New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model

In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.Comment: 8 Pages, The Journal Thermal Science, 201

New numerical approach for fractional differential equations

In the present case, we propose the correct version of the fractional Adams-Bashforth methods which take into account the nonlinearity of the kernels including the power law for the Riemann-Liouville type, the exponential decay law for the Caputo-Fabrizio case and the Mittag-Leffler law for the Atangana-Baleanu scenario. The Adams-Bashforth method for fractional differentiation suggested and are commonly use in the literature nowadays is not mathematically correct and the method was derived without taking into account the nonlinearity of the power law kernel. Unlike the proposed version found in the literature, our approximation, in all the cases, we are able to recover the standard case whenever the fractional power $\alpha=1$.Comment: 19 pages, 3 figure

Development Of Modified Biopolymer Adsorbents From Natural Polysaccharides For Renewal Of Abattoir Wastewater

DissertationThe wastewater effluents produced by poultry and the red meat industries were analysed in the quest to detect the presence of heavy metals in abattoir wastewater and to establish and optimize alternative methods of purifying wastewater from Bloemfontein abattoirs in an effort to reduce water pollution. Water samples were randomly collected from two categories of local abattoirs in Bloemfontein, namely poultry and red meat abattoirs. The samples were found to contain high levels of alkali and alkaline earth metals (Ca, Mg, K and Na) at rates above 100 mg/ℓ. Other elements present in the wastewater samples that were analyzed included Cr, Ni, Cu and Pb, which are elements that have been reported to cause devastating effects in animals and the environment. Analyses of the Cr, Ni, Cu and Pb using ICP-OES showed the presence of ultra-trace levels (0.05 – 0.2 mg/ℓ) in both wastewater solutions. These elements confirmed the presence of heavy metals in the water bodies at the abattoirs. A chromatographic technique using different chitosan products as adsorbents was developed. Some cross-linked chitosan products were synthesized from different chitin (mussel, prawn, pang and silver) products. The modified chitosan products were obtained from cross-linking the chitin with glutaraldehyde, formaldehyde, epichlorohydrine, maleic anhydride, p-benzoquinone, poly (ethylene) glycol diglycidyl ether (PEG diglycidyl ether), 1-vinyl-2-pyrrolidone, 1,3-dichloroaceone, acrylic acid and s-methyl-benzylamine. Characterization of these cross-linked chitosan products was performed using FTIR, SEM and viscometer assessments. The results obtained from the analyses using SEM spectroscopy revealed that the different products had different morphological structures. The results of the analyses showed significant adsorption rates of alkali and alkaline earth metals (Ca, Mg, K and Na) using shrimp chitosan that was cross-linked with maleic anhydride (J1) and shrimp chitosan that was cross-linked with acrylic acid (I2) chitosan products. The shrimp and crab chitosan starch that was cross-linked with formaldehyde (C1 and C2) was also shown to effectively adsorb the alkali and alkaline earth metals present in the waste samples. Lower concentrations of heavy metals were recovered (0.05 - 0.2 mg/ℓ) for Cr, Ni, Cu and Pb using these chitosan products. Although no complete adsorption of these elements was achieved in both the wastewater samples, the results showed a substantial improvement of the water eluted which demonstrated the effectiveness of the method using synthesized chitosan products

Analytical solutions for the recovery tests after constant-discharge tests in confined aquifers

A new analytical solution for residual drawdown during the recovery period after a constant rate pumping test is described. A comparison between the proposed solution, existing solutions and experimental data from field observation are presented. The proposed analytical solution is in perfect agreement with the experimental data for α = 0.01, in contrast to the Cooper-Jacob solution. A new analytical solution for the determination of the skin factor without any restriction on the variables t and t’ is derived. An analytical solution for the drawdown response in a confined aquifer that is pumped step-wise or intermittently at a different discharge rate is suggested. On the basis of the suggested solution, a new analytical solution for the analysis of residual drawdown data after a pumping test with step-wise or intermittently changing discharge rates is provided.Keywords: recovery equations, residual drawdown, skin effect, variable discharge

Phenotypic diversity in fruit and seed traits, and neutral genetic diversity in Allanblackia Floribunda

