Search results for "Elastic"
showing 10 items of 2162 documents
Defining relations of the noncommutative trace algebra of two 3×3 matrices
2006
The noncommutative (or mixed) trace algebra $T_{nd}$ is generated by $d$ generic $n\times n$ matrices and by the algebra $C_{nd}$ generated by all traces of products of generic matrices, $n,d\geq 2$. It is known that over a field of characteristic 0 this algebra is a finitely generated free module over a polynomial subalgebra $S$ of the center $C_{nd}$. For $n=3$ and $d=2$ we have found explicitly such a subalgebra $S$ and a set of free generators of the $S$-module $T_{32}$. We give also a set of defining relations of $T_{32}$ as an algebra and a Groebner basis of the corresponding ideal. The proofs are based on easy computer calculations with standard functions of Maple, the explicit prese…
The Lie algebra of polynomial vector fields and the Jacobian conjecture
1998
The Jacobian conjecture for polynomial maps ϕ:Kn→Kn is shown to be equivalent to a certain Lie algebra theoretic property of the Lie algebra\(\mathbb{D}\) of formal vector fields inn variables. To be precise, let\(\mathbb{D}_0 \) be the unique subalgebra of codimensionn (consisting of the singular vector fields),H a Cartan subalgebra of\(\mathbb{D}_0 \),Hλ the root spaces corresponding to linear forms λ onH and\(A = \oplus _{\lambda \in {\rm H}^ * } H_\lambda \). Then every polynomial map ϕ:Kn→Kn with invertible Jacobian matrix is an automorphism if and only if every automorphism Φ of\(\mathbb{D}\) with Φ(A)\( \subseteq A\) satisfies Φ(A)=A.
Homomorphisms on spaces of weakly continuous holomorphic functions
1999
Let X be a Banach space and let $X^{\ast }$ be its topological dual space. We study the algebra ${\cal H}_{w^\ast}(X^{\ast})$ of entire functions on $X^{\ast }$ that are weak-star continuous on bounded sets. We prove that every m-homogeneous polynomial of finite type P on $X^*$ that is weak-star continuous on bounded sets can be written in the form $P=\textstyle\sum\limits _{j=1}^q x_{1j}\cdots x_{mj}$ where $x_{ij} \in X$ , for all i,j. As an application, we characterize convolution homomorphisms on ${\cal H}_{w^\ast}(X^{\ast})$ and on the space ${\cal H}_{wu}(X)$ of entire functions on X which are weakly uniformly continuous on bounded subsets of X, assuming that X * has the approximation…
Multiple positive solutions of some elliptic problems via the Morse theory and the domain topology
1994
We use Morse theory to estimate the number of positive solutions of an elliptic problem in an open bounded setΩ ∉ ℝN. The number of solutions depends on the topology ofΩ, actually onP t (Ω), the Poincare polynomial ofΩ. More precisely, we obtain the following Morse relations: $$\sum\limits_{u \in K} {t^{\mu \left( u \right)} } = tP_t \left( \Omega \right) + t^2 [P_t \left( \Omega \right) - 1] + t\left( {1 + t} \right)\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{O} \left( t \right)$$ , where $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{O} \left( t \right)$$ is a polynomial with non-negative integer coefficients,K is the set of positive solutions …
Chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes-Renner relation
2010
The next to leading order chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes- Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order P…
Preparation and mechanical properties of intercalated PP/OMMT nanocomposites
2007
The preparation of polymer nanocomposites by melt compounding polypropylene (PP) with organically modified montmorillonite using maleic anhydride modified PP as compatibilizer is described. Compositions with organomontmorillonite content 0, 5, 10 wt.% were prepared and tested. Data on the influence of organomontmorillonite content on the tensile stress?strain curves, elastic modulus, strength, and ultimate elongation of the nanocomposites are obtained. The concentration dependences of elastic properties of materials with differently oriented plate like nanoparticles analyses taking into account hierarchical structure features of nanocomposites is considered. Theoretical analysis results are…
Thermal and Mechanical Properties of Unvulcanized Polypropylene Blends with Different Elastomers: Ethylene-Propylene-Diene Terpolymer, Nitrile-Butadi…
2013
In this work, composites of isotactic polypropylene (PP) with three unvulcanized elastomers – terpolymer of ethylene-propylene-dicyclopentadiene (EPDM), chlorinated polyethylene (CPE) and copolymer of acrylonitrile-butadiene (NBR) – have been investigated. The purpose of the investigation was to create PP/elastomer blend composites of significantly different compositions (with an excess of PP, intermediate ones, and with an excess of elastomer) and to study the dependence of tensile behaviour and elastic properties on the blends with different component ratio. Tensile properties have been recognized from the stress-strain curves. The changes of elastic modulus have been characterized with r…
Structure and Mechanical Properties of Melt Intercalated Po1lypropylene–Organomontmorillonite Nanocomposites
2010
The preparation and properties of polymer nanocomposites, obtained by melt-compounding of polypropylene (PP) and organomontmorillonite (OMMT) modified by different alkyl ammonium salts, are described. A copolymer of maleic anhydride and PP was used as a compatibilizing additive. Nanocomposites with OMMT content of 1, 5 and 10 wt% were prepared and tested. The influence of OMMT content on the tensile stress–strain curves, elastic modulus, yield and tensile strength, and ultimate elongation of the nanocomposites is determined. The results of measuring the microhardness and impact strength of polymer nanocomposites are presented. Long-term creep tests were performed to predict the long-term de…
Accelerated weathering of polypropylene/wood flour composites
2008
Abstract Wood–plastic composites (WPCs) have received increasing attention during the last decades, because of many advantages related to their use. Some of their main applications are represented by outdoor furnishing and decking; therefore, it is important to assess their behaviour under UV exposure. In this work, polypropylene/wood flour composites were prepared and their resistance to photooxidation investigated. The composites were prepared by extrusion and compression moulding, and were subjected to mechanical tests, FTIR analysis and molecular weight measurements. The results showed that the composites retained a higher fraction of the original mechanical properties after accelerated…
Characterization of blends of polypropylene with a semirigid liquid-crystal copolyester
1991
Abstract Blends with a liquid-crystal polymers (LCP) as one component show, in general, very interesting properties. Reduction of shear viscosity and improvement of mechanical properties are very remarkable. High melting temperatures and high costs of the LCP limit the use of these blends. A new class of thermotropic LCPs with flexible spaces, with relatively low melting temperatures, can overcome the first problem. In this work, rheological and mechanical properties of blends of polypropylene with low contents of this LCP are presented. Torque during extrusion and viscosity decrease with LCP content. Elastic modulus is remarkably increased when the LCP phase is oriented.