Pointwise Sum of two Maximal Monotone Operators

∗ Cette recherche a été partiellement subventionnée, en ce qui concerne le premier et le dernier auteur, par la bourse OTAN CRG 960360 et pour le second auteur par l’Action Intégrée 95/0849 entre les universités de Marrakech, Rabat et Montpellier.The primary goal of this paper is to shed some light on the maximality of the pointwise sum of two maximal monotone operators. The interesting purpose is to extend some recent results of Attouch, Moudafi and Riahi on the graph-convergence of maximal monotone operators to the more general setting of reflexive Banach spaces. In addition, we present some conditions which imply the uniform Brézis-Crandall-Pazy condition. Afterwards, we present, as a consequence, some recent conditions which ensure the Mosco-epiconvergence of the sum of convex proper lower semicontinuous functions

Study on survival and growth rate of three Artemia species fed with Dunaliella tertiolecta, Tetraselmis suecica and Nannochloropsis oculata

In recent years, Artemia has proven to be one of the easiest to prepare and the most nutritious food available to aquaculture. In this research, the process of hatching of Artemia cyst into larval stage using algae as a diet was investigated. The cysts used for this experiment belonged to three species Artemia urmiana, Artemia parthenogenetica and Artemia franciscana. The algae species used for the feeding of the Artemia included Dunaliella tertiolecta, Tetraselmis suecica and Nannochloropsis oculata. The effect of algae feeding on growth rate and survival of the Artemia species from hatching to maturation during 15 days was investigated. The results showed that A. franciscana had better growth rate and survival compared to the other two species

Reliability assessment using combination of polynomial chaos and simulations: application to nonlinear fracture mechanics

This paper presents a probabilistic approach based on polynomial chaos expansion, in order to provide accurate explicit approximation of the structural response to be considered in the limit state function. The main difficulties in this approach are related to the calculation of the expansion coefficients which are defined by multi-dimensional integrals. As an alternative to the quadrature methods, Monte-Carlo simulations based on low discrepancy Halton sequence have been used for this issue. The accuracy and the efficiency of the proposed approach have been approved through analytical models. It is shown that the use of low discrepancy sequence provides more rapidly converging estimates. The proposed approach has been applied to assess the integrity of a cracked pipe

Chiral nature of magnetic monopoles in artificial spin ice

Micromagnetic properties of monopoles in artificial kagome spin ice systems are investigated using numerical simulations. We show that micromagnetics brings additional complexity into the physics of these monopoles that is, by essence, absent in spin models: besides a fractionalized classical magnetic charge, monopoles in the artificial kagome ice are chiral at remanence. Our simulations predict that the chirality of these monopoles can be controlled without altering their charge state. This chirality breaks the vertex symmetry and triggers a directional motion of the monopole under an applied magnetic field. Our results also show that the choice of the geometrical features of the lattice can be used to turn on and off this chirality, thus allowing the investigation of chiral and achiral monopoles.Comment: 10 pages, 4 figure

Combining Strong Convergence, Values Fast Convergence and Vanishing of Gradients for a Proximal Point Algorithm Using Tikhonov Regularization in a Hilbert Space

In a real Hilbert space $\mathcal{H}$. Given any function $f$ convex differentiable whose solution set $\argmin_{\mathcal{H}}\,f$ is nonempty, by considering the Proximal Algorithm x_{k+1}=\text{prox}_{\b_k f}(d x_k), where $0<d<1$ and (\b_k) is nondecreasing function, and by assuming some assumptions on (\b_k), we will show that the value of the objective function in the sequence generated by our algorithm converges in order $\mathcal{O} \left( \frac{1}{ \beta _k} \right)$ to the global minimum of the objective function, and that the generated sequence converges strongly to the minimum norm element of $\argmin_{\mathcal{H}}\,f$, we also obtain a convergence rate of gradient toward zero. Afterward, we extend these results to non-smooth convex functions with extended real values

Three-component ambient noise beamforming in the Parkfield area

ACKNOWLEDGEMENTS Many thanks to Andrew Curtis and Ian Main for their critical and perceptive comments and to Sjoerd de Ridder for fruitful discussions. We are particularly grateful to Elmer Ruigrok for his detailed and constructive review, which has substantially improved our manuscript. We acknowledge the facilities of the IRIS Data Management System for providing access to the seismic data. This work is funded within the DFG project ‘SynPaTh’ and the EU project ‘GEMex’.Peer reviewedPublisher PD

Numerical analysis of timber fracture due to mechanical and thermal loads: an approach based on invariant integral

International audienc

Strong convergence towards the minimum norm solution via temporal scaling and Tikhonov approximation of a first-order dynamical system

Given a proper convex lower semicontinuous function defined on a Hilbert space and whose solution set is supposed nonempty. For attaining a global minimizer when this convex function is continuously differentiable, we approach it by a first-order continuous dynamical system with a time rescaling parameter and a Tikhonov regularization term. We show, along the generated trajectories, fast convergence of values, fast convergence of gradients towards origin and strong convergence towards the minimum norm element of the solution set. These convergence rates now depend on the time rescaling parameter, and thus improve existing results by choosing this parameter appropriately. The obtained results illustrate, via particular cases on the choice of the time rescaling parameter, good performances of the proposed continuous method and the wide range of applications they can address. Numerical illustrations for continuous example are provided to confirm the theoretical results.Comment: arXiv admin note: substantial text overlap with arXiv:2309.1320

Phytoplankton of Aras dam reservoir (Iran): an attempt to assess water quality

The Aras reservoir, located in the north-west of Iran, plays an important role in fisheries, drinking and agricultural water supplies and recreational activities in the region. This study was performed to characterize the seasonal fluctuations of phytoplankton communities and their relationship with environmental factors in the Aras reservoir from August 2013 to May 2014. Sampling was carried out seasonally from 5 sampling locations. In each location three samples were taken for phytoplankton identification and enumeration, chemical analysis and chlorophyll a determination. In total, 72 species belonging to 5 divisions were determined. Cyanobacteria contained the highest density (74%) during the study period with Pseudanabaena limnetica as the most abundant species. This group retained its dominance the whole year round which indicated the poor quality and high nutrient load of the Aras reservoir, mainly due to human activities. On average, Trophic State Index (TSI) showed that water in the reservoir was eu-hypereutrophic. The results indicated that phytoplankton density negatively correlated with Secchi disc depth (R^2 = -0.479), total alkalinity (R^2 = -0.564), total hardness (R^2 = -0.727) and HCO_3 concentration (R^2 = -0.589). On the other hand, there was a positive correlation between the phytoplankton density and TP (R^2 = 0.734). A comparison between the present and a previous study indicated that the cyanobacterial bloom pattern in the Aras reservoir has shifted from warm season toward an all year round cycle which in addition to basin pollution due to anthropogenic activities, can be related to global warming and climate change