A Kato class for the Khon Laplacian

Positivity - In this paper we establish an upper estimate and a 3G-theorem for the Green function of the Khon Laplacian $$\Delta _{{\mathbb {H}}}$$ on a domain D of the Heisenberg group $${{\mathbb...     

Problème de Dirichlet relatif à une perturbation non lineaire des espaces harmoniques

In this paper, we prove for a more general semi-linear perturbation of linear harmonic spaces, the existence and the unicity of the solution of the Dirichlet problem and we apply our results for the non-linear stationary Schrödinger equation.     

On the Existence of Positive Eigenvalues for Linear and Nonlinear Equations with Indefinite Weight

We prove the existence of positive eigenvalues for two types of equations having an indefinite weight. We consider the linear case, and we show the existence of a positive principal eigenvalue corresponding to a positive eigenfunction. For the nonlinear case, we show that the set of positive eigenvalues is an unbounded interval, and that the corresponding eigenfunctions are positive.     

A novel method for designing S-box based on chaotic map and Teaching–Learning-Based Optimization

A new method for obtaining strong S-boxes based on chaotic map and Teaching–Learning-Based Optimization (TLBO) is presented in this paper. Our method presents eight rounds; each round contains two transformations: row left shifting and columnwise rotation. The vectors for the transformations are different from one round to another, and they are controlled by two keys to the logistic map. These two keys are optimized by using TLBO which aims to construct a strong S-box that satisfies to the criteria set in advance. Test for the following criteria such as bijectivity, nonlinearity, strict avalanche criteria, equiprobable inputs/outputs XOR distribution is analyzed. Additionally, we will provide many comparisons with other S-boxes and test of the sensitivity to keys. The results of performance test show that the proposed design S-boxes presents good cryptography proprieties and can resist to several attacks.     

Comment on “Modified Baptista type chaotic cryptosystem via matrix secret key” [Phys. Lett. A 372 (2008) 5427]

In this comment, we analyze a recently proposed Baptista-like cryptosystem and show that it is not invertible. Others weaknesses are also reported. A modified version of this cryptosystem is proposed to show how to overcome the non-invertibility.     

On the Existence of Positive Eigenvalues for Semilinear Elliptic Equation on all of R d

In this paper, we consider a problem of the form

On the security of a spatiotemporal chaotic cryptosystem

Recently, Tang et al. [Phys Lett. A 318, 388 (2003)] proposed a spatiotemporal cryptosystem based on one-way coupled map lattices. They claim that it has high security, fast encryption speed, and short synchronization transient. This work proves that this scheme has some security weaknesses. Indeed, we propose an attack which the system cannot withstand.     

Succinimido–Ferrocidiphenol Complexed with Cyclodextrins Inhibits Glioblastoma Tumor Growth In Vitro and In Vivo without Noticeable Adverse Toxicity

SuccFerr (N-[4-ferrocenyl,5-5-bis (4-hydroxyphenyl)-pent-4-enyl]-succinimide) has remarkable antiproliferative effects in vitro, attributed to the formation of a stabilized quinone methide. The present article reports in vivo results for a possible preclinical study. SuccFerr is lipophilic and insoluble in water, so the development of a formulation to obviate this inconvenience was necessary. This was achieved by complexation with randomly methylated cyclodextrins (RAMEßCDs). This supramolecular water-soluble system allowed the in vivo experiments below to proceed. Application of SuccFerr on the glioblastoma cancer cell line U87 indicates that it affects the cellular cycle by inducing a blockade at G0/G1 phase, linked to apoptosis, and another one at the S phase, associated with senescence. Using healthy Fischer rats, we show that both intravenous and subcutaneous SuccFerr: RAMEßCD administration at 5 mg/kg lacks toxic effects on several organs. To reach lethality, doses higher than 200 mg/kg need to be administered. These results prompted us to perform an ectopic in vivo study at 1 mg/kg i.v. ferrocidiphenol SuccFerr using F98 cells xenografted in rats. Halting of cancer progression was observed after six days of injection, associated with an immunological defense response linked to the active principle. These results demonstrate that the properties of the selected ferrocidiphenol SuccFerr transfer successfully to in vivo conditions, leading to interesting therapeutic perspectives based on this chemistry.     

Structural and dielectric properties of Ba0.8 La0.133 Ti0.90 Sn0.1 O3

Perovskite type Ba_0.8 La_0.133 Ti_0.90 Sn_0.1 O₃ ceramic has been prepared through a solid-state reaction route. The effects of cationic substitution of La³⁺ and Sn⁴⁺ for titanium in the A and B sites for BaTiO₃ perovskite lattice on symmetry and dielectric properties were investigated. The samples are of single phase with rhombohedral structure of R$\overline{3}$ C space group. Impedance spectrum results indicate that the electrical properties are strongly dependent on temperature and have a good correlation with the sample microstructure in different temperature. Nyquist plots (Z″versus Z′) show that the conductivity behavior is accurately represented by an equivalent circuit model which consists of a parallel combination of a bulk resistance and constant phase elements (CPE). The near value of activation energies obtained from the analyses of modulus and conductivity data confirms that the transport is through ion hopping mechanism in the investigated materials.