Bilinear optimality constraints for the cone of positive polynomials

For a proper cone \({{\mathcal K}\subset\mathbb{R}^n}\) and its dual cone \({{\mathcal K}^*}\) the complementary slackness condition \({\langle{\rm {\bf x}},{\rm {\bf s}}\rangle=0}\) defines an n-dimensional manifold \({C({\mathcal K})}\) in the space \({{\mathbb R}^{2n}}\) . When \({{\mathcal K}}\) is a symmetric cone, points in \({C({\mathcal K})}\) must satisfy at least n linearly independent bilinear identities. This fact proves to be useful when optimizing over such cones, therefore it is natural to look for similar bilinear relations for non-symmetric cones. In this paper we define the bilinearity rank of a cone, which is the number of linearly independent bilinear identities valid for points in \({C({\mathcal K})}\) . We examine several well-known cones, in particular the cone of positive polynomials \({{\mathcal P}_{2n+1}}\) and its dual, and show that there are exactly four linearly independent bilinear identities which hold for all \({({\rm {\bf x}},{\rm {\bf s}})\in C({\mathcal P}_{2n+1})}\), regardless of the dimension of the cones. For nonnegative polynomials over an interval or half-line there are only two linearly independent bilinear identities. These results are extended to trigonometric and exponential polynomials. We prove similar results for Müntz polynomials.     

Antimicrobial graphene polymer (PVK-GO) nanocomposite films

The first report on the fabrication and application of a nanocomposite containing poly-N-vinyl carbazole (PVK) polymer and graphene oxide (GO) as an antimicrobial film was demonstrated. The antimicrobial film was 90% more effective in preventing bacterial colonization relative to the unmodified surface. More importantly, the nanocomposite thin film showed higher bacterial toxicity than pure GO-modified surface.     

Dynamics of a hybrid vibro-impact oscillator: canonical formalism

Nonlinear Dynamics - Hybrid vibro-impact (HVI) oscillations is a strongly nonlinear dynamical regime that involves both linear oscillations and collisions under periodic, impulsive, or stochastic...     

Water Pollution Threat to the Environment by a Urea Plant

Disposal of untreated industrial effluents is drastically deteriorating the quality of underground water. Research work has been conducted to analyze the effect of disposal of urea plant effluent on the quality of ground water of the District Mianwali Daudkhail, Pakistan. For this purpose the effluent and ground water samples were analyzed for pH, TDS, TSS, Cl, F, COD, BOD, Fe, Zn, Pb, Cu, Cr, Cd, Mn, and As. Results obtained were compared with WHO and NEQS standards for drinking and effluent emission limits, respectively. Moreover, effluent samples were also evaluated for irrigation purposes and results compared with criteria recommended for irrigation water. Results showed though the effluents were according to the standards given by National Environmental Quality Standards (NEQS) for liquid emission and fit for irrigation purposes, the quality of underground water was below standard due to having a higher quantity of total dissolved solids than permissible.     

Addendum to “Unstable crack motion is predictable” [2005. JMPS 53, 1071]

Using a scaling relationship discussed in an earlier paper [Abraham, F. F., 2005. Unstable crack motion is predictable. J. Mech. Phys. Solids 53, 1071-1075], we find that the steady-state speed of a unidirectional crack moving in a hyperelastic solid equals the crack speed in a linear solid with our “effective spring constant”.     

Monte Carlo simulation using the Fourier transform of the interatomic potential

When doing Monte Carlo simulations using continuous potentials, the evaluation of the configurational potential energy ink-space by Fourier transformation is shown to be a computationally attractive scheme for systems where the long-range interatomic interaction spans a dimension comparable to the size of the simulated system.     

Synthesis and protein degradation capacity of photoactivated enediynes

[structure: see text] The viability of proteins as targets of thermally and photoactivated enediynes has been confirmed at the molecular level. Model studies using a labeled substrate confirmed the efficacy of atom transfer from diyl radicals produced from enediynes to form captodatively stabilized carbon centered aminoacyl radicals, which then undergo either fragmentation or dimerization. To exploit this finding, a family of enediynes was developed using an intramolecular coupling strategy. Derivatives were prepared and used to target specific proteins, showing good correlation between affinity and photoinduced protein degrading activity. The findings have potential applications in the design of artificial chemical proteases and add to our understanding of the mechanism of action of the clinically important enediyne antitumor antibiotics.     

On the validity of the capillarity approximation in the rate theory of homogeneous nucleation

An Einstein model is used to calculate the internal vibrational free energy of approximately spherical fcc crystallites as a function of crystallite size at T/θ = 1. It is found that the free energy per surface atom does not become convergent until a size of about 3 × 10⁷ atoms is reached. The excess free energy at convergence is used to define the macroscopic surface tension for use in the capillarity approximation. The internal free energy of microcrystallites containing of the order of 100 atoms is fortuitously well described by the capillarity approximation. A good estimate of the total free energy of the microcrystallite (nucleus) is obtained from the capillarity approximation only by adding the contributions from free translation and rotation and the replacement partition function.     

A computer simulation of an amorphous thin film on a crystalline substrate

We employ the Monte Carlo simulation method of classical statistical mechanics to study the structure and energetics of the crystal/amorphous interface. The interface is found to be approximately four atomic layers thick and provides good bonding between the amorphous and crystalline phases.