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Extended b-metric spaces and the related approximate fixed point results
Full text linkIn this paper, we investigate some approximate fixed point results in extended b-metric spaces using several contraction mappings such as the Mohseni-Saheli contraction, the B-contraction, and their consequences. Additionally, we prove some ϵ-fixed point results by using rational type contraction mappings, which were discussed mainly in Dass and Gupta [1975] and Jaggi [1977]. Also, a few examples are included to illustrate the results. Finally, we discuss some applications that support our main results in the field of applied mathematic
Gaussian Twin Neighborhood Prime Labeling on Fan Digraphs
Full text linkGaussian integers are complex numbers of the form \gamma=x+iy where x and y are integers and i^2=-1. The set of Gaussian integers is usually denoted by \mathbb{Z}[i]. A Gaussian integer \gamma=a+ib\in\mathbb{Z}[i] is prime if and only if either \gamma=\pm(1\pm i),N(\gamma)= a^2+b^2 is a prime integer congruent to 1(mod4), or \gamma=p+0i or =0+pi where p is a prime integer and |p|\equiv3(mod4). Let D=(V,A) be a digraph with |V|=n. An injective function f:V(D)\rightarrow\left[\gamma_n\right] is said to be a Gaussian twin neighborhood prime labeling of D, if it is both Gaussian in and out neighborhood prime labeling. A digraph which admits a Gaussian twin neighborhood prime labeling is called a Gaussian twin neighborhood prime digraph. In this paper, we introduce some definitions of fan digraphs. Further, we establish the Gaussian twin neighborhood prime labeling in fan digraphs using Gaussian integers
Mathematical modelling and application of reduced differential transform method for river pollution
Full text linkThis paper presents the mathematical model of pollutant transport in a river. To effectively find the analytical solution of the advectiondiffusion equation under various forms of suitable initial conditions, the reduced differential transform method (RDTM) is used. Three different initial concentration function cases, including rational, exponential, and power, are analyzed for the present model. A 2D and 3D visual comparison of the solutions obtained for each case is also shown. This article discusses the sufficient condition for convergence of the reduced differential transform approach to solving non-linear differential equations. The convergence results for the concentration functions in each case are briefly described. The present method is highly effective and more efficient in solving real-world problems. For all cases, the amount of phosphate pollutant concentration at various distances and time levels has been examined using numerical and graphical representations. While analyzing actual world problems, the current study demonstrates its effectiveness
Superior domination polynomial of cycles
Full text linkSuperior domination polynomial SD(G, x) is a polynomial in which the power of the variable denotes the cardinality of a superior dominating set and the total number of sets of same cardinality forms the coefficient of the variable. In this paper we find the SD(Cn, x) of cycle graphs. The results related to the polynomial SD(Cn, x) is stated and the proved
Near Mean Labeling in Dicyclic Snakes
Full text linkK. Palani et al. defined the concept of near mean labeling in digraphs. Let D=(V,A) be a digraph where Vthe vertex is set and A is the arc set. Let f:V\rightarrow{0,\ 1,\ 2,\ \ldots,q} be a 1-1 map. Define f^\ast:A\rightarrow{1,\ 2,\ \ldots,q} byf^\ast\left(e=\vec{uv}\right)=\left\lceil\frac{f\left(u\right)+f(v)}{2}\right\rceil. Letf^\ast\left(v\right)=\left|\sum_{w\in V}{f^\ast(\vec{vw})}-\sum_{w\in V}{f^\ast(\vec{wv})}\right|. Iff^\ast\left(v\right)\le2\ \ \forall\ v\in A(D), then f is said to be a near mean labeling of D and D is said to be a near mean digraph. In this paper, different dicyclic snakes are defined and the existence of near mean labeling in them is checked
A Dynamical Analysis of a Mathematical Model on Type-2 Diabetic From Obestiy
Full text linkThe aim of this research is to construct a model for type-2 diabeticfrom obesity using parameters based on the female population in India.We have introduced two control variables as diet with physicalactivity and medication. The positive endemic equilibrium is obtained.The local and global stability of the model are analyzed withsome specific conditions. Numerical simulations are carried out to exhibitthe flow of variables with controls. Our study mainly highlightsthe awareness of metabolic risk by healthy diet, physical activitiesand medications
On abduction, dualities and reason
