Let/. It :0 ---0 G be any two self maps of a compact connected oriented Lie group G. In this paper, for each positive integer k , we associate an integer with fk,hi . We relate this number with Lefschetz coincidence number. We deduce that for any two differentiable maps f, there exists a positive integer k such that k 5.2+1 , and there is a point x C G such that ft (x) = (x) , where A is the rank of G . Introduction Let G be an n-dimensional com -pact connected Lie group with multip-lication p ( .e 44:0 xG--+G such that p ( x , y) = x.y ) and unit e . Let [G, G] be the set of homotopy classes of maps G G . Given two maps f , f G ---• Jollowing [3], we write f. f 'to denote the map G-.Gdefined by 01.11® =A/WO= fiat® ,sea Given a point g

In this research, the methods of Kernel estimator (nonparametric density estimator) were relied upon in estimating the two-response logistic regression, where the comparison was used between the method of Nadaraya-Watson and the method of Local Scoring algorithm, and optimal Smoothing parameter λ was estimated by the methods of Cross-validation and generalized Cross-validation, bandwidth optimal λ has a clear effect in the estimation process. It also has a key role in smoothing the curve as it approaches the real curve, and the goal of using the Kernel estimator is to modify the observations so that we can obtain estimators with characteristics close to the properties of real parameters, and based on medical data for patients with chro

TRIPS agreement was The first to apply protection by patents. However, this type of protection, which grants exclusive and monopoly rights to patent owners, came at the expense of developing countries which are considered rich in biodiversity and also at the expense of traditional and poor knowledge of modern technologies. The release of new plant varieties has led to the emergence of biopiracy and looting of the rights of developing countries without a license

A UV-Vis spectrophotometry method was developed for the determination of metoclopramide hydrochloride in pure and several pharmaceutical preparations, such as Permosan tablets, Meclodin syrups, and Plasil ampoules. The method is based on the diazotization reaction of metoclopramide hydrochloride with sodium nitrate and hydrochloric acid to yield the diazonium salt, which is then reacted with 3,5-dimethyl phenol in the presence of sodium hydroxide to form a yellow azo dye. Calibration curves were linear in the range from 0.3 to 6.5 µg/mL, with a correlation coefficient of 0.9993. The limits of detection and quantification were determined and found to be 0.18 and 0.61 µg/mL, respectively. Accuracy and precision were also determined b

Copper selenide (Cu2Se) thin films were prepared by thermal evaporation at RT with thickness 500 nm. The heat-treating for (400 &500) K for the absorber layer has been investigated. This research includes, studying the structural properties of X-ray diffraction (XRD) that show the Cu2Se thin film (Cubic) and has a polycrystalline orientation prevalent (220). Moreover, studying the effect of annealing on their surface morphology properties by using Atomic Force Microscopy AFM. Optical properties were considered using the transmittance and absorbance spectra had been recorded when wavelength range (400 - 1000) nm in order to study the absorption coefficient and energy gap. It was found that these films had allowed direct transitio

In the present work studies were carried out to extract a cationic dye (Methylene Blue MB) from an aqueous solution using emulsion liquid membrane process (ELM). The organic phase (membrane phase) consists of Span 80 as emulsifier, sulfuric acid solution as stripping agent and hexane as diluent. 

In this study, important factors influencing the extraction of methylene blue dye were studied. These factors include H₂SO₄ concentration in the stripping phase, agitation speed in the dye permeation stage, Initial dye concentration and diluent type.

   More than (98%) of Methylene blue dye was extracted at the following conditions: H₂SO₄ concentration (1.25) M, agitation

A novel encapsulated deep eutectic solvent (DES) was introduced for biodiesel production via a two-step process. The DES was encapsulated in medical capsules and were used to reduce the free fatty acid (FFA) content of acidic crude palm oil (ACPO) to the minimum acceptable level (< 1%). The DES was synthesized from methyltriphenylphosphonium bromide (MTPB) and p-toluenesulfonic acid (PTSA). The effects pertaining to different operating conditions such as capsule dosage, reaction time, molar ratio, and reaction temperature were optimized. The FFA content of ACPO was reduced from existing 9.61% to less than 1% under optimum operating conditions. This indicated that encapsulated MTPB-DES performed high catalytic activity in FFA esterificatio