In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.
This study is about the role of the Internet in spreading rumors, especially through social networking sites "Facebook" model as the effectiveness of social networks lies in the speed of transmission of events; these two characteristics are important to the public, making the Internet a strong contender for television and its relationship with the public. That's why we find that the Internet today has become a fertile environment for the growth and spread of rumors. The more limited the platforms and places of publication, the greater the responsibility in the search for the original source in spreading this or that rumor, as the Internet is considered an easy means in the production, spreading and re-spreading of
... Show MoreAbstract: A novel design of Mach Zehnder Interferometer (MZI) in terms of using special type of optical fiber that has double clad with graded distribution of the refractive index that can be easily implemented practically was suggested and simulated in this work. The suggested design is compact, rapid, and is simple to be modified and tested. The simulated design contains a MZI of 1546.74 nm of central wavelength that is constructed using special type of double clad optical fiber that has two different numerical apertures. The first aperture will supply single mode propagation via its core, while the second numerical aperture supports a zigzag wave propagation (multimode) in the first clad region. The interferometer’s
... Show MoreThe tourism industry has undergone exponential transformation, reshaped by online travel agencies (OTAs), shifting consumer preferences, and technological advancements. Established OTAs like TripAdvisor and Travelocity face pressures to adapt their strategies to capitalize on these disruptive landscape changes. This research involves a comparative analysis examining the key challenges confronting TripAdvisor and Travelocity, with a focus on opportunities to leverage artificial intelligence (AI) in enhancing personalization and the traveler experience. The study utilizes publicly available data on the companies and academic literature on AI innovation diffusion. Findings reveal that while TripAdvisor has actively developed AI-based trip plan
... Show MoreLet G be a graph with p vertices and q edges and be an injective function, where k is a positive integer. If the induced edge labeling defined by for each is a bijection, then the labeling f is called an odd Fibonacci edge irregular labeling of G. A graph which admits an odd Fibonacci edge irregular labeling is called an odd Fibonacci edge irregular graph. The odd Fibonacci edge irregularity strength ofes(G) is the minimum k for which G admits an odd Fibonacci edge irregular labeling. In this paper, the odd Fibonacci edge irregularity strength for some subdivision graphs and graphs obtained from vertex identification is determined.
The 3-parameter Weibull distribution is used as a model for failure since this distribution is proper when the failure rate somewhat high in starting operation and these rates will be decreased with increasing time .
In practical side a comparison was made between (Shrinkage and Maximum likelihood) Estimators for parameter and reliability function using simulation , we conclude that the Shrinkage estimators for parameters are better than maximum likelihood estimators but the maximum likelihood estimator for reliability function is the better using statistical measures (MAPE)and (MSE) and for different sample sizes.
Note:- ns : small sample ; nm=median sample
... Show MoreThe present study aims at finding out the (effect of the Caroll’s pattern on the second intermediate class pupils' achievement in geography)
The partial experimental design of two groups, experimental and control, with pre-post tests is used. The sample is represented in (74) female pupils. The sample is divided into two groups (38) experimental group and (36) control one. The sample is selected from first intermediate class pupils ( Am Salama Secondary School for girls) \ Baghdad\ Al-karkh-1, for academic year 2015-2016.
The researcher has equalized the two groups in several variables: the previous achievement tests, intelligence, age in months, the scor
... Show MoreTelevision culture has become the most dangerous of our time. It manipulates with minds and hearts together; and forms consciousness. It transforms societies into actual forces rejecting certain principles by guiding the media landscape through visible connotations acceptable to the public; or provokes the citizen against elements that put a burden on the viewer or the public in order to create a positive reaction to the subject of combating terrorism by combining these ads in line with what the public wants of security and tranquility and a decent living after suffering from terrorism in the past years.
Therefore, this research deals with television advertisements as one of the most important fo
... Show MoreIn this study, we set up and analyze a cancer growth model that integrates a chemotherapy drug with the impact of vitamins in boosting and strengthening the immune system. The aim of this study is to determine the minimal amount of treatment required to eliminate cancer, which will help to reduce harm to patients. It is assumed that vitamins come from organic foods and beverages. The chemotherapy drug is added to delay and eliminate tumor cell growth and division. To that end, we suggest the tumor-immune model, composed of the interaction of tumor and immune cells, which is composed of two ordinary differential equations. The model’s fundamental mathematical properties, such as positivity, boundedness, and equilibrium existence, are exami
... Show MoreThe avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels
... Show MoreThe objectives of this research are to determine and find out the reality of crops structure of greenhouses in association of Al-Watan in order to stand on the optimal use of economic resources available for the purpose of reaching a crop structure optimization of the farm that achieves maximize profit and gross and net farm incomes , using the method of linear programming to choose the farm optimal plan with the highest net income , as well as identifying production plans farm efficient with (income - deviation) optimal (E-A) of the Association and derived, which takes into account the margin risk wich derived from each plan using the model( MOTAD), as a model of models of linear programming alternative programming m
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