Full text linkWe integrate dualistic conceptions of the real with Peirce's perspectives about reality and abduction, emphasizing the concept of reason underlying Peirce's thoughts. Peirce's abduction is related to the notions of retrogression and grounding in Hegel, later re-encountered in Hansonian-abduction.Abduction in turn is considered in relation to abstraction acquiring its fullest sense as a stage in the process of producing a theory. The process is iterative and self improving, it incorporates ``turbid thinking'' making it increasingly ``clear'' at successive iterations that incorporate the lessons taught by failed predictions, i.e., refutations. The cycle of thoughts promoted by doubts comes to rest when belief is reached. We discuss how this coming to rest depends on a criterion for cessation of doubts. The observation is illustrated with two different criteria, one proposed by Mach that only demands analogy and the criteria of dualists such as Goethe and Whewell that inspire the present work. Hence, it is possible to produce, and socially accept, imperfect theories unless we demand the highest level of rationality, avoiding any leftover of the turbid thoughts that have been used in the early developments. This work rests upon the existence of some objective form of reason. Influenced by a constructivist, Piagetian, perspective of science, we propose and discuss a small number of conditions that we identify as characteristics of rational abduction: rules for the rational construction of theories. We show how a classical example of belief that satisfiestoday's most common definition of abduction does not match the standards of rational retroduction. We further show how the same rules indicate the partial detachment of Special Relativity from the observable world, a fact actually known to Einstein. We close arguing that there is an urgent need to develop a critical epistemology incorporating dualistic perspectives
G-Supra and G-Infra space
Full text linkThe main idea of this paper is to generate supra and infra topologies from simple undirected graphs. For this, we have introduced two new operators namely supra and infra operators which are defined on the power set of the vertex set of a graph. Moreover, we have also proved that the supra operator satisfying Kuratowski’s closure axiom will yield a topology. Further it was extended to develop the concept of connectedness and separation axioms on G-supra and G-infra spaces
Short-time fourier transform based ensemble classifiers for detection of atrial fibrillation from ECG datasets
Full text linkAtrial Fibrillation (Afib) is a common cardiac arrhythmia characterized by irregular and often rapid heart rate, leading to inefficient blood pumping from the atria. It increases the risk of stroke, heart failure, and other heart-related complications. Afib is often associated with symptoms like palpitations, shortness of breath, and fatigue. Diagnosis typically involves electrocardiography (ECG) to detect irregular electrical activity in the heart. Treatment options range from medication to procedures like catheter ablation, aimed at restoring normal heart rhythm and reducing associated risks. Soft computing methods can aid in automating the classification of cardiovascular diseases, assisting clinicians in diagnosing arrhythmias. In this research paper, ensemble classifiers are employed for the classification of Atrial Fibrillation based on ECG datasets. When utilizing the Catboost Classifier in conjunction with the STFT-based GEO implementation, the results indicate an average perfect classification rate of approximately 99%, an error rate of 1%, and a kappa coefficient of 0.9689% for detection of Afib
DNA pedagogy: between sociology of science and historical-epistemic issues (Pedagogia del DNA: tra sociologia della scienza e questioni storico-epistemiche)
Full text linkThe pedagogical function of science teaching may benefit from an analysis of the historical-epistemic dimension, without neglecting the socio-political context in which a given research was carried out. In the case of DNA structure, the background of its discovery is particularly complex. Starting from the analysis of some papers, the view on the circumstances that led to their drafting broadens. We try to answer the fundamental question for any educator: why teach all that? Ethics issues are related to the general organisation of research, increasingly focused on speed and competition. Even teaching is affected by these dynamics, not only in higher education, but also at secondary level; students should be made aware of this trend. The history of science could therefore favour a more general awareness.SUNTOLa funzione pedagogica dell’insegnamento scientifico può trarre vantaggio da un’analisi della dimensione storico-epistemica, senza trascurare il contesto socio-politico nel quale una determinata ricerca è stata condotta. Nel caso della struttura del DNA, i retroscena della sua scoperta sono particolarmente complessi. Dopo l’analisi di alcuni articoli, si allarga gradualmente la vista sulle circostanze che hanno condotto alla loro stesura. Si cerca di rispondere a una domanda fondamentale per ogni educatore: perché insegnare tutto ciò? Le questioni etiche riguardano l’organizzazione generale della ricerca, sempre più tesa alla velocità e alla competizione. Persino l’insegnamento è influenzato da dinamiche simili, non solo in ambito accademico, ma anche a livello secondario; gli studenti dovrebbero essere a conoscenza di questa tendenza. La storia della scienza può dunque favorire una maggiore consapevolezza