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.
Long memory analysis is one of the most active areas in econometrics and time series where various methods have been introduced to identify and estimate the long memory parameter in partially integrated time series. One of the most common models used to represent time series that have a long memory is the ARFIMA (Auto Regressive Fractional Integration Moving Average Model) which diffs are a fractional number called the fractional parameter. To analyze and determine the ARFIMA model, the fractal parameter must be estimated. There are many methods for fractional parameter estimation. In this research, the estimation methods were divided into indirect methods, where the Hurst parameter is estimated fir
... Show More
Piracy on phonograms is now, rightly, the crime of the electronic age. Despite the protection sought by States to provide for such registrations, whether at the level of national legislation or international agreements and conventions, but piracy has been and continues to pose a significant threat to the rights of the producers of those recordings, especially as it is a profitable way for hackers to get a lot of money in a way Illegal, which is contrary to the rules of legitimate competition. Hence, this research highlights the legal protection of producers of phonograms in light of the Iraqi Copyright Protection Act No. (3) of 1971, as amended.
One of the diseases on a global scale that causes the main reasons of death is lung cancer. It is considered one of the most lethal diseases in life. Early detection and diagnosis are essential for lung cancer and will provide effective therapy and achieve better outcomes for patients; in recent years, algorithms of Deep Learning have demonstrated crucial promise for their use in medical imaging analysis, especially in lung cancer identification. This paper includes a comparison between a number of different Deep Learning techniques-based models using Computed Tomograph image datasets with traditional Convolution Neural Networks and SequeezeNet models using X-ray data for the automated diagnosis of lung cancer. Although the simple details p
... Show More
(1)
Over the past few decades, the surveying fieldworks were usually carried out based on classical positioning methods for establishing horizontal and vertical geodetic networks. However, these conventional positioning techniques have many drawbacks such as time-consuming, too costly, and require massive effort. Thus, the Global Navigation Satellite System (GNSS) has been invented to fulfill the quickness, increase the accuracy, and overcome all the difficulties inherent in almost every surveying fieldwork. This research assesses the accuracy of local geodetic networks using different Global Navigation Satellite System (GNSS) techniques, such as Static, Precise Point Positioning, Post Processing Kinematic, Session method, a
... Show More
(2)
(1)
The paper generates a geological model of a giant Middle East oil reservoir, the model constructed based on the field data of 161 wells. The main aim of the paper was to recognize the value of the reservoir to investigate the feasibility of working on the reservoir modeling prior to the final decision of the investment for further development of this oilfield. Well log, deviation survey, 2D/3D interpreted seismic structural maps, facies, and core test were utilized to construct the developed geological model based on comprehensive interpretation and correlation processes using the PETREL platform. The geological model mainly aims to estimate stock-tank oil initially in place of the reservoir. In addition, three scenarios were applie
... Show More
(7)
(2)
Alginate is one of the natural biopolymers that is widely used for drug formulations, combination of alginate with other polymers, such as gum acacia, pectin, and carrageenan can increase mechanical strength, therefore, can reduce leakage of the encapsulated active pharmaceutical ingredient from the polymer matrix. Interaction of alginate and these polymers can occur via intermolecular hydrogen bonds causing synergism, which is determined from the viscosity of polymer mixture.
Alginate was combined with gum acacia/pectin/carrageenan in different blending ratios (100:0, 75:25, 50:50, 25:75, and 0:100) with and without addition of CaCl2. The synergism effect is obtained from the design of experimental (DoE), and calculati
... Show More
(11)
(7)
Samples of gasoline engine oil (SAE 5W20) that had been exposed to various oxidation times were inspected with a UV-Visible (UV-Vis) spectrophotometer to select the best wavelengths and wavelength ranges for distinguishing oxidation times. Engine oil samples were subjected to different thermal oxidation periods of 0, 24, 48, 72, 96, 120, and 144 hours, resulting in a range of total base number (TBN) levels. Each wavelength (190.5 – 849.5 nm) and selected wavelength ranges were evaluated to determine the wavelength or wavelength ranges that could best distinguish among all oxidation times. The best wavelengths and wavelength ranges were analyzed with linear regression to determine the best wavelength or range to predict oxidation t
... Show More
(16)
(16)
This report explores emerging techniques to boost multimedia transfer effectiveness, given the escalating need for improved quality and performance in multimedia interactions. The analysis involves a thorough literature assessment and comparison of present strategies to pinpoint key tendencies and propose novel approaches. The methodology involves examining recent technological enhance ments in video coding standards, quality appraisal methods, and compression tech niques. Specific domains investigated comprise firmware component architectures, 4D indexing structures, and iterative filtering frameworks. The study in addition weighs tradeoffs between video quality, encoding intricacy, and bitrate demands. Key determinations consist of
... Show More