Boletim da Sociedade Paranaense de Matemática

A study on the temperature Sombor energy and entropy of a graph

Sharathkumar H T, Narahari Narasimha Swamy, Shrikanth C K, Vignesh Ravi — Thu, 09 Oct 2025 00:00:00 +0000

The temperature Sombor index is one of the variations of the recently introduced Sombor index, a degree based topological index, found to have nice mathematical properties and very useful applications. In our current study, we introduce the temperature Sombor matrix $\mathcal{T}(G)$, an associated matrix of the temperature Sombor index of a graph $G$, and present certain bounds on its eigenvalues. Additionally, we define the temperature Sombor energy $\mathcal{ET(G)}$ of $G$ and determine some bounds on it. We also discuss the chemical applicability of this parameter by comparing it with the $\pi$-electron energy of certain organic compounds. Additionally, we perform the regression analysis of the temperature Sombor energy with the graph energy of trees with fixed orders $n=8, 9, \dots, 18$. Further, we compute the temperature Sombor entropy of the silicon carbide compound and analyze it in conjunction with its temperature Sombor energy.

Balanced Graphs from Lexicographic Products of Open Neighborhood Graphs

RUDRAPATI BHUVANESWARA PRASAD, A. Mallikarjuna Reddy , G. Shobhalatha — Thu, 09 Oct 2025 21:28:29 +0000

This paper investigates the structural balance properties of Lexicographic Product graphs formed
by combining standard graph classes with their corresponding Open Neighborhood graphs. Specifically, we
construct the Lexicographic Product G′ = G[N(G)], where G is a standard graph and N(G) denotes its
open neighborhood graph. We examine the balance of the resulting signed graphs under various edge sign
assignments. For each graph class considered, we rigorously demonstrate that the resulting Lexicographic
Product graph is both regular and structurally balanced. The sign assignment methodology is derived from
adjacency relationships in both G and N(G). Through detailed examples and structural proofs, we confirm
that the signed Lexicographic Product graphs consistently exhibit balance, underscoring their significance in
the study of signed and structured networks.

RT-conjugate codes in the Rosenbloom-Tsfasman metric

Sai Gopinadh Bodigiri, Venkatrajam Marka — Thu, 09 Oct 2025 21:34:01 +0000

Linear Complementary Dual (LCD) codes are a special class of linear error-correcting code used in data transmission and storage. These codes possess specific algebraic properties that make them useful in applications, such as communication systems, cryptography, and data storage devices. These are particularly valuable in scenarios that require a high degree of error detection and correction. This study explores the characteristics of RT-conjugate codes within the Rosenbloom-Tsfasman metric (RT-metric). In this study, we focus on a specific subclass of LCD codes characterized by conjugate conditions. In particular, we establish sufficient conditions under which a linear code in the RT metric qualifies as an LCD code through its conjugate structure. We also analyzed the weight distribution of the dual of these codes in terms of their type and proposed several construction methods for RT-conjugate codes.

On the Existence of Optimal Binary LCD Codes Under Hierarchical Poset Metrics

Rohini More, Venkatrajam Marka — Thu, 09 Oct 2025 21:40:38 +0000

A linear code is referred to as a linear complementary dual (LCD) code when it has only a trivial intersection with its dual. LCD codes have gained prominence in research due to their application in cryptography, communication systems, and data storage.

”This article explores the binary LCD hierarchical poset code, wherein the dimension is determined by the rank of the Gramian of its generator matrix. By employing the canonical systematic form of the generator matrix of the hierarchical poset code, the corresponding Gramian matrix is specified by imposing certain conditions on the support of basis elements. Utilizing the Griesmer bound of linear code under Hamming metric and the canonical decomposition of the hierarchical poset code, a upper bound is established on the maximum distance

of the hierarchical poset code with any hull dimension under specified conditions. Furthermore, the study investigates the existence of optimal binary LCD codes under a hierarchical poset metric when $n$ is equivalent to $a$ mod $8$ where, $a$ ranges from $0$ to $7$.”

