Journal Vol – 17 No -11, November 2022

AN OPENING OF A NEW HORIZON IN THE THEORY OF QUADRATIC EQUATION : PURE AND PSEUDO QUADRATIC EQUATION – A NEW CONCEPT

Authors:

Prabir Chandra Bhattacharyya

DOI NO:

https://doi.org/10.26782/jmcms.2022.11.00001

Abstract:

In this paper, the author has opened a new horizon in the theory of quadratic equations. The author proved that the value of x which satisfies the quadratic equation cannot be the only criteria to designate as the root or roots of an equation. The author has developed a new mathematical concept of the dimension of a number. By introducing the concept of the dimension of number the author structured the general form of a quadratic equation into two forms: 1) Pure quadratic equation and 2) Pseudo quadratic equation. First of all the author defined the pure and pseudo quadratic equations. In the case of pure quadratic equation ax^2+bx+c=0 , the root of the equation will be a two-dimensional number having one root only while in the case of pseudo quadratic equation ax^2+bx+c=0, the root of the equation will be a one-dimensional number having two roots only. The author proved that all pseudo quadratic equation is factorizable but all factorizable quadratic equation is not a pseudo quadratic equation. The author begs to differ from the conventional theorem: "A quadratic equation has two and only two roots." By introducing the concept that any quadratic surd is a two-dimensional number, the author developed a new theorem: “In a quadratic equation with rational coefficients, irrational roots cannot occur in conjugate pairs” and proved it. Any form of quadratic equation ax^2+bx+c=0, can be solved by the application of the ‘Theory of Dynamics of Numbers’ even if the discriminant b^2-4ac<0 in real number only without introducing the concept of an imaginary number. Therefore, the question of imaginary roots does not arise in the method of solution of any quadratic equation

Keywords:

Dimension of Numbers,Dynamics of Numbers,,Quadratic Equation,Rectangular Bhattacharra’s Coordinates,significance of roots of a Quadratic Equation,

Refference:

I. Bhattacharyya, Prabir Chandra. : “AN INTRODUCTION TO THEORY OF DYNAMICS OF NUMBERS: A NEW CONCEPT”. J. Mech. Cont. & Math. Sci., Vol.-17, No.-1, January (2022). pp 37-53

II. Bhattacharyya, Prabir Chandra. : “A NOVEL CONCEPT IN THEORY OF QUADRATIC EQUATION”. J. Mech. Cont. & Math. Sci., Vol.-17, No.-3, March (2022) pp 41-63

III. Bhattacharyya, Prabir Chandra. : “AN INTRODUCTION TO RECTANGULAR BHATTACHARYYA’S CO-ORDINATES: A NEW CONCEPT”. J. Mech. Cont. & Math. Sci., Vol.-16, No.-11, November (2021). pp 76-86.

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BREAST CANCER HISTOLOGICAL IMAGES CLASSIFICATION AND PERFORMANCE EVALUATION OF DIFFERENT CLASSIFIERS

Authors:

Md. Rakibul Islam, Shariful Islam, Md. Shahadot Hosen (Rony) , Md. Nur Alam

DOI NO:

https://doi.org/10.26782/jmcms.2022.11.00002

Abstract:

                  Breast cancer is a serious trouble and one of the greatest causes of death for women throughout the world. Computer-aided diagnosis (CAD) techniques can help the doctor make more credible decisions. We have determined the possibility of knowledge transfer from natural to histopathological [IX][XII] images by employing a pre-trained network ResNet-50.This pre-trained network has been utilized as a feature generator and extracted features are used to train support vector machine (SVM), random forest, decision tree, and K nearest neighbor(KNN) classifiers[X]. We altered the softmax layer to support the vector machine classifier, random forest classifier, decision tree classifier, and k-nearest neighbor classifier, to evaluate the classifier performance of each algorithm. These approaches are applied for breast cancer classification and evaluate the performance and behavior of different classifiers on a publicly available dataset named Bttheeak-HIS dataset. In order to increase the efficiency of the ResNet[III] model, we preprocessed the data before feeding it to the network. Here we have applied to sharpen filter and data augmentation techniques, which are very popular and effective image pre-processing techniques used in deep models.

Keywords:

Machine learning,Support Vector Machine (SVM),K-Nearest Neighbor (KNN),RESNET (Residual Network) model,Random Forest.[VII],

Refference:

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VI. B. E. Bejnordi, G. Zuidhof, M. Balkenhol et al., “Contextaware stacked convolutional neural networks for classifcation of breast carcinomas in whole-slide histopathology images,” Journal of Medical Imaging, vol. 4, no. 04, p. 1, 2017.
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VIII. George, Yasmeen Mourice, Hala Helmy Zayed, Mohamed Ismail Roushdy, and Bassant Mohamed Elbagoury. “Remote computer-aided breast cancer detection and diagnosis system based on cytological images.” IEEE Systems Journal 8, no. 3 (2014): 949-964.

