Computing Eigenelements of Real Symmetric Matrices via Optimization

In certain circumstances, it is advantageous to use an optimization approach in order to solve the generalized eigenproblem, Ax = Bx, where A and B are real symmetric matrices and B is positive definite. In particular, this is the case when the matrices A and B are very large the computational cost, prohibitive, of solving, with high accuracy, systems of equations involving these matrices. Usually, the optimization approach involves optimizing the Rayleigh quotient.We first propose alternative objective functions to solve the (generalized) eigenproblem via (unconstrained) optimization, and we describe the variational properties of these functions.We then introduce some optimization algorithms (based on one of these formulations) designed to compute the largest eigenpair. According to preliminary numerical experiments, this work could lead the way to practical methods for computing the largest eigenpair of a (very) large symmetric matrix (pair).     

Dynamic stability of functionally graded cantilever cylindrical shells under distributed axial follower forces

In this paper, flutter of functionally graded material (FGM) cylindrical shells under distributed axial follower forces is addressed. The first-order shear deformation theory is used to model the shell, and the material properties are assumed to be graded in the thickness direction according to a power law distribution using the properties of two base material phases. The solution is obtained by using the extended Galerkin's method, which accounts for the natural boundary conditions that are not satisfied by the assumed displacement functions. The effect of changing the concentrated (Beck's) follower force into the uniform (Leipholz's) and linear (Hauger's) distributed follower loads on the critical circumferential mode number and the minimum flutter load is investigated. As expected, the flutter load increases as the follower force changes from the so-called Beck's load into the so-called Leipholz's and Hauger's loadings. The increased flutter load was calculated for homogeneous shell with different mechanical properties, and it was found that the difference in elasticity moduli bears the most significant effect on the flutter load increase in short, thick shells. Also, for an FGM shell, the increase in the flutter load was calculated directly, and it was found that it can be derived from the simple power law when the corresponding increase for the two base phases are known.     

Local minima of quadratic forms on convex cones

We study the local minima and the critical values of a quadratic form on the trace of a convex cone. This variational problem leads to the development of a spectral theory that combines matrix algebra and facial analysis of convex cones.      

Determination of the thermal stress wave propagation in orthotropic hollow cylinder based on classical theory of thermoelasticity

The thermoelasticity problem in a thick-walled orthotropic hollow cylinder is solved analytically using finite Hankel transform and Laplace transform. Time-dependent thermal and mechanical boundary conditions are applied on the inner and the outer surfaces of the cylinder. For solving the energy equation, the temperature itself is considered as boundary condition to be applied on both the inner and the outer surfaces of the orthotropic cylinder. Two different cases are assumed for solving the equation of motion: traction–traction problem (tractions are prescribed on both the inner and the outer surfaces) and traction–displacement (traction is prescribed on the inner surface and displacement is prescribed on the outer surface of the hollow orthotropic cylinder). Due to considering uncoupled theory, after obtaining temperature distribution, the dynamical structural problem is solved and closed-form relations are derived for radial displacement, radial and hoop stress. As a case study, exponentially decaying temperature with respect to time is prescribed on the inner surface of the cylinder and the temperature of the outer surface is considered to be zero. Owing to solving dynamical problem, the stress wave propagation and its reflections were observed after plotting the results in both cases.     

Valeurs propres relatives à un cône convexe : caractérisation et résultats de cardinalité

Let A be an n×n real matrix, and $\text{K?}\text{R}{}^{\mathrm{n}}$ be a closed convex cone. The spectrum of A relative to K, denoted by σ(A,K), is the set of all $\text{λ∈}\text{R}$ for which the linear complementarity problem

$\text{x∈K,}\text{Ax?λx∈K}{}^{\mathrm{+}}\text{,}\text{〈x,Ax?λx〉=0}$

admits a nonzero solution $\text{x∈}\text{R}{}^{\mathrm{n}}$. The aim of this Note is to study the main properties of the set-valued mapping $\text{σ(·}\text{,K)}$, and discuss some structural differences existing between the polyhedral case (i.e., K is finitely generated) and the non-polyhedral case. To cite this article: A. Seeger, M. Torki, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Novel Pomegranate-Nanoparticles Ameliorate Cisplatin-Induced Nephrotoxicity and Improves Cisplatin Anti-Cancer Efficacy in Ehrlich Carcinoma Mice Model

