i-manager's Journal on Mathematics (JMAT)


Volume 12 Issue 1 January - June 2023

Research Paper

Performance Analysis of Convolutional Neural Networks for Image Classification with Appropriate Optimizers

Sana Danish* , Jamshaid Ul Rahman**, Gulfam Haider***
* Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
** School of Mathematical Sciences, Jiangsu University 301 Xuefu road, Zhenjiang, China.
*** FAST University of Computer and Emerging Sciences (NUCES), Chiniot Faisalabad (CFD), Campus, Pakistan.
Danish, S., Rahman, J. U., and Haider, G. (2023). Performance Analysis of Convolutional Neural Networks for Image Classification with Appropriate Optimizers. i-manager’s Journal on Mathematics, 12(1), 1-8. https://doi.org/10.26634/jmat.12.1.19398

Abstract

Optimizers in Convolutional Neural Networks play an important role in many advanced deep learning models. Studies on advanced optimizers and modifications of existing optimizers continue to hold significant importance in the study of machine tools and algorithms. There are a number of studies to defend and the selection of these optimizers illustrate some of the challenges on the effectiveness of these optimizers. Comprehensive analysis on the optimizers and alteration with famous activation function Rectified Linear Unit (ReLU) offered to protect effectiveness. Significance is determined based on the adjustment with the original Softmax and ReLU. Experiments were performed with Adam, Root Mean Squared Propagation (RMSprop), Adaptive Learning Rate Method (Adadelta), Adaptive Gradient Algorithm (Adagrad) and Stochastic Gradient Descent (SGD) to examine the performance of Convolutional Neural Networks for image classification using the Canadian Institute for Advanced Research dataset (CIFAR-10).

Research Paper

The Behavior of Jump Discontinuous Function in Timbre

Paul Nishanth F.*
Loyola College, Chennai, Tamil Nadu, India.
Nishanth, F. P. (2023). The Behavior of Jump Discontinuous Function in Timbre. i-manager’s Journal on Mathematics, 12(1), 9-20. https://doi.org/10.26634/jmat.12.1.19342

Abstract

The structure of every musical instrument is related to the applied topics of mathematics like logarithms, golden ratio, etc., and this paper practically explores into this topic to know how music is related to the mathematical concepts. It can be realized that our sensitivity to sound is linked to the logic of our brains. Every musical instrument has distinct sounds while playing the same frequency. Many people know that music is continuous in one frequency. But in the quality of the sound, the discontinuity occurs in some musical instruments. We can see how discontinuity occurs in such behavior of the musical waveform in one frequency.

Research Paper

Parabolic Form of Casson Fluid Flow based on Angle of Inclination in Conducting Field

Mummadisetty Umamaheswar* , Poli Chandra Reddy**, Singamala Harinath Reddy***, Baddela Hari Babu****
*-*** Department of Mathematics, Annamacharya Institute of Technology and Sciences, Rajampet, Andhra Pradesh, India.
**** Department of Mathematics, PACE Institute of Technology & Sciences (Autonomous), Ongole, Andhra Pradesh, India.
Umamaheswar, M., Reddy, P. C., Reddy, S. H., and Babu, B. H. (2023). Parabolic Form of Casson Fluid Flow based on Angle of Inclination in Conducting Field. i-manager’s Journal on Mathematics, 12(1), 21-28. https://doi.org/10.26634/jmat.12.1.19628

Abstract

A considerable analysis has been performed to draw out the flow properties of MHD Casson fluid in parabolic movement with several parameters. The novelty in the examination is the angle of inclination with the permeable vertical plate. The purpose of the work is to analyze the impact of some parameters on the flow in two cases namely, obtuse angle and acute angle. The solution of the flow governed equations is attained by the utilization of the finite divergence technique in explicit type. The nature of the fluid velocity is observed in the cases of acute angle and obtuse angle and described accordingly with the use of graphs and tables. One of the major findings is that for increasing values of porosity the velocity enhances in the case of acute angle and falls down in the case of obtuse angle.

Research Paper

Common Fixed-Point Theorems via Notion of Pairwise Semi-Compatible Mappings and Occasionally Weakly Compatible Mappings (OWC) for Six Self-Mappings in Fuzzy Metric Spaces

RAKESH*
Department of Mathematics, Aurora's Technological and Management Academy, Hyderabad, Telangana, India.
Singh, T. R. (2023). Common Fixed-Point Theorems via Notion of Pairwise Semi-Compatible Mappings and Occasionally Weakly Compatible Mappings (OWC) for Six Self-Mappings in Fuzzy Metric Spaces. i-manager’s Journal on Mathematics, 12(1), 29-36. https://doi.org/10.26634/jmat.12.1.19308

Abstract

The notion of occasionally weakly compatible mappings, and Semi compatible mappings in fuzzy metric space is discussed in this research. The paper investigates the Common fixed-point theorems in fuzzy metric spaces. By taking the property of commutativity of pair mappings, the pairwise semi-compatible mappings and occasionally weakly compatible mappings, satisfying constructive type condition for six self-mappings the common fixed-point theorems in fuzzy metric spaces were proved. The result improves and generalizes other similar results in the literature.

Research Paper

Study of Goal Programming Approach in Resource Allocation in Acute Care Hospitals

Mandala Krishna* , Sobhan Babu Kappala**
* Department of Mathematics, Raghu Institute of Technology, Visakhapatnam, Andhra Pradesh, India.
** Department of Mathematics, JNTUK, Andhra Pradesh, India.
Krishna, M., and Kappala, S. B. (2023). Study of Goal Programming Approach in Resource Allocation in Acute Care Hospitals. i-manager’s Journal on Mathematics, 12(1), 37-43. https://doi.org/10.26634/jmat.12.1.19263

Abstract

In this study, the goal programming approach is discussed which is used in hospitals to allocate resources. Two linear goal-programming models are included in the process. One model fixes the ratio of different types of cases that doctors see each year, while the other translates case mix decisions into a set of practice changes for doctors. Decision-makers may use the models to find the optimal case mix that maximizes profitability for the institution while minimizing negative impacts on physician compensation and clinical workflow.