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Open Access
Some fixed point theorems in intuitionistic fuzzy metric space with certain contractive conditions
(G.B. Pant University of Agriculture and Technology, Pantnagar, District Udham Singh Nagar, Uttarakhand. PIN - 263145, 2022-09) Dimri, Ritikesh; Sanjay Kumar
In the present research work fixed point theorems in complete fuzzy metric space due to Wairojjana et al. (2015) and Patir et al. (2018) are extended to complete intuitionistic fuzzy metric space with certain contractive conditions using altering distance functions. The work is presented in five chapters. Chapter one focuses on the basic preliminaries and definitions related to metric spaces, fuzzy metric spaces, intuitionistic fuzzy metric spaces, contractive mapping, altering distance function and fixed point. Chapter two presents a review of the literature which is studied during the proposed work. In chapter three definition of increasing and decreasing altering distance function is given.Fixed point theorems due to Wairojjana et al. (2015) and Patir et al. (2018) for complete fuzzy metric space extented to complete intuitionistic fuzzy metric spaceare proved in this chapter. In chapter four, the theorems proved are supported by few examples. Chapter five summarizes the work in brief along with the conclusions. The literature used in the course of the study has been referred under the section of literature cited
Open Access
Binary classification of Pneumothorax in chest X-Ray images using deep neural network
(G.B. Pant University of Agriculture and Technology, Pantnagar, District Udham Singh Nagar, Uttarakhand. PIN - 263145, 2022-08) Kaur, Manjeet; Arun Kumar
Currently, lung diseases are extremely common throughout the globe and few of which include chronic obstructive pulmonary disease, pneumonia, pneumothorax, tuberculosis etc. Air in the pleural cavity is thought to be as “pneumothorax". This is a state when the lung surface or chest wall is breached, allowing air to enter the pleural space and causing the lung to collapse, it is a serious situation and might be life-threatening. Chest radiographs are the foremost significant and extensively used diagnostic techniques to detect thoracic or lung diseases among various medical imaging technologies. Pneumothorax can be diagnosed by chest X-rays, CT scans or ultrasound techniques but chest X-ray is the most often used accessible radiological method for screening and diagnosing thoracic diseases. The diagnosis from the chest X-Ray can be of great efficiency and time saving if done through automated systems instead of manual image reading. Tremendous research works are being conducted to develop reliable automatic diagnostic systems for detecting diseases within the chest radiographs. Artificial Intelligence (AI) tools have proven to be effective in optimizing the medical industry. Several framework-supported computing techniques have been proposed for the automated identification of pneumothorax from chest radiographs. Numerous models for pneumothorax automated diagnosis are certainly available. In this study, we have taken chest X-ray images and then used the Deep Transfer Learning technique along with Machine Learning to detect the presence or absence of pneumothorax in chest X-ray images. We have aggregated the unique and computational attributes of Deep Learning and Machine Learning. We have used the Deep Transfer Learning technique which is a pre-trained model that is a Residual Network for image feature extraction and the Support Vector Machine (SVM) algorithm which creates the best decision boundary known as “Hyperplane” to classify data points, is a Machine Learning model used for pneumothorax binary classification. To achieve effective outcomes, a balancing data technique with augmentation is used to create a balance between the training and validation dataset, as well as an automatic adjusting learning rate technique called "ReduceLROnPlateau" to monitor validation loss and obtain optimal learning rates. As an implementation tool, “Google Colab” is used. In our proposed method model, it outperforms in terms of metrics that include accuracy, recall (Sensitivity), f-1 score, precision, loss, and AUC(Area Under The Curve). The performance of the framework is evaluated on a dataset that is available on “Kaggle” which is chest X-ray images. This research work has set a new record with a good performance by achieving state-of-the-art results as 0.8831 in terms of AUC and 0.4375 in terms of loss. The Precision, Recall, and f-1 score is obtained as 0.78, 0.81, and 0.794 respectively.
