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On the influencing facets of infant mortality in Karnataka: A study based on birth orders
The infant mortality rate (IMR) is used to assess the overall physical health of any community. Reducing this and spreading awareness among people can improve the well-being of society. In India, IMR is high due to the complex and challenging health policies and increased population, but various socio-economic and demographic factors play a significant role in determining the infant mortality rate. This study majorly focuses on identifying the factors influencing infant mortality, and a model has been proposed to estimate the likelihood of an infant's survival in Karnataka. For the empirical analysis, data has been taken from the National Family Health Survey-4 (2015-16), India. It is found that mothers' education and female literacy are the most significant factors affecting the IMR irrespective of the birth order. It is also found that the various socio-economic and demographic factors do not have a significant influence on the survival status of an infant as the birth order increases. Other factors like preceding birth interval, wealth index, caste, and religion also influence infant mortality. Hence, it is suggested that parents should have access to quality education and health facilities near their place of residence to reduce infant mortality at each order of birth. 2025 Author(s). -
On the Investigation of Environmental Effects of ChatGPT Usage via the Newly Developed Mathematical Model in Caputo Sense
This study explores the interconnection between the variables of ChatGPT usage, energy consumption, water consumption, and carbon dioxide CO2 emissions. A new integer and fractional order model using the Caputo derivative is proposed to comprehend the long-term dependencies of these variables. Boundedness, and global and local stability are examined for the fractional order model. The equilibrium points of these variables are shown to determine the stability of the model. The RungeKutta 7 numerical method is employed for the integer order model, whereas the semi-implicit linear interpolation (L1) method is used for the fractional order model. The parameter sensitivity is conducted on the systems parameters to understand the variables impact by varying the relevant parameters for the system. To increase the efficacy of our analysis, we used machine learning approaches to model and predict the dynamics of CO2 emissions, energy and water consumption, and ChatGPT usage. The Prophet ML model stood out among the other methods because it is adept at identifying long-term growth trends, seasonal changes, and the impact of outside variables in intricate time-series data. It is extremely beneficial for research centered on sustainability, where accurate projections are essential for wellinformed decision-making, because it can produce robust, interpretable forecasts against missing values and outliers. Using the Prophet ML model, our research guarantees precise and expandable predictions and provides valuable information that can direct tactics to balance environmental sustainability and technological progress. 2026 by the authors. -
On the k-Forcing Number of Some DS-Graphs
Amos et al. introduced the notion of k-forcing number as a generalization of Zero forcing number and is denoted by Fk(G) where k> 0 is any positive integer, the k -forcing number of a graph is the minimum cardinality among all k -forcing sets of a graph G. In this paper, many bounds for k -forcing number of degree splitting graph DS(G) for different graph classes are found. We evaluate the value of k -forcing number of degree splitting graph of some of the Cartesian product graph for different values of k. Also we observed that for Tur graph Tn , t, upper and lower bound is given by, Fk(Tn , t) ? Fk(DS(Tn , t) ) ? Fk(Tn , t) + 1. 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. -
On the Laplacian energy of interval valued fuzzy graphs
Interval valued fuzzy Laplacian matrix (IVFLM) associated with an interval valued fuzzy graph (IVFG) is studied in this paper. We define spectrum, energy, Laplacian spectrum and Laplacian energy and obtain some bounds for energy and Laplacian energy. 2020 Author(s). -
On the Mass Accretion Rate and Infrared Excess in Herbig Ae/Be Stars
The present study makes use of the unprecedented capability of the Gaia mission to obtain the stellar parameters such as distance, age, and mass of HAeBe stars. The accuracy of Gaia DR2 astrometry is demonstrated from the comparison of the Gaia DR2 distances of 131 HAeBe stars with the previously estimated values from the literature. This is one of the initial studies to estimate the age and mass of a confirmed sample of HAeBe stars using both the photometry and distance from the Gaia mission. Mass accretion rates are calculated from H? line flux measurements of 106 HAeBe stars. Since we used distances and the stellar masses derived from the Gaia DR2 data in the calculation of the mass accretion rate, our estimates are more accurate than previous studies. The mass accretion rate is found to decay exponentially with age, from which we estimated a disk dissipation timescale of 1.9 0.1 Myr. The mass accretion rate and stellar mass exhibit a power-law relation of the form . From the distinct distribution in the values of the infrared spectral index, n2-4.6, we suggest the possibility of difference in the disk structure between Herbig Be and Herbig Ae stars. 2019. The American Astronomical Society. All rights reserved.. -
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On the Maximization of Some Graph Coloring Problems
