A line arrangement of 3n lines in CP2 satisfies the Hirzebruch property if each line intersect others in n + 1 points. Hirzebruch asked in 1985 if all such arrangements are related to finite complex reflection groups. We give a positive answer to this question in the case when the line arrangement in CP2 is real, confirming that there exist exactly four such arrangements.

We prove that any symplectic Fano 6-manifold M with a Hamiltonian S1-action is simply connected and satisfies c1c2(M)=3D24. This is done by showing that the fixed submanifold Mmin subset of M on which the Hamiltonian attains its minimum is diffeomorphic to either a del Pezzo surface, a 2-sphere or a point. In the case when dim(Mmin)=3D4, we use the fact that symplectic Fano 4-manifolds are symplectomorphic to del Pezzo surfaces. The case when dim(Mmin)=3D2 involves a study of six-dimensional Hamiltonian S1-manifolds with Mmin diffeomorphic to a surface of positive genus. By exploiting an analogy with the algebro-geometric situation we construct in each such 6-manifold an S1-invariant symplectic hypersurface F(M) playing the role of a smooth fibre of a hypothetical Mori fibration over Mmin. This relies upon applying Seiberg-Witten theory to the resolution of symplectic 4-orbifolds occurring as the reduced spaces of M.

We prove that a compact 4-manifold which supports a circle-invariant fat SO(3)-bundle is diffeomorphic to either S-4 or (C) over bar(P) over bar (2). The proof involves studying the resulting Hamiltonian circle action on an associated symplectic 6-manifold. Applying our result to the twistor bundle of Riemannian 4-manifolds shows that S-4 and (C) over bar(P) over bar (2) are the only 4-manifolds admitting circle-invariant metrics solving a certain curvature inequality. This can be seen as an analogue of Hsiang-Kleiner's theorem that only S-4 and (C) over bar(P) over bar (2) admit circle-invariant metrics of positive sectional curvature.

We observe that the maximal open set of constant curvature k in a Riemannian manifold of curvature >= k or <= k has a convexity-type property, which we call two-convexity. This statement is used to prove a number of rigidity statements in comparison geometry.

Liiv, Jueri
Zekker, Ivar
Panov, Dmitri
Sammelselg, Vaeino
Tenno, Toomas
Jaerv, Jaak

Polyvinylidene fluoride particles and film were chemically modified by grafting with polystyrene without a preliminary treatment of the fluoropolymer surface. The modification was performed using surface-initiated atom transfer radical polymerization with Cu+-Tris (2-aminoethyl)amine as the catalytic system in a styrene/acetonitrile mixture. A small amount of Cu(II)Cl-2 was added to control the polymerization process. The amount of covalently bound polystyrene was quantified using Fourier transform infrared spectroscopy, and the extent of grafting was found to be a time-dependent process at 60 degrees C. The formation of polystyrene brushes, which may form a uniform polystyrene layer over the surface of fluoropolymer particles, was observed via scanning electron microscopy. Polymer Journal (2013) 45, 313-317; doi:10.1038/pj.2012.148; published online 8 August 2012

Given an integer b and a finitely presented group G, we produce a compact symplectic 6-manifold with c(1)=0, b(2)> b, b(3)> b and pi(1)=G. In the simply connected case, we can also arrange for b(3)=0; in particular, these examples are not diffeomorphic to Kahler manifolds with c(1)=0. The construction begins with a certain orientable, four-dimensional, hyperbolic orbifold assembled from right-angled 120-cells. The twistor space of the hyperbolic orbifold is a symplectic Calabi-Yau orbifold; a crepant resolution of this last orbifold produces a smooth symplectic manifold with the required properties.

The present invention relates to a wood protection method, as well as to the resulting wood product. The present invention provides in particular non-metal impregnation fluids based on plant oils and processes for modification of wood to protect it against biological decay, to improve the physical properties and ensure dimensional stability of the material.

We use hyperbolic geometry to construct simply connected symplectic or complex manifolds with trivial canonical bundle and with no compatible Kahler structure. We start with the desingularisations of the quadric cone in C(4) : the smoothing is a natural S(3)-bundle over H(3), its holomorphic geometry is determined by the hyperbolic metric; the small-resolution is a natural S(2)-bundle over H(4) with symplectic geometry determined by the metric. Using hyperbolic geometry, we find orbifold quotients with trivial canonical bundle; smooth examples are produced via crepant resolutions. In particular, we find the first example of a simply connected symplectic 6-manifold with c(1) = 0 that does not admit a compatible Kahler structure. We also find infinitely many distinct complex structures on 2(S(3) x S(3)) # (S(2) x S(4)) with trivial canonical bundle. Finally, we explain how an analogous construction for hyperbolic manifolds in higher dimensions gives symplectic non-Kahler "Fano" manifolds of dimension 12 and higher.

