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.
In recent years, the world witnessed a rapid growth in attacks on the internet which resulted in deficiencies in networks performances. The growth was in both quantity and versatility of the attacks. To cope with this, new detection techniques are required especially the ones that use Artificial Intelligence techniques such as machine learning based intrusion detection and prevention systems. Many machine learning models are used to deal with intrusion detection and each has its own pros and cons and this is where this paper falls in, performance analysis of different Machine Learning Models for Intrusion Detection Systems based on supervised machine learning algorithms. Using Python Scikit-Learn library KNN, Support Ve
... Show MoreClassifying an overlapping object is one of the main challenges faced by researchers who work in object detection and recognition. Most of the available algorithms that have been developed are only able to classify or recognize objects which are either individually separated from each other or a single object in a scene(s), but not overlapping kitchen utensil objects. In this project, Faster R-CNN and YOLOv5 algorithms were proposed to detect and classify an overlapping object in a kitchen area. The YOLOv5 and Faster R-CNN were applied to overlapping objects where the filter or kernel that are expected to be able to separate the overlapping object in the dedicated layer of applying models. A kitchen utensil benchmark image database and
... Show MoreNaproxen is non-steroidal anti-inflammatory drug, which has antipyretic and anti-inflammatory effect. It is extensively bound to plasma albumin, and exhibits gastric toxicity, so it may be more efficient to deliver the drug in its sustained release dosage form and adequate blood level is achieved. Three liquid formulations with in situ gelling properties have been assessed for their potential for the oral sustained delivery of naproxen . The formulations were dilute solutions of: (a) pectin; (b) gellan gum and; (c) sodium alginate, all containing complexed calcium ion that form gels when these ions are released in the acidic environment of the stomach . The viscosity of the sols and drug release were measured, and was found to be depende
... Show MoreThis research aims to improve the radiation shielding properties of polymer-based materials by mixing PVC with locally available building materials. Specifically, two key parameters of fast neutron attenuation (removal cross-section and half-value layer) were studied for composite materials comprising PVC reinforced with common building materials (cement, sand, gypsum and marble) in different proportions (10%, 30% and 50% by weight). To assess their effectiveness as protection against fast neutrons, the macroscopic neutron cross-section was calculated for each composite. Results show that neutron cross-section values are significantly affected by the reinforcement ratios, and that the composite material PVC + 50% gypsum is an effect
... Show MoreWe manufactured the nanoparticles light emitting diode (NPs-LED) for organic and inorganic semiconductors to achieve electroluminescence (EL). The nanoparticles of Europium oxide(Eu2O3) were incorporated into the thin film layers of the organic compounds, poly(3,4,- ethylene dioxythiophene)/polystyrene sulfonic acid (PEDOT:PSS), N,N’–diphenyl-N,N’ –bis(3-methylphenyl)-1,1’-biphenyl 4,4’- diamine (poly TPD) and polymethyl methacrylate (PMMA), by the spin coating and with the help of the phase segregation method. The EL of NPs-LED, was study for the different bias voltages (20, 25, 30) V at the room temperature, from depending on the CIE 1931 color spaces and it was generated the white light at 20V, t
... Show MoreBackground: Surface treatment of machined dental zirconia for enhancement of the adhesion to resin cement, using Er,Cr:YSGG Laser. Materials and Methods: Total number of 42 zirconia disc specimens (9 mm diameter, and 2 mm height) was sintered according to the manufacturer instruction. They are divided into six groups, each group of seven samples. Laser groups (Experiment parameters) were depend on laser total irradiation time, pulse duration, and power. Group (A): 20 sec., 60 µs pulse duration. Group (B): 30 sec., 60 µs pulse duration. Group (C): 40 sec., 60 µs pulse duration. Group (D): 20 sec., 700 µs pulse duration. Group (E): 30 sec., 700 µs pulse duration, with different powers used (1, 1
... Show MoreA lower extracellular pH is one of the few well-documented physiological differences between tumour and normal tissues. On the other hand, elevated glutathione (GSH) level has been detected in many tumours compared with healthy surrounding tissues. The compound II: 3-(9H-purin-6-yl-thio) carbonothionyl methyl-8-oxo-7-(2-thiophen-2-yl) acetamido-5-thia-1-azabicyclo-4-octo-ene-carboxylic acid was a cephalothin derivative contain 6-mercaptopurine (6-MP). Compound II react with general base catalysis in slightly acidic pH or with sulfhydryl nucleophiles to release the chemotherapeutic drug 6-MP. The generation of compound II was accomplished following multistep reaction procedures. The structure of compound II and its intermediate was confir
... Show MoreThe aim of this paper, is to study different iteration algorithms types two steps called, modified SP, Ishikawa, Picard-S iteration and M-iteration, which is faster than of others by using like contraction mappings. On the other hand, the M-iteration is better than of modified SP, Ishikawa and Picard-S iterations. Also, we support our analytic proof with a numerical example.
This work deals with the preparation of a zeolite/polymer flat sheet membrane with hierarchical porosity and ion-exchange properties. The performance of the prepared membrane was examined by the removal of chromium ions from simulated wastewater. A NaY zeolite (crystal size of 745.8 nm) was prepared by conventional hydrothermal treatment and fabricated with polyethersulfone (15% PES) in dimethylformamide (DMF) to obtain an ion-exchange ultrafiltration membrane. The permeate flux was enhanced by increasing the zeolite content within the membrane texture indicating increasing the hydrophilicity of the prepared membranes and constructing a hierarchically porous system. A membrane contain