A model of dynamics of group structures of human institutions

Given is a review of the substantial theories of cognitivist's trend and also of static and dynamic models of group structures that are based on them. A model of human institutiosn is constructed that explains the origin of balanced structures. This model is realized by a system of locally interacting automatons which are connected by a system of relations and endowed with the ability to react.     

Crystal structure of a new small-pore zirconosilicate Na2ZrSi2O7·H2O and its relation to stoichiometrically and topologically similar compounds

The small-pore zirconosilicate Na₂ZrSi₂O₇·H₂O crystallizes in monoclinic system with space group C2/c, a = 5.4715(4); b = 9.4111(6); c = 13.0969(8) Å, β = 92.851(7)°. Its framework consists of layers built of ZrO₆ octahedra and SiO₄ tetrahedra and forming condensed [Si₂O₇] pyrogroups by connection. The sodium ions and water molecules are placed in channels set up between the layers. The stoichiometric and structural similarities of the studied phase with anhydrous compounds having general chemical formula A₂₍₃₎MT₂O₇ (A = Na,K; M = Zr,Lu,Sc; T = Si,Ge) are discussed. The topological relationship of their structures is interpreted in the light of spatial combination of silicon and zirconium polyhedra as basic building units into larger composite building units and their three-dimensional arrangement.     

Tricyanovinylation of 2-aryl-1-vinylpyrroles: solvent- and substituent controlled chemo- and regioselectivity

2-Aryl-1-vinylpyrroles in acetone, THF and benzene react with tetracyanoethene chemo- and regiospecifically across the vinyl group to give 3-(2-arylpyrrol-1-yl)-1,1,2,2-cyclobutanetetracarbonitriles in 88-94% yield. The latter, upon recrystallization from EtOH, eliminates HCN and entirely rearranges to afford stereospecifically trans-(3E)-4-(2-arylpyrrol-1-yl)-1,3-butadiene-1,1,2-tricarbonitriles. In DMSO, along with the above [2+2]-cycloaddition, tricyanovinylation of the pyrrole ring occurs to form the corresponding 3- and 5-tricyanovinylpyrroles, the product ratio being dependent on the substituents in the pyrrole ring and the reaction conditions.     

Cytotoxic properties of platinum(IV) and dinuclear platinum(II) complexes and their ligand substitution reactions with guanosine-5′-monophosphate

The substitution reaction of the Pt(IV) complex [PtCl₄(bipy)] with guanosine-5??-monophosphate (5??-GMP) was studied by UV?CVis spectrophotometry. This reaction was investigated under pseudo-first-order conditions at 37?°C in 25?mM Hepes buffer (pH?=?7.2) in the presence of 10?mM NaCl to prevent the hydrolysis of the complex. The substitution of chlorides in [{trans-Pt(NH₃)₂Cl}₂(??-1,2-bis(4-pyridyl)ethane)](ClO₄)₂ (Pt3) complex by 5??-GMP was followed by ¹H NMR spectroscopy under second-order conditions. Very similar values for the rate constants of both substitution steps were obtained. The Pt(IV) complexes, [PtCl₄(bipy)] and [PtCl₄(dach)], as well as dinuclaer Pt(II) [{trans-Pt(NH₃)₂Cl}₂(??-pyrazine)](ClO₄)₂ (Pt1), [{trans-Pt(NH₃)₂Cl}₂(??-4,4??-bipyridyl)](ClO₄)₂?·?DMF (Pt2) and [{trans-Pt(NH₃)₂Cl}₂(??-1,2-bis(4-pyridyl)ethane)](ClO₄)₂ (Pt3) complexes, displayed potent cytotoxic activity against human ovarium carcinoma cell line TOV21G and lower activity toward human colon carcinoma HCT116 cell line at the same concentrations. Our data indicate that these platinum complexes could be explored further, as potential therapeutic agents for ovarian cancer.     