Natural convection flow of magnetohydrodynamic micropolar fluid in a dome-shaped enclosures

Kathyayani Gandrakota, Maheswari Siddamsetti, Venkata Ramudu Gattu — Thu, 09 Oct 2025 23:21:16 +0000

This study conducts a numerical investigation into laminar flow and natural convection heat transfer of micropolar fluid within dome-shaped enclosures (DSEs). The enclosure features adiabatic left and right walls, while the bottom wall is maintained at constant temperatures, with top dome-shape wall is cold. The study examines how the unique geometry of DSEs influences natural convection (N.C.) and flow characteristics under varying parameters such as Rayleigh number (Ra), Prandtl number (Pr), Hartmann number (Ha), micropolar parameter (K), and radiation parameter (Rd). The developed mathematical model, based on the vorticity-stream function method, investigates the influence of magnetic field strength and direction, micropolar fluid characteristics, and radiative heat transfer on both thermal and flow behavior. The results reveal significant modifications in velocity profiles, temperature distribution, and microrotation patterns due to changes in magnetic and radiative effects. This comprehensive analysis contributes to a deeper understanding of MHD natural convection in micropolar fluids with thermal radiation, aiding progress in advanced heat management systems and industrial applications.

Constrained Rational Cubic Fractal Interpolation Using Function Values

Rajesh Lenkalapelly, Mahipal Reddy Komandla — Thu, 09 Oct 2025 23:29:50 +0000

This paper presents the development of a constrained rational cubic fractal interpolation using
function values based on iterated function systems. The rational cubic fractal interpolation function is
constructed using a cubic polynomial in the numerator and a linear polynomial in the denominator, with
convergence properties that offer flexibility for modeling complex datasets exhibiting fractal-like behavior.
We show that the proposed approximation converges to the original function as the discretization parameter
trends to zero. The framework incorporates a single shape-control parameter and enforces constraints through
(i) piecewise linear functions, (ii) linear functions, and (iii) rectangular bounds that confine the interpolated
curve within a specified range. A detailed performance analysis is provided, along with a systematic approach
for selecting scaling factors and shape parameters. The effectiveness of the proposed method is validated
through extensive numerical experiments.

Characterization of Roughness in Gamma Near Algebras

Rajani K, P. Narasimha Swamy, B. Harika, T. Srinivas — Thu, 09 Oct 2025 23:37:30 +0000

Rough sets offer a way to deal with uncertain or imprecise data. Gamma near algebra (GNA) is a
broadening of near algebra (NA) and gamma near ring (GNR). In this paper we introduce the notions of rough
sub gamma near algebras (RSGNAs) and rough ideals (RIs) in a GNA and derive their key characteristics.
We further investigate the relationship between upper and lower approximations of these rough frameworks
and their images under homomorphism.

Significance of Cross Diffusion on the Transient Behaviour of Radiating Casson Fluid near a Heated Slanted Plate

Venkateswarlu Malapati, Chennaiah M. B, Noor Md — Thu, 09 Oct 2025 23:40:47 +0000

High heat is used to destroy tumors and abnormal tissues through thermal ablation. The use of hyperthermia with chemotherapy and radiation therapy has been shown to increase their efficacy by damaging cancer cells and enhancing drug delivery. It is possible to use heat therapies to target tumors precisely while causing minimal damage to normal tissues at the same time. Diffusion thermo and thermo diffusion effects can affect local concentrations of therapeutic agents and heat transfer, potentially enhancing hyperthermia treatment effectiveness. The properties of Casson fluids, which intimately resemble blood motion in capillaries, are principally relevant in the design of biomedical devices such as artificial organs. A study of heat transfer in fluid flows can also assist in recognition of pollutant dispersion from technical sources and correcting combustion productivity for reducing transmission. The analysis presented here investigates the unsteady flow of Casson fluid across an impulsively initiated slanted plate, under the influence of thermo diffusion, diffusion thermo, and thermal radiation. In this study, the controlling flow equations are integrated adopting the Laplace transform mechanism, and the consequences emphasize concentration, temperature, and velocity distributions based on disparate parameter estimates. Tables analyze Sherwood number, Nusselt number, and skin friction factors. The consequences show that increasing the thermal radiation and plate inclination angle increases the fluid velocity, while decreasing the wall friction is found for opposing and assisting buoyancy forces. The Nusselt number and fluid temperature are increased by heat source and diffusion thermo effects. In a similar vein, the Sherwood number lowers with thermal radiation and rises with the thermo-diffusion effect.

