In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:

 respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.

The Cu(II) was found using a quick and uncomplicated procedure that involved reacting it with a freshly synthesized ligand to create an orange complex that had an absorbance peak of 481.5 nm in an acidic solution. The best conditions for the formation of the complex were studied from the concentration of the ligand, medium, the eff ect of the addition sequence, the eff ect of temperature, and the time of complex formation. The results obtained are scatter plot extending from 0.1–9 ppm and a linear range from 0.1–7 ppm. Relative standard deviation (RSD%) for n = 8 is less than 0.5, recovery % (R%) within acceptable values, correlation coeffi cient (r) equal 0.9986, coeffi cient of determination (r2) equal to 0.9973, and percentage capita

Leucine amino peptidases (LAP; EC 3.4.11.1) constitute a diverse set of exopeptidases that catalyze the hydrolysis of leucine residues from the amino-terminal of protein or peptide substrates, (LAP) are present in animals, plants, and microbes. In this study, leucine amino peptidase was purified partial from Arachis hypogaea seeds by using gel filtration chromatography Sephadex G-100. The enzyme was purified 3.965 fold with a recovery of 29.4%. Its pH and temperature optimum were(8.7) and (37oC), respectively. The results show novel properties of LAP from Arachis hypogaea L. or peanut. The Km value for LAP (77 mM), with V max (1538 m mole min-1). We recommend a separate isoenzymeof the enzyme (LAP) from Arachis hypogaea on L. peanut seeds a

Endoglucanase produced from Aspergillus flavus was purified by several steps including precipitation with 25 % ammonium sulphate followed by Ion –exchange chromatography, the obtained specific activity was 377.35 U/ mg protein, with a yield of 51.32 % .This step was followed by gel filtration chromatography (Sepharose -6B), when a value of specific activity was 400 U/ mg protein, with a yield of 48 %. Certain properties of this purified enzyme were investigated, the optimum pH of activity was 7 and the pH of its stability was 4.5, while the temperature stability was 40 °C for 60 min. The enzyme retained 100% of its original activity after incubation at 40 °C for 60 min; the optimum temperature for enzyme activity was 40 °C.

The activity of peroxidase (POD) in cabbage was evaluated using
spectrophotometric method. The enzyme was extracted from the cabbage leaves
with 0.1 M phosphate buffer solution pH 7. 0 . POD activity was determined using
(O-dianisidine) as a substrate. The effects of the amounts of enzyme extract,
substrate concentration, pH and temperature were investigated. The highest activity
of POD was recored at 2 mg/ml. The highest activity of POD was optimized with
16 mM O-dianisidine, The optimum pH was 7.0 for POD , The optimum
temperature was 30°C for POD. These optimum conditions were used to
determined the enzyme activities in cabbage sample. Acetone fractionated
peroxidase from crude extract of Brassica oleracea

Beta-lactamase was purified from local isolate Klebsiella pneumonia by several steps included precipitation with ammonium sulphate at 20-40% saturation, DEAE- ion exchange chromatography and gel filtration on Sephacryl S-200 column. The obtained purification fold and recovery were 32.66; 47.04% respectively. The characterization of the purified beta-lactamase showed that the molecular weight was about 4000 daltons as determined by gel filtration.Purified enzyme had an optimal pH of 7 for activity and an optimal stability between pH 6.5-7.5, results shows that the optimal temperature appear to be 35 ? C .During storage the enzyme retained 72% at -20 ? C and retained 25% of the activity at the same period at 4 ? C.

Probiotics are live microbes that give many health benefits to human beings and animals, the most studied and commonly used probiotics are Gram-positive bacteria; lactobacilli and bifidobacteria. At nowadays, Lactobacillus spp. constitute more than two-thirds of the total numbers of probiotic species. The present study aimed to characterize Lactobacillus that locally isolated from human mouth and feces as probiotics. A total of three Lactobacillus isolates; Lactobacillus fermentum Lb2, Lactobacillus rhamnosus Lb9, and Lactobacillus paracasei Lb10 were investigated in respect to acid and bile salts tolerance, antibiotics susceptibility, and cell surface hydrophobicity in vitro using bacterial adhesion to hydrocarbons method. In compa

Oxidation of sulfur compounds in fuel followed by an adsorption process were studied using two modes of operation, batch mode and continuous mode (fixed bed). In batch experiment oxidation process of kerosene with sulfur content 2360 ppm was achieved to study the effect of amount of hydrogen peroxide(2.5, 4, 6 and 10) ml at different temperature(40, 60 and 70)°C. Also the effect of amount acetic acid was studied  at the optimal conditions of the oxidation step(4ml H₂O₂ and 60 °C).Besides, the role of acetic acid different temperatures(40, 60, 70) °C and 4ml H₂O₂, effect of reaction time(5, 30, 60, 120, 300) minutes at temperatures(40,60) °C, 4ml H₂O₂ and 1 mlHAC)&

Some new mono isoimides of asymmetrical pyromillitdiimide derived from pyromellitic dianhydride were synthesized and studied by their melting points, FTIR, and 1HNMR spectroscopy and CHN analysis (for some of them) and it was proved that the mechanism of the formation of these isoimides followed, the mechanism suggested by Cotter et al. by using N, N─-dicyclohexylcarbodiimide as dehydrating agent, in spite of the groups attached to the phenyl moiety as mentioned in literatures.

    Some new mono isoimides of asymmetrical pyromillitdiimide derived from pyromellitic dianhydride were synthesized and studied by their melting points , FTIR , and 1HNMR spectroscopy and C.H.N analysis (for some of them) and it was proved that the mechanism of the formation of these isoimides followed , the mechanism suggested by Cotter et al . by using N, N─- dicyclohexylcarbodiimide as dehydrating agent , in spite of the groups attached to the phenyl moiety as mentioned in literatures .