Nilpotency degree of cohomology rings in characteristic 3

The purpose of this note is to provide a -group whose mod-3 cohomology ring has a nilpotent element satisfying .

     

Theory of spherofibrous composites. 2. Fundamental equations

Fundamental equations of the theory of spatially reinforced media with a matrix reinforced by spherical particles are proposed on the basis of a linearly reinforced layer and tl.e hypothesis of a longitudinal state. For an arbitrary orientation of the fibers, the generalized elasticity equation for composites was found to contain 21 elastic constants and approximate formulas were derived for their determination.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga. Latvia (October, 1995).Communication 1. see preceding article.A. A. Blagonravov Institute of Mechanical Engineering. Russian Academy of Sciences, Moscow. Russian. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 306–316, May–June, 1996.     

On the Relation between Curvature,Diameter, and Volume of a Complete Riemannian Manifold

In this note, we prove that if N is a compact totally geodesic submanifold of a complete Riemannian manifold M, g whose sectional curvature K satisfies the relation K ≥ k > 0, then for any point m ∈ M. In the case where dim M = 2, the Gaussian curvature K satisfies the relation K ≥ k ≥ 0, and γ is of length l, we get Vol (M, g) ≤ if k ≠ 0 and Vol (M, g ≤ 2ldiam (M) if k = 0.__________Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1576–1583, November, 2004.     

Study on the isomeric ratios of (γ,p) photonuclear reactions with isotopes 40 92 Zr and 74 183 W in the giant dipole resonance region

We have carried out the study on the isomeric ratios in (γ,p) photonuclear reactions with isotopes ₄₀ ⁹² Zr and ₇₄ ¹⁸³ W in the giant dipole resonance (GDR) region. The targets were irradiated with bremsstrahlungs produced by electron accelerator Microtron MT-25 of the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, Dubna, Russia. Spectra of the irradiated samples were measured with a spectroscopic system consisting of 8192-channel analyzer CANBERRA and high-energy resolution semiconductor detector CANBERRA. The results were discussed and compared with those of other authors. The text was submitted by the authors in English.     

Hydrogenated Graphene and Hydrogenated Silicene: Computational Insights

Density functional calculations are performed to study the energetic, structural, and electronic properties of graphene and silicene functionalized with hydrogen. Our calculations predict that H atoms bind much more strongly to silicene than to graphene. The adsorbed H atoms tend to cooperatively stabilize each other leading to a two‐dimensional nucleation and growth mechanism. The different structural and electronic modifications induced by H in fully functionalized graphene and silicene (known as graphane and silicane) are also explained. Finally, the electronic properties of defective graphane with multiple hydrogen vacancies are investigated. Engineering the vacancies in graphane offers a way to modify the electronic properties of this material.     

Synthesis, structure of [H3dien]·(MF6)·H2O (M=Cr, Fe) and Fe Mössbauer study of [H3dien]·(FeF6)·H2O

Single crystals of [H₃dien]·(FeF₆)·H₂O (I) and [H₃dien]·(CrF₆)·H₂O (II) are obtained by solvothermal synthesis under microwave heating. I is orthorhombic (Pna2₁) with a=11.530(2) Å, b=6.6446(8) Å, c=13.787(3) Å, V=1056.3(2) Å³ and Z=4. II is monoclinic (P2₁/c) with a=13.706(1) Å, b=6.7606(6) Å, c=11.3181(9) Å, β=99.38(1)°, V=1034.7(1) Å³ and Z=4. The structure determinations, performed from single crystal X-ray diffraction data, lead to the R₁/wR₂ reliability factors 0.028/0.066 for I and 0.035/0.102 for II. The structures of I and II are built up from isolated FeF₆ or CrF₆ octahedra, water molecules and triprotonated amines. In both structures, each octahedron is connected by hydrogen bonds to six organic cations and two water molecules. The iron-based compound is also characterized by ⁵⁷Fe Mössbauer spectrometry: the hyperfine structure confirms the presence of Fe³⁺ in octahedral coordination and reveals the existence of paramagnetic spin fluctuations.     

Quantum magnetism in the paratacamite family: towards an ideal kagomé lattice

We report muon spin rotation measurements on the S=1/2 (Cu2+) paratacamite ZnxCu4-x(OH)6Cl2 family. Despite a Weiss temperature of approximately -300 K, the x=1 compound is found to have no transition to a magnetic frozen state down to 50 mK as theoretically expected for the kagomé Heisenberg antiferromagnet. We find that the limit between a dynamical and a partly frozen ground state occurs around x=0.5. For x=1, we discuss the relevance to a singlet picture.     

Invariant manifolds of partial functional differential equations

This paper is concerned with the existence, smoothness and attractivity of invariant manifolds for evolutionary processes on general Banach spaces when the nonlinear perturbation has a small global Lipschitz constant and locally C^k-smooth near the trivial solution. Such a nonlinear perturbation arises in many applications through the usual cut-off procedure, but the requirement in the existing literature that the nonlinear perturbation is globally C^k-smooth and has a globally small Lipschitz constant is hardly met in those systems for which the phase space does not allow a smooth cut-off function. Our general results are illustrated by and applied to partial functional differential equations for which the phase space (where r>0 and being a Banach space) has no smooth inner product structure and for which the validity of variation-of-constants formula is still an interesting open problem.     

Electronic states of 1,4-bis(phenylethynyl)benzene: A synchrotron radiation linear dichroism investigation

The electronic transitions of 1,4-bis(phenylethynyl)benzene (BPEB) were investigated by UV synchrotron radiation linear dichroism (SRLD) spectroscopy in the range 25,000-58,000 cm⁻¹ (400-170 nm) on molecular samples aligned in stretched polyethylene. The investigation was supported by variable temperature spectroscopy and by quantum chemical calculations in the LCOAO and TD-DFT models. The molecular alignment of BPEB in stretched polyethylene was found to be remarkably efficient, leading to an orientation factor equal to 0.95 for the long molecular axis. The observed band shape depended strongly on the degree of stretching and on temperature. The combined experimental and theoretical evidence leads to the characterization of several previously unobserved transitions and supports the assumption that BPEB adopts a nearly planar conformation in stretched polyethylene.     

Unexpected Radical Telomerisation of Vinylidene Fluoride with 2-Mercaptoethanol

The radical telomerisation of vinylidene fluoride (VDF) with 2-mercaptoethanol as chain transfer agent (CTA) was studied to synthesise fluorinated telomers which bear a hydroxy end-group, such as H(VDF)_nS(CH₂)₂OH, under thermal (di-tert-butyl peroxide as the initiator) or photochemical initiations. A careful structural study of a typical H-VDF-S(CH₂)₂OH telomer was performed by ¹H and ¹⁹F NMR spectroscopy. These analytical methods allowed us to explore the selective addition of the thiyl radical onto the hydrogenated side of VDF, and the telomer containing one VDF unit was obtained selectively. Surprisingly, for higher [VDF]_o initial concentrations, a monoadduct telomer was produced as well as PVDF homopolymer. This feature was related to the fast consumption of the CTA. The kinetics of radical telomerisation led to a quite high transfer constant of the CTA (40 at 140 °C) that evidences the formation of a monoadduct as the only telomer formed.