In this paper a mathematical model that describes the flow of infectious disease in a population is proposed and studied. It is assumed that the disease divided the population into four classes: susceptible individuals (S), vaccinated individuals (V), infected individuals (I) and recover individuals (R). The impact of immigrants, vaccine and external sources of disease, on the dynamics of SVIRS epidemic model is studied. The existence, uniqueness and boundedness of the solution of the model are discussed. The local and global stability of the model is studied. The occurrence of local bifurcation as well as Hopf bifurcation in the model is investigated. Finally the global dynamics of the proposed model is studied numerically.

A trademark is one of the most valuable elements in advertising. At the same time, it is a guarantee for both the producer and the consumer. It prevents the mixing of products with a certain mark with similar products bearing another mark; and creates confidence in the goods of the product.

With the increase in the types of goods and products and the emergence of similar goods, producers have turned to the use of the brand to identify their products and seek perfection in manufacture to maintain quality and continuous improvement which ensures good reputation and fame.

Hence, commercials for goods and services focused on the brand because they give in-depth connotations with the recipients of these ads. T

The main object of this paper is to study the representations of monomial groups and characters technique for representations of monomial groups. We refer to monomial groups by M-groups. Moreover we investigate the relation of monomial groups and solvable groups. Many applications have been given the symbol G e.g. group of order 297 is an M-group and solvable. For any group G, the factor group G/G? (G? is the derived subgroup of G) is an M-group in particular if G = Sn, SL(4,R).

With the quick grow of multimedia contents, from among this content, face recognition has got a lot of significant, specifically in latest little years. The face as object formed of various recognition characteristics for detect; so, it is still the most challenge research domain for researchers in area of image processing and computer vision. In this survey article, tried to solve the most demanding facial features like illuminations, aging, pose variation, partial occlusion and facial expression. Therefore, it indispensable factors in the system of facial recognition when performed on facial pictures. This paper study the most advanced facial detection techniques too, approaches: Hidden Markov Models, Principal Component Analysis (PCA)

The current research aims to identify the Vocational Self of the educational counselors as well as to identify the significant difference in the professional self according to the gender variable (male-female). The researcher adopted the scale of al-hasani (2015), which consisted of (34) items. It was applied to a sample of (300) school counselors (male-female) who were randomly selected from the six directorates in the Baghdad governorate for the academic year 2020/2021. The results showed that the research sample of educational counselors has a vocational self-concept. There are no statistically significant differences in the vocational self-concept between males and females among the educational counselors.

Experimental and theoretical investigations are presented on flocculation process in pulsator clarifier. Experimental system was designed to study the factors that affecting the performance of pulsator clarifier. These factors were water level in vacuum chamber which range from 60 to 150 cm , rising time of water in vacuum chamber which having times of 20,30 & 40 seconds , and sludge blanket height which having heights of 20,30 & 40 cm .The turbidity and pH of raw water used were 200 NTU and 8.13 respectively. According to the jar test, the alum dose required for this turbidity was 20 mg/l .The performance parameters of pulsator clarifier such as , turbidity ,total solid TS , shear rate , volume concentration of sludge blanket an

I attended some amides non grassy substitutes such as acrylic compounds Amaid Electron Amaid and Alsinamamaid interaction unsaturated acids such as acrylic acid or Ketronk ????????? with primary amines Malkhtlfah of acrylic monomers Alamayd

The aim of this study was the production of aspartame by using immobilized thermolysin in bentonite clay. The yield of immobilized thermolysin in bentonite was 92% of the original enzyme amount. pH profile of free and immobilized enzyme was 7.0 and 7.5 respectively which was stable at 6.5-9.0 for 30min. The optimum temperature of both enzymes was 50°C, while they were stable at 65°C for 30min. however, they lost 52.73 and 61.72% from its main activity at 80°C respectively. Immobilized thermolysin has retained all activity within 27 days, but it kept 68.27% of initial activity when stored for 60 days at 4°C whereas, it retained a full activity after 20 continue usage. In addition, it retained 86.53% of its original activity af

Roller Compacted Concrete (RCC) is a technology characterized mainly by the use of rollers for compaction; this technology achieves significant time and cost savings in the construction of dams and roads. The primary scope of this research is to study the durability and performance of roller compacted concrete that was constructed in the laboratory using roller compactor manufactured in local market. A total of (60) slab specimen of (38×38×10) cm was constructed using the roller device, cured for 28 days, then 180 sawed cubes and 180 beams are obtained from RCC slab. Then, the specimens are subjected to 60 cycles of freezing and thawing, sulfate attack test and wetting and drying. The degree of effect of the type of coarse aggregate (c

The acidity of spent lubricant was treated using sodium hydroxide solution. The effect of three variables on the treatment have been studied . These are mixing time rangingfrom 5-35 minutes, NaOH to lubricant weight ratio ranging from  0.25-1.25 and weight percentage  of NaOH ranging from  2-6 % .

The experimental design of Box-Wilson method is adopted to find a useful relationship between the three controllable variables and the lowering in the acidity of the spent lubricant. Then the effective variables and interactions are identified using the statistical analysis(F-test) of  three variable fractional design. The mathematical model is well represented  by a second order polynomial.

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