The indivisibility of the homogeneous Kn-free graphs

AbstractWe will prove that for each n ≥ 3 the homogeneous Kn-free graph Hn is indivisible. That means that for every partition of Hn into two classes R and B there is an isomorphic copy of Hn in R or in B. This extends a result of Komjáth and Rödl [Graphs Combin., 2 (1986), 55–60] who have shown that H3 is indivisible

Indivisible homogeneous directed graphs and a game for vertex partitions

AbstractLet T be a set of finite tournaments. We will give a necessary and sufficient condition for the T-free homogeneous directed graph HT to be divisible; that is, that there is a partition of HT into two sets neither of which contains an isomorphic copy of HT

Synthesis and Cytotoxicity Screening of Some Novel Benzofuranoyl-pyrazole Derivatives against Liver and Cervix Carcinoma Cell Lines

A series of new pyrazole, thiazole and thiazolinone derivatives incorporated into benzofuran were synthesized by using 3-(benzofuran-2-yl)-1-phenyl-1H-pyrazol-4-carboxaldehyde as starting material. A total of 41 novel compounds were synthesized. Some of these synthesized compounds were evaluated for cytotoxicity activity against HEPG2 (liver carcinoma cell line) and HELA (cervix carcinoma cell line). The tested compounds (1, 2c, 7c, 8b, 9b, 13b and 14b) showed better activities at low concentration against the commonly used human carcinoma cell lines. A detailed synthesis, spectroscopic data and cytotoxicity screening for the new compounds are described.Keywords: Pyrazole, thiazolinone, benzofuran, benzofuranoyl-pyrazoles, cytotoxic screening, HEPG2, HELAPDF and Supplementry file attache

Piecewise Approximate Analytical Solutions of High-Order Singular Perturbation Problems with a Discontinuous Source Term

A reliable algorithm is presented to develop piecewise approximate analytical solutions of third- and fourth-order convection diffusion singular perturbation problems with a discontinuous source term. The algorithm is based on an asymptotic expansion approximation and Differential Transform Method (DTM). First, the original problem is transformed into a weakly coupled system of ODEs and a zero-order asymptotic expansion of the solution is constructed. Then a piecewise smooth solution of the terminal value reduced system is obtained by using DTM and imposing the continuity and smoothness conditions. The error estimate of the method is presented. The results show that the method is a reliable and convenient asymptotic semianalytical numerical method for treating high-order singular perturbation problems with a discontinuous source term

On progressive wave solution for non-planar KDV equation in a plasma with q-nonextensive electrons and two oppositely charged ions

In this paper, the ion-acoustic wave is investigated in a plasma with q-nonextensive electrons and two oppositely charged ions with varying masses. These parameters are found to modify the linear dispersion relation and nonlinear solitary structures. The reductive perturbation method is employed to derive modified Korteweg-de Vries (KdV) equation. To solve the obtained governing evolution equation, the exact solution in the planar geometry is obtained and used to obtain an analytical approximate progressive wave solution for the nonplanar evolution equation. The analytical approximate solution so obtained is compared with the numerical solution of the same nonplanar evolution equation and the results are presented in 2D and 3D figures. The results revealed that both solutions are in good agreement. A parametric study is carried out to investigate the effect of different physical parameters on the nonlinear evolution solution behavior. The obtained solution allows us to study the impact of various plasma parameters on the behavior of the nonplanar ion-acoustic solitons. The suitable application of the present investigations can be found in laboratory plasmas, where oppositely charged ions and nonthermal electrons dwell.The second author is partially supported by the Deanship of Scientific Research at Prince Sattam bin Abdulaziz University under grant No. 2019/1/11000.Publisher's Versio

Mathematical Modeling of Heat-Transfer for a Moving Sheet in a Moving Fluid

A mathematical model was developed for determining the heat transfer between a moving sheet that passes through a moving fluid environment to simulate the fabrication process of sheet and fiber-like materials. Similarity transformations were introduced to reduce the governing equations to two nonlinear ordinary differential equations. For high values Prandtl number, the energy equation became much stiffer or singularly perturbed and the standard numerical methods failed to handle it. An innovative procedure combining shooting and singular perturbation technique was developed. The results show that the heat transfer depends on the relative velocity between the moving fluid and the moving sheet to a certain value after that value the relative velocity has no effect. If blowing effect is found the thermal layer becomes thinner and temperature profiles are backed together

