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Volume mean operator and differentiation results associated to root systems
Chaabane Rejeb 대한수학회 2017 대한수학회보 Vol.54 No.6
Let $R$ be a root system in $\mathbb{R}^d$ with Coxeter-Weyl group $W$ and let $k$ be a nonnegative multiplicity function on $R$. The generalized volume mean of a function $f\in L^1_{loc}(\mathbb{R}^d,m_k)$, with $m_k$ the measure given by $dm_k(x):=\omega_k(x)dx:=\prod_{\alpha\in R}|\mathop{\langle\alpha,x\rangle}|^{k(\alpha)}dx$, is defined by: $\forall\ x\in \mathbb{R}^d$, $\forall\ r>0$, $M_B^r(f)(x):=\frac{1}{m_k[B(0,r)]}\int_{\mathbb{R}^d}f(y)h_k(r,x,y)\omega_k(y)dy$, where $h_k(r,x,\cdot)$ is a compactly supported nonnegative explicit measurable function depending on $R$ and $k$. In this paper, we prove that for almost every $x\in\mathbb{R}^d$, $\lim_{r\rightarrow0}M_B^r(f)(x)=f(x)$.
VOLUME MEAN OPERATOR AND DIFFERENTIATION RESULTS ASSOCIATED TO ROOT SYSTEMS
Rejeb, Chaabane Korean Mathematical Society 2017 대한수학회보 Vol.54 No.6
Let R be a root system in $\mathbb{R}^d$ with Coxeter-Weyl group W and let k be a nonnegative multiplicity function on R. The generalized volume mean of a function $f{\in}L^1_{loc}(\mathbb{R}^d,m_k)$, with $m_k$ the measure given by $dmk(x):={\omega}_k(x)dx:=\prod_{{\alpha}{\in}R}{\mid}{\langle}{\alpha},x{\rangle}{\mid}^{k({\alpha})}dx$, is defined by: ${\forall}x{\in}\mathbb{R}^d$, ${\forall}r$ > 0, $M^r_B(f)(x):=\frac{1}{m_k[B(0,r)]}\int_{\mathbb{R}^d}f(y)h_k(r,x,y){\omega}_k(y)dy$, where $h_k(r,x,{\cdot})$ is a compactly supported nonnegative explicit measurable function depending on R and k. In this paper, we prove that for almost every $x{\in}\mathbb{R}^d$, $lim_{r{\rightarrow}0}M^r_B(f)(x)= f(x)$.
Raja Chaabane-Banaoues,Myriam Oudni-M’rad,Selim M’rad,Habib Mezhoud,Hamouda Babba 대한기생충학열대의학회 2016 The Korean Journal of Parasitology Vol.54 No.1
Hydatidosis has become a real concern for health care institutions and animal rearers in Tunisia. The Tunisian endemicity is aggravated by the growing number of dogs and the difficulty of getting rid of contaminated viscera because of the lack of equipment in most slaughterhouses. Therefore, microscopic and molecular tools were applied to evaluate the role of slaughterhouses in canine infection and Echinococcus granulosus sensu lato (s. l.) egg dissemination. Exposure risk to E. granulosus s. l. eggs in urban and rural areas was explored in order to implant preventive and adapted control strategies. Microscopic examinations detected taeniid eggs in 152 amongst 553 fecal samples. The copro-PCR demonstrated that 138 of 152 taeniid samples analyzed were positive for E. granulosus s. l. DNA. PCR-RFLP demonstrated that all isolated samples belonged to E. granulosus sensu stricto (s. s.). An important environmental contamination index (25.0%) by E. granulosus s. l. eggs was demonstrated. The average contamination index from the regions around slaughterhouses (23.3%; 95% CI: 17.7-28.9%) was in the same range as detected in areas located far from slaughterhouses (26.0%, 95% CI: 21.3-30.8%). Echinococcosis endemic areas were extended in both rural (29.9%, 95% CI: 24.8-34.9%) and urban locations (18.1%, 95% CI: 13.0-22.9%). The pathogen dissemination is related neither to the presence/absence of slaughterhouses nor to the location in urban or rural areas, but is probably influenced by human activities (home slaughtering) and behavior towards the infected viscera.
Lynda Amel Chaabane,Fouad Bourada,Mohamed Sekkal,Sara Zerouati,Fatima Zohra Zaoui,Abdeldjebbar Tounsi,Abdelhak Derras,Abdelmoumen Anis Bousahla,Abdelouahed Tounsi 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.71 No.2
In this investigation, study of the static and dynamic behaviors of functionally graded beams (FGB) is presented using ahyperbolic shear deformation theory (HySDT). The simply supported FG-beam is resting on the elastic foundation (Winkler-Pasternak types). The properties of the FG-beam vary according to exponential (E-FGB) and power-law (P-FGB) distributions. Thegoverning equations are determined via Hamilton’s principle and solved by using Navier’s method. To show the accuracy of thismodel (HySDT), the current results are compared with those available in the literature. Also, various numerical results are discussedto show the influence of the variation of the volume fraction of the materials, the power index, the slenderness ratio and the effect ofWinkler spring constant on the fundamental frequency, center deflection, normal and shear stress of FG-beam.
