The synthesis of pyrazolo[1,2-a]pyrazoles. Regio- and stereo-selective 1,3-dipolar cycloadditions of (1Z)-rel-(4R,5R)-1-arylmethylene-4-benzoylamino-5-phenyl-3-pyrazolidinon-1 -azomethinimines

Reaction of rel-(4R,5R)-4-benzoylamino-5-phenyl-3-pyrazolidinone (4) with aromatic aldehydes 5a-f gave the corresponding (1Z)-rel-(4R,5R)-1-arylmethylene-4-benzoylamino-5-phenyl-3-pyrazolidinon-1-azomethinimines 6a-f . 1,3-Dipolar cycloadditions of azomethinimines 6a-f to various dipolarophiles, which were found to proceed regio- and stereo-selectively, afforded the corresponding pyrazolo[1,2-a]-pyrazoles 8a-f, 10 , and 13–16 . Reaction of azomethinimine 6a with hydrogen cyanide gave rel-(5R,6R)-6-benzoylamino-5,6-dihydro-3,5-diphenyl-1-oxo-1H,7H-pyrazolo[1,2-a][1,2,3]triazole (18) as a representative of a new ring system.     

Synthesis and NMR characterization of 4-[(2-tetrahydro-pyranyloxy)methyl]piperidine and intermediates

4-(Hydroxymethyl)piperidine was selectively protected with tetrahydropyranyl group in several steps to give the title compound. Use of ¹H and ¹⁹F nmr spectra in structure determination is discussed.     

A non-commutative Priestley duality

We prove that the category of left-handed strongly distributive skew lattices with zero and proper homomorphisms is dually equivalent to a category of sheaves over local Priestley spaces. Our result thus provides a non-commutative version of classical Priestley duality for distributive lattices and generalizes the recent development of Stone duality for skew Boolean algebras.     

Sumsets being squares

Alon, Angel, Benjamini and Lubetzky [1] recently studied an old problem of Euler on sumsets for which all elements of A+B are integer squares. Improving their result we prove: 1. There exists a set A of 3 positive integers and a corresponding set B?[0,N] with |B|?(logN)^15/17, such that all elements of A+B are perfect squares. 2. There exists a set A of 3 integers and a corresponding set B?[0,N] with |B|?(logN)^9/11, such that all elements of the sets A, B and A+B are perfect squares. The proofs make use of suitably constructed elliptic curves of high rank.     

Carrier concentration and shallow electron states in Sb-doped hydrothermally grown ZnO

In order to obtain p-type ZnO, the incorporation of group-V elements on oxygen sites has received lots of attention. Recently, the implantation of Sb+ ions into ZnO has been shown to lead to reduced n-type conduction. However, a compensating effect due to implantation damage could not be ruled out. Therefore, single-crystal ZnO has been hydrothermally grown with additional Sb₂O₃, Sb₂O₅, and K(SbO)C₄H₄O₆ in the solution. Schottky barrier contacts have been deposited onto the () face. Capacitance–voltage measurements and thermal admittance spectroscopy have been used for electrical characterization, and secondary ion mass spectrometry was used to measure the Sb content in the samples. Clearly, all samples exhibited n-type conduction. A competition between the incorporation of oxygen and antimony is suggested.     

Technical and radiological characterisation of fly ash and bottom ash from thermal power plant

Journal of Radioanalytical and Nuclear Chemistry - Huge quantities of fly ash and bottom ash are generated from thermal power plants and it presents great concern for country, mainly due...     

Coefficients of Orthogonal Polynomials on the Unit Circle and Higher-Order Szego Theorems

Let be a nontrivial probability measure on the unit circle the density of its absolutely continuous part, its Verblunsky coefficients, and its monic orthogonal polynomials. In this paper we compute the coefficients of in terms of the . If the function is in , we do the same for its Fourier coefficients. As an application we prove that if and if is a polynomial, then with and S the left-shift operator on sequences we have