A Global Convergence Result with Applications to Periodic Solutions

AbstractWe establish a global convergence result and then apply it to show that under appropriate hypotheses every positive solution of the difference equation xn+1=∑i=0mAixn−2i,n=0,1,…,converges to a period two solution

Solutions Form for Some Rational Systems of Difference Equations

We deal with the form of the solutions for the following systems of rational difference equations , , with nonzero real numbers initial conditions. Also we investigate some properties of the obtained solutions and present some numerical examples

On a System of Difference Equations of an Economic Model

We study some qualitative properties of the solutions of a system of difference equations, which describes an economic model. The study of the local stability of the equilibrium points is carried out. We give some important results of the invariant and the boundedness of the solutions to the considered system. The global convergence of the solutions is presented and investigated

Daily flight activity rhythms of the peach and mediterranean fruit flies using sexual and olfactory attractants

The periodicity of insect activity is affected by endogenous and exogenous factors, and these factor thresholds often limit its activity. The flight activity within 24 h circadian rhythm is often influenced by light, whereas the abundance is affected by temperature. This study aimed to hourly follow the flight activity of the peach (PFF) and Mediterranean (MFF) fruit flies, at guava orchard, using sexual and olfactory attractants. The flight of PFF males usually started before that of females, whereas that of MFF males was in the same time as females. As temperature rose above 30 °C, the flight activity of males affected, but that of females not. Thus, flight activities of males were negatively, and females were positively, correlated with temperature. On the contrary, males were positively, and females were negatively, correlated with relative humidity. The sexual attractant attracted more PFF males than MFF, but the olfactory attractants attracted more PFF females than MFF. The highest male captures were between 7:00 am and 10:00 am, and females between 11:00 am and 5:00 pm, suggesting males fly actively during the morning to locate their mates, whereas females fly actively during the afternoon to locate their food and/or distribute their eggs. This also suggests that PFF and MFF are diurnal species. For management of both species, the spray treatments therefore should be taken during the time interval 7:00 am and 10:00 am for males (to disrupt mating) and 11:00 am and 5:00 pm for females (to disrupt feeding and oviposition)

Oleuropein and oleic acid: A novel emerging dietary target for human chronic diseases

263-268The human chronic metabolic disease is predominantly associated with the disturbance in the lipid, proteins and nucleic acid biological balance due to the attack of free radicals generated from oxidative stress. Currently, the available synthetic antioxidants are synthesized by food industries are very effective and inexpensive but as chronic use, it exhibits many toxicological health effects like synthetic drugs. Hence, plant origin antioxidants gained increasing attention all over the world. In this regards, Olive tree (Olea europaea L.) belongs to Oleaceae family and its by-products such as olive leaves and olive oil are highly focused by many researcher due to its potential therapeutic effects in a reversal of various chronic diseases without any side effects. Oleuropein and Oleic acid are the major components in the olive by products and attributes olive as a holly natural remedy and also olive oil considered as a potential food ingredient in the Mediterranean diet. The fat content in olive fruits is higher than olive leaves. Whereas, the protein ratio is higher in olive leaves and more abundance of Oleuropein, which contributes major health benefits as compared to olive oil. Oleic acid with high MUFA ratio contributes to the major health benefits of olive oil to several human chronic diseases

Priabonian Sharks and Rays (Late Eocene: Neoselachii) From Minqar Tabaghbagh In The Western Qattara Depression, Egypt

http://deepblue.lib.umich.edu/bitstream/2027.42/90948/1/Contributions32no06-c04-30-2012.pd