In this article we introduce the notion of polyhedral Kahler manifolds, even dimensional polyhedral manifolds with unitary holonomy. We concentrate on the 4-dimensional case, prove that such manifolds are smooth complex surfaces and classify the singularities of the metric. The singularities form a divisor and the residues of the flat connection on the complement of the divisor give us a system of cohomological equations. A parabolic version of the Kobayshi-Hitchin correspondence of T Mochizuki permits us to characterize polyhedral Kahler metrics of nonnegative curvature on CP(2) with singularities at complex line arrangements.

Ploom, Anu
Panov, Dmitri
Jaerv, Jaak
Tuulmets, Ants

Kinetics of tetraethoxysilane reaction with n-butylmagnesium chloride, specifically solvated with dibutyl ether, diethyl ether, THF, and triethylamine, was studied in toluene. Also isopropylmagnesium chloride, isopropyltriethoxysilane, and diisopropylketone were involved in a similar investigation. The pseudo first-order rate constants determined at a great excess of these organomagnesium compounds were used for separation of the appropriate equilibrium and rate constants. An advantage of the method consists in preclusion of non-specific solvation effects when effects of donor solvents are considered. In separate experiments, thermodynamic parameters were determined for rate and equilibrium constants, measured for the reaction of tetraethoxysilane with n-butylmagnesium chloride solvated with dibutyl ether in toluene, and also in bulk dibutyl ether. The implication of steric and solvation effects on this reaction is discussed. (C) 2008 Elsevier B. V. All rights reserved.

Grignard reactions with alkoxysilanes or carbonyl compounds produce alkoxymagnesium halides as by-products. Kinetic measurements for reactions of silanes and of a ketone were performed with Grignard reagents, enriched in alkoxymagnesium halides and taken in a great excess. The alkoxide-type reaction products complex tightly with Grignard reagents and enhance in this way their nucleophilicity, thus accelerating the reaction. However, alkoxides branched at alpha-C atom exert an unfavorable steric hindrance to reaction resulting in a decrease in the reaction rate. (c) 2006 Published by Elsevier B.V.

Rate constants for the reactions of methylvinyldichlorosilane and tetraethoxysilane with alkylmagnesium chlorides RMgCl (R = Et, n-Bu, i-Bu, i-Pr, s-Bu, t-Bu) in diethyl ether were determined. Excellent correlations of rate data with steric constants E-S(Si) by Cartledge and v' by Charton were found for the reaction of methylvinyldichlorosilane. Linear correlations with break points were obtained for the tetraethoxysilane reaction. It was assumed that this could be referred to a change in the reaction mechanism.

In this article we address a number of features of the moduli space of spherical metrics on connected, compact, orientable surfaces with conical singularities of assigned angles, such as its non-emptiness and connectedness. We also consider some features of the forgetful map from the above moduli space of spherical surfaces with conical points to the associated moduli space of pointed Riemann surfaces, such as its properness, which follows from an explicit systole inequality that relates metric invariants (spherical systole) and conformal invariant (extremal systole).

Temiz, Ali
Kose, Gaye
Panov, Dmitri
Terziev, Nasko
Alma, Mehmet Hakki
Palanti, Sabrina
Akbas, Selcuk

In this article, the effects of bio-oil and epoxidized linseed oil (ELO) on water absorption, tangential swelling, decay and insect resistance, thermo-gravimetric analysis, and mechanical properties of treated wood samples were studied. The bio-oil used in this article was by-product of ThermoWood thermal modification process. Linseed oil and hydrogen peroxide were used to prepare ELO. The results indicated that the samples treated with bio-oil had lower water absorption than that of the control group. The second treatment with ELO significantly reduced further the water absorption. The decay resistance of treated wood samples with 20% of bio-oil against brown (Coniophora puteana) and white rot (Trametes versicolor) fungi was very high. According to the insect test results, increasing bio-oil concentration from 10% to 20% significantly decreased surviving rate of Hylotrupes bajulus. Thermo-gravimetric analysis showed that all treated samples had higher initial deterioration temperature than that of the control group. Regarding the wood strength, the impregnated bio-oil generally reduced the mechanical properties of wood except modulus of elasticity (MOE). (c) 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 1562-1569, 2013