G) − 12, and satisfying one of the following conditions: (i) 0 ≦α(G) ≦ 4; (ii) 5 ≦α(G) ≦ 10 andS(G) solvable.     

On coderivatives and Lipschitzian properties of the dual pair in optimization

In this paper, we apply the concept of coderivative and other tools from the generalized differentiation theory for set-valued mappings to study the stability of the feasible sets of both the primal and the dual problem in infinite-dimensional linear optimization with infinitely many explicit constraints and an additional conic constraint. After providing some specific duality results for our dual pair, we study the Lipschitz-like property of both mappings and also give bounds for the associated Lipschitz moduli. The situation for the dual shows much more involved than the case of the primal problem.