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.
(102)
(101)
Drug solubility and dissolution remain a significant challenge in pharmaceutical formulations. This study aimed to formulate and evaluate repanglinide (RPG) nanosuspension-based buccal fast-dissolving films (BDFs) for dissolution enhancement. RPG nanosuspension was prepared by the antisolvent-precipitation method using multiple hydrophilic polymers, including soluplus®, polyvinyl alcohol, polyvinyl pyrrolidine, poloxamers, and hydroxyl propyl methyl cellulose. The nanosuspension was then directly loaded into BDFs using the solvent casting technique. Twelve formulas were prepared with a particle size range of 81.6-1389 nm and PDI 0.002-1 for the different polymers. Nanosuspensions prepared with soluplus showed a favored mean particle size o
... Show More
(5)
(5)
(14)
High peak to average power ration (PAPR) in orthogonal frequency division multiplexing (OFDM) is an important problem, which increase the cost and complexity of high power amplifiers. One of the techniques used to reduce the PAPR in OFDM system is the tone reservation method (TR). In our work we propose a modified tone reservation method to decrease the PAPR with low complexity compared with the conventional TR method by process the high and low amplitudes at the same time. An image of size 128×128 is used as a source of data that transmitted using OFDM system. The proposed method decrease the PAPR by 2dB compared with conventional method with keeping the performance unchanged. The performance of the proposed method is tested with
... Show More
(8)
(1)
This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.
Finally, all algori
... Show More
(23)
(10)
<span>As a result of numerous applications and low installation costs, wireless sensor networks (WSNs) have expanded excessively. The main concern in the WSN environment is to lower energy consumption amidst nodes while preserving an acceptable level of service quality. Using multi-mobile sinks to reduce the nodes' energy consumption have been considered as an efficient strategy. In such networks, the dynamic network topology created by the sinks mobility makes it a challenging task to deliver the data to the sinks. Thus, in order to provide efficient data dissemination, the sensor nodes will have to readjust the routes to the current position of the mobile sinks. The route re-adjustment process could result in a significant m
... Show More
(4)
(2)
Alzheimer’s disease (AD) is a progressive disorder that affects cognitive brain functions and starts many years before its clinical manifestations. A biomarker that provides a quantitative measure of changes in the brain due to AD in the early stages would be useful for early diagnosis of AD, but this would involve dealing with large numbers of people because up to 50% of dementia sufferers do not receive formal diagnosis. Thus, there is a need for accurate, low-cost, and easy to use biomarkers that could be used to detect AD in its early stages. Potentially, electroencephalogram (EEG) based biomarkers can play a vital role in early diagnosis of AD as they can fulfill these needs. This is a cross-sectional study that aims to demon
... Show More
(68)
(53)
This paper describes the use of microcomputer as a laboratory instrument system. The system is focused on three weather variables measurement, are temperature, wind speed, and wind direction. This instrument is a type of data acquisition system; in this paper we deal with the design and implementation of data acquisition system based on personal computer (Pentium) using Industry Standard Architecture (ISA)bus. The design of this system involves mainly a hardware implementation, and the software programs that are used for testing, measuring and control. The system can be used to display the required information that can be transferred and processed from the external field to the system. A visual basic language with Microsoft foundation cl
... Show More
(2)
A method has been demonstrated to synthesise effective zeolite membranes from existing crystals without a hydrothermal synthesis step.
(27)
(25)
(9)