On stationarity and second-order properties of bilinear random fields

One-dimensional indexed bilinear (BL) models are widely used for modeling non Gaussian time series. Extending BL models to multidimensional indexed (spatial) SBL one, yields a novel class of models which are capable of taking into account the important characteristic of non Gaussianity and spatiality behavior. Our main contribution here is to extend various results on BL processes to SBL one. Our attention is thus focussed on the probabilistic structure of some SBLmodels. So, we establish necessary and sufficient conditions for the existence of regular stationary and ergodic solutions in term of their transfer functions. As a consequence, we observe that the second order structure is similar to a spatial ARMA model with some uncorrelated white noise. So, it is necessary to look into higher-order moments in order to distinguish between linear and nonlinear random fields. Our study may be applied to GARCH or ARMA random fields.     

Time dependent Lyapunov functions for some Kolmogorov semigroups perturbed by unbounded potentials

We study global regularity properties of transition kernels associated to second order differential operators in \mathbb R^N{\mathbb {R}^N} with unbounded drift and potential terms. Under suitable conditions, we prove pointwise upper bounds. We use time dependent Lyapunov function techniques allowing us to gain a better time behaviour of such kernels.     

Renormalized solution for Stefan type problems: existence and uniqueness

We consider a class of nonlinear degenerate problems of Stefan type: $u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)$ where β is a maximal monotone graph in ${\mathbb{R}^2,}We consider a class of nonlinear degenerate problems of Stefan type:

