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.
Sentiment analysis refers to the task of identifying polarity of positive and negative for particular text that yield an opinion. Arabic language has been expanded dramatically in the last decade especially with the emergence of social websites (e.g. Twitter, Facebook, etc.). Several studies addressed sentiment analysis for Arabic language using various techniques. The most efficient techniques according to the literature were the machine learning due to their capabilities to build a training model. Yet, there is still issues facing the Arabic sentiment analysis using machine learning techniques. Such issues are related to employing robust features that have the ability to discrimina
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The fluctuation and expansion ratios have been studied for cylindrical gas-solid fluidized columns by using air as fluidizing medium and Paracetamol as the bed material. The variables were the column diameter (0.0762, 0.15, and 0.18 m), static bed height (0.05, 0.07, and 0.09 m), and air velocity to several times of minimum fluidization velocity. The results showed that both the fluctuation and expansion ratios had a direct relation with air velocity and an inverse one with column diameter and static bed height. A good agreement was between the experimental results and the calculated values by using the correlation equations from the literature.
A Pap test can identify the pre-cancerous and cancerous problem in the vagina and uterine cervix. Cervical tumour is the easiest gynecologic disease to be diagnosed, treated and prevented using regular screening tests and follow-up. This review aimed to explore the opinion of specialists about cytological changes and the precancerous lesions with Pap smear test and visual inspection of the cervices, also to determine the relationship of this malignancy with demographic characteristics of patients. Results showed that few cervical cancer and pre-cancer were with women in postmenopausal period, but more were with women in the premenopausal period. Visual inspection of the cervix can show erosion lesions by gross inspection. Upon cytology exam
... Show MoreData-driven models perform poorly on part-of-speech tagging problems with the square Hmong language, a low-resource corpus. This paper designs a weight evaluation function to reduce the influence of unknown words. It proposes an improved harmony search algorithm utilizing the roulette and local evaluation strategies for handling the square Hmong part-of-speech tagging problem. The experiment shows that the average accuracy of the proposed model is 6%, 8% more than HMM and BiLSTM-CRF models, respectively. Meanwhile, the average F1 of the proposed model is also 6%, 3% more than HMM and BiLSTM-CRF models, respectively.
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Carrying strength is one of the important physical capabilities in the field of competitive sports, which affects the success of the sports training process and helps players to continue to perform skillfully, physically and tactically for as long as possible, and the capacity for endurance varies depending on the type of sports activities, it may sometimes be very short. And with a high level of intensity, such as gymnastics and wrestling movements, and it may be long, and with a medium level of intensity, as in basketball, football and other games. The research community represents a sample of Baghdad players for teams (football, basketball, handball, volleyball, wrestling, weightlifting) and for the sports season (2017-2018 AD) for ages
... Show MoreThe aim of the present study was to develop theophylline (TP) inhalable sustained delivery system by preparing solid lipid microparticles using glyceryl behenate (GB) and poloxamer 188 (PX) as a lipid carrier and a surfactant respectively. The method involves loading TP nanoparticles into the lipid using high shear homogenization – ultrasonication technique followed by lyophilization. The compositional variations and interactions were evaluated using response surface methodology, a Box – Behnken design of experiment (DOE). The DOE constructed using TP (X1), GB (X2) and PX (X3) levels as independent factors. Responses measured were the entrapment efficiency (% EE) (Y1), mass median
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Solutions of dyes Rhodamine 6G (Rh6G) and Coumarin480(C480) were prepared at five concentrations (1x10-3, 5x10-4, 1x10-4, 5x10-5 and1x10-5) mol/l, the mixing was stirred to obtain on a homogenous solution, the(poly methyl-methacrylate) (PMMA) was solved by chloroform solvent with certain ratio, afterward (PMMA+Rh6G) and (PMMA+C480) thin films were prepared by casting method on glass block which has substrate with dimensions (7.5 x2.5)cm2, the prepared samples were left in dark place at room temperature for 24 hours to obtain uniform and homogenous thin films. UV-VIS absorption spectra, transmission spectra and fluorescence spectra were done to measure linear refractive index and linear absorption coefficient. The nonlinear optical proper
... Show MoreThe present work concerns with simulating unsteady state equilibrium model for production of methyl oleate (biodiesel) from reaction of oleic acid with methanol using sulfuric acid as a catalyst in batch reactive distillation. MESHR equations of equilibrium model were solved using MATLAB (R2010a). The validity of simulation model was tested by comparing the simulation results with a data available in literature. UNIQUAC liquid phase activity coefficient model is the most appropriate model to describe the non-ideality of OLAC-MEOH-MEOL-H2O system. The chemical reactions rates results from EQ model indicating the rates are controlled by chemical kinetics. Several variables was studied such as molar ratio of methanol to oleic acid 4:1, 6:1
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