Re-Evaluating the Classical Falling Body Problem

This paper re-analyzes the falling body problem in three dimensions, taking into account the effect of the Earth’s rotation (ER). Accordingly, the analytic solution of the three-dimensional model is obtained. Since the ER is quite slow, the three coupled differential equations of motion are usually approximated by neglecting all high order terms. Furthermore, the theoretical aspects describing the nature of the falling point in the rotating frame and the original inertial frame are proved. The theoretical and numerical results are illustrated and discussed.The authors would like to thank the referees for their valuable comments and suggestions, which helped to improve the manuscript. Moreover, the first author thanks Prince Sattam bin Abdulaziz University and Deanship of Scientific Research at Prince Sattam bin Abdulaziz University for their continuous support and encouragement.info:eu-repo/semantics/publishedVersio

Détection de l'adultération du beurre par la margarine

Une méthode analytique permettant de détecter l’adultération du beurre par la margarine a été développée. Elle est basée sur la détermination de la composition en acides gras et en stérols par chromatographie en phase gazeuse. Plusieurs niveaux d’adultération du beurre par la margarine (3, 5 et 10% p/p) ont été préparés puis analysés. Les résultats montrent que l’acide linoléique et les stérols permettent de détecter la margarine dans le beurre à un seuil de 3%

Préparation du fromage frais à partir du lait recombiné

Le but de cette étude a été d'évaluer les possibilités de préparation du fromage frais à partir du lait recombiné qui a été pasteurisé puis conservé pendant une nuit à 6°C pour faciliter la réhydratation. Le lait a été ensuite inoculé avec le levain constitué à parts égales de L. lactis subsp. lactis, L. lactis subsp. lactis var. diacetylactis et L. casei subsp casei à raison de 3% puis maintenu entre 30 et 37°C pour activer la fermentation. À pH 5,0 à 5,5, la présure a été ajoutée puis le moulage a été réalisé à température ambiante lorsque le pH a atteint une valeur comprise entre 4,3 .. 5,0. L'adoption de cette procédure normalisée de préparation du fromage frais a donné lieu à des produits de composition physico-chimique régulière et de qualité microbiologique satisfaisante. L'analyse sensorielle du fromage frais a montré que les produits élaborés à partir du lait recombiné uniquement (100%), ont été moins appréciés que ceux préparés à partir du lait recombiné additionné de 25 ou 50% de lait frais.Manufacture of fresh cheese from recombined milkThis study was carried out to evaluate the possibility of making fresh cheese from recombined milk. For this preparation, recombined milk was pasteurized and cooled overnight at 6°C to improve the powder rehydration. Then, milk was inoculated with 3% of a lactic starter composed of L.lactis subsp. lactis, L. lactis subsp.lactis var. diacetylactis and L. ca sei subsp. casei, and kept at 30 - 3TC to activate fermentation. At pH 5,0 - 5,5, the rennet was added and moulding was realized at ambient temperature when the pH reached a value of 4,3 to 5,0. Standardization of the processing gave fresh cheese with a regular chemical composition and a satisfactory microbiological quality. The sensory evaluation of fresh cheese showed that the products made with 100% recombined milk were less appreciated than those prepared from recombined milk added up with 20 to 25% fresh milk

Assessing the effect of organic residue quality on active decomposing fungi in a tropical Vertisol using 15N-DNA stable isotope probing

15N-DNA stable isotope probing (15N-DNA-SIP) combined with 18S rRNA gene-based community analysis was used to identify active fungi involved in decomposition of 15N-labeled maize and soybean litter in a tropical Vertisol. Phylogenetic analysis of 15N-labeled DNA subjected to 18S rRNA gene-based community fingerprinting showed that organic residue quality promoted either slow (i.e. Penicillium sp., Aspergillus sp.) or fast growing (i.e. Fusarium sp., Mortierella sp.) fungal decomposers in soils treated with maize or soybean residues, respectively, whereas Chaetomium sp. were found as dominant decomposers in both residue treatments. Therefore, we have clear evidence that specific members of the fungal community used 15N derived from the two different organic resources for growth and stimulated early decomposition of maize or soybean decomposition. In conclusion, our study showed that 15N-DNA-SIP-based community analyses cannot only follow the flow of N from organic resources into bacteria, but also into the actively decomposing fungal communities of soils