Hyperparameter Optimization in Neural Networks Approach to Singular Matrix Differential Systems

Venkata Sundaranand Putcha, Praveen Kumar Ulebeedu Matam — Thu, 09 Oct 2025 23:44:06 +0000

Singular Matrix Differential Systems (SMDS) or, alternatively, semi-state, degenerate, descriptor, constrained, or differential-algebraic systems (DAEs) are key to modeling dynamic processes experiencing abrupt structural or parametric changes. It becomes difficult to solve initial value problems (IVPs) for these systems as classical methods are ineffective to apply owing to singularity and a lack of closed-form solutions. This paper introduces an adaptive neural network solution to linear singular matrix differential systems (LSMDS) with a semi-supervised learning framework. Singular systems, a commonplace within engineering models and constraint-laden physical models, are extremely computationally challenging with stiffness, index intricacy, and inconsistent initial conditions. Standard numerical solvers are afflicted by similar challenges, especially with singular matrices. To compensate, we propose a hybrid neural structure joining (i) a systematic search with activation functions and (ii) a two-stage optimizer sequence joining Adam's strengths with those of L-BFGS. The structure learns precise approximations without mesh-based discretizations. We build a task-specific loss function comprising differential-algebraic systems (DAEs) to guide optimizer training. We also undertake a detailed hyperparameter study, comprising network depth, width, activation function choosing, and optimizer switching plans, to establish suitable configurations. We evaluate our approach with a number of benchmark singular systems, achieving better accuracy, robustness, and generalization beyond standard solvers. This paper provides a flexible, data-efficient substitute to solving challenging constraint-laden systems, with significant applications to scientific computation and real-world modeling.

Thermo-fluidic Behaviour of Maxwell - Type Hybrid Nano fluids under MHD and Radiative Effects with Wall Slip

RAVI UMMIDI, Madhusudan Patro, Karanam Sreelatha — Thu, 09 Oct 2025 23:48:50 +0000

Mathematicalmodellingisvital forunderstandingandoptimizingNanofluiddynamics in
electroniccoolingsystems. Itenablesresearcherstopredictfluidbehavior,enhanceheattransferperfor
mance,anddesignmoreefficientsystemswithfewerexperimentaltrials.Thisstudypresentsacomprehensive
computational analysis of hybridgraphene-basedNanofluidflowover a stretching surface, incorporating
magnetohydrodynamic(MHD)effects,nonlinearthermalradiation,chemicalreactions,andviscoelasticprop
erties. ThehybridNanofluidcomprisesgrapheneoxideandcoppernanoparticlesdispersedinaNewtonian
basefluid. TheBuongiornomodel accounts fornanoparticlemigrationdue toBrownianmotionandther
mophoresis,while theMaxwellmodel capturesViscoelasticbehavior.Second-order slipboundaryconditions
areimposedtoreflectmicroscaleeffectsrelevantinbiomedicalandmicrofluidicsystems.
Thegoverningpartial differential equations formomentum, energy, andnanoparticleconcentrationare
transformedintoasystemofcoupled,nonlinearordinarydifferentialequationsusingsimilaritytransformations.
Thesearesolvednumericallyviatheshootingmethodcombinedwiththefourth-orderRunge–Kuttaalgorithm
andNewton’siteration.Tovalidatetheresults,MATLAB’sbuilt-insolverbvp4cisalsoemployed.
Theimpactofvariousdimensionlessparameters, includingthemagneticfieldstrength,Weissenbergnum
ber, radiationparameter,Brownianmotion, thermophoresis,andslipcoefficients, issystematicallyanalyzed.
Findings indicatethatanincreasedmagneticfieldreducesfluidvelocityviatheLorentz forceandthickens
thethermalboundarylayer.Thermalradiationelevatesfluidtemperature,whileslipeffectsreducewallshear
stressandheattransferrates.Enhancedthermophoresisleadstoincreasednanoparticlemigration, influencing
bothtemperatureandconcentrationfields.
Comparisonswithexistingliteraturevalidatethemodelandhighlightitsrelevancetothedesignofadvanced
thermal systems,biomedicaldevices,andmicrofluidicapplications. Thisstudyoffersarobustmathematical
frameworkforanalyzinghybridnanofluidbehaviorundercomplexphysicalconditions.