Allanblackia floribunda est un arbre des forêts denses humides tropicales valorisé pour la teneur élevée en acides gras de ses graines, essentiellement constitués d’acides stéarique et oléique dont l’efficacité dans la réduction du mauvais cholestérol de l’organisme humain a été prouvée. Pour cette raison, les graines de A. floribunda collectées en milieu naturel sont commercialisées. Toutefois, les travaux sur la culture de cette espèce sont encore à leur phase initiale. Nous avons déterminé la possibilité d’amélioration génétique de cette espèce en échantillonnant 17 à 40 fruits par arbre de 70 arbres distribués sur quatre sites en milieu naturel. La matière grasse a été extraite des graines, et les teneurs en acides stéarique et oléique estimées à l’aide de méthodes développées au cours de cette étude. La variation phénotypique des traits des fruits et des graines a été caractérisée dans et entre les arbres, et entre les sites. Les estimations de répétabilité des caractères mesurés ont été effectuées. Des corrélations phénotypiques entre les traits étudiés ont aussi été estimées, et quatre traits ont été retenus pour effectuer la sélection multi-caractère de 20 arbres-plus qui constitueront la population d’amélioration de cette espèce pour la production des graines. Nous avons par la suite isolé 10 marqueurs moléculaires de type microsatellite polymorphes à partir de A. floribunda, et sept de ces marqueurs étaient polymorphes à la fois chez Allanblackia gabonensis et Allanblackia stanerana. La variation de huit loci microsatellites a permis de caractériser la structure génétique neutre de 10 populations de A. floribunda de zone de forêt naturelle du Cameroun, puis d’inférer l’histoire récente des forêts humides d’Afrique Centrale. Aucune différence significative n’a été observée entre les paramètres génétiques de la population d’amélioration et celle existant en milieu naturel indiquant qu’une amélioration de cette espèce à partir des 20 arbres sélectionnés ne réduirait pas sa diversité génétique neutre. Toutefois, une légère augmentation du taux de consanguinité a été observée dans la population d’amélioration, et des recommandations sont formulées pour la conservation des ressources génétiques durant l’amélioration de A. floribunda.Allanblackia floribunda or tallow tree is a tropical forest-tree species that is valued for its seeds, which are rich in hard fat consisting mostly of stearic and oleic acids, reported to lower plasma cholesterol levels, thus reducing the risks of heart attack. Owing to this fat profile, Allanblackia oil is used for margarine production and in soap and ointments manufacture, and seeds extracted from Allanblackia fruits by local communities are traded. We determined whether the species could be genetically improved for fruit/seed production by sampling 17 to 40 fruits from each of 70 trees that were distributed among four sites in wild stands. Fat was extracted from the seeds, and stearic and oleic acid content of the fat was estimated using methods developed in this study. Phenotypic variation in fruit/seed traits was assessed within- and among-trees, and among sites. Repeatabilities were estimated for measured characters, and relationships between these characters investigated. Twenty “plus trees” were selected for breeding, and implications for improvement discussed. Then we isolated and characterized ten microsatellite primer pairs for A. floribunda. Seven of these microsatellite loci were polymorph for both Allanblackia gabonensis and Allanblackia stanerana species as well. Using eight informative microsatellite loci, we have characterized the genetic structure of A. floribunda natural populations from Cameroon, and inferred the recent history of rainforests from Central Africa. No significant difference was identified in genetic parameters between wild stands and the breeding population, indicating that breeding A. floribunda from 20 trees would not reduce nuclear genetic diversity. However, a slight increase in inbreeding was observed in the breeding population, and recommendations for genetic diversity conservation during tree improvement in the species are made

Les facteurs d’efficacite des ecoles secondaires au Cameroun

L’objectif principal de cet article est d’identifier les facteurs d’efficacité des écoles secondaires au Cameroun. Pour cela, l’auteur utilise l’approche non paramétrique pour générer les niveaux d’efficacité des écoles et développe un modèle Tobit pour identifier lesdits facteurs d’efficacité. Les données proviennent de l’institut national de la statistique du Cameroun. Les résultats démontrent que le niveau moyen d’efficacité des écoles secondaires est estimé à 0,60 et les écoles secondaires du milieu rural sont les plus efficientes. En ce qui concerne l’analyse de l’efficacité par ordre d’enseignement, les résultats démontrent que les écoles privées protestantes sont les plus efficientes et les écoles secondaires privées laïques, les plus inefficientes. Enfin, les résultats des estimations prouvent que les écoles les plus efficientes sont celles qui sont relativement mieux dotées en ressources. Ils confirment l’importance de la discipline au sein des écoles et témoignent la valeur de la coopération entre les écoles et les parents d’élèves.MOTS CLES: éducation; école; système éducatif; efficacité; élève