Open Access
Flow and heat transfer in hybrid nanofluid flow over a vertical plate with heat absorption and viscous dispersion
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2021-07) Gumber, Priya; Manoj Kumar
Present work intends to address the issue of flow and heat transfer in nanofluids over a vertical plate with heat absorption and viscous dispersion. The various flow regime conditions including different physical phenomenon like suction/injection effect, volume fraction, Eckert number, heat generation/ absorption and shape parameter etc. have been incorporated, to study their effects on velocity, temperature and micro- rotation profiles. The physical quantities of interest viz. skin friction coefficient, Nusselt number have also been calculated and their analysis is included in this study. The study presented in the thesis comprises of five chapters. The first chapter is aimed to fulfill the basic need of introducing the various concepts and foundation needed for fluid mechanics. Chapter two throw light on majority of passed research work related with the present work. Chapter three covers the mathematical formulation of the problem and its detailed description. A proper description of used methodology, together with the details of the numerical solution is also presented. Chapter four describes the result and discussion of the considered problem taken in chapter three. The work has been summarized in chapter five. In along with the finding of the study, the literature used in the course of the study has been referred under the section of literature cited. The related study may be helpful to applied scientific fields and different branch of engineering and applied mathematics.
Open Access
Cattaneo-Christov heat flux model in flow of hybrid nanofluid over a wedge and a cone
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2021-07) Garia, Rashmi; Manoj Kumar
The current study deals with the flow and heat transfer near two different geometries i.e. cone and wedge and implements Cattaneo-Christov heat flux model to scrutinize the fluid flow. The flow environment is featured with the effects of thermal radiation, suction, heat generation/injection, magnetic field, volume fraction. The condition of zero mass flux is also incorporated near the surface. The influence of these aforementioned effects are studied via velocity and temperature profiles. The numeric values of engineering interest parameters i.e. skin friction parameter and heat transfer parameter are evaluated. The statistical analysis has also been performed, includes the evaluation of correlation coefficient between the pertinent parameters and the skin friction coefficient and heat transfer coefficient alongside with the evaluation of probable error and statistical declaration. The current work bounds five chapters. The very first chapter delivers the basics and foundational knowledge of fluid mechanics. The second chapter presents the cited literatures which are found to be helpful for the performing the task. The next chapter three focuses on the elaboration of mathematical formulation and numerical methodology is also described. Chapter four illustrates the results and discusses them in comprehensive manner. The summary of the fluid flow problem is presented in chapter five. The work will be applicable in the arena of engineering and applied mathematics.
Open Access
Fixed point theorem using quasicontraction mapping in metric space
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2020-10) Chundriyal, Suraj Prakash; Pal, A.K.
In the present research work proved a fixed point theorem due to Lj. B. CIRIC (1974) with the help of quasi-contraction condition in metric space. Thesis work present in five chapters. The first chapter consists of the basic preliminaries and definitions related to metric space, fixed point, contraction and contractive mappings. Banach contraction principle and some applications of this theorem are also discussed in this section. In the second chapter presents a review of the literature which is studied during the proposed work. The chapter three starts with some primary definitions like generalized contraction and quasicontraction, etc. Fixed point theorem due to Lj. B. Ciric (1974) are proved in this chapter. In chapter four, the theorems proved are supported by an example. In the fifth chapter, summarizes the thesis work in brief along with the conclusions. References that are helpful during research work given in the literature cited.