SYNTHESIS, ANTICANCER ACTIVITY AND MOLECULAR DOCKING STUDY OF NOVEL 1, 3-DIHETEROCYCLES INDOLE DERIVATIVES

Objective: The present work aimed to synthesize some new 1, 3-diheterocyles indolyl derivatives and study their cytotoxic activity. In addition, explore the probability of the most promising antiproliferative compounds to inhibit TopoI enzyme theoretically via molecular docking study.Methods: Reaction of ethyl 2-(3-formyl-1H-indol-1-yl)acetate (1) with 2-cyanoacetic acid hydrazide, 3-amino-5-pyrazolone and 2'-acetyl-2-cyanoacetohydrazide in an equal molar ratio led to the formation of compounds 2, 6, 8 and 10, respectively, which in turn reacted with another molecule of 2-cyanoacetic acid hydrazide and/or 3-amino-5-pyrazolone (1:1 molar ratio) to give novel series of 1,3-dipyrazole indole derivatives 3, 7, 9 and 11, respectively. On the other hand, Knoevenagel condensation of 1 with malononitrile gave ethyl 2-(3-(2, 2-dicyanovinyl)-1H-indol-1-yl) acetate (11). Reaction of 11 with 2-cyanoacetic acid hydrazide, 3-amino-5-pyrazolone, hydrazine hydrate, urea, thiourea and/or guanidine yielded 1, 6-diaminopyridine 12, pyrano(2,3-c)pyrazole 14, pyrazole 16 and pyrimidine derivatives 18a-c, respectively. Reaction of the latter compounds with 3-amino-5-pyrazolone furnished a novel series of 1, 3-diheterocycle indole derivatives 13, 15, 17 and 19a-c, respectively. Ten new target compounds 3, 6, 8, 10, 13, 15, 17 and 19a-c were tested for in vitro antiproliferative activity against A-549, MCF7, HCT-116 and HEPG2 cancer cell lines. In addition, molecular docking study of the most promising antiproliferative compounds against human DNA Topoisomerase I (PDB ID: 1T8I) theoretically is discussed.Results: Compounds 3, 6, 8 and 17 showed potent in vitro antiproliferative activity. Docking scores of the latter compounds were observed better than co-crystalline ligand.Conclusion: Further work is recommended to confirm the inhibition of TopoI in a specific bioassay

Isolation of biologically active metabolites from Bougainvillea spectabilis Willd. cultivated in Egypt

Bougainvillea spectabilis Willd.  is an ornamental plant cultivated in tropical, subtropical regions and other places as Egypt. The present study aimed to perform bioassay guided fractionation and isolation of some of the bioactive compounds from the Egyptian cultivate. The total ethanol extracts of the leaves (T.ET.L.), stems (T.ET.S.) and flowers (T.ET.F.) were screened for some pharmacological activities viz. in vivo anti-oxidant and anti-hepatotoxic, in addition to in vitro cytotoxic activities. The anti-oxidant effect was assessed by measuring serum glutathione level (GSH) in alloxan-induced diabetic rats. The anti-hepatotoxic activity was evaluated via measuring serum markers level viz. alanine aminotransferase (ALT), aspartate aminotransferase (AST), and alkaline phosphatase (ALP) in CCl4-induced hepatotoxicity in rats. In vitro cytotoxicity of the different extracts was estimated for liver cancer cell line (HEPG2) adopting Sulforhodamine B stain assay. T.ET.L. exhibited significantly potent anti-oxidant and anti-hepatotoxic activities, while T.ET.S. showed the highest cytotoxic activity. Through biological guided fractionation, leaves and stems were subjected to successive solvent extraction, whereas the leaves ethyl acetate (Et.Ac.L.) and the stems ethanol 70% (Et.70%S.) extracts showed highly potent activities. Thus, different chromatographic techniques were performed on Et.Ac.L. and Et.70%S. extracts leading to the isolation of five bioactive metabolites. Three flavonoids were isolated from Et.Ac.L.; genistein-7-O-rutinoside (1), formononetin-7-O-rutinoside (2) and myricetin (3), while orobol-7-O-glucoside (4) and hesperidin (5) were isolated from Et.70%S. This work demonstrated the importance of the plant as a promising anti-oxidant, anti-hepatotoxic and cytotoxic product for nutraceutical use