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.
Abstract:
The internal control is the tool through which it is possible to verify and ensure the implementation of tasks in accordance with the established plans and programs and to evaluate the level of performance that is implemented within the different companies.
A guarantee from the supplier with the absence of a specialized technical committee that follows up the stages of implementing the contract and disbursing all amounts of financial dues to the supplier before completing the implementation of the contract and overlooking the non-implementation of some clauses of the contract by the committee in charge of
... Show MoreImpact Resistance training with and against the trajectory of the motor in some physical abilities and the BioA 100-meter, mechanical racing run for young people. That Training Jogging for different distances Melt -Rubber ropes According to direction and reversed movement With Obligations To the border of scientific of components Pregnancy Training represents to a training trend Aimed To Events Developments In The link between Starting and running, According to the specific mechanical requirements Have It Of Development of force Explosive and quick and their components which To give Border To the level Special speed for Stages Sprint run 100 m and amounts Efforts Required instantaneous powers. Noted Researcher In That Over there Repeat For
... Show MoreThe study aimed to determine of some Optimum conditions for bioremediation and removing of seven mineral elements included hexavalent chromium, nickel, cobalt, cadmium, lead, iron and copper as either alone or in group by living and heat treated cells of baker’s yeast Saccharomyces cerevisiae. The dried baker's yeast from Aldnaamaya China Company was used in this study. Biochemical tests was used to ensure yeast belonging to S. cerevisiae and then used to remove the mentioned mineral elementes under different conditions which included incubation period, pH, and temperature. It was found that the best of these conditions was 60 minutes for duration of incubation, 6 for pH, 25 ᵒC for temperature. During the study the behavior of living
... Show MoreThe current research attempts to examine the relationship between social-psychological conflict and their relation to family upbringing approaches among the adolescents of intermediate stage according to sex and economical level. To do this, the researcher prepared a questionnaire to measure social-psychological conflict that consisted of (32) item divided on four dimensions, and also she prepared a questionnaire to measure family upbringing approaches which composed of (28) item divided on four dimensions. The sample was (260) male and female student from intermediate stage chosen randomly. The results revealed that there were significant differences between social-psychological conflict which went to male, there was a negative correlat
... Show MoreIt has become necessary to change from a traditional system to an automated system in production processes, because it has high advantages. The most important of them is improving and increasing production. But there is still a need to improve and develop the work of these systems. The objective of this work is to study time reduction by combining multiple sequences of operations into one process. To carry out this work, the pneumatic system is designed to decrease\ increase the time of the sequence that performs a pick and place process through optimizing the sequences based on the obstacle dimensions. Three axes are represented using pneumatic cylinders that move according to the sequence used. The system is implemented and
... Show MoreAbstract
This paper represents a study of the effect of the soil type, the drilling parameters and the drilling tool properties on the dynamic vibrational behavior of the drilling rig and its assessment in the drilling system. So first, an experimental drilling rig was designed and constructed to embrace the numerical work.
The experimental work included implementation of the drill-string in different types of soil with different properties according to the difference in the grains size, at different rotational speeds (RPM), and different weights on bit (WOB) (Thrust force), in a way that allows establishing the charts that correlate the vibration acceleration, the rate of penetration (ROP), and the power
... Show MoreSupport vector machine (SVM) is a popular supervised learning algorithm based on margin maximization. It has a high training cost and does not scale well to a large number of data points. We propose a multiresolution algorithm MRH-SVM that trains SVM on a hierarchical data aggregation structure, which also serves as a common data input to other learning algorithms. The proposed algorithm learns SVM models using high-level data aggregates and only visits data aggregates at more detailed levels where support vectors reside. In addition to performance improvements, the algorithm has advantages such as the ability to handle data streams and datasets with imbalanced classes. Experimental results show significant performance improvements in compa
... Show MoreIn this research, we have added nano anatase TiO2 as a partial replacement of Portland cement by a weight percentage of (0.25 to 1%) for the development of properties for protection against bacteria. The control mix was made by using "the cement to sand" proportion about (1: 2.75) with the "water to cement" proportion of (0.5) to study the structure, porosity, water absorption, density, mechanical properties, as well as anti-bacterial behavior. Inspections have been done such as scanning electron microscopy (SEM), and atomic force microscope (AFM) for mortar. Experimental results showed that after the addition of Nano powders in cement mortar, the structural properties improved significantly with the development of hydration o
... Show More