Exploiting the Massey Gap

In this paper, we find new refinements to the Massey inequality, which relates the Shannon and guessing entropies, introducing a new concept: the Massey gap. By shrinking the Massey gap, we improve all previous work without introducing any new parameters, providing closed-form strict refinements, as well as a numerical procedure improving them even further.     

The first coordination compound containing three different types of spin carriers: 2p-3d-4f (TCNQ.-, Cu2+ and Gd3+)

A novel heterospin system, [(CuL)2Gd(TCNQ)2].TCNQ-.CH3OH.2CH3CN, is obtained by reacting the mononuclear complex, [CuL], with gadolinium(III) nitrate, followed by the substitution of the nitrato ions with anionic organic radicals.     

Some Polynuclear Coordination Compounds Precursors of Chromites Synthesis,Physicochemical Characterization and Thermal Stability

The polynuclear coordination compounds LnCr(tartrate)₃·nH₂O where Ln(III)=La-Er, obtained through a precipitation method, were characterized on the basis of elemental analysis, their electronic and vibrational spectra and magnetic susceptibility measurements. The possibility of obtaining chromites through the transformations of the polynuclear coordination compounds in the solid state was considered. The thermal decompositions of these compounds, studied by TG and DTA methods, were found to follow an almost uniform pattern. The decompositions occurred in six-eight steps. The first two steps involved dehydration, and the third the transformation of tartrate anions to oxalate, followed by conversion to carbonate and oxocarbonate intermediates. The final product in each case was LnCrO₃. A non-isothermal kinetic analysis of the first decomposition steps was performed, the most probable decomposition mechanism being selected and the kinetic parameters evaluated. The final products of the transformations were characterized. This revised version was published online in August 2006 with corrections to the Cover Date.     

Family constraining of iterative algorithms

In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image processing situations when a single constraining operator was used. In the field of image reconstruction from projections a priori information about the original image, such as smoothness or that it belongs to a certain closed convex set, may be used to improve the reconstruction quality. We study here constraining of iterative processes by a family of operators rather than by a single operator.     

Almost Hamiltonian Groups

In this paper we investigate the following problem in Group Theory: which properties $cal P$ transfer (or do not transfer) from all cyclic subgroups, or all abelian subgroups to all arbitrary subgroups? We solve this problem completely when $cal P$ is the property of having finite index in its normal closure, proving that $cal P$ carries from abelian, but not from cyclic to arbitrary subgroups. We use primarily some results of B.H. Neumann.     

Fibonacci numbers that are not sums of two prime powers

In this paper, we construct an infinite arithmetic progression of positive integers such that if , then the th Fibonacci number is not a sum of two prime powers.

     

p-Catalan numbers and squarefree binomial coefficients

In this paper, we consider the generalized Catalan numbers , which we call s-Catalan numbers. For p prime, we find all positive integers n such that p^q divides F(p^q,n), and also determine all distinct residues of , q?1. As a byproduct we settle a question of Hough and the late Simion on the divisibility of the 4-Catalan numbers by 4. In the second part of the paper we prove that if pq?99999, then is not squarefree for n?τ₁(p^q) sufficiently large (τ₁(p^q) computable). Moreover, using the results of the first part, we find n<τ₁(p^q) (in base p), for which may be squarefree. As consequences, we obtain that is squarefree only for n=1,3,45, and is squarefree only for n=1,4,10.     

Synthesis,characterisation and thermal behaviour of some complexes with ligands having 1,3,4-thiadiazole moieties

Summary The investigations concerning the thermal behaviour of a series of Ni(II) and Cu(II) complexes of type [MLCl_n]·mH₂O ((1) M:Ni, L:L(1), n=1, m=2; (2) M:Cu, L:L(2), n=1, m=2; (3) M:Ni, L:L(3), n=2, m=0; (4) M:Cu, L:L(3), n=1, m=2) are presented in this paper. The ligands L(1)-L(3) have been synthesised by template condensation of 1,2-diaminoethane with formaldehyde and 2-amino-1,3,4-thiadiazole-5-thiole or 2-acetamino-1,3,4-thiadiazole-5-sulfonamide. The bonding and stereochemistry of the complexes have been characterised by IR, electronic and magnetic studies at room temperature. The thermal behaviour provided confirmation of the complex composition as well as the number and the nature of water molecules and the intervals of thermal stability. The different nature of the ligands and/or the metallic ions generates a different thermal behaviour for complexes. The complexes do not show biological activity against HIV virus.