Ferric Hydrogensulfate Catalysed Schmidt Reaction of Ketones to Amides under Solvent‐Free Conditions

A new, efficient and convenient method has been developed for the one‐pot synthesis of amides from ketones and sodium azide in the presence of ferric hydrogensulfate in solvent‐free media. Advantages of this method are chemoselectivity, with high yields in a simple operation, and short reaction time under solvent‐free conditions.     

An investigation on two cracks perpen-dicular to the interfaces in a piezolectric layer bonded to two half spaces by the schmidt method

The behavior of two collinear anti-plane shear cracks in'a piezoelectric layer bonded to two half spaces is investigated by the Schmidt method. The cracks are vertically to the interfaces of the piezoelectric layer. By using the Fourier transform, the problem can be solved with two pairs of triple integral equations. These equations are solved using the Schmidt method. This process is quite different from that adopted previously. Numerical examples are provided to show the effect of the geometry of the interacting cracks and the piezoelectric constants of the material upon the stress intensity factor of the cracks. Project supported by the Post Doctoral Science Foundation of Heilongijang Province, the Natural Science Foundation of Heilongjing Province and the Science Research Foundation of Harbin Institute of Technology(HIT. 2000. 30).     

Characterization and Authentication of “Ricotta” Whey Cheeses through GC-FID Analysis of Fatty Acid Profile and Chemometrics

The fatty acid (FA) profiles of 240 samples of ricotta whey cheese made from sheep, goat, cow, or water buffalo milk were analyzed by gas-chromatography (GC). Then, sequential preprocessing through orthogonalization (SPORT) was used in order to classify samples according to the nature of the milk they were made from. This strategy achieved excellent results, correctly classifying 77 (out of 80) validation samples. Eventually, since 36 (over 114) sheep ricotta whey cheeses were PDO products, a second classification problem, finalizing the discrimination of PDO and Non-PDO dairies, was faced. In this case, two classifiers were used, SPORT and soft independent modelling by class analogy (SIMCA). Both approaches provided more than satisfying results; in fact, SPORT properly assigned 63 (of 65) test samples, whereas the SIMCA model accepted 14 PDO individuals over 15 (93.3% sensitivity) and correctly rejected all the other samples (100.0% specificity). In conclusion, all the tested approaches resulted as suitable for the two fixed purposes. Eventually, variable importance in projection (VIP) analysis was used to understand which FAs characterize the different categories of ricotta. Among the 22 analyzed compounds, about 10 are considered the most relevant for the solution of the investigated problems.     

Copper-mediated trimethylsilyl azide in amination of bromoflavonoids to synthesize unique aminoflavonoids

Aminoflavonoids are unique antioxidants comparing to other abundant flavonoids in nature. Their syntheses and biological activities were scarcely reported. An effectively copper-mediated amination of the corresponding bromoflavonoids to synthesize a series of new aminoflavonoids is described.     

Dynamic stress intensity factors of two 3D rectangular cracks in a transversely isotropic elastic material under a time-harmonic elastic P-wave

The dynamic stress intensity factors (DSIFs) of two 3D rectangular cracks in a transversely isotropic elastic material under an incident harmonic stress wave are investigated by generalized Almansi’s theorem and the Schmidt method in the present paper. Using 2D Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, three pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the geometric shape of the rectangular crack, the characteristics of the harmonic wave and the distance between two rectangular cracks on the DSIFs of the transversely isotropic elastic material.     

精确计算非旋波近似下二能级系统的能谱和动力学性质

利用相干态正交化展开法,精确求解了非旋波近似下Jaynes-Cummings模型的能谱和动力学性质.与近似下解析解比较发现,在弱耦合和强耦合区近似解析解与数值精确解符合很好,但在中间耦合区符合较差. 关键词： 相干态正交化展开 非旋波近似 Jaynes-Cummings模型     

A new method for pyrrole peri-annulation: synthesis of 1H-1,5,7-triazacyclopenta[c,d]phenalenes from 1H-perimidines

New methods for the synthesis of 1H-1,5,7-triazacyclopenta[c,d]phenalenes have been developed based on a sequence involving Schmidt reaction of keto-perimidines and acylation of the intermediate amides with 1,3,5-triazines or carboxylic acids. The same synthetic sequence starting from the corresponding alkylperimidine includes acylation with acetic acid as the first step.     

Exact classical solutions of nonlinear sigma models on supermanifolds

We study two-dimensional nonlinear sigma models with target spaces being the complex super-Grassmannian manifolds, that is, coset supermanifolds G(m,p|n,q)≅U(m|n)/[U(p|q)⊗U(m−p|n−q)]$G(m,p|n,q)\cong U(m|n)/[U(p|q)\otimes U(m-p|n-q)]$ for 0?p?m$0?p?m$, 0?q?n$0?q?n$ and 1?p+q$1?p+q$. The projective superspace CPm−1|n${\mathbf{CP}}^{m-1|n}$ is a special case of p=1$p=1$, q=0$q=0$. For the two-dimensional Euclidean base space, a wide class of exact classical solutions (or harmonic maps) are constructed explicitly and elementarily in terms of Gramm–Schmidt orthonormalisation procedure starting from holomorphic bosonic and fermionic supervector input functions. The construction is a generalisation of the non-super-case published more than twenty years ago by one of the present authors.     

Intramolecular and Intermolecular Schmidt Reactions of Alkyl Azides with Aldehydes

Despite recent advances in the use of alkyl azides in ring expansion reactions of ketones, there has been little work done on the corresponding chemistry of aldehydes. In the present study, the Lewis acid-promoted reactions of alkyl azides with aldehydes were studied in both intermolecular and intramolecular contexts. The intramolecular reactions of azidoalkyl aldehydes in which the azide and carbonyl groups were separated by 2-5 carbons were examined. Although the examples having the shortest tether failed (3-azidopropanals), each of the other systems gave good yields of either NH-substituted lactams (resulting from hydride migration in the initially formed azidohydrin adduct) or formamides (alkyl migration). The product formed was dependent on the chain length of the starting azido aldehyde. The intermolecular reactions were less efficient, requiring TiCl₄ promotion for even moderate yields, and in each case gave mixtures of products resulting from hydride and alkyl migration.