i-manager Publications

i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 13 Issue 2

Mathematical Modeling of Higher Overtone Vibrational Frequencies in Dichlorine Monoxide
Some Types of Generalized Closed and Generalized Star Closed Sets in Topological Ordered Spaces
Optimizing Capsule Endoscopy Detection: A Deep Learning Approach with L-Softmax and Laplacian-SGD
Kernel Ideals in Semigroups
Modeling the Dynamics of Covid-19 with the Inclusion of Treatment, Vaccination and Natural Cure
Calculation of Combined Vibrational Frequencies in Cl₂O using Lie Algebraic Method

Most Cited

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).

References

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[2]. Ahlawat, S., Choudhary, A., Nayyar, A., Singh, S., & Yoon, B. (2020). Improved handwritten digit recognition using convolutional neural networks (CNN). Sensors, 20(12), 3344.

[3]. Babu, D. V., Karthikeyan, C., & Kumar, A. (2020, December). Performance analysis of cost and accuracy for whale swarm and RMSprop optimizer. In IOP Conference Series: Materials Science and Engineering, 993(1), 012080. IOP Publishing.

[4]. Bashar, A. (2019). Survey on evolving deep learning neural network architectures. Journal of Artificial Intelligence, 1(2), 73-82.

[5]. Bottou, L. (2012). Stochastic gradient descent tricks. In G. Montavon, G. B. Orr, & K. R. Müller (Eds), Neural Networks: Tricks of the Trade (pp. 421-436).

[6]. Cui, X., Zhang, W., Tüske, Z., & Picheny, M. (2018). Evolutionary stochastic gradient descent for optimization of deep neural networks. Advances in Neural Information Processing Systems, 31.

[7]. Gu, J., Wang, Z., Kuen, J., Ma, L., Shahroudy, A., Shuai, B., ... & Chen, T. (2018). Recent advances in convolutional neural networks. Pattern Recognition, 77, 354-377.

[8]. Hayou, S., Doucet, A., & Rousseau, J. (2019, May). On the impact of the activation function on deep neural networks training. In International Conference on Machine Learning (pp. 2672-2680). PMLR.

[9]. Jais, I. K. M., Ismail, A. R., & Nisa, S. Q. (2019). Adam optimization algorithm for wide and deep neural network. Knowledge Engineering and Data Science, 2(1), 41-46.

[10]. Ketkar, N., & Santana, E. (2017). Deep Learning with Python (Vol. 1). Springer, Berkeley, CA.

[11]. Kingma, D. P., & Ba, J. (2014). Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980.

[12]. Lei, X., Pan, H., & Huang, X. (2019). A dilated CNN model for image classification. IEEE Access, 7, 124087-124095.

[13]. Li, H., Liu, H., Ji, X., Li, G., & Shi, L. (2017). Cifar10-dvs: an event-stream dataset for object classification. Frontiers in Neuroscience, 11, 309.

[14]. Li, Y. (2022, January). Research and application of deep learning in image recognition. In 2022 IEEE 2nd International Conference on Power, Electronics and Computer Applications (ICPECA) (pp. 994-999). IEEE.

[15]. Li, Y., & Yuan, Y. (2017). Convergence analysis of two-layer neural networks with relu activation. Advances in Neural Information Processing Systems, 30.

[16]. Li, Z., Liu, F., Yang, W., Peng, S., & Zhou, J. (2021). A survey of convolutional neural networks: analysis, applications, and prospects. IEEE Transactions on Neural Networks and Learning Systems, 33(12), 6999-7019.

[17]. Lydia, A., & Francis, S. (2019). Adagrad-an optimizer for stochastic gradient descent. International Journal of Information and Computing Science, 6(5), 566-568.

[18]. Mahajan, A., & Chaudhary, S. (2019, June). Categorical image classification based on representational deep network (RESNET). In 2019 3rd International conference on Electronics, Communication and Aerospace Technology (ICECA) (pp. 327-330). IEEE.

[19]. Maharjan, S., Alsadoon, A., Prasad, P. W. C., Al-Dalain, T., & Alsadoon, O. H. (2020). A novel enhanced softmax loss function for brain tumour detection using deep learning. Journal of Neuroscience Methods, 330, 108520.

