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Ptolemy Scientific Research Press (PSR Press)is a highly regarded publisher of scientific literature dedicated to bringing the latest research and findings to a broader audience. With a focus on cutting-edge research and technology, Ptolemy Scientific Research Press offers a range of publications catering to professionals, researchers, and student’s needs. Whether looking for information on the latest breakthroughs in physics, biology, engineering, or computer science, you can trust Ptolemy Scientific Research Press to deliver insightful, accurate, and engaging content. With its commitment to quality, accessibility, and innovation, Ptolemy Scientific Research Press is an essential resource for anyone interested in science and technology.

Latest Published Articles

Minimization of layer feed cost using linear programming

EASL-Vol. 6 (2023), Issue 1, pp. 01 – 10 Open Access Full-Text PDF

Gabriel Obed Fosu, Jones Brefo Konadu, and Michael Yaw Yeboah

Abstract:Poultry farms in Ghana are experiencing a decline, and some are at risk of collapsing due to the high cost of poultry feed. The aim of this paper is to assist poultry farmers in increasing their profits by reducing the cost of poultry feed. The linear programming technique is implemented to utilize locally available feed ingredients to formulate layer feed mix for the various stages of poultry growth, which includes chick mash (starter), grower, and prelayer. Mathematical models are constructed based on the nutrient requirements of the layers, nutrient composition of the available ingredients, and any other restrictions on the available ingredients for the formulation. Seven decision variables and eleven constraints are identified. Compared to the existing practice, it is estimated that the LP model’s optimal solution can reduce feed formulation costs by approximately 30%, 19%, and 14% in chick mash, grower, and prelayer, respectively.

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Identification of parameters in parabolic partial differential equation from final observations using deep learning

OMA-Vol. 7 (2023), Issue 1, pp. 10 – 31 Open Access Full-Text PDF

Khalid Atif, El-Hassan Essouf and Khadija Rizki

Abstract:In this work, we propose a deep learning approach for identifying parameters (initial condition, a coefficient in the diffusion term and source function) in parabolic partial differential equations (PDEs) from scattered final observations in space and noisy a priori knowledge. In Particular, we approximate the unknown solution and parameters by four deep neural networks trained to satisfy the differential operator, boundary conditions, a priori knowledge and observations. The proposed algorithm is mesh-free, which is key since meshes become infeasible in higher dimensions due to the number of grid points explosion. Instead of forming a mesh, the neural networks are trained on batches of randomly sampled time and space points. This work is devoted to the identification of several parameters of PDEs at the same time. The classical methods require a total a priori knowledge which is not feasible.
While they cannot solve this inverse problem given such partial data, the deep learning method allows them to resolve it using minimal a priori knowledge.

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The local fractional natural transform and its applications to differential equations on Cantor sets

OMA-Vol. 7 (2023), Issue 1, pp. 01 – 09 Open Access Full-Text PDF

Djelloul Ziane, and Mountassir Hamdi Cherif

Abstract:The work that we have done in this paper is the coupling method between the local fractional derivative and the Natural transform (we can call it the local fractional Natural transform), where we have provided some essential results and properties. We have applied this method to some linear local fractional differential equations on Cantor sets to get nondifferentiable solutions. The results show this transform’s effectiveness when we combine it with this operator.

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The Galerkin method and hinged beam dynamics

OMS-Vol. 7 (2023), Issue 1, pp. 236 – 247 Open Access Full-Text PDF

David Raske

Abstract:In this paper we prove large-time existence and uniqueness of high regularity weak solutions to some initial/boundary value problems involving a nonlinear fourth order wave equation. These sorts of problems arise naturally in the study of vibrations in beams that are hinged at both ends. The method used to prove large-time existence is the Galerkin approximation method.

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Some arguments for the wave equation in quantum theory 3

OMS-Vol. 7 (2023), Issue 1, pp. 196 – 235 Open Access Full-Text PDF

Tristram de Piro

Abstract:In this paper, we proved that solutions \((\rho,J)\) exist for the 1-dimensional wave equation on \([-\pi,\pi]\). When \((\rho,J)\) is extended to a smooth solution \((\rho,\overline{J})\) of the continuity equation on a vanishing annulus \(Ann(1,\epsilon)\) containing the unit circle \(S^1\), a corresponding causal solution \((\rho,\overline{J}’ \overline{E}, \overline{B})\) to Maxwell’s equations can be obtained from Jefimenko’s equations. The power radiated in a time cycle from any sphere \(S(r)\) with \(r>0\) is \(O\left(\frac{1}{r}\right)\), which ensure that no power is radiated at infinity over a cycle.

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Thyroid volume and its correlation with thyroid function in central India

TCMS-Vol. 3 (2023), Issue 2, pp. 15 – 23 Open Access Full-Text PDF

Dr. Alka Agrawal, Dr. Gaurav Bhandari, Dr. Ashish Sahoo, Dr. Mohd. Asif and Dr. Mengpi Jamoh

Abstract:Introduction: Thyroid gland volume is highly variable as it is greatly influenced by age, gender, anthropometric measurements, and geographical location. It has become essential for every population to determine the reference range of their normal thyroid gland volume in healthy individuals. This, in turn, will help the population in grading goitre and guide large-scale iodine monitoring programs. Ultrasound, being more precise than clinical examination in identifying enlarged thyroid glands, overcomes the problems of overestimation of goitre prevalence and marked interobserver variability associated with palpation estimates. A nomogram of thyroid volume in our environment is important to serve as a reference point in managing patients with thyroid pathologies, especially goitre. The purpose of this study was to establish reference ranges of total thyroid volume among the normal adult population in central India using ultrasonography and correlate it with thyroid function tests.
Methods and Material: A prospective cross-sectional study was conducted in a tertiary care hospital. A total of 410 healthy subjects were included. B-mode Ultrasonography was used to measure the total thyroid volume by combining the volume of both lobes obtained using the ellipsoid formula. Blood samples were taken for thyroid function tests. Age-specific reference values for thyroid volume were obtained.
Statistical analysis used: IBM Statistical Package for the Social Sciences (SPSS) software for Windows, Version 26.0. Armonk, NY: IBM Corp was used for analysis.
Results: The mean total thyroid gland volume of all study subjects was \(6.90\pm1.74\) ml. Males had a significantly higher gland volume (\(7.30\pm1.86\) ml) compared to females (\(6.63\pm1.61\) ml) (\(P<0.001\)). The volume of the right lobe was significantly greater than that of the left lobe in both genders (\(3.76\pm0.96\) ml vs \(3.14\pm0.89\) ml, \(P<0.001\)). No significant correlation was found between gland volume and thyroid function tests.
Conclusions: We attempted to contribute to establishing the reference values for our local population, and further large studies are required to establish nationwide reference values of thyroid gland volume.

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BOOK-foundations-of-mathematical-analysis-and-semigroups-theory

BOOK - NULL CONTROLLABILITY OF DEGENERATE AND NON-DEGENERATE SINGULAR PARABOLIC