An Inexact Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds

In this paper, we present an inexact version of the steepest descent method with Armijo’s rule for multicriteria optimization in the Riemannian context given in Bento et al. (J. Optim. Theory Appl., 154: 88–107, 2012). Under mild assumptions on the multicriteria function, we prove that each accumulation point (if any) satisfies first-order necessary conditions for Pareto optimality. Moreover, assuming that the multicriteria function is quasi-convex and the Riemannian manifold has nonnegative curvature, we show full convergence of any sequence generated by the method to a Pareto critical point.     

Deformation and rigidity results for the 2k‐Ricci tensor and the 2k‐Gauss‐Bonnet curvature

We present several deformation and rigidity results within the classes of closed Riemannian manifolds which either are 2k‐Einstein (in the sense that their 2k‐Ricci tensor is constant) or have constant 2k‐Gauss‐Bonnet curvature. The results hold for a family of manifolds containing all non‐flat space forms and the main ingredients in the proofs are explicit formulae for the linearizations of the above invariants obtained by means of the formalism of double forms.     

Degree of equivariant maps between generalized G-manifolds

Yasuhiro Hara in [Topology Appl. 148 (2005), 113–121] and Jan Jaworowski in [J. Fixed Point Theory Appl. 1 (2007), 111–121] studied, under certain conditions, the degree of equivariant maps between free G-manifolds, where G is a compact Lie group. The main results obtained by them involve data provided by the classifying maps of the orbit spaces. In this paper, we extend these results by replacing the free G-manifolds by free generalized G-manifolds over ${\mathbb{Z}}$ .     

Vibrational resonance in a time-delayed genetic toggle switch

Biological oscillators can respond in a surprising way when they are perturbed by two external periodic forcing signals of very different frequencies. The response of the system to a low-frequency signal can be enhanced or depressed when a high-frequency signal is acting. This is what is known as vibrational resonance (VR). Here we study this phenomenon in a simple time-delayed genetic toggle switch, which is a synthetic gene-regulatory network. We have found out how the low-frequency signal changes the range of the response, while the high-frequency signal influences the amplitude at which the resonance occurs. The delay of the toggle switch has also a strong effect on the resonance since it can also induce autonomous oscillations.     

Constructal design of T-shaped cavity for several convective fluxes imposed at the cavity surfaces

The purpose here is to investigate, by means of the constructal principle, the influence of the convective heat transfer flux at the cavity surfaces over the optimal geometry of a T-shaped cavity that intrudes into a solid conducting wall. The cavity is cooled by a steady stream of convection while the solid generates heat uniformly and it is insulated on the external perimeter. The convective heat flux is imposed as a boundary condition of the cavity surfaces and the geometric optimization is achieved for several values of parameter a = (2hA^1/2/k)^1/2. The structure of the T-shaped cavity has four degrees of freedom: L₀/L₁ (ratio between the lengths of the stem and bifurcated branches), H₁/L₁ (ratio between the thickness and length of the bifurcated branches), H₀/L₀ (ratio between the thickness and length of the stem), and H/L (ratio between the height and length of the conducting solid wall) and one restriction, the ratio between the cavity volume and solid volume (φ). The purpose of the numerical investigation is to minimize the maximal dimensionless excess of temperature between the solid and the cavity. The simulations were performed for fixed values of H/L = 1.0 and φ = 0.1. Even for the first and second levels of optimization, (L₁/L₀) _○○ and (H₀/L₀)_○, the results revealed that there is no universal shape that optimizes the cavity geometry for every imposed value of a. The T-shaped cavity geometry adapts to the variation of the convective heat flux imposed at the cavity surfaces, i.e., the system flows and morphs with the imposed conditions so that its currents flow more and more easily. The three times optimal shape for lower ratios of a is achieved when the cavity has a higher penetration into the solid domain and for a thinner stem. As the magnitude of a increases, the bifurcated branch displaces toward the center of the solid domain and the number of highest temperature points also increases, i.e., the distribution of temperature field is improved according to the constructal principle of optimal distribution of imperfections.     

Antioxidising activity of cinnamic acid derivatives against oxidative stress induced by oxidising radicals

Cinnamic acid and its derivatives react with hydroxyl radical (HO^?), in neutral medium, to give hydroxylation products, whether on the benzene ring or on the exocyclic chain, and decarboxylation products. The latter compounds are also obtained after oxidation of the same substrates by the SO₄^?? radical anion. Evidence was provided for the protecting effects afforded by cinnamic acid and hydroxylated derivatives against oxidative reaction mediated by HO^?. By using adenine as a model compound, the results obtained suggest that the high protective effect is due to an antioxidising cascade process. Copyright © 2013 John Wiley & Sons, Ltd.     

Ricci dark energy in Chern–Simons modified gravity

In this work, we have considered the Ricci dark energy model, where the energy density of the universe is proportional to the Ricci scalar curvature, in the dynamic Chern–Simons modified gravity. We show that in this context the evolution of the scale factor is similar to that displayed by the modified Chaplygin gas.     

Mechanical properties of kaolinite ‘macro-crystals’

The mechanical properties of a rare sample of kaolinite macroscopic crystals were evaluated using instrumented indentation. The crystals were also characterized by X-ray diffraction, scanning electron microscopy, atomic force microscopy and Fourier transform infrared spectroscopy before and after heat treatment at 1100°C. The results are explained in terms of the fracture process occurring in the layered structure of kaolinite, and of the effect of roughness on the hardness and elastic modulus. Data analysis using One-way ANOVA (p?<?0.05) showed that the values of hardness and elastic modulus obtained are statistically homogeneous. Before heat treatment, the sample was composed essentially of kaolinite, with hardness of 42?MPa and elastic modulus equal to 1.3?GPa. After calcination at 1100°C, the sample keeps its layered habit and consists of amorphous metakaolinite. The hardness increases to 360?MPa and the elastic modulus increases to 6.9?GPa.     

Plane waves in noncommutative fluids

We study the dynamics of the noncommutative fluid in the Snyder space perturbatively at the first order in powers of the noncommutative parameter. The linearized noncommutative fluid dynamics is described by a system of coupled linear partial differential equations in which the variables are the fluid density and the fluid potentials. We show that these equations admit a set of solutions that are monochromatic plane waves for the fluid density and two of the potentials and a linear function for the third potential. The energy–momentum tensor of the plane waves is calculated.