[20]. Martin-Donas, J. M., Gomez, A. M., Gonzalez, J. A., & Peinado, A. M. (2018). A deep learning loss function based on the perceptual evaluation of the speech quality. IEEE Signal Processing Letters, 25(11), 1680-1684.

[21]. Monga, V., Li, Y., & Eldar, Y. C. (2021). Algorithm unrolling: Interpretable, efficient deep learning for signal and image processing. IEEE Signal Processing Magazine, 38(2), 18-44.

[22]. Postalcıoğlu, S. (2020). Performance analysis of different optimizers for deep learning-based image recognition. International Journal of Pattern Recognition and Artificial Intelligence, 34(2), 2051003.

[23]. Qu, Z., Yuan, S., Chi, R., Chang, L., & Zhao, L. (2019). Genetic optimization method of pantograph and catenary comprehensive monitor status prediction model based on adadelta deep neural network. IEEE Access, 7, 23210-23221.

[24]. Reddy, R. V. K., Rao, B. S., & Raju, K. P. (2018, June). Handwritten Hindi digits recognition using convolutional neural network with RMSprop optimization. In 2018 Second International Conference on Intelligent Computing and Control Systems (ICICCS) (pp. 45-51). IEEE.

[25]. Shinde, P. P., & Shah, S. (2018, August). A review of machine learning and deep learning applications. In 2018 Fourth International Conference on Computing Communication Control and Automation (ICCUBEA) (pp. 1-6). IEEE.

[26]. Sun, S., Cao, Z., Zhu, H., & Zhao, J. (2019). A survey of optimization methods from a machine learning perspective. IEEE Transactions on Cybernetics, 50(8), 3668-3681.

[27]. Traoré, C., & Pauwels, E. (2021). Sequential convergence of AdaGrad algorithm for smooth convex optimization. Operations Research Letters, 49(4), 452-458.

[28]. Ul Rahman, J., Ali, A., Ur Rehman, M., & Kazmi, R. (2020b). A unit softmax with Laplacian smoothing stochastic gradient descent for deep convolutional neural networks. In Intelligent Technologies and Applications: Second International Conference, INTAP 2019 (pp. 162-174). Springer, Singapore.

[29]. Ul Rahman, J., Chen, Q., & Yang, Z. (2020a). Additive parameter for deep face recognition. Communications in Mathematics and Statistics, 8, 203-217.

[30]. Ul Rahman, J., Makhdoom, F., Ali, A., & Danish, S. (2023). Mathematical modeling and simulation of biophysics systems using neural network. International Journal of Modern Physics B, 2450066.

[31]. Van Rossum, G., & Drake Jr, F. L. (1995). Python Tutorial (Vol. 620). Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands.

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[33]. Xiang, J., Dong, T., Pan, R., & Gao, W. (2020). Clothing attribute recognition based on RCNN framework using L-Softmax loss. IEEE Access, 8, 48299-48313.

[34]. Xu, J., Zhang, Z., Friedman, T., Liang, Y., & Broeck, G. (2018, July). A semantic loss function for deep learning with symbolic knowledge. In International Conference on Machine Learning (pp. 5502-5511). PMLR.

[35]. Zeiler, M. D. (2012). Adadelta: an adaptive learning rate method. arXiv preprint arXiv:1212.5701.

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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.

References

[1]. Benson, D. (2008). Music: A Mathematical Offering. Cambridge University Press, New York.

[2]. Jessop, S. (2017). The historical connection of Fourier analysis to music. The Mathematics Enthusiast, 14(1), 77-100.

[3]. Jones, S. (2021). ADSR Envelopes In Music Explained.

[4]. Krumhansl, C. L., & Iverson, P. (1992). Perceptual interactions between musical pitch and timbre. Journal of Experimental Psychology: Human Perception and Performance, 18(3), 739-751.

[5]. Lam, J. R., & Saitis, C. (2021). The timbre explorer: A synthesizer interface for educational purposes and perceptual studies. International Conference on New Interfaces for Musical Expression (pp. 1-9).

[6]. Lucas, J. R. (2001). Theory of Electricity-Analysis of Non-Sinusoidal Waveform-Part 1.

[7]. Parker. (2009). Timbre – Music and Math.

[8]. Petersen, M. (2001). Mathematical Harmonies.