ut- Dw -?F(u,w) = g(·,u),  w ? b(u)u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)      54. Design of a new and highly effective chiral auxiliary for Diels-Alder reaction of 1-aminodiene   总被引：1，自引：0，他引：1   Robiette R  Cheboub-Benchaba K  Peeters D  Marchand-Brynaert J 《The Journal of organic chemistry》2003,68(25):9809-9812 A theoretical investigation of the facial selectivity of optically active oxazolidin-2-one-substituted dienes has been realized. This analysis enabled the development of (R)-4-phenyloxazolidin-2-thione as a very effective chiral auxiliary for cycloaddition of 1-aminodiene.      55. Insights into the structure of triethylammoniumbis(pyridine-2,6-dicarboxylato-iron(III)): Crystallographic and theoretical study      Karima Benhamed  Boulanouar Messaoudi  Samira Louhibi  Thierry Roisnel 《Molecular Crystals and Liquid Crystals》2017,658(1):140-152       56. Biological Investigation of Amaryllidaceae Alkaloid Extracts from the Bulbs of Pancratium trianthum Collected in the Senegalese Flora      Seydou Ka  Natacha Mrindol  Insa Seck  Simon Ricard  Abdoulaye Diop  Cheikh Saad Bouh Boye  Karima Landelouci  Benoit Daoust  Lionel Berthoux  Genevive Ppin  Matar Seck  Isabel Desgagn-Penix 《Molecules (Basel, Switzerland)》2021,26(23) Amaryllidaceae plants are rich in alkaloids with biological properties. Pancratium trianthum is an Amaryllidaceae species widely used in African folk medicine to treat several diseases such as central nervous system disorders, tumors, and microbial infections, and it is used to heal wounds. The current investigation explored the biological properties of alkaloid extracts from bulbs of P. trianthum collected in the Senegalese flora. Alkaloid extracts were analyzed and identified by chromatography and mass spectrometry. Alkaloid extracts from P. trianthum displayed pleiotropic biological properties. Cytotoxic activity of the extracts was determined on hepatocarcinoma Huh7 cells and on acute monocytic leukemia THP-1 cells, while agar diffusion and microdilution assays were used to evaluate antibacterial activity. Antiviral activity was measured by infection of extract-treated cells with dengue virus (DENVGFP) and human immunodeficiency virus-1 (HIV-1GFP) reporter vectors. Cytotoxicity and viral inhibition were the most striking of P. trianthum’s extract activities. Importantly, non-cytotoxic concentrations were highly effective in completely preventing DENVGFP replication and in reducing pseudotyped HIV-1GFP infection levels. Our results show that P. trianthum is a rich source of molecules for the potential discovery of new treatments against various diseases. Herein, we provide scientific evidence to rationalize the traditional uses of P. trianthum for wound treatment as an anti-dermatosis and antiseptic agent.      57. Investigation on the effect of cellulosic nanoparticles’ morphology on the properties of natural rubber based nanocomposites      Abdelkader Bendahou  Hamid Kaddami 《European Polymer Journal》2010,46(4):609-136 Cellulose whiskers and microfibrillated cellulose (MFC) were extracted from the rachis of date palm tree and characterized. These cellulosic nanoparticles were used as reinforcing phase to prepare nanocomposite films using latex of natural rubber as matrix. These films were obtained by the casting/evaporation method. The properties of the ensuing nanocomposite films were investigated using differential scanning calorimetry, toluene and water uptake experiments, dynamic mechanical analysis and tensile tests. The stiffness of the natural rubber was significantly increased above its glass-rubber transition temperature upon nanoparticles addition. The reinforcing effect was shown to be higher for nanocomposites with MFC compared to whiskers. It was ascribed to the higher aspect ratio and possibility of entanglements of the former. The presence of residual lignin, extractive substances and fatty acids at the surface of MFC was also suggested to promote higher adhesion level with the polymeric matrix.      58. A green protocol for one-pot three-component synthesis of 1-(benzothiazolylamino) methyl-2-naphthol catalyzed by oxalic acid      Malek Taher Maghsoodlou  Mahsa Karima  Mojtaba Lashkari  Belghais Adrom  Jasem Aboonajmi 《Journal of the Iranian Chemical Society》2017,14(2):329-335       59. D'Alembert‐type solution of the Cauchy problem for the Boussinesq‐Klein‐Gordon equation      Karima R. Khusnutdinova  Matthew R. Tranter 《Studies in Applied Mathematics》2019,142(4):551-585 In this paper, we construct a weakly‐nonlinear d'Alembert‐type solution of the Cauchy problem for the Boussinesq‐Klein‐Gordon (BKG) equation. Similarly to our earlier work based on the use of spatial Fourier series, we consider the problem in the class of periodic functions on an interval of finite length (including the case of localized solutions on a large interval), and work with the nonlinear partial differential equation with variable coefficients describing the deviation from the oscillating mean value. Unlike our earlier paper, here we develop a novel multiple‐scales procedure involving fast characteristic variables and two slow time scales and averaging with respect to the spatial variable at a constant value of one or another characteristic variable, which allows us to construct an explicit and compact d'Alembert‐type solution of the nonlinear problem in terms of solutions of two Ostrovsky equations emerging at the leading order and describing the right‐ and left‐propagating waves. Validity of the constructed solution in the case when only the first initial condition for the BKG equation may have nonzero mean value follows from our earlier results, and is illustrated numerically for a number of instructive examples, both for periodic solutions on a finite interval, and localized solutions on a large interval. We also outline an extension of the procedure to the general case, when both initial conditions may have nonzero mean values. Importantly, in all cases, the initial conditions for the leading‐order Ostrovsky equations by construction have zero mean, while initial conditions for the BKG equation may have nonzero mean values.      60. Multiple positive fixed points for the sum of expansive mappings and k‐set contractions      Lyna Benzenati  Karima Mebarki 《Mathematical Methods in the Applied Sciences》2019,42(13):4412-4426 In this work, we are concerned with the existence of multiple positive fixed points for the sum of an expansive mapping with constant h > 1 and a k‐set contraction when 0 ≤ k < h ? 1. In particular, the case of the sum of an expansive mapping with constant h > 1 and an e‐concave operator and an e‐convex operator is considered. Two examples of application illustrate some of the theoretical results.      [首页] « 上一页 [1] [2] [3] [4] [5] 6 [7] [8] 下一页 » 末  页»

Design of a new and highly effective chiral auxiliary for Diels-Alder reaction of 1-aminodiene

A theoretical investigation of the facial selectivity of optically active oxazolidin-2-one-substituted dienes has been realized. This analysis enabled the development of (R)-4-phenyloxazolidin-2-thione as a very effective chiral auxiliary for cycloaddition of 1-aminodiene.     

