Theoretical study on the group 2 atoms + N2O reactions

The electronic structure aspects of the M (1S,3P) + N2O(X 1sigma+) (M = Be, Mg, Ca) reactions are investigated using the CASSCF/MRMP2 (complete active space SCF and the multireference M?ller-Plesset perturbation theory of the second order) computational methodology. The lowest adiabatic 1 1A' and 1 3A' potential energy surfaces (PESs) favor the bending dissociation mechanism of N2O in all studied cases. The rate-limiting channels are determined by the classical barriers that decrease in the series Be (8.9) > Mg (7.0) > Ca (1.2) kcal/mol, whereas the spin-forbidden reaction channels are found to be less important. A comparison with elaborated kinetic results (Plane et al. J. Phys. Chem. 1990, 94, 5255; Gas-Phase Metal Reactions; Elsevier: Amsterdam, 1992; Vinckier et al. J. Phys. Chem. A 1999, 103, 5328) on the Ca (1S) + N2O(X 1sigma+) reaction is presented, and the differences in the kinetic behavior of the title reactions are discussed. Our results also indicate that the techniques based on the multiconfigurational wave functions are unavoidable if a correct topology of the PESs governing these reactions is needed.     

Ordered Mesoporous Silicas with 2,5-Dimercapto-1,3,4-Thiadiazole Ligand: High Capacity Adsorbents for Mercury Ions

This work reports two-step synthesis of novel ordered mesoporous silicas (OMS), which contain mercury-specific multifunctional ligand and have high surface area and well-developed porosity. One pot co-condensation synthesis was employed to introduce chloropropyl functionality on the mesopore walls of hexagonally ordered silica. In the next step, 2,5-dimercapto-1,3,4-thiadiazole was reacted with chloropropyl groups during template-displacement process, which resulted in high affinity adsorbent towards mercury ions. The maximum adsorption capacity of this adsorbent for mercury ions from aqueous solutions was as high as 1.7 g/g, which is about three times higher than the concentration of surface ligand. This study shows that the surface properties of OMS can be tailored by proper choice of chemical modification method, which affects the ligand bonding density and determines the adsorbent capacity and affinity towards heavy metal ions. Three methods, one-pot synthesis, template-displacement and post-synthesis modification, were used for the introduction of surface ligands into MCM41 and SBA15 mesostructures to prepare mercury-specific adsorbents. In addition, adsorption properties of these adsorbents as well as their effectiveness for mercury removal from aqueous solutions were comparatively studied.     

On the derived algebra of a centraliser

Let g be a classical Lie algebra, e∈g a nilpotent element and ge⊂g the centraliser of e. We prove that ge=[ge,ge] if and only if e is rigid. It is also shown that if e∈[ge,ge], then the nilpotent radical of ge coincides with [ge(1),ge], where ge(1)⊂ge is an eigenspace of a characteristic of e corresponding to the eigenvalue 1.     

Estimates of a sum of Dirichlet series

We study the Dirichlet series with an arbitrary abscissa of absolute convergence. The lower and upper estimates for sums of these series are found. The above results allow us to establish some relations between the maximum modulus and the maximal term of Dirichlet series, especially to find conditions that ensure that the maximum modulus and the maximal term have the same many-term asymptotics.     

Approximation of Fractional Brownian Motion by Martingales

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exists a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.     

Special Lie superalgebras with maximality condition for subalgebras

We consider finitely generated Lie superalgebras over a field of characteristic zero satisfying Capelli identities. We prove that any such an algebra with the maximality condition for abelian subalgebras is finite dimensional. In particular, any special Lie superalgebra with the maximality condition for its subalgebras has a finite dimension. We also prove that the universal enveloping algebra U(L) of special Lie superalgebra L is Noetherian if and only if $\dim L<\infty$ .     

Ce20Mg19Zn81: a new structure type with a giant cubic cell

Icosacerium nonadecamagnesium henoctacontazinc, Ce₂₀Mg₁₉Zn₈₁, synthesized by fritting of the pure elements with subsequent arc melting, crystallizes with an unusually large cubic unit cell [space group F3m, a = 21.1979 (8) Å] and represents a new structure type among the technologically important family of ternary rare earth–transition metal–magnesium intermetallics. The majority of atoms (two Ce and five Zn) display .3m site symmetry, two Ce and one Mg atom occupy three 2.mm positions, one Mg and one Zn have 3m site symmetry, one Mg and three Zn atoms sit in ..m positions, and one Zn atom is in a general position. The Ce₂₀Mg₁₉Zn₈₁ structure can be described using the geometric concept of nested polyhedral units, by which it consists of four different polyhedral units, viz.A (Zn+Zn₄+Zn₄+Zn₁₂+Ce₆), B (Mg+Zn₁₂+Ce₄+Zn₂₄+Ce₄), C (Zn₄+Zn₁₂+Mg₆) and D (Zn₄+Zn₄+Mg₁₂+Ce₆), with the outer construction unit being an octahedron or tetrahedron. All interatomic distances in the structure indicate metallic‐type bonding.     

Polynomials whose coefficients coincide with their zeros

In this paper we consider monic polynomials such that their coefficients coincide with their zeros. These polynomials were first introduced by S. Ulam. We combine methods of algebraic geometry and dynamical systems to prove several results. We obtain estimates on the number of Ulam polynomials of degree N. We provide additional methods to obtain algebraic identities satisfied by the zeros of Ulam polynomials, beyond the straightforward comparison of their zeros and coefficients. To address the question about the existence of orthogonal Ulam polynomial sequences, we show that the only Ulam polynomial eigenfunctions of hypergeometric type differential operators are the trivial Ulam polynomials \(\{x^N\}_{N=0}^\infty \). We propose a family of solvable N-body problems such that their stable equilibria are the zeros of certain Ulam polynomials.     

Isobornylchalcones as Scaffold for the Synthesis of Diarylpyrazolines with Antioxidant Activity

The pyrazoline ring is defined as a “privileged structure” in medicinal chemistry. A variety of pharmacological properties of pyrazolines is associated with the nature and position of various substituents, which is especially evident in diarylpyrazolines. Compounds with a chalcone fragment show a wide range of biological properties as well as high reactivity which is primarily due to the presence of an α, β-unsaturated carbonyl system. At the same time, bicyclic monoterpenoids deserve special attention as a source of a key structural block or as one of the pharmacophore components of biologically active molecules. A series of new diarylpyrazoline derivatives based on isobornylchalcones with different substitutes (MeO, Hal, NO₂, N(Me)₂) was synthesized. Antioxidant properties of the obtained compounds were comparatively evaluated using in vitro model Fe²⁺/ascorbate-initiated lipid peroxidation in the substrate containing brain lipids of laboratory mice. It was demonstrated that the combination of the electron-donating group in the para-position of ring B and OH-group in the ring A in the structure of chalcone fragment provides significant antioxidant activity of synthesized diarylpyrazoline derivatives.