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.
Solar cells has been assembly with electrolytes including I−/I−3 redox duality employ polyacrylonitrile (PAN), ethylene carbonate (EC), propylene carbonate (PC), with double iodide salts of tetrabutylammonium iodide (TBAI) and Lithium iodide (LiI) and iodine (I2) were thoughtful for enhancing the efficiency of the solar cells. The rendering of the solar cells has been examining by alteration the weight ratio of the salts in the electrolyte. The solar cell with electrolyte comprises (60% wt. TBAI/40% wt. LiI (+I2)) display elevated efficiency of 5.189% under 1000 W/m2 light intensity. While the solar cell with electrolyte comprises (60% wt. LiI/40% wt. TBAI (+I2)) display a lower efficiency of 3.189%. The conductivity raises with the
... Show MoreCopper nanoparticles (CuNPs) were prepared with different diameters by sonoelectrodeposition technique using Electrodeposition process coupled with high-power ultrasound horn (Sonoelectrodeposition). The particle diameter of the CuNPs was adjusted by varying CuSO4 solution acidity (pH) and current density. The morphology and structure of the CuNPs were examined by X-ray diffraction (XRD) and Scanning Electron Microscopy (SEM). It was found that the size of the produced copper nanoparticles ranged between 22 to 77 nm, where the diameter of CuNPs increases with reduction the solution acidity from 0.5 to 1.5 pH and increasing the current density of the deposition from 100 to 400 nm. Finally the produced CuNPs were pressed to fabricate disc
... Show MoreThe present work describes guggul as a novel carrier for some anti-inflammatory drugs. Guggulusomes containing different concentration of guggul with aceclofenac were prepared by sonication method and characterized for vesicle shape, size, size-distribution, pH, viscosity, spread ability, homogeneity, and accelerated stability in-vitro drug permeation through mouse skin. The vesicles exhibited an entrapment efficiency of 93.2 ± 12%, vesicle size of 0.769 ± 3μm and a zeta potential of - 6.21mV. In vitro drug release was analyzed using Franz’s diffusion cells. The cumulative release of the guggulusomes gel (G2) was 75.8% in 18 hrs, which is greater than that all the gel formulation. The stability profile of prepare
... Show MoreAlloys of GaxSb1-x system with different Ga concentration (x=0.4, 0.5, 0.6) have been prepared in evacuated quartz tubes. The structure of the alloys were examined by X-ray diffraction analysis (XRD) and found to be polycrystalline of zincblend structure with strong crystalline orientation (220). Thin films of GaxSb1-x system of about 1.0 μm thickness have been deposited by flash evaporation method on glass substrate at 473K substrate temperature (Ts) and under pressure 10-6 mbar. This study concentrated on the effect of Ga concentration (x) on some physical properties of GaxSb1-x thin films such as structural and optical properties. The structure of prepared films for various values of x was polycrystalline. The X-ray diffraction analy
... Show MoreAbstract:
Objectives: This study aims to (1) find out the association between patients' age, years of getting the disease, and their spiritual coping ability, and (2) investigate the differences in illness perception and spiritual coping ability between gender groups, level of education groups, monthly income groups, residence groups and satisfaction with health services groups.
Methodology
A descriptive correlational design is used in this study. The study sample includes a convenience sample of (158) patients with chronic kidney failure.
The study instrument consists of two parts; the first one focuses on participants’ sociodemographic characteristics, and the second part deals with participants’ spiritual coping by us
Advances in gamma imaging technology mean that is now technologically feasible to conduct stereoscopic gamma imaging in a hand-held unit. This paper derives an analytical model for stereoscopic pinhole imaging which can be used to predict performance for a wide range of camera configurations. Investigation of this concept through Monte Carlo and benchtop studies, for an example configuration, shows camera-source distance measurements with a mean deviation between calculated and actual distances of <5 mm for imaging distances of 50–250 mm. By combining this technique with stereoscopic optical imaging, we are then able to calculate the depth of a radioisotope source beneath a surfa
Recent research has shown that a Deoxyribonucleic Acid (DNA) has ability to be used to discover diseases in human body as its function can be used for an intrusion-detection system (IDS) to detect attacks against computer system and networks traffics. Three main factor influenced the accuracy of IDS based on DNA sequence, which is DNA encoding method, STR keys and classification method to classify the correctness of proposed method. The pioneer idea on attempt a DNA sequence for intrusion detection system is using a normal signature sequence with alignment threshold value, later used DNA encoding based cryptography, however the detection rate result is very low. Since the network traffic consists of 41 attributes, therefore we proposed the
... Show MoreThe most popular medium that being used by people on the internet nowadays is video streaming. Nevertheless, streaming a video consumes much of the internet traffics. The massive quantity of internet usage goes for video streaming that disburses nearly 70% of the internet. Some constraints of interactive media might be detached; such as augmented bandwidth usage and lateness. The need for real-time transmission of video streaming while live leads to employing of Fog computing technologies which is an intermediary layer between the cloud and end user. The latter technology has been introduced to alleviate those problems by providing high real-time response and computational resources near to the
... Show MoreA particulate composite material was prepared by adding the Titanium dioxide (TiO2) with a particle size of (75-150) µm to Epoxy resin at weight percentage of (10%,20%,30%,40%,50%).The following some mechanical properties were studied,fracture toughness, hardness.casting preparation methods were used in this study includes preparing plate of matrix and composites. specimens were prepared according to ASTM for the Mechanical properties tests. After that Another samples were heat treated for three and six hour at 65C?. Fracture toughness (Kic) represent for stress intensity factor results were showed that the curve of three hours aging increases in fracture toughness (Kic) for composites but for six hours aging increases fracture tough
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