Biological Investigation of Amaryllidaceae Alkaloid Extracts from the Bulbs of Pancratium trianthum Collected in the Senegalese Flora

Amaryllidaceae plants are rich in alkaloids with biological properties. Pancratium trianthum is an Amaryllidaceae species widely used in African folk medicine to treat several diseases such as central nervous system disorders, tumors, and microbial infections, and it is used to heal wounds. The current investigation explored the biological properties of alkaloid extracts from bulbs of P. trianthum collected in the Senegalese flora. Alkaloid extracts were analyzed and identified by chromatography and mass spectrometry. Alkaloid extracts from P. trianthum displayed pleiotropic biological properties. Cytotoxic activity of the extracts was determined on hepatocarcinoma Huh7 cells and on acute monocytic leukemia THP-1 cells, while agar diffusion and microdilution assays were used to evaluate antibacterial activity. Antiviral activity was measured by infection of extract-treated cells with dengue virus (DENV_GFP) and human immunodeficiency virus-1 (HIV-1_GFP) reporter vectors. Cytotoxicity and viral inhibition were the most striking of P. trianthum’s extract activities. Importantly, non-cytotoxic concentrations were highly effective in completely preventing DENV_GFP replication and in reducing pseudotyped HIV-1_GFP infection levels. Our results show that P. trianthum is a rich source of molecules for the potential discovery of new treatments against various diseases. Herein, we provide scientific evidence to rationalize the traditional uses of P. trianthum for wound treatment as an anti-dermatosis and antiseptic agent.     

Investigation on the effect of cellulosic nanoparticles’ morphology on the properties of natural rubber based nanocomposites

Cellulose whiskers and microfibrillated cellulose (MFC) were extracted from the rachis of date palm tree and characterized. These cellulosic nanoparticles were used as reinforcing phase to prepare nanocomposite films using latex of natural rubber as matrix. These films were obtained by the casting/evaporation method. The properties of the ensuing nanocomposite films were investigated using differential scanning calorimetry, toluene and water uptake experiments, dynamic mechanical analysis and tensile tests. The stiffness of the natural rubber was significantly increased above its glass-rubber transition temperature upon nanoparticles addition. The reinforcing effect was shown to be higher for nanocomposites with MFC compared to whiskers. It was ascribed to the higher aspect ratio and possibility of entanglements of the former. The presence of residual lignin, extractive substances and fatty acids at the surface of MFC was also suggested to promote higher adhesion level with the polymeric matrix.     

D'Alembert‐type solution of the Cauchy problem for the Boussinesq‐Klein‐Gordon equation

In this paper, we construct a weakly‐nonlinear d'Alembert‐type solution of the Cauchy problem for the Boussinesq‐Klein‐Gordon (BKG) equation. Similarly to our earlier work based on the use of spatial Fourier series, we consider the problem in the class of periodic functions on an interval of finite length (including the case of localized solutions on a large interval), and work with the nonlinear partial differential equation with variable coefficients describing the deviation from the oscillating mean value. Unlike our earlier paper, here we develop a novel multiple‐scales procedure involving fast characteristic variables and two slow time scales and averaging with respect to the spatial variable at a constant value of one or another characteristic variable, which allows us to construct an explicit and compact d'Alembert‐type solution of the nonlinear problem in terms of solutions of two Ostrovsky equations emerging at the leading order and describing the right‐ and left‐propagating waves. Validity of the constructed solution in the case when only the first initial condition for the BKG equation may have nonzero mean value follows from our earlier results, and is illustrated numerically for a number of instructive examples, both for periodic solutions on a finite interval, and localized solutions on a large interval. We also outline an extension of the procedure to the general case, when both initial conditions may have nonzero mean values. Importantly, in all cases, the initial conditions for the leading‐order Ostrovsky equations by construction have zero mean, while initial conditions for the BKG equation may have nonzero mean values.     

Multiple positive fixed points for the sum of expansive mappings and k‐set contractions

In this work, we are concerned with the existence of multiple positive fixed points for the sum of an expansive mapping with constant h > 1 and a k‐set contraction when 0 ≤ k < h ? 1. In particular, the case of the sum of an expansive mapping with constant h > 1 and an e‐concave operator and an e‐convex operator is considered. Two examples of application illustrate some of the theoretical results.