iosr-Jm   Volume-18 ~ Issue-2 ~ Mar. – Apr. 2022

Abstract:The proof of the four-color theorem is led from its definition to the notion of a "complete triangular network" CTN(n) to a description of its construction to see if it is possible to construct a CTN(n) enforcing the 5th color. A negative answer then allows us to claim that the four-color theorem is thereby proved.1 MSC 54C99

Key words:Four-color theorem, complete triangular network, graph map, color forcing

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Abstract: A campaign is a series of ads that is aimed to fulfill a purpose, such as generating leads or increasing the number of app installs. Machine learning techniques are used in ad campaigning. In machine learning, there are many types of algorithms, such as classification algorithm, regression algorithm, clustering algorithm, etc. Among the clustering algorithms, K-means algorithm is widely used because it is a simple and fast algorithm. Random forest algorithms are used for classification and regression both. In this paper clustering and regression both techniques are used for ad campaigning analysis and sales prediction. First, ad groups are created using the K-means clustering algorithm then Random Forest Regressor algorithm is used to optimize sales conversion and predict future sales.

Key words: Supervised learning, Clustering, Regression, K-means, Random Forest, advertising data

[1]. R. Balabantaray, C. Sarma and M. Jha, "Document Clustering using K-means and K-Medoids", International Journal of Knowledge Based Computer System, 1(1), pp. 7-13, 2013.
[2]. I. Alsmadi and I. Alhami, "Clustering and classification of email contents", Journal of King Saud University – Computer and Information Sciences, 27(1), pp. 46-57, 2015.
[3]. R. Shreyas, D.M Akshata, B.s Mahanand, B. Shagun and C.M Abhishek, "Predicting Popularity of Online Articles using Random Forest Regression", Institute of Electrical and Electronics Engineers, 8(13), pp. 1-5, 2017.
[4]. M. Syakur, B. Khotimah, E. Rochman and B. Satoto, "Integration K-means Clustering Method and Elbow Method For Identification of The Best Customer Profile Cluster", Institute of Physics : Material Science and Engineering, 336(1), pp. 1-6, 2018.
[5]. X. Gao, J. Wen and C. Zhang, "An Improved Random Forest Algorithm for Predicting Employee Turnover", Hindawi : Mathematical Problems in Engineering, 2019(4), pp. 1-12, 2019

Abstract: Restaurants or any other shopping websites are growing their business these days. And the mass group of costumers tend to trust on ratings given to the products. Prior prediction of rating the product before launching, with the help of product features, would be beneficial for the business firm. Here restaurant ratings are predicted with the Back propagation neural network model. For experimental results three different optimizers are used. The proposed model shows 70% of the accuracy.

Keywords: Back propagation, Artificial Neural Networks, Optimizers, Ratings

[1]. Atharva Kulkarni, Divya Bhandari and Sachin Bhoite, "Restaurants Rating Prediction using Machine Learning Algorithms", International Journal of Computer Applications Technology and Research, Volume 8–Issue 09, pp. 375-378, 2019.
https://ijcat.com/archieve/volume8/issue9/ijcatr08091008.pdf
[2]. Diederik P. Kingma, Jimmy Ba, "Adam: A Method for Stochastic Optimization", 3rd International Conference for Learning Representations, San Diego, 2015. https://arxiv.org/abs/1412.6980
[3]. Djork-Arne Clevert, Thomas Unterthiner and Sepp Hochreiter, "Fast and accurate Deep network learning by Exponential linear units (Elus)", ICLR conference, 2016. https://arxiv.org/abs/1511.07289
[4]. Huang, "Using Artificial Neural Networks to Predict Restaurant Industry Service Recovery", International Journal of Advancements in Computing Technology (IJACT), Volume-4, pp. 315-321, 2012.
https://www.researchgate.net/publication/289463707_Using_artificial_neural_networks_to_predict_restaurant_industry_service_recovery
[5]. Hyewon Youn and Zheng Gu, "Predict US restaurant firm failures: The artificial neural network model versus logistic regression mode", 2010. https://www.jstor.org/stable/23745462

Abstract: In this study, we investigated the effect of cholesterol on drug distribution in the body. This work also involves mathematical models that represent drug concentration in the blood and in the tissue by introducing a constant cholesterol parameter and treatment in previous works stated in the literature, in an attempt to understand the behavior of a drug administered in the human body over time. In addition, the models help to study and assess the behavior of medication distribution in the body associated with a high or low level of cholesterol. The analytical solutions for the drug concentration in the bloodstream and that of the tissues were obtained using the Laplace's........

