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.
In this article, performing and deriving te probability density function for Rayleigh distribution is done by using ordinary least squares estimator method and Rank set estimator method. Then creating interval for scale parameter of Rayleigh distribution. Anew method using is used for fuzzy scale parameter. After that creating the survival and hazard functions for two ranking functions are conducted to show which one is beast.
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The study examined the assessment of raw water and drinking water projects of Diyala Governorate for the year 2017, amounting to (24) projects, The average per capita supply of potable water (0.396 m3 / day/person), which is less than the global standard for the average per capita of drinking water, and constitute water rumors within the network of water transport in the province (3%), and the water of raw and drinking value within the limits allowed to be used by Iraq and the global indicators of {Total acidity, alkaline, acidic function, chlorides, magnesium, Electrical conductivity, total soluble salts, sodium, potassium, sulfates, turbidity other than (raw water)}. While the index of calcium only a value higher than the limits
... Show MoreThis article will address autoclave design considerations and
manufacturing working with high pressure low temperature
supercritical drying technique to produce silica aerogel. The design
elects carbon dioxide as a supercritical fluid (31.7 oC and 72.3 bar).
Both temperature and pressure have independently controlling
facility through present design. The autoclave was light weight (4.5
kg) and factory-made from stainless steel. It contains a high pressure
window for monitoring both transfer carbon dioxide gas to liquid
carbon dioxide and watching supercritical drying via aerogel
preparation process. In this work aerogel samples were prepared and
the true apparent densities, total pore volume and pore size
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This article aims to explore the importance of estimating the a semiparametric regression function ,where we suggest a new estimator beside the other combined estimators and then we make a comparison among them by using simulation technique . Through the simulation results we find that the suggest estimator is the best with the first and second models ,wherealse for the third model we find Burman and Chaudhuri (B&C) is best.
A new two-way nesting technique is presented for a multiple nested-grid ocean modelling system. The new technique uses explicit center finite difference and leapfrog schemes to exchange information between the different subcomponents of the nested-grid system. The performance of the different nesting techniques is compared, using two independent nested-grid modelling systems. In this paper, a new nesting algorithm is described and some preliminary results are demonstrated. The validity of the nesting method is shown in some problems for the depth averaged of 2D linear shallow water equation.
Construction and operation of (2 m) parabolic solar dish for hot water application were illustrated. The heater was designed to supply hot water up to 100 oC using the clean solar thermal energy. The system includes the design and construction of solar tracking unit in order to increase system performance. Experimental test results, which obtained from clear and sunny day, refer to highly energy-conversion efficiency and promising a well-performed water heating system.
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The human kidney is one of the most important organs in the human body; it performs many functions
and has a great impact on the work of the rest of the organs. Among the most important possible treatments is
dialysis, which works as an external artificial kidney, and several studies have worked to enhance the
mechanism of dialysate flow and improve the permeability of its membrane. This study introduces a new
numerical model based on previous research discussing the variations in the concentrations of sodium,
potassium, and urea in the extracellular area in the blood during hemodialysis. We simulated the differential
equations related to mass transfer diffusion and we developed the model in MATLAB Simu
In this work ,medical zinc oxide was produced from zinc scraps instead of traditional method which used for medical applications such as skin diseases, Iraq is importing around 50 ton/year for samarra plant the producted powder has apartical size less than 5 micron and the purity was more than 99.98%,also apilot plant of yield capacitiy 15 kg/8hours wsa designed and manufactured .
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