A graph coloring problem involves labeling the vertices or edges in a graph with newlinecolors or numbers subject to some constraints. The most frequently known graph newlinecoloring problems are the ones that usually minimize the number of colors used in newlinecoloring the vertices or edges. The chromatic number of a graph G, denoted by and#967;(G), is the least number of colors used in a proper coloring of G. The chromatic sum of a graph G, denoted as P(G), was introduced in [1], which is to and the smallest possible coloring sum in a proper coloring of the graph G using natural numbers. Lately, a few studies have endured in a distinct area of the literature where the number of colors used in a graph coloring problem is maximized under certain conditions. Some of these works have applications in network sciences. newlineThe concerned study focuses on the maximization of three dierent edge coloring newlineconcepts, viz., the vertex induced kand#8722;edge coloring, vertex incident kand#8722;edge coloring, newlineand edge incident 2and#8722;edge coloring of a simple connected graph G, where k and#8805; 2. The newlinenumber of colors assigned to the edges of the graph G has been maximized under certain conditions. The vertex induced kand#8722;edge coloring and the vertex incident newlinekand#8722;edge coloring concepts are the generalized version of the edge coloring approach newlineintroduced and studied in [2]. Furthermore, the concept of the achromatic sum of a graph G has also been introduced here. This concept is to and the greatest possible coloring sum of the graph G in an improper edge coloring using natural numbers. An extensive study newlineon three achromatic sums, namely the vertex induced 2and#8722;edge coloring sum, the vertex incident 2and#8722;edge coloring sum, and the edge incident 2and#8722;edge coloring sum are carried out. A few bounds for these parameters on a simple connected graph G and the exact values for some elementary graph classes have been investigated. A few comparative results between some of these parameters have also been obtained. -
On the Motion of Non-Newtonian EyringPowell Fluid Conveying Tiny Gold Particles Due to Generalized Surface Slip Velocity and Buoyancy
In the painting industry, space science and biomedical science, the nature of relaxation in the flow of non-Newtonian fluid (i.e. blood) containing gold (Ag) suits the characteristics of EyringPowell fluid flow induced by generalized surface slip velocity and buoyancy. However, flow of various non-Newtonian fluids on the horizontal surface of a slanted paraboloid of revolution objects (i.e. rocket, as in space science), over a bonnet of a car and over a pointed surface of an aircraft is of importance to experts in all these fields. In this article, the analysis of the motion within the thin layer formed on a horizontal object which is neither a perfect horizontal nor vertical and neither an inclined surface nor a cone/wedge is presented. The transformed governing equations which model the flow was non-dimenzionalized, parameterized and solved numerically using a well-known RungeKutta integration procedure along with shooting technique. The influence of increasing the magnitude of major parameters on the temperature distribution, local heat transfer rate, concentration of the fluid, local skin friction coefficient and velocity of the flow are illustrated graphically and discussed. Velocity slip parameter is found to be a decreasing function of temperature distribution across the flow. Heat transfer rate (NuxRex-1/2) at the wall (?= 0) is an increasing function of velocity slip parameter. Maximum coefficient of concentration of homogeneous bulk fluid at the wall exists at larger values of the emerged velocity slip and volume fraction parameters. 2018, Springer Nature India Private Limited. -
On the Non-Inverse Graph of a Group
Let (G, ?) be a finite group and S = {u G|u u-1}, then the inverse graph is defined as a graph whose vertices coincide with G such that two distinct vertices u and v are adjacent if and only if either u ? v S or v ? u S. In this paper, we introduce a modified version of the inverse graph, called i?-graph associated with a group G. The i?-graph is a simple graph with vertex set consisting of elements of G and two vertices x, y ? are adjacent if x and y are not inverses of each other. We study certain properties and characteristics of this graph. Some parameters of the i?-graph are also determined. 2022 Javeria Amreen et al., published by Sciendo. -
On the quick estimation of probability of recovery from COVID-19 during first wave of epidemic in India: a logistic regression approach
The COVID-19 pandemic has recently become a threat all across the globe with the rising cases every day and many countries experiencing its outbreak. According to the WHO, the virus is capable of spreading at an exponential rate across countries, and India is now one of the worst-affected country in the world. Researchers all around the world are racing to come up with a cure or treatment for COVID-19, and this is creating extreme pressure on the policy makers and epidemiologists. However, in India the recovery rate has been far better than in other countries, and is steadily improving. Still in such a difficult situation with no effective medicine, it is essential to know if a patient with the COVID-19 is going to recover or die. To meet this end, a model has been developed in this article to estimate the probability of a recovery of a patient based on the demographic characteristics. The study used data published by the Ministry of Health and Family Welfare of India for the empirical analysis. Hemlata Joshi, S. Azarudheen, M. S. Nagaraja, Singh Chandraketu. -
