Synthesis and polymerization of o-hexylaniline: Characterization of the corresponding polyaniline

In the field of research on soluble conducting polymers, the poly(o-alkylanilines) are very interesting because we can expect them to give more soluble polymers and new properties. Like poly(o-propylaniline) (POP), which is more soluble than polyaniline (PANi), poly(o-hexylaniline) (POH) appears to be more soluble in organic solvents than POP because of the longer alkyl groups in the 2-position. The higher solubility confers better processability on this new polymer, and because of this solubility, an NMR study in solution became possible.The nitration of hexylbenzene and the reduction of the resulting product to o-hexylaniline were performed according to the literature. The chemical polymerization was easy and it is possible to produce this polymer in large quantities.The polymerization carried out in anhydrous NH₄F, 2.35 HF medium and in 5 M perchloric acid gave a polymer with almost quantitative yield. The electrochemical behaviour of POH displayed faster electron transfers than PANi in organic solvents, depending on the acido-basicity level of the aqueous solutions. Unlike PANi, fractal growth was not observed.     

Application of a separating transformation to estimates of inner radii of open sets

We obtain solutions of new extremal problems of the geometric theory of functions of a complex variable related to estimates for the inner radii of nonoverlapping domains. Some known results are generalized to the case of open sets. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1313–1321, October, 2007.     

Differential Conditions for Constrained Nonlinear Programming via Pareto Optimization

We deal with the differential conditions for local optimality. The conditions that we derive for inequality constrained problems do not require constraint qualifications and are the broadest conditions based on only first-order and second-order derivatives. A similar result is proved for equality constrained problems, although the necessary conditions require the regularity of the equality constraints.     

On the weakened Siegel’s conjecture

In the paper, we prove that two definitions of E-functions present in mathematics are equivalent if E-functions satisfy second-order linear differential equations. For this set of functions, a weakened variant of the well-known Siegel conjecture about representability of any E-function by a polynomial of hypergeometric functions is also proved. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 33–39, 2005.     

The σ<Emphasis Type="Italic">g</Emphasis>-Drazin Inverse and the Generalized Mbekhta Decomposition

In this paper we define and study an extension of the g-Drazin for elements of a Banach algebra and for bounded linear operators based on an isolated spectral set rather than on an isolated spectral point. We investigate salient properties of the new inverse and its continuity, and illustrate its usefulness with an application to differential equations. Generalized Mbekhta subspaces are introduced and the corresponding extended Mbekhta decomposition gives a characterization of circularly isolated spectral sets.     

Regularization of singular systems of linear algebraic equations by shifts

Regularization of singular systems of linear algebraic equations by shifts is examined. New equivalent conditions for the shift regularizability of such systems are derived.     

Impact of two mass scale oscillations on the analysis of atmospheric and reactor neutrino data

We study the stability of the results of the three-neutrino oscillation analysis of atmospheric and reactor neutrino data under departures of the one dominant mass scale approximation. In order to do so we perform the analysis of atmospheric and reactor neutrino data in terms of three-neutrino oscillations where the effect of both mass differences is explicitly considered. We study the allowed parameter space resulting from this analysis as a function of the mass splitting hierarchy parameter which parameterizes the departure from the one dominant mass scale approximation. We consider schemes with both direct and inverted mass ordering. Our results show that in the analysis of the atmospheric data the derived range of the largest mass splitting, , is stable, while the allowed ranges of mixing angles and are wider than those obtained in the one dominant mass scale approximation. Inclusion of the CHOOZ reactor data in the analysis results in the reduction of the parameter space in particular for the mixing angles. As a consequence the final allowed ranges of the parameters from the combined analysis are only slightly broader than when obtained in the one dominant mass scale approximation. Received: 31 May 2002 / Revised version: 10 July 2002 / Published online: 31 October 2002     

Monstrous Branes

 We study D-branes in the bosonic closed string theory whose automorphism group is the Bimonster group (the wreath product of the Monster simple group with ℤ₂). We give a complete classification of D-branes preserving the chiral subalgebra of Monster invariants and show that they transform in a representation of the Bimonster. Our results apply more generally to self-dual conformal field theories which admit the action of a compact Lie group on both the left- and right-moving sectors. Received: 20 February 2002 / Accepted: 17 August 2002 Published online: 19 December 2002 Communicated by R.H. Dijkgraaf     

Convergence of Weighted Sums and Laws of Large Numbers in D([0,1]; E)

Convergence properties of weighted sums of functions in D([0, 1]; E) (E a Banach space) are investigated. We show that convergence in the Skorokhod J₁-topology of a sequence (x_n) in D([0, 1]; E) does not imply convergence of a sequence ( _n) of averages. Convergence in the J₁-topology of a sequence ( _n) of averages is shown, under the growth condition x_n ∞ = o(n), to be equivalent to the convergence of ( _n) in the uniform topology. Convergence of a sequence (x_n,) is shown to imply convergence of the sequence ( _n) of averages in the M₁ and M₂ topologies. The strong law of large numbers in D[0, 1] is considered and an example is constructed to show that different definitions of the strong law of large numbers are nonequivalent.