IX. Gupta, Vibha, and Arnav Bhavsar. “Breast Cancer Histopathological Image Classification: Is Magnification Important?.” In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pp. 17- 24. 2017.
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XII. Han, Zhongyi, Benzheng Wei, Yuanjie Zheng, Yilong Yin, Kejian Li, and Shuo Li. “Breast cancer multi-classification from histopathological images with structured deep learning model.” Scientific reports 7, no. 1 (2017): 4172
XIII. Kahya, Mohammed Abdulrazaq, Waleed Al-Hayani, and Zakariya Yahya Algamal. “Classification of breast cancer histopathology images based on adaptive sparse support vector machine.” Journal of Applied Mathematics and Bioinformatics 7.1 (2017): 49
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XVII. Pan, S.J. And Yang, Q., 2010. A Survey On Transfer Learning. Ieee Transactions On Knowledge And Data Engineering, 22(10), Pp.1345–1359.
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XXI. Rokach, Lior; Maimon, O. (2008). Data Mining With Decision Trees: Theory And Applications. World Scientific Pub Co Inc.
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XXIV. Simonyan, K. And Zisserman, A., 2014. Very Deep Convolutional Networks For Large-Scale Image Recognition. Arxiv Preprint Arxiv:1409.1556.
XXV. Spanhol, Fabio A., Luiz S. Oliveira, Caroline Petitjean, and Laurent Heutte. “A dataset for breast cancer histopathological image classification.” IEEE Transactions on Biomedical Engineering 63, no. 7 (2016): 1455-1462.
XXVI. Spanhol, Fabio Alexandre, Luiz S. Oliveira, Caroline Petitjean, and Laurent Heutte. “Breast cancer histopathological image classification using convolutional neural networks.” In Neural Networks (IJCNN), 2016 International Joint Conference on, pp. 2560-2567. IEEE, 2016.
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XXXIII. Zhang, Yungang, Bailing Zhang, Frans Coenen, and Wenjin Lu. “Breast cancer diagnosis from biopsy images with highly reliable random subspace classifier ensembles.” Machine vision and applications 24, no. 7 (2013): 1405-1420.

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ONLINE SKILL TEST PLATFORM

Authors:

Mehria Nawaz, Twinkle Agarwal, Dilip Kumar Gayen

DOI NO:

https://doi.org/10.26782/jmcms.2022.11.00003

Abstract:

Information communication and technology are the most important skills for 21st-century learning and help promote other skills, including life and career skills and learning and innovation skills. This kind of learning allows the learner to connect as a learning network without barriers or borders. The growth of online education has taken our education system to another level. Now anyone can learn from anywhere, anytime as per convenience. In different platforms, questions link are shared with a submission time. Although, learners are taking up unfair means to clear the test provided online in which students usually search up the topic, use different means to get the answers, and get good marks. Hence, teachers cannot get an idea of who is good in the class and who needs extra attention. So, our idea is to make such a platform where the teacher will be taking the test just like our offline classes. In this platform, the teacher will be discussing every question after the students submit the answer in a time duration which will also be proctored and at the same time, the teacher will get the top performer and their submission time. This way we can assure minimal malpractice and identify the students who need more explanation for the questions. This will clear their doubts and the teacher understands the actual performance ratio.

Keywords:

Skill test platform,MongoDB,MERN Stack, MongoDB,student's performance,

Refference:

I. C. Ying-ying, “The Design and Implementation of Online Examination System with Characteristics of Cloud Service”, Beijing University of Posts and Telecommunications. 2013.
II. H-R. Ouyang, H-F. Wei, H-X. Li, A-Q. Pan, Y. Huang, “Checking Causal Consistency of MongoDB”, Journal of Computer Science and Technology. Vol. 37, pp: 128–146, 2022.
III. M. Radoev, “A Comparison between Characteristics of NoSQL Databases and Traditional Databases,” Comput. Sci. Inf. Technol. vol. 5, no. 5, pp: 149–153, 2017.
IV. M.Yagci, M. Unal, “Designing and implementing an adaptive online examination system”, Procedia – Social and Behavioral Sciences. Vol. 116, pp: 3079-3083, 2014.
V. W. Schultz, T. Avitabile, A. Cabral, “Tunable consistency in MongoDB.”, Proc. VLDB Endow. Vol. 12, No. 12, pp 2071-2081, 2019.
VI. Z. Yong-Sheng, F. Xiu-Mei and B. Ai-Qin, “The Research and Design of Online Examination System,” 2015 7th International Conference on Information Technology in Medicine and Education (ITME). pp.: 687-691, 2015.

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GENERAL ANALYTICAL SOLUTION OF AN ELASTIC BEAM UNDER VARYING LOADS WITH VALIDATION

Authors:

Hafeezullah Channa, Muhammad Mujtaba Shaikh, Kamran Malik

DOI NO:

https://doi.org/10.26782/jmcms.2022.11.00004

Abstract:

In this paper, we take into account the system of differential equations with boundary conditions of a fixed elastic beam model (EBM). Instead of finding a solution of EBM for a particularly specified load, which is the usual practice, we derive the general analytical solution of the model using techniques of integrations. The proposed general analytical solutions are not load-specific but can be used for any load without having to integrate successively again and again. We have considered load in a general polynomial form and obtained a general analytical solution for the deflection and slope parameters of EBM. Direct solutions have been determined under two types of loads: uniformly distributed load and linearly varying load. The formulation derived has been validated on the known cases of uniformly distributed load as appears frequently in the literature.

Keywords:

Elastic beam,General analytical solution,Deflection,Slope,

Refference:

I. Babak Mansoori, Ashkan Torabi, Arash Totonch (2020). ‘Numerical investigation of the reinforced concrete beams using cfrp rebar, steel sheets and gfrp’. J. Mech. Cont.& math. Sci., vol.-15, no.-3, pp 195-204.
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IV. Malik, Kamran, Shaikh, Abdul Wasim and Shaikh, Muhammad Mujtaba. (2021). “An efficient finite difference scheme for the numerical solution of Timoshenko beam model. Journal of mechanics of continua and mathematical sciences”, 16 (5): 76-88..
V. Malik, Kamran, Shaikh, Muhammad Mujtaba and Shaikh, Abdul Wasim. (2021).“On exact analytical solutions of the Timoshenko beam model under uniform and variable loads. Journal of mechanics of continua and mathematical sciences”, 16 (5): 66-75.
VI. Timoshenko SP (1921). On the correction for shear of the differential equation for transverse Vibrations of prismatic bars, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 41(245): 744-746.
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