Nonlinearity of davenport—Schinzel sequences and of generalized path compression schemes

Davenport—Schinzel sequences are sequences that do not contain forbidden subsequences of alternating symbols. They arise in the computation of the envelope of a set of functions. We show that the maximal length of a Davenport—Schinzel sequence composed ofn symbols is Θ (nα(n)), where α(n) is the functional inverse of Ackermann’s function, and is thus very slowly increasing to infinity. This is achieved by establishing an equivalence between such sequences and generalized path compression schemes on rooted trees, and then by analyzing these schemes. Work on this paper by the second author has been supported in part by a grant from the U.S.-Israeli Binational Science Foundation.     

Mechanisms of reaction of aminoxyl (nitroxide), iminoxyl, and imidoxyl radicals with alkenes and evidence that in the presence of lead tetraacetate, N-hydroxyphthalimide reacts with alkenes by both radical and nonradical mechanisms

1,2-dideuterio-cyclohexene, 1,2-dideuterio-cyclooctene, and trans-3,4-dideuterio-hex-3-ene were reacted with three >NO* radicals: 4-hydroxyTempo, di-tert-butyliminoxyl, both used as the actual radicals, and phthalimide-N-oxyl (PINO) generated from N-hydroxyphthalimide (NHPI) by its reaction with tert-alkoxyl radicals (t-RO*) and with lead tetraacetate. In all cases, except the NHPI/Pb(OAc)4 system, only mono >NO-substituted alkenes were produced. The 2H NMR spectra imply that 88-92% of monoadducts were formed by the initial abstraction of an allylic H-atom, followed by capture of the allylic radical by a second >NO*, while the remaining 12-8% appear to be formed by an initial addition of >NO* to the double bond followed by H-atom abstraction by a second >NO*. A substantial and sometimes the major product formed with the NHPI/Pb(OAc)4 system has two PINO moieties added across the double bond. Since such diadducts are not formed with the NHPI/t-RO* system, a heterolytic mechanism is proposed, analogous to that known for the Pb(OAc)4-induced acetoxylation of alkenes. A detailed analysis of the NHPI/Pb(OAc)4/alkene products indicates that monosubstitution occurs by both homolytic and heterolytic processes.     

On a semilinear volterra integrodifferential equation

The Volterra integrodifferential equation $$\begin{array}{*{20}c} {u_t (t,x) + \smallint '_0 a(t - s)( - \Delta u(s,x) + f(x,u(s,x)))ds = h(t,x),,} \\ {t > 0,x \in \Omega \subset R^N ,} \\ \end{array} $$ together with boundary and initial conditions is considered. The existence of global solutions (in time) is established under weak assumptions onf. An application in heat flow is also indicated.     

The first example of a hetero-tetranuclear [(VO)Gd](2) complex: synthesis, crystal structure and magnetic properties of [VOLGd(hfa)(2)CH(3)OH](2).2CH(3)OH.2(CH(3))(2)CO

A cyclic tetranuclear [V(IV)O-Gd(III)](2) complex with VO and Gd ions alternately arrayed, behaves, from the magnetic point of view, as two independent dinuclear entities each having a S= 4 ground state, as a consequence of an active and ferromagnetic VO-Gd interaction through the double phenoxo bridge and a magnetically inactive VO-Gd interaction through the amide bridge.     

Linear equations and interpolation in Boolean algebra

The authors generalize the classical interpolation formula for Boolean functions of n variables. A characterization of all interpolating systems with 2ⁿ elements is obtained. The methods of proof used are intimately related to the solution of linear Boolean equations.     

Existence of multiple solutions with precise sign information for superlinear Neumann problems

We consider a nonlinear Neumann problem driven by the p-Laplacian differential operator and having a p-superlinear nonlinearity. Using truncation techniques combined with the method of upper–lower solutions and variational arguments based on critical point theory, we prove the existence of five nontrivial smooth solutions, two positive, two negative and one nodal. For the semilinear (i.e., p = 2) problem, using critical groups we produce a second nodal solution. This paper was completed while N.S. Papageorgiou was visiting the University of Aveiro as an invited scientist. The hospitality and financial support of the host institution are gratefully acknowledged. V. Staicu acknowledges partial financial support from the Portuguese Foundation for Sciences and Technology (FCT) under the project POCI/MAT/55524/2004.     

A new diamine containing disiloxane moiety and some derived Schiff bases: synthesis,structural characterisation and antimicrobial activity

A new siloxane diamine, 1,3-bis(amino-phenylene-ester-methylene)tetramethyldisiloxane (1), was obtained by a two-step procedure and used to prepare a series of Schiff bases (2–5), by reaction with different carbonylic compounds: salicylaldehyde, 3,5-dibromosalicylaldehyde, 5-chlorosalicylaldehyde and 3,5-di-tert-butyl-2-hydroxybenzaldehyde. All compounds, separated in crystalline form, were characterised by spectral (FTIR, UV–vis and NMR) analysis as well as by single-crystal X-ray diffraction. In these structures, different packing motifs occur depending on the different association degree determined by intra- and intermolecular π–π stacking interactions. Antimicrobial activity of the compounds was evaluated against three fungi and two bacteria, where the Schiff bases derived from salicylaldehyde and in special 5-chlorosalicylaldehyde showed remarkable activity.     

Synthesis,characterization, molecular docking studies and in vitro screening of new metal complexes with Schiff base as antimicrobial and antiproliferative agents

A series of Cu(II), Co(II), Pd(II), Pt(II), Zn(II), Cd(II) and Fe(III) complexes were designed and synthesized using Schiff base 1‐phenyl‐2,3‐dimethyl‐4‐(N‐3‐formyl‐6‐methylchromone)‐3‐pyrazolin‐5‐one (HL). The new metal complexes were investigated using various physicochemical techniques including elemental and thermal analyses, molar electric conductivity and magnetic susceptibility measurements, as well as spectroscopic methods. Also, the crystal structures of ligand HL and the Pd(II) complex were determined using single‐crystal X‐ray diffraction analysis. For all compounds, the antimicrobial activity was studied against a series of standard strains: Staphylococcus aureus, Bacillus cereus, Enterococcus faecalis, Escherichia coli, Acinetobacter baumannii, Candida albicans, Candida krusei and Cryptococcus neoformans. The in vitro antiproliferative activity of the ligand and complexes was evaluated against ten cancer cell lines: MSC, A375, B16 4A5, HT‐29, MCF‐7, HEp‐2, BxPC‐3, RD, MDCK and L20B. At 10 μM concentration a significant cytotoxic effect of the Co(II), Pd(II) and Cd(II) complexes was observed against B16 4A5 murine melanoma cells. The Zn(II) complex is active against HEp‐2, RD and MDCK cancer cell lines, where IC₅₀ values vary between 1.0 and 77.6 and for BxPC‐3 the activity index versus doxorubicin is 3.7 times higher.