Analysis of DSC curve of dodecyl methacrylate polymerization by two-peak deconvolution method

Free radical polymerization of n-dodecyl methacrylate (DDMA) in bulk has been investigated by differential scanning calorimetry (DSC). Autoacceleration of reaction was observed at the temperatures 70, 80, and 90 °C, with 0.25, 0.5, and 1 wt% of initiator, and was absent at 100 °C. DSC curves obtained at the temperatures below 100 °C were characterized by two maxima. Two-peak deconvolution was used to separate DSC curve into two constitutive unimodal curves, i.e., to calculate the contribution of polydodecyl methacrylate formed before (first maximum) and after (second maximum) the onset of autoacceleration. The share of second maximum decreases as the polymerization temperature and initiator concentration are increased. As the organization of monomer is known to decrease with increasing temperature, it can be expected that the fraction of polymerized disordered phase of monomer (first maximum in DSC curve) is the highest at 90 °C. Our results confirm this prediction and are in good agreement with those observed from conversion versus time curves of DDMA polymerization.     

Boundary-driven phase transitions in open driven systems with an umbilic point

Different phases in open driven systems are governed by either shocks or rarefaction waves. A presence of an isolated umbilic point in bidirectional systems of interacting particles stabilizes an unusual large scale excitation, an umbilic shock (U-shock). We show that in open systems the U-shock governs a large portion of phase space, and drives a new discontinuous transition between the two rarefaction-controlled phases. This is in contrast to strictly hyperbolic case where such a transition is always continuous. Also, we describe another robust phase which takes place at the phase governed by the U-shock, if the umbilic point is not isolated.     

Fundamentals of Bicomplex Pseudoanalytic Function Theory: Cauchy Integral Formulas, Negative Formal Powers and Schrödinger Equations with Complex Coefficients

The study of the Dirac system and second-order elliptic equations with complex-valued coefficients on the plane naturally leads to bicomplex Vekua-type equations (Campos et al. in Adv Appl Clifford Algebras, 2012; Castañeda et al. in J Phys A Math Gen 38:9207–9219, 2005; Kravchenko in J Phys A Math Gen 39:12407–12425, 2006). To the difference of complex pseudoanalytic (or generalized analytic) functions (Bers in Theory of pseudo-analytic functions. New York University, New York, 1952; Vekua in Generalized analytic functions. Nauka, Moscow (in Russian); English translation Oxford, 1962. Pergamon Press, Oxford, 1959) the theory of bicomplex pseudoanalytic functions has not been developed. Such basic facts as, e.g., the similarity principle or the Liouville theorem in general are no longer available due to the presence of zero divisors in the algebra of bicomplex numbers. In the present work we develop a theory of bicomplex pseudoanalytic formal powers analogous to the developed by Bers (Theory of pseudo-analytic functions. New York University, 1952) and especially that of negative formal powers. Combining the approaches of Bers and Vekua with some additional ideas we obtain the Cauchy integral formula in the bicomplex setting. In the classical complex situation this formula was obtained under the assumption that the involved Cauchy kernel is global, a very restrictive condition taking into account possible practical applications, especially when the equation itself is not defined on the whole plane. We show that the Cauchy integral formula remains valid with the Cauchy kernel from a wider class called here the reproducing Cauchy kernels. We give a complete characterization of this class. To our best knowledge these results are new even for complex Vekua equations. We establish that reproducing Cauchy kernels can be used to obtain a full set of negative formal powers for the corresponding bicomplex Vekua equation and present an algorithm which allows one their construction. Bicomplex Vekua equations of a special form called main Vekua equations are closely related to stationary Schrödinger equations with complex-valued potentials. We use this relation to establish useful connections between the reproducing Cauchy kernels and the fundamental solutions for the Schrödinger operators which allow one to construct the Cauchy kernel when the fundamental solution is known and vice versa. Moreover, using these results we construct the fundamental solutions for the Darboux transformed Schrödinger operators.     

How to measure chi(3) of a nanoparticle

Most of the known methods to measure the nonlinear optical properties of materials deal with the bulk properties, but there are many demanding applications that require those measurements to be done on a single particle or a single molecule. We report a novel application of nonlinear optics to measure the third-order nonlinear optical susceptibility of nanoparticles in solutions. By measuring the power of the third harmonic generated in a diluted solution of nanoparticles, both the size and chi(3) can be extracted from a simple set of measurements.