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ISSN: 2523-0212 (online) 2616-4906 (Print)
ISSN: 2616-8111 (online) 2616-8103 (Print)
ISSN: 2617-9687 (online) 2617-9679 (Print)
ISSN: 2618-0758 (online) 2618-074X (Print)
ISSN: 2617-9709 (online) 2617-9695 (Print)
ISSN: 2791-0814 (online) 2791-0806 (Print)
Open Journal of Mathematical Science (OMS)
ISSN: 2523-0212 (online) 2616-4906 (Print)
Open Journal of Mathematical Analysis (OMA)
ISSN: 2616-8111 (online) 2616-8103 (Print)
Open Journal of Discrete Applied Mathematics (ODAM)
ISSN: 2617-9687 (online) 2617-9679 (Print)
Ptolemy Journal of Chemistry (PJC)
ISSN: 2618-0758 (online) 2618-074X (Print)
Engineering and Applied Science Letters (EASL)
ISSN: 2617-9709 (online) 2617-9695 (Print)
Trends in Clinical and Medical Sciences (TCMS)
ISSN: 2791-0814 (online) 2791-0806 (Print)
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.
A famous conjecture of Ryser states that any \(r\)-partite set system has transversal number at most \(r-1\) times their matching number. This conjecture is only known to be true for \(r\leq3\) in general, for \(r\leq5\) if the set system is intersecting, and for \(r\leq9\) if the set system is intersecting and linear. In this note, we deal with Ryser’s conjecture for intersecting \(r\)-partite linear systems: if \(\tau\) is the transversal number for an intersecting \(r\)-partite linear system, then \(\tau\leq r-1\). If this conjecture is true, this is known to be sharp for \(r\) for which there exists a projective plane of order \(r-1\). There has also been considerable effort to find intersecting \(r\)-partite set systems whose transversal number is \(r-1\). In this note, we prove that if \(r\geq2\) is an even integer, then \(f_l(r)\geq3r-5\), where \(f_l(r)\) is the minimum number of lines of an intersecting \(r\)-partite linear system whose transversal number is \(r-1\). Aharoni \emph{et al.,} [R. Aharoni, J. Barát and I.M. Wanless, \emph{Multipartite hypergraphs achieving equality in Ryser’s conjecture}, Graphs Combin. {\bf 32}, 1–15 (2016)] gave an asymptotic lower bound: \(f_l(r)\geq3\).\(052r+O(1)\) as \(r\to\infty\). For some small values of \(r\) (\(r\geq2\) an even integer), our lower bound is better. Also, we prove that any \(r\)-partite linear system satisfies \(\tau\leq r-1\) if \(\nu_2\leq r\) for all \(r\geq3\) odd integer and \(\nu_2\leq r-2\) for all \(r\geq4\) even integer, where \(\nu_2\) is the maximum cardinality of a subset of lines \(R\subseteq\mathcal{L}\) such that any three elements chosen in \(R\) do not have a common point.
The vertex-degree based (VDB) topological index (or graphical function-index) \(TI_{f}(G)\) of \(G\) with edge-weight function \(f(x,y)\) was defined as \(TI_{f}(G)=\sum\limits_{uv\in E(G)}f(d(u),d(v))\), where \(d(u)\) is the degree of vertex \(u\) in \(G\). In this paper, we use a unified way to determine the extremal values of VDB indices of connected \((n,m)\)-graphs. When \(f(x,y)\) satisfies some special properties, we determine the connected \((n,m)\)-graphs with maximum (or minimum) \(TI_{f}(G)\) is the almost regular graphs. Our results generalize the results of paper [Aashtab, A., Akbari, S., Madadinia, S., Noei, M., \& Salehi, F. (2022) On the graphs with minimum Sombor index. MATCH Commun. Math. Comput. Chem., {88}, 553-559].
For all positive even integers \(n\), graphs of order \(n\) with degree sequence \(S_{n}:1,2,\dots,n/2,n/2,n/2+1,n/2+2,\dots,n-1\) naturally arose in the study of a labeling problem in [1].This fact motivated the authors of the aforementioned paper to study these sequences and as a result of this study they proved that there is a unique graph of order \(n\) realizing \(S_{n}\) for every even integer \(n\). The main goal of this paper is to generalize this result.
The Sombor index has gained lot of attention in the recent days for its mathematical properties and chemical applicabilities. Here, we initiated the novel block number version of the classical Sombor index and its matrix representation of a graph. The Block Sombor index \(BS(G)\) is defined as the sum total of square root of the sum of squares of block numbers of adjacent vertices, where the block number of a vertex is the number of blocks to which that vertex belongs to. The main purpose of this paper is to obtain some bounds and characterizations of \(BS(G)\) and its Block Sombor energy \(E_{BS}\). Also, we estimate some properties of spectral radius of Block Sombor matrix \(A_{BS}(G)\).
This study aims to model the statistical behaviour of extreme maximum temperature values in Rwanda. To achieve such an objective, the daily temperature data from January 2000 to December 2017 recorded at nine weather stations collected from the Rwanda Meteorological Agency were used. The two methods, namely the block maxima (BM) method and the Peaks Over Threshold (POT), were applied to model and analyse extreme temperatures in Rwanda. Model parameters were estimated, while the extreme temperature return periods and confidence intervals were predicted. The model fit suggests that Gumbel and Beta distributions are the most appropriate for the annual maximum daily temperature. Furthermore, the results show that the temperature will continue to increase as estimated return levels show it.
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