Cisplatin (CISP) is one of the most widely used anti-cancer chemotherapeutic agents with remarkable efficacy against various types of cancers. However, it has been associated with nephrotoxicity amongst other undesirable side effects. Pomegranate (PE) is a potent antioxidant and anti-inflammatory agent effective against cancer, with a superior benefit of not being associated with the common toxicities related to the use of conventional chemotherapeutic agents. However, the application of PE is limited by its reduced solubility and decreased bioavailability. We investigated the potential of a novel nanoparticle (NP) enclosing PE to enhance its solubility and improve its bioavailability, and efficacy to prevent CISP-associated nephrotoxicity in a mice model of Ehrlich solid carcinoma (ESC). All mice were grouped into four cohorts: (I) control, (II) tumor, (III) CISP, and (IV) CISP + PE-NPs. The data obtained demonstrated that PE-NPs was beneficial in potently ameliorating CISP-induced nephrotoxicity in ESC mice. PE-NPs significantly attenuated CISP-induced oxidative stress and lipid peroxidation in the kidney via improving activities of antioxidants (SOD, GSH, and CAT). Additionally, PE-NPs considerably decreased CISP-induced inflammation in the kidney by decreasing the levels of NF-kB, IL-1β, and TNF-α. Notably, PE-NPs did not assuage the antitumor efficacy of CISP as revealed by histological assessment and tumor weight data. In summary, PE-NPs may be a potent alternative anticancer therapy devoid of nephrotoxicity.     

Simultaneous determination of nitrite and nitrate in potato and water samples using negative electrospray ionization ion mobility spectrometry

Nowadays, nitrite and nitrate ions are analyzed in biological samples using laborious and expensive methods; such as HPLC, CE, MS-MS. In this work, the simultaneous analysis of nitrite and nitrate ions was conducted by electrospray ionization-ion mobility spectrometry (ESI-IMS), without using any complicated or laborious derivitization step. Ion mobility spectrometry with low cost, inexpensive maintenance and very fast analysis makes an attractive technique for the simultaneous determination of these ions in foodstuff and drinking water samples. The analyte interference was systematically investigated for binary mixture analysis. The obtained results provided detection limits of 3.8 and 4.7 μg/L for nitrite and nitrate, respectively. A linear dynamic range of about 2 orders of magnitude, and relative standard deviations below 5% were obtained by the proposed method for the analysis of both ions. Also, the proposed method was used to analyze various real samples of potato and drinking water samples, and the obtained results confirmed the capability of negative ESI-IMS for the simultaneous detection of nitrite and nitrate.     

Centers of sets with symmetry or cyclicity properties

We introduce an axiomatic formalism for the concept of the center of a set in a Euclidean space. Then we explain how to exploit possible symmetries and possible cyclicities in the set in order to localize its center. Special attention is paid to the determination of centers in cones of matrices. Despite its highly abstract flavor, our work has a strong connection with convex optimization theory. In fact, computing the so-called “incenter” of a solid closed convex cone is a matter of solving a nonsmooth convex optimization program. On the other hand, the concept of the incenter of a solid closed convex cone has a bearing on the complexity analysis and design of algorithms for convex optimization programs under conic constraints.     

RuIII(OTf)SalophenCH2–NHSiO2–Fe: an efficient and magnetically recoverable catalyst for trimethylsilylation of alcohols and phenols with hexamethyldisilazane

Efficient trimethylsilylation of alcohols and phenols with hexamethyldisilazane (HMDS) catalyzed by ruthenium(III) complex of chloromethylated Salophen supported on nanomagnetic materials is reported. First, the iron nanomagnets were silica coated, functionalized with amine and then ruthenium CM‐Salophen was successfully bonded to their surface. The catalyst, Ru^III(OTf)SalophenCH₂–NHSiO₂–Fe, was characterized by elemental analysis, FT‐IR and UV–visible spectroscopic techniques, transmission electron microscopy and inductively coupled plasma (ICP). The Ru^III(OTf)SalophenCH₂–NHSiO₂–Fe catalyzed trimethylsilylation of primary and secondary alcohols as well as phenols, and the corresponding TMS ethers were obtained in high yields and short reaction times at room temperature. This new heterogenized trimethylsilylation catalyst is easily recovered with a magnet and showed no appreciable loss of activity even after five consecutive runs. Copyright © 2014 John Wiley & Sons, Ltd.