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.
SnS has been widely used in photoelectric devices due to its special band gap of 1.2-1.5 eV. Here, we reported on the fabrication of SnS nanosheets and the effect of synthesis condition together with heat treatment on its physical properties. The obtained band gap of the SnS nanosheets is in the rage of 1.37-1.41 eV. It was found that the photo-current density of a thin film comprised of SnS nanosheets could be enhanced significantly by annealing treatment. The maximum photo-current density of the stack structure of FTO/SnS/CdS/Pt was high as 389.5 mu A cm(-2), rendering its potential application in high efficiency solar hydrogen production.
(10)
(10)
The present study describes employing zero-, 1st - and 2nd -order derivative spectrophotometric methods have been developed for determination of lorazepam (LORA) and clonazepam (CLON) in commercially available tablets. LORA was determined by means of 1st (D1), 2nd (D2) derivative spectrophotometric techniques using zero cross, peak height, and Peak area. D1 used for the determination of CLON by using zero cross and peak height while D2 (zero cross) was used for the determination of CLON. The method was established to be linear in concentration containing different ratios of LORA and CLON range of (20-200 mg/L) and (5-35 mg/L) at wavelength range (250 -370 nm), (210-370nm) respectively. The proposed techniques are highly sensitive, precise a
... Show MoreProtection of the oil pipelineswhich extracted from the wells was found to shut the well and prevent the leakage of oil when broken using safety valve. This valve is automatically activated by loss of pressure between the well and pipelines, which take the pressure, signal from hydraulic pressure sensor through pressure control valve which has constant or variable value but it is regulated manually. The manual regulatory process requires the presence of monitoring workers continuously near the wells which are always found in remote areas. In this paper, a smart system has been proposed that work with proportional pressure control valve and also electronic pressure sensor through Arduino controller, which is programmed in a way that satisfie
... Show MoreAn experimental study was carried out to improve the surface roughness quality of the stainless steel 420 using magnetic abrasive finishing method (MAF). Four independent operation parameters were studied (working gap, coil current, feed rate, and table stroke), and their effects on the MAF process were introduced. A rotating coil electromagnet was designed and implemented to use with plane surfaces. The magnetic abrasive powder used was formed from 33%Fe and 67% Quartz of (250µm mesh size). The lubricant type SAE 20W was used as a binder for the powder contents. Taguchi method was used for designing the experiments and the optimal values of the selected parameters were found. An empirical equation representing the r
... Show MoreIn every country in the world, there are a number of amputees who have been exposed to some accidents that led to the loss of their upper limbs. The aim of this study is to suggest a system for real-time classification of five classes of shoulder girdle motions for high-level upper limb amputees using a pattern recognition system. In the suggested system, the wavelet transform was utilized for feature extraction, and the extreme learning machine was used as a classifier. The system was tested on four intact-limbed subjects and one amputee, with eight channels involving five electromyography channels and three-axis accelerometer sensor. The study shows that the suggested pattern recognition system has the ability to classify the sho
... Show More
(5)
(5)
Airlift reactors are widely used in the chemical and biochemical applications as effective contactors for mass and heat transfer. The main advantages of airlift contactor compared with simple bubble column are ease of construction, low shear rate, high capacity, good mixing and liquid circulation without mechanical agitators and circulating pumps.
In this work, growth characteristics of Chlorella vulgaris microalgae were studied in an internal loop airlift photobioreactor for biomass production. The bioreactor operated under batch and semi-continuous culture mode using commercially available 20:20:20+TE NPK fertilizer as nutrients. The experiments were conducted to evaluate the growth rate and biomass productivity of
... Show MoreIn this study, condensation polymerization was used to synthesize a number of novel liquid crystal polymers with 1,3,4-oxadiazole rings based on melamine. The new synthesized polymers were characterized by Fourier transform infrared (FTIR) and proton nuclear magnetic resonance (1HNMR) spectroscopy. Differential scanning calorimetry (DSC) and optical polarization microscopy (OPM) were used to investigate their liquid crystalline properties. The results demonstrated that throughout a wide temperature range, most of the polymers exhibited columnar (CohX) and nematic (N) liquid crystalline phases.
(1)
(1)
Electronic remote identification (ER-ID) is a new radio frequency (RF) technology that is initiated by the Federal Aviation Authorities (FAA). For security reasons, traffic control, and so on, ER-ID has been applied for drones by the FAA to enable them to transmit their unique identification and location so that unauthorized drones can be identified. The current limitation of the existing ER-ID algorithms is that the application is limited to the Wi-Fi and Bluetooth wireless controllers, which results in a maximum range of 10–20 m for Bluetooth and 50–100 m for Wi-Fi. In this study, a mathematical computing technique based on finite state automaton (FSA) is introduced to expand the range of the ER-ID RF system and reduce the ene
... Show More
(5)
(6)
There is no doubt that teachers are the leaders of positive changing in community where they directed the students and build their brains. In our current generation that characterized by accelerated technological development that communication changes, economic and politics, needs from the teacher an active leadership skills that match with the soul of our generation and contribute in confrontation the current challenges and the future challenges in the form that lead to create a conscious generation where they will be a basic brick for the future community where the listeners looking forward the education where they support the continuity communication of develop process, economy, scientifically and in all life fields. In our study we take
... Show More