Marble wastes as amendments to stabilize heavy metals in Zn-Electroplating sludge
Riahi, Khalifa,Chaabane, Safa,Thayer, Bechir Ben Techno-Press 2017 Advances in environmental research Vol.6 No.1
Powdered marble wastes (PMW) generated by Utique marble cutting industries (North of Tunisia) with abundant amounts were used in this study as low-cost materials to investigate the stabilization of heavy metals (Pb, Zn, Fe) in sludge generated from a local Zn-Electroplating factory. Powdered marble wastes were evaluated by means of chemical fractions of heavy metals in sludge and concentrations of heavy metals in leachate from columns to determine their ability to stabilize heavy metals in contaminated sludge. Results indicated that chemical fractions of heavy metals in sludge were affected by application of the PMW mineral materials and pH, however, the effects varied with heavy metals. Application of the powdered marble wastes mineral materials reduced exchangeable metals in the sequence of Pb (60.5%)>Fe (40.5%)>Zn (30.1%). X-ray diffraction and hydro-geochemical transport code PHREEQC analysis were successfully carried out to get a better understanding of the mechanisms of reactive mineral phases involved in reduced exchangeable heavy metals in sludge after PMW material amendments. Therefore, metal immobilization using powdered marble wastes materials is an effective stabilization technique for industrial metallic hydroxide sludge.
Tedjeddine Bendisari,Lynda A. Chaabane,Feriel Tires,Assma L. Mazouzi,Wissam Y. Bouayed,Abderrahman Lalimi,Kadid Moufek Techno-Press 2023 Advances in materials research Vol.12 No.4
The main objective of this article is to highlight the progress made in the development of new materials that have been gradually used by humans until today. Of course, this progress must be associated with other parameters in order to guarantee sustainable development. For this, today, it has become urgent to reduce the consumption of cement by resorting to its partial or total replacement by other similar materials in order to reduce CO<sub>2</sub> emissions in our environment. This should certainly help to develop greener building materials. In this study, it was decided to proceed with the partial or total replacement of Portland cement type CEM II/B-L-42.5N by slate and lime that had not undergone any previous transformation. The results obtained revealed that the mortar whose substitution compared to the replacement of cement (100%) cement and sand (0/4) confers better kinetics than those of the series composed of(100%) cement and fraction rubble (0/1).
Afef Be´jaoui,He´dia Chaabane,Maroua Jemli,Abdennacer Boulila,Mohamed Boussaid 한국식품영양과학회 2013 Journal of medicinal food Vol.16 No.12
Variation in the quantity and quality of the essential oil (EO) of wild population of Origanum vulgare at different phenological stages, including vegetative, late vegetative, and flowering set, is reported. The oils of air-dried samples were obtained by hydrodistillation. The yield of oils (w/w%) at different stages were in the order of late vegetative (2.0%), early vegetative (1.7%), and flowering (0.6%) set. The oils were analyzed by gas chromatography (GC) and GC–mass spectrometry (GC-MS). In total, 36, 33, and 16 components were identified and quantified in vegetative, late vegetative, and flowering set, representing 94.47%, 95.91%, and 99.62% of the oil, respectively. Carvacrol was the major compound in all samples. The ranges of major constituents were as follows: carvacrol (61.08–83.37%), p-cymene (3.02– 9.87%), and c-terpinene (4.13–6.34%). Antibacterial activity of the oils was tested against three Gram-positive and two Gram-negative bacteria by the disc diffusion method and determining their diameter of inhibition and the minimum inhibitory concentration (MIC) values. The inhibition zones and MIC values for bacterial strains, which were sensitive to the EO of O. vulgare subsp. glandulosum, were in the range of 9–36mm and 125–600 lg/mL, respectively. The oils of various phenological stages showed high activity against all tested bacteria, of which Bacillus subtilis was the most sensitive and resistant strain, respectively. Thus, they represent an inexpensive source of natural antibacterial substances that exhibited potential for use in pathogenic systems.
Polynomial Dynamic Output-feedback Controllers for Positive Polynomial Fuzzy Systems with Time Delay
Imen Iben Ammar,Hamdi Gassara,Mohamed Chaabane,Ahmed El Hajjaji 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.8
This paper investigates the stability and stabilization problems of positive polynomial fuzzy uncertain interval models with time delay. Using the polynomial output feedback fuzzy control strategy, the design problem is firstly studied by considering the unmeasured states and measurable premise variables. Then, the control design problem is extended for both the unmeasurable states and unmeasurable premise variables. To study the considered analysis and design problems, a line-integral polynomial fuzzy Lyapunov function with polynomial terms depending of the estimated states is proposed. For each case, the proposed design conditions of the polynomial dynamic output feedback fuzzy controllers guarantying both the stability and the positivity of the resulting closed loop systems, are solved using the Sum of Squares (SOS) approach with tacking into account the positivity of the error signals. Finally, simulation examples are given to show the effectiveness of the proposed approaches.
Design of Robust Fault Detection Observer for Takagi-Sugeno Models Using the Descriptor Approach
Maha Bouattour,Mohammed Chadli,Mohamed Chaabane,Ahmed El Hajjaji 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.5
This paper deals with the design of a robust fault detection observer for a Takagi-Sugeno (T-S) fuzzy model affected by sensor and actuator faults and unknown bounded disturbances simultaneously. An observer based on the technique of descriptor systems is studied. Indeed, by considering faults as auxiliary state variables, both states and faults are estimated simultaneously. In order to guarantee the best robustness to disturbances and sensitivity to faults, the developed observer combine the H__/H_∞ performances. Then, based on Lyapunov method, asymptotic stability conditions are given to design the observer parameters. In order to get convenient and reliable faults estimator in computations, an iterative linear matrix inequality (LMI) algorithm is developed. This algorithm, solved easily using existing numerical tools, allows to minimize influences of disturbances and maximize the ones of faults. Finally, a numerical example is proposed to illustrate the effectiveness of the result.