[9]. Pierce, A. (2014). Partial Differential Equations, Lecture 15: Convergence of Fourier series.

[10]. Shah, S. (2010). An Exploration of the Relationship between Mathematics and Music (Doctoral dissertation, Manchester Institute for Mathematical Sciences, The University of Manchester).

[11]. Weiss, T. (2016). Musical Sound: A Mathematical Approach to Timbre.

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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.

References

[1]. Akbar, N. S., & Khan, Z. H. (2015). Metachronal beating of cilia under the influence of Casson fluid and magnetic field. Journal of Magnetism and Magnetic Materials, 378, 320-326.

[2]. Chamkha, A. J. (2000). Transient hydromagnetic three-dimensional natural convection from an inclined stretching permeable surface. Chemical Engineering Journal, 76(2), 159-168.

[3]. Endalew, M. F., & Sarkar, S. (2021). Incidences of aligned magnetic field on unsteady MHD flow past a parabolic accelerated inclined plate in a porous medium. Heat Transfer, 50(6), 5865-5884.

[4]. Goud, B. S., Srilatha, P., & Shekar, M. R. (2018). Study of Hall current and radiation effects on MHD free convective flow past an inclined parabolic accelerated Plate with variable temperature in a Porous medium. International Journal of Mechanical Engineering and Technology (IJMET), 9(7), 1268-1276.

[5]. Hamid, M., Zubair, T., Usman, M., Khan, Z. H., & Wang, W. (2019). Natural convection effects on heat and mass transfer of slip flow of time-dependent Prandtl fluid. Journal of Computational Design and Engineering, 6(4), 584-592.

[6]. Hayat, T., Shafiq, A., Alsaedi, A., & Asghar, S. (2015). Effect of inclined magnetic field in flow of third grade fluid with variable thermal conductivity. AIP Advances, 5(8), 087108.

[7]. Iftikhar, N., Riaz, M. B., Awrejcewicz, J., & Akgül, A. (2021). Effect of magnetic field with parabolic motion on fractional second grade fluid. Fractal and Fractional, 5(4), 163.

[8]. Jha, B. K., & Aina, B. (2021). MHD mixed convection flow in an inclined porous channel having time-periodic boundary condition (MHD mixed convection flow in an inclined porous channel). Journal of Porous Media, 24(6), 69-91.

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[10]. Kaushik, P., & Mishra, U. (2021). Numerical solution of free stream MHD flow with the effect of velocity slip condition from an inclined porous plate. Journal of Mathematical and Computational Science, 12, 1-14.

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[12]. Matao, P., Reddy, B. P., & Sunzu, J. (2022). Hall and rotation effects on radiating and reacting mhd flow past an accelerated permeable plate with Soret and Dufour effects. Trends in Sciences, 19(5), 2879-2879.

[13]. Patel, H. R. (2019). Effects of cross diffusion and heat generation on mixed convective MHD flow of Casson fluid through porous medium with non-linear thermal radiation. Heliyon, 5(4), e01555.

[14]. Rajput, U. S., & Kumar, G. (2016). Chemical reaction effect on unsteady MHD flow past an impulsively started oscillating inclined plate with variable temperature and mass diffusion in the presence of Hall current. Applied Research Journal, 2(5), 244-253.

[15]. Rao, B. M., Gopal, D., Kishan, N., Ahmed, S., & Prasad, P. D. (2020). Heat and mass transfer mechanism on threedimensional flow of inclined magneto Carreau nanofluid with chemical reaction. Archives of Thermodynamics, 41(2), 223- 238.

[16]. Reddy, B. P. (2019). Radiation and chemical reaction effects on unsteady MHD free convection parabolic flow past an infinite isothermal vertical plate with viscous dissipation. International Journal of Applied Mechanics and Engineering, 24(2), 343-358.

[17]. Reddy, P. C., Umamheswar, M., Reddy, S. H., Raju, A. M., & Raju, M. C. (2022). Numerical study on the parabolic flow of MHD fluid past a vertical plate in a porous medium. Heat Transfer, 51(4), 3418-3430.

[18]. Taid, B. K., & Ahmed, N. (2022). MHD free convection flow across an inclined porous plate in the presence of heat source, Soret effect, and chemical reaction affected by viscous dissipation Ohmic heating. Biointerface Research in Applied Chemistry, 12(5), 6280-6296.

