Elastic Properties of Carbon Nanotubes and Nanoropes

Elastic properties of carbon nanotubes and nanoropes are investigated using an empirical force-constant model. For single and multi-wall nanotubes the elastic moduli are shown to be insensitive to details of the structure such as the helicity, the tube radius and the number of layers. The tensile Young's modulus and the torsion shear modulus calculated are comparable to that of the diamond, while the the bulk modulus is smaller. Nanoropes composed of single-wall nanotubes possess the ideal elastic properties of high tensile elastic modulus, flexible, and light weight.Comment: 10 page

Unavoidable Multicoloured Families of Configurations

Balogh and Bollob\'as [{\em Combinatorica 25, 2005}] prove that for any $k$ there is a constant $f(k)$ such that any set system with at least $f(k)$ sets reduces to a $k$-star, an $k$-costar or an $k$-chain. They proved $f(k)<(2k)^{2^k}$. Here we improve it to $f(k)<2^{ck^2}$ for some constant $c>0$. This is a special case of the following result on the multi-coloured forbidden configurations at 2 colours. Let $r$ be given. Then there exists a constant $c_r$ so that a matrix with entries drawn from $\{0,1,...,r-1\}$ with at least $2^{c_rk^2}$ different columns will have a $k\times k$ submatrix that can have its rows and columns permuted so that in the resulting matrix will be either $I_k(a,b)$ or $T_k(a,b)$ (for some $a\ne b\in \{0,1,..., r-1\}$), where $I_k(a,b)$ is the $k\times k$ matrix with $a$'s on the diagonal and $b$'s else where, $T_k(a,b)$ the $k\times k$ matrix with $a$'s below the diagonal and $b$'s elsewhere. We also extend to considering the bound on the number of distinct columns, given that the number of rows is $m$, when avoiding a $t k\times k$ matrix obtained by taking any one of the $k \times k$ matrices above and repeating each column $t$ times. We use Ramsey Theory.Comment: 16 pages, add two application

Fast Ridge Regression with Randomized Principal Component Analysis and Gradient Descent

We propose a new two stage algorithm LING for large scale regression problems. LING has the same risk as the well known Ridge Regression under the fixed design setting and can be computed much faster. Our experiments have shown that LING performs well in terms of both prediction accuracy and computational efficiency compared with other large scale regression algorithms like Gradient Descent, Stochastic Gradient Descent and Principal Component Regression on both simulated and real datasets

A process yields large quantities of pure ribosome subunits

Development of process for in-vitro protein synthesis from living cells followed by dissociation of ribosomes into subunits is discussed. Process depends on dialysis or use of chelating agents. Operation of process and advantages over previous methods are outlined

Iron-based layered superconductor LaO1−x_{1-x}Fx_xFeAs: an antiferromagnetic semimetal

We have studied the newly found superconductor compound LaO$_{1-x}$F$_x$FeAs through the first-principles density functional theory calculations. We find that the parent compound LaOFeAs is a quasi-2-dimensional antiferromgnetic semimetal with most carriers being electrons and with a magnetic moment of $2.3\mu_B$ located around each Fe atom on the Fe-Fe square lattice. Furthermore this is a commensurate antiferromagnetic spin density wave due to the Fermi surface nesting, which is robust against the F-doping. The observed superconduction happens on the Fe-Fe antiferromagnetic layer, suggesting a new superconductivity mechanism, mediated by the spin fluctuations. An abrupt change on the Hall measurement is further predicted for the parent compound LaOFeAs.Comment: 4 pages, 7 figure

Phenomenological Analysis of pppp and pˉp\bar{p}p Elastic Scattering Data in the Impact Parameter Space

We use an almost model-independent analytical parameterization for $pp$ and $\bar{p}p$ elastic scattering data to analyze the eikonal, profile, and inelastic overlap functions in the impact parameter space. Error propagation in the fit parameters allows estimations of uncertainty regions, improving the geometrical description of the hadron-hadron interaction. Several predictions are shown and, in particular, the prediction for $pp$ inelastic overlap function at $\sqrt{s}=14$ TeV shows the saturation of the Froissart-Martin bound at LHC energies.Comment: 15 pages, 16 figure

Focusing by Plano-Concave lens using Negative Refraction

We demonstrate focusing of a plane microwave by a plano-concave lens fabricated from a photonic crystal (PhC) having negative refractive index and left-handed electromagnetic properties. An inverse experiment, in which a plane wave is produced from a source placed at the focal point of the lens is also reported. A frequency dependent negative refractive index, is obtained for the lens from the experimental data which matches well with that determined from band structure calculations