Open Access
Fuzzy rule based expert system for multi assets portfolio optimization
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2020-09) Bisht, Garima; Sanjay Kumar
Fuzzy logic has been established as an appropriate tool to handle the uncertainty in the system which occurs due to imprecise information, uncertainty, vagueness and other uncontrolled parameters. Portfolio Optimization has always been an important topic for researchers in the area of Financial Mathematics due to its unpredictable behavior. Combination of fuzzy logic and portfolio optimization problems gives an efficient way of selecting the optimal portfolio. Portfolio optimization means combining assets in such a way so as to get maximum return or minimum risk. In the present study we develop multi input single output (MISO) Mamdani FIS for three assets to maximize return and minimize risk using triangular and gaussian membership functions. We also compare the performance of different FIS by calculating the RMSE values as compared to statistical model for portfolio optimization. Chapter 1. gives the introduction of FIS and portfolio optimization. Chapter 2. gives the literature review pertaining to FIS and applications of fuzzy logic in portfolio optimization. Chapter 3. gives materials and methods used during course of investigations. Chapter 4. gives the results obtained by Mamdani FIS. The work has been summarized in Chapter 5.
Open Access
Flow and heat transfer of Cu-water nanofluid over stretching sheet with Stefan blowing Effect
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2020-07) Negi, Shubham; Manoj Kumar
Present work deals with the problem of flow and heat transfer in nanofluids past a stretching porous sheet mainly Cattaneo-Christov double diffusive model is applied to study the flow problem. The various flow conditions including different physical phenomenon like magnetic effect, activation energy effect, Stefan blowing effect, volume fraction and the condition of zero mass flux has been incorporated at the boundary, to study their effects on velocity, temperature and concentration profiles. The physical quantities of interest viz. skin friction coefficient and Nusselt number have also been calculated and their analysis is included in this study. The study presented in the thesis comprises of five chapters. The first chapter is aimed to fulfill the basic need of introducing the various concepts and foundation needed for fluid mechanics. Chapter two throw light on majority of passed research work related with the present work. Chapter three covers the mathematical formulation of the problem and its detailed description. A proper description of used methodology, together with the details of the numerical solution is also presented. Chapter four describes the result and discussion of the considered problem taken in chapter three. The work has been summarized in chapter five. In along with the finding of the study, the literature used in the course of the study has been referred under the section of literature cited. The related study may be helpful to applied scientific fields and different branch of engineering and applied mathematics.
Open Access
Reliability estimation of some SENs using UGF method
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2020-07) Bisht, Vaibhav; Singh, S.B.
In this research work, author has developed two different models which are given as: 1. Reliability assessment of 8×8 shuffle Exchange network with one stage less (SEN-) by using universal generating function method. 2. Reliability assessment of 4×4 shuffle exchange network (SEN) by using universal generating function method. In the first model, 8×8 SEN- MIN does not satisfy the basic condition of MIN of full connectivity as some of the inputs nodes are not connected to all output nodes. So 2×1 MUX and 1×2 DEMUX have been used at source end and destination end respectively of 8×8 SEN- to achieve full connectivity. The reliability block diagram of the terminal, broadcast and network reliability of 8×8 SEN- was presented and its reliability was calculated by universal generating function method. In the second model we have considered three 4×4 shuffle exchange networks, namely, 4×4 SEN, 4×4 SEN+ and 4×4 SEN+2. The reliability block diagram of terminal, broadcast and network reliability for each of these networks was presented. The reliability of 4×4 SEN, 4×4 SEN+ and 4×4 SEN+2 was calculated by using universal generating function method unlike done before. Both the presented models are demonstrated by appropriate illustrative examples.
Open Access
A study of thermo-magnetic effects on static state of cholesteric liquid crystal between two hot co-axial circular cylinders
(G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2009-06) Gangwar, Sukhdev Singh; Sharma, A.K.
Liquid crystal the fourth state of matter is observed between the crystalline solid and amorphous liquid states. It exihibits the properties of liquids as well as that of crystalline solid state. In the present study we have considered an infinite static layer of cholesteric liquid crystal lying between two infinite hot co-axial circular cylinders in the presence of azimuthal magnetic field when both the cylinders are held at different temperatures and are lying at rest. We have examined the thermo-magnetic effects in this problem. After obtaining the system of governing differential equations we have solved it numerically by Newton Raphson method. The results are then graphically plotted. It has been observed that orientation of molecules varies with the variation of magnetic field and temperature gradient parameters.

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