On the rainbow neighbourhood number of Mycielski type graphs
A rainbow neighbourhood of a graph G is the closed neighbourhood N[v] of a vertex v ? V (G) which contains at least one colored vertex of each color in the chromatic coloring C of G. Let G be a graph with a chromatic coloring C defined on it. The number of vertices in G yielding rainbow neighbourhoods is called the rainbow neighbourhood number of the graph G, denoted by rX(G). In this paper, we discuss the rainbow neighbourhood number of the Mycielski type graphs of graphs. 2018 Academic Publications. -
On the rainbow neighbourhood number of set-graphs
In this paper, we present results for the rainbow neighbourhood numbers of set-graphs. It is also shown that set-graphs are perfect graphs. The intuitive colouring dilemma in respect of the rainbow neighbourhood convention is clarified as well. Finally, the new notion of the maximax independence, maximum proper colouring of a graph and a new graph parameter called the i-max number of G are introduced as a new research direction. 2020 the author(s). -
ON THE SECURE EQUITABLE DOMINATION IN GRAPHS
A secure equitable dominating set S of a graph G is a dominating set in which for any vertex v ? V (G) \ S there exists at least one vertex u ? S such that u ? Ne(v), where Ne(v) indicate the equitable neighbourhood of v, and if we swap the vertex u with v, the equitable domination property of the graph will be unharmed. ?esec(G) represents the secure equitable domination number of G, which is the cardinality of the minimum secure equitable dominating set in G. The improved bounds of the secure equitable domination number of some fundamental kinds of graphs are established in this study. Furthermore, we incorporate specific results based on the diameter, girth, and degree. Additionally, we determine the bounds of the secure equitable domination number of specific special classes of graphs. I??k University, Department of Mathematics, 2025; all rights reserved. -
On the secure vertex cover pebbling number
A new graph invariant called the secure vertex cover pebbling number, which is a combination of two graph invariants, namely, secure vertex cover and cover pebbling number, is introduced in this paper. The secure vertex cover pebbling number of a graph, G, is the minimum number m so that every distribution of m pebbles can reach some secure vertex cover of G by a sequence of pebbling moves. In this paper, the complexity of the secure vertex cover problem and secure vertex cover pebbling problem are discussed. Also, we obtain some basic results and the secure vertex cover pebbling number for complete r-partite graphs, paths, Friendship graphs, and wheel graphs. 2023 World Scientific Publishing Co. Pte Ltd. All rights reserved. -
On the Temporal Causal Relationship Between Macroeconomic Variables: Empirical Evidence From India
The present study examines the dynamic interactions among macroeconomic variables such as real output, prices, money supply, interest rate (IR), and exchange rate (EXR) in India during the pre-economic crisis and economic crisis periods, using the autoregressive distributed lag (ARDL) bounds test for cointegration, Johansen and Juselius multivariate cointegration test, Granger causality/Block exogeneity Wald test based on Vector Error Correction Model, variance decomposition analysis and impulse response functions. The empirical results reveal a stronger long-run bilateral relationship between real output, price level, IR, and EXR during the pre-crisis sample period. Moreover, the empirical results confirm a unidirectional short-run causality running from price level to EXR, IR to price level, and real output to money supply during the pre-crisis period. Also, it is evident from the test results that there exist short-run bidirectional relationships running between real output and EXR, price level and IR, and IR and EXR in the pre-crisis era, respectively. Most importantly, long-run bidirectional causality is found between real output, EXR, and IR during the economic crisis period. And the study results indicate short-run bidirectional causality between money supply and EXR, IR and price level, and IR and output in India during the crisis era. Also, a short-run unidirectional causality runs from prices to real output in the crisis period. The Author(s) 2014. -
On the Wave Propagation and Dynamic Response of a Spherical Cavity in Piezoelectric Microstructures via Rabotnov Kernel-Based MooreGibsonThompson Thermoelasticity Theory
This study investigates the transient dynamic response and thermomechanical stability of a transversely isotropic piezoelectric medium featuring a spherical cavity. To accurately model the small-scale effects inherent in advanced structural components, a spatiotemporal nonlocal elasticity framework of the KleinGordon type is employed, incorporating both internal length and intrinsic time scale parameters. The governing equations of the MooreGibsonThompson (MGT) thermoelastic model are reformulated using a nonsingular Rabotnov-type fractional exponential kernel, providing a robust mathematical formulation to capture memory-dependent interactions without the paradox of infinite propagation speeds. The structural boundary of the cavity is subjected to a ramp-type thermal loading and electrical grounding, simulating realistic operational conditions for sensors and actuators. Using the Laplace transform technique and the Zakian numerical inversion method, the transient distributions of temperature, displacement, stress, and electric potential are derived. The results highlight the significant influence of the Rabotnov fractional parameter and spatiotemporal nonlocality on the structural stability and wave-front characteristics. This research provides a unique medium for understanding the latest developments in fractional-order dynamics for piezoelectric micro- and nano-structures, offering practical insights for civil, aerospace, and mechanical engineering applications. 2026 World Scientific Publishing Company. -
