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 EC and a differ-entiable map F: G G , write GA to denote the tangent space of G at g [4,p.10] , and denote by d x F the linear map rig F :Tx0 T, (x)G induced by F , it is called the differential of Fat g [4,p.22]. Let LA, Rx :0 G be respec-tively the left translation Lx(i)=4..(g,e) , and the right translation Rx(1)./..(gcg). Then there is a natural homomorphism Ad ,the adjoin representation, from G to GL(G•), (the group of nonsingular linear transformations of Qdefined as follows:- Ad(g)= deRe, od,Lx. Note that d xRc, ad.; =d(4,( Lx(e)))0 de; =d.(4, 04)=4(40 Re) = d(4(4, (e)))0 (44, =d ar, o (44, . Since G is connected , the image of Ad belongs to the connected component of G(G)containing the identity,i.e. for each g E 0, detAd(g) > 0 . By Exercise Al • Dr.-Prof.-Department of Mathematics- College of Science- University of Baghdad. •• Dr.-Department of Mathematics- College of Science for Woman- University of Baghdad.
This paper provides an attempt for modeling rate of penetration (ROP) for an Iraqi oil field with aid of mud logging data. Data of Umm Radhuma formation was selected for this modeling. These data include weight on bit, rotary speed, flow rate and mud density. A statistical approach was applied on these data for improving rate of penetration modeling. As result, an empirical linear ROP model has been developed with good fitness when compared with actual data. Also, a nonlinear regression analysis of different forms was attempted, and the results showed that the power model has good predicting capability with respect to other forms.
Art of legend was arisen out of pillars of theatre which casts light on those legends that were written to glorify powers and situations surpass level of human beings . So we find that legend was transformed through its doctrine sides over level of concept and realization on field of subjects where by which Greek theatre was founded . As soon as it was adopted by drama art as legendary ritual phenomena with its stories . With that modes of social , spiritual expressions were differentiated within communities , peoples over all different countries and civilizations . This explains us the apparent difference in cases of legends , alike if they were within thoughtful , social or cultural sides between civilizations . Since drama art is mirr
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Objective: To establish growth curve for a sample of infertile women and to assess Body Mass Index.
Methodology: Non-probability (purposive sample) of (100) infertile women, who visit Kamal Al-Samaraee
Hospital/ fertility and IVF center . The data are collected through the use of constructed questionnaire, which
consists of two parts. Part 1: consists of (5) items about demographic characteristics, part 2: consists of (4) items
about reproductive status, descriptive statistical analysis procedures (frequency, percentage, Contingency
coefficients, polynomial cube order).
Results: Revealed that the infertile women in the study group had decrease in their Body Mass Index with aging
(with increase of infertility duration
Objective: To evaluate nurses' practices concerning isolation techniques for Adult Leukemic Patients (ALP).
Methodology: A descriptive study was carried out at the isolation rooms at leukemic wards in Baghdad Teaching
Hospitals, starting from Jan. 27th 2008 up to the 27th of Apr. 2008. To achieve the objectives of study, a non-probability
"purposive" sample of (50) nurse was selected out of four Teaching Hospitals in Baghdad city were selected according
to the criteria of the study sample.
The study instrument consisted of two major parts. It is based on the review of literature. First is concerned with
demographic data for nurses; and the second part is observational tool (checklist) is composed of (83) item. The conte
Learn new methods of teaching mathematics contribute to raising the level of pupils to acquire mathematical concepts primary stage
Attempt advancement in the level of mathematics teaching for the better through the use of modern teaching strategies. The research aims at the progress in the acquisition of mathematical concepts schoolgirls after subjecting the fourth grade to teach in active learning strategies, the number of research sample (60) schoolgirl, by (30) schoolgirl experimental group and 30 pupils of the control group. Clear from the results shown the presence of a statistically significant difference between the acquisition of concepts of schoolgirls two groups (experimental and control) for the benefit of pupils of the exp
An experimental study was carried out to improve the surface roughness quality of the stainless steel 420 using magnetic abrasive finishing method (MAF). Four independent operation parameters were studied (working gap, coil current, feed rate, and table stroke), and their effects on the MAF process were introduced. A rotating coil electromagnet was designed and implemented to use with plane surfaces. The magnetic abrasive powder used was formed from 33%Fe and 67% Quartz of (250µm mesh size). The lubricant type SAE 20W was used as a binder for the powder contents. Taguchi method was used for designing the experiments and the optimal values of the selected parameters were found. An empirical equation representing the r
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In this research, beam expander, BEX, is explained and designed for illuminating the
remote flying target. The BEX is optically designed to be suited for Nd:YAG laser of given
specifications. The BEX is modified to be zoom one to meet the conditions of preventing the
receiving unit; i.e the photodetector, from getting saturated at near and far laser tracking.
Decollimation could be achieved by automatic motor, which controls zoom lens of the BEX
according to the required expansion ratio of beam expander
As a well-known oral and intravenous antifungal, voriconazole (VRN) has an extensive history of usage in the medical field. Solid lipid nanoparticles (SLNs) have been produced to treat ocular fungal keratitis in the eye. A 32Box-behnken design was used to produce a variety of new formulas for hot-melt extrusion. The SLNs were evaluated by entrapment efficiency (EE percent), particle size (PS), polydispersity index (PDI), and zeta potential (ZP). A series of in-vitro and in-vivo studies were carried out on the new formula. The produced vesicles’ EE, PS, PDI, and ZP values were all good. SLNs eye drops were numerically adjusted to include carbopol, a stabilizer, lipids, and a surfactant, among other substances. ZP of -36.5 ± 0.20 m
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: zonal are included in phraseological units, form metaphorical names for a person, give him various emotional and evaluative characteristics. This article examines the topic of zoomorphic metaphors that characterize a person in the Russian and Arabic languages in the aspect of their comparative analysis, since the comparative analysis of the metaphorical meanings of animalisms is an important method for studying cultural linguistics, since zoomorphic metaphors are a reflection of culture in a language.