[19]. Zeeshan, A., Majeed, A., Akram, M. J., & Alzahrani, F. (2021). Numerical investigation of MHD radiative heat and mass transfer of nanofluid flow towards a vertical wavy surface with viscous dissipation and Joule heating effects using Keller-box method. Mathematics and Computers in Simulation, 190, 1080-1109.

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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.

References

[1]. Abbas, M., Altun, I., & Gopal, D. (2009). Common fixed point Theorems for non compatible mappings in fuzzy metric spaces. Bulletin of Mathematical Analysis and Applications [Electronic only], 1(2), 47-56.

[2]. Al-Thagafi, M. A., & Shahzad, N. (2008). Generalized I-nonexpansive selfmaps and invariant approximations. Acta Mathematica Sinica, English Series, 24, 867-876.

[3]. Al-Thagafi, M. A., & Shahzad, N. (2009). A note on occasionally weakly compatible maps. International Journal of Mathematical Analysis, 3(2), 55-58.

[4]. Cho, Y. J., Sharma, B. K., & Sahu, D. R. (1995). Semi-compatibility and fixed points. Mathematica Japonicae, 42(1), 91-98.

[5]. Gupta, V., Deep, R., & Tripathi, A. K. (2018). Some common fixed point theorems in fuzzy metric spaces and their applications. Boletim da Sociedade Paranaense de Matemática, 36(3), 141-153.

[6]. Jain, A., & Chaudhary, B. (2013). On common fixed point theorems for semi-compatible and occasionally weakly compatible mappings in Menger space. International Journal of Research and Reviews in Applied Sciences, 14(3), 662- 670.

[7]. Jungck, G. (1986). Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences, 9(4), 771-779.

[8]. Kaleva, O., & Seikkala, S. (1984). On fuzzy metric spaces. Fuzzy Sets and Systems, 12(3), 215-229. https://doi.org/10. 1016/0165-0114(84)90069-1

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[14]. Singh, B., & Jain, S. (2005a). Semicompatibility and fixed point theorems in fuzzy metric space using implicit relation. International Journal of Mathematics and Mathematical Sciences, 2005(16), 2617-2629.

[15]. Singh, B., & Jain, S. (2005b). Weak compatibility and fixed point theorems in fuzzy metric spaces. Ganita, 56(2), 167-176.

[16]. Subrahmanyam, P. V. (1995). A common fixed point theorem in fuzzy metric spaces. Information Sciences, 83(3-4), 109-112.

[17]. Zadeh, L. (1965). Fuzzy sets. Inform Control, 8, 338-353.

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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.

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[1]. Feldstein, M. S. (1967). Economic Analysis for Health Service Efficiency. North-Holland.

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[3]. Fleck, L. M. (1994). Just caring: Oregon, health care rationing, and informed democratic deliberation. The Journal of Medicine and Philosophy, 19(4), 367-388.

[4]. Galbraith, J. K. (1967). The New Industrial State. Boston (Houghton Mifflin Company).

[5]. Garrison, R. H., Noreen, E. W., Brewer, P. C., & Mardini, R. U. (2003). Managerial Accounting. New York: McGraw-Hill/Irwin.

[6]. Gass, S. I. (1983). Decision-aiding models: Validation, assessment, and related issues for policy analysis. Operations Research, 31(4), 603-631.

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[8]. Tengs, T. O., Meyer, G., Siegel, J. E., Pliskin, J. S., Graham, J. D., & Weinstein, M. C. (1996). Oregon's Medicaid ranking and cost-effectiveness: Is there any relationship?. Medical Decision Making, 16(2), 99-107.

[9]. Turing, A. M. (2015). Computing Machinery and Intelligence. Mind, 59(9), 433-460.

[10]. Winston, W. (2017). Operations Research: Applications and Algorithms. Boston, PWS-Kent Publishing Company.

i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 13 Issue 2

Most Read

Most Cited

Volume 12 Issue 1 January - June 2023

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

References

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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

References

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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

References

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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

References

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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

References

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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.

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.

* Department of Mathematics, Raghu Institute of Technology, Visakhapatnam, Andhra Pradesh, India.

** Department of Mathematics, JNTUK, Andhra Pradesh, India.