This paper is devoted to a study of the numerical solution of the thermoelastic model describing the contact problem between the body and a rigid foundation that is thermally conducting. The linear thermoelastic constitutive law describes the behavior of the material. The contact is frictionless and described with Signorini’s condition and a thermal contact condition when the heat exchange coefficient depends on the contact pressure. We aim to present a detailed description of the numerical modeling of the problem. on this end, we use a penalty method to approximate the constraints. Finally, we provide numerical simulations to study a two-dimensional example and compare the penalty problem with the Lagrangian one.

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.

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.

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.

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.

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.

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.

Background: Smoking is currently the most preventable cause of diseases and death worldwide and is one of the causative risk factors for developing cancer in different organs. Therefore, smoking patients must be carefully monitored for alterations in buccal mucosa caused by tobacco abuse.
Aim and Objective: The aim of the study is to investigate cytological changes in buccal mucosa cells and establish a correlation with the morphometric analysis of mouth opening among smokers and non-smokers.
Materials and Methods: A comparative study was conducted on 200 individuals aged between 20 and 60 years. The subjects were randomly chosen from inpatients and outpatients of the Medicine Department at Index Medical College and Hospital. Buccal smears of these patients were processed in the Department of Anatomy.
Results: Significant differences were observed between non-smokers and smokers for cells with binucleation, pyknosis, perinuclear halo, cytoplasmic granules, karyolysis, karyorrhexis, and micronuclei in buccal mucosal cells. However, no significant difference was found for cytoplasmic vacuoles between non-smokers and smokers. Similar studies have reported findings consistent with our non-smoking population.
Conclusion: The present study indicates that almost all cytomorphological findings were higher in smokers than in non-smokers. Early detection of oral cancers becomes complex as they are mostly innocuous and asymptomatic during their initial stages. Cytomorphometric analysis can be used regularly to detect these cell alterations.

Childhood constipation is a prevalent issue globally. Certain children experience persistent constipation and soiling, either as a result of surgical repair of anorectal malformations or underlying medical conditions that present management challenges. These refractory cases of constipation significantly affect the psychological well-being of both patients and their families. The available treatment options for refractory constipation are not clearly established. However, prompt and appropriate management of constipation contributes to an enhanced health-related quality of life. This article explores the current modalities available for treating children with challenging constipation and examines their impact on health-related quality of life.

Using coalescence and cones, this study defines three types of graphs formed by amalgamating vertices of disjoint unions of complete graphs. The three types include the cone over a disjoint union of two complete graphs (C1), the cone over a disjoint union of \(k\) complete graphs (C2), and the \(l\) cone over a disjoint union of two complete graphs (C3). Coalescence of complete graphs (C1, C3) and the \(l\) cone (C3) are determined by their Laplacian spectra, a novel finding. Their Laplacian spectra reveal the size of the vertex cutset. Applications include the analysis of corporate networks, where individuals form coalescence of complete graphs through joint membership of two or more company boards.