On the Way to Oneself : An Existential Study of the Select Plays of Sreeja K V and Sajitha Madathil
The perennial inquiries into human identity and the purpose of existence persist as enduring mysteries, often evoking a sense of introspection and existential angst. Amidst the quest for elucidation, individuals frequently find themselves entangled in the web of maya (appearance), wherein perceptions of reality become distorted, leading to emotional responses including jealousy, greed, guilt, and disappointment. However, amidst this labyrinth of existence, philosophical frameworks such as Existentialism and Advaita Vedanta offer invaluable lenses through which to perceive and engage with these existential inquiries. Existentialism prompts individuals to confront the subjective nature of their existence and assert autonomy in defining their identities and purpose. In contrast, Advaita Vedanta seeks to transcend the illusory veil of ego and perceive the ultimate reality of the Self (atman) as indistinguishable from the eternal consciousness (Brahman). Through the exploration of these philosophical paradigms, one can embark on a journey of Self- discovery, ultimately unveiling insights into the timeless questions of human existence. It is possible to identify this kind of crisis in the lives of the characters in the selected plays of Sreeja K V and Sajitha Madathil. Therefore, this thesis examines the selected plays of twenty-first-century Malayalam playwrights Sreeja K V and Sajitha Madathil through the lens of Simone de Beauvoir's existentialism and the pramana of Advaita Vedanta. It aims to explore the concept of the Self and how certain circumstances and experiences contribute to its realisation. By analysing the protagonists of these plays, the thesis seeks to uncover the notion that the Self is not merely a product of causality but rather the observer and creator of existence itself. This investigation raises further questions regarding the manifestation of the Self in one's life and the potential for misconceptions about its nature. The plays provide insights into the interaction between worldly illusions and the true essence of the Self, prompting consideration of how individuals often conflate these realms and succumb to materialistic temptations. Additionally, the thesis explores whether negative experiences are transient and whether individuals ultimately learn to overcome them. The selected plays open up the scope to understand the interplay of illusions of the world and the Self. This exploration leads to further questions like how does the Self appear in ones life? Is the Self mistaken? How often do people superimpose these two together and fall prey to the materialistic aspects? Is it true that the negative experiences are momentary, and often, one learns to survive from those experiences? Through the application of analytical frameworks of Existentialism and Advaita Vedanta into the select plays, this research endeavours to provide insights into these inquiries. -
On the zero forcing number of complementary prism graphs
The zero forcing number of a graph is the minimum cardinality among all the zero forcing sets of a graph G. The aim of this article is to compute the zero forcing number of complementary prism graphs. Some bounds on the zero forcing number of complementary prism graphs are presented. The remainder of this article discusses the following result. Let G and ? be connected graphs. Then Z(G?) ? n ? 1 if and only if there exists two vertices vi, vj ? V (G) and i 6? j such that, either N(vi) ? N(vj) or N[vi] ? N[vj] in G. 2025 Azarbaijan Shahid Madani University. -
On the zero forcing number of graphs and their splitting graphs
In [10], the notion of the splitting graph of a graph was introduced. In this paper we compute the zero forcing number of the splitting graph of a graph and also obtain some bounds besides finding the exact value of this parameter. We prove for any connected graph ? of order n ? 2, Z[S(?)] ? 2Z(?) and also obtain many classes of graph in which Z[S(?)] = 2Z(?). Further, we show some classes of graphs in which Z[S(?)] < 2Z(?). Journal Algebra and Discrete Mathematics. -
On thermal performance of spine fin in magnetized hybrid fluid rooted with Cu and MoS4 nanoparticles
This study examines the thermal performance of diverse profiles of spine fins with variable thermal conductivity. A hybrid nanofluid comprising Cu, and MoS4 with water as the base fluid, is modeled mathematically. Both the cylindrical and concave parabolic profiles are taken into account. The comparative outcomes are inferred from numerical and semi-analytical methods. The non-dimensional temperature profiles are analyzed graphically while considering the fin tip to be insulated, and the effects of various thermal parameters are also investigated. We have observed that the heat transfer rate shows an opposite trend toward convective-conduction and porosity parameter. The study also revealed that the concave parabolic profile emits more heat in comparison with the cylindrical profile. 2024 Author(s).