Keywords: Mathematical Models, Pharmacokinetics, Cholesterol, Drug Distribution, Ordinary Differential Equations, Lipid

[1]. Haines, C., & Crouch, R. (2007). Mathematical modelling and applications: Ability and competence frameworks. In Modelling and applications in mathematics education (pp. 417-424). Springer, Boston, MA.
[2]. Bunonyo, K. W., & Eli, I. C. (2020). Mathematical Modeling of an Oscillatory MHD Blood Flow through a Lipid Saturated Porous Channel with Metabolic Heat and Magnetic Field. Communication in Physical Sciences, 6(1),783-792
[3]. Bunonyo, K. W., Ebiwareme, L., & Awomi, P. Z. (2022). The Effects of Cholesterol and Treatment on Drug Concentration in the Blood Stream and Stomach. European Journal of Mathematics and Statistics, 3(2), 1-9.
[4]. Heather, M., Ofanoa, M., Ofanoa, S. M., Tu'akoi, S., Lutui, H., Dalbeth, N.,& Goodyear-Smith, F. (2021). Design and implementation of a Pacific intervention to increase uptake of urate-lowering therapy for gout: a study protocol. International journal for equity in health, 20(1), 1-7.
[5]. Hrydziuszko, O., Wrona, A., Balbus, J., & Kubica, K. (2014). Mathematical two-compartment model of human cholesterol transport in application to high blood cholesterol diagnosis and treatment. Electronic Notes in Theoretical Computer Science, 306, 19-30.

Abstract: The flow of nanofluid flow through a porous medium has attracted several authors in the field of science, engineering and several industries over the decades. The viscous force in Newtonian and non-Newtonian fluids causes friction in the motion of several fluids. However, Buoyancy effect on MHD nanofluid flow and the characteristics of the thermophysical properties of copper (Cu) -nanofluid over a porous medium in the presence of Dufour and Ohmic heating is considered in this study. The transformed governing equation is solved numerically using midpoint methods known as midrich method with Richardson extrapolation enhancement or deferred correction.....

Keywords: Buoyancy effect, MHD, Nanofluid, Porous Medium, Dufour, Ohmic heating, thermal radiation. Thermo-physical properties, Richardson extrapolation

[1] Yahaya, S. D. and Simon, K. D., (2015), "Effect of Buoyancy and Thermal Radiation on MHD flow over a Stretching Porous Sheet using Homotopy Analysis Method".
[2] Subhas, M. A., Klkarni, A. K. and Ravikumara, R., (2011), "MHD flow and heat transfer with effects of buoyancy, viscosity and Joules dissipation over a nonlinear vertical stretching porous sheet with partial slip"., vol.3, No. 3, Doi:10.4236/eng.2011.33033
[3] Lakshmi, G. D., Niranja, H. and Sivasankara, S. (2021), "Effects of chemical reaction, radiation and activation energy on MHD buoyancy induced nanofluid flow past a vertical surface", Transsaction B: Mechanical engineering, scientific Iranica B (2022) 29(1), 90-100, DOI: 10.24200sci.56835.4934
[4] Animasaun I. L. and Sandeep, N., (2016) "Buoyancy induced model for the flow of 36 nm alumina-water nanofluid along upper horizontal surface of a paraboloid of revolution with variable thermal conductivity and viscosity" Power Technology 301, 858 - 867. doi: /10.1016/j.powtec.2016.07.023
[5] Nguyen, C. T., (2012), "Fundamentals of Mass Transport in microscale,"., second edition, http://doi.org/1016/B978 - 1 - 4377-3520-8.00002 – 4.

Abstract: In this paper, a coupled fixed-point theorem for maps satisfying contractive conditions in perspective of complex valued dislocated metric spaces have been established. Our main result generalizes, extends and improves the some known result in the existing literature of [10] and [16]. Also provide an example in support of our main result.

Keywords: Coupled fixed point, Complex valued dislocated metric spaces, Contractive condition. MSC:47H10, 54 H25

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Abstract: For a graph , a binary vertex labeling function of is called a biconditional cordial labeling if an induced edge labeling function defined by , satisfies the two conditions: and 1 where and denotes respectively the number of vertices and edges of having label . A graph is called biconditional cordial graph if it admits biconditional cordial labeling. In this manuscript we have proved that the crown graph, armed crown, helms, closed helms, gears and flower graphs are biconditional cordial graphs.

Keywords: Crown graph; Flower graph; Biconditional cordial labeling; Biconditional cordial graph.

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[2]. J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, 24, \#DS6, 2021.
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