HYBRID BLOCK METHOD TO SOLVING FIRST ORDER INITIAL VALUE PROBLEM IN ORDINARY DIFFERENTIAL EQUATIONS

Seeta Vitala, Y. Rajashekar Reddy — Thu, 09 Oct 2025 23:53:28 +0000

This study examines the hybrid block method (HBM) derivation for solving first order initial
value problems (FOIVP) in ordinary differential equations (ODEs). Using the collocation and interpolation
procedure at equally spaced locations in the interval of consideration, a continuous formula is generated from
the estimated answer, which is assumed to be in the form of power series. The accuracy of the procedure is
significantly influenced by the advantage of using data off-step points. The efficacy of the suggested approach
is demonstrated by a few numerical examples that show how close the answers are to the precise solutions.
All types of FOIVP involving ODEs can be solved utilizing this method.

CRHKS- Character Recognition in Handwritten Kadamba Script: A Dataset-Based Approach

Beebi Naseeba, Yuktharasi Yalavarthi — Thu, 09 Oct 2025 23:59:43 +0000

The Kadamba manuscript is an early South Indian script derived from the Brahmi script

developed in the fourth century by the Kadamba dynasty. It is an ancient and historically significant writing

system from South India, yet its preservation and computational analysis remain challenging due to the absence

of standardized digital representation.It plays a pivotal role in the development of Kannada and Telugu scripts

and is frequently found in early inscriptions.This paper presents a novel dataset specifically designed for the

recognition of handwritten Kadamba script. The Kadamba script data set comprises 29 consonants, 5 vowels,

and 10 numerals. Data were collected from 100 participants representing a diverse range of ages and genders.

Participants were provided with sample templates and instructed to write isolated characters using regular

pens on A4 sheets.To emulate the appearance of traditional manuscripts, characters were written by individuals

of various backgrounds. The data set collected was stored in both CSV and image formats. Each handwritten

sheet was scanned and processed through a structured pipeline to enhance image quality and ensure uniformity.

To preserve the structural integrity of the script, the samples underwent digitization and preprocessing steps,

including adaptive binarization and contour-based segmentation. These processed samples were then used to

build machine learning models. This work addresses the lack of Kadamba script resources by introducing a

benchmark dataset. This contribution systematically bridges the gap by offering a standardized benchmark

Kadamba script for numeral and vowel recognition, which are highly valuable in the context of manuscript

analysis and research like OCR, Historical and Cul

SOME RELATIONS AND APPLICATIONS OF FUZZY AUTOMATION SUB SEMI-GROUPS

Lakshmi Harini Gundugula, E.Keshava Reddy — Fri, 10 Oct 2025 00:03:02 +0000

1,3] In this research paper, to showing that A, besides B, remain two sets. Formerly, a relative
ρ from A to B may be defined as a subset of A × B [1,3,8]. For each a ∈ A, we then define aρ in the obvious
way, to find the aρ = {b ∈ B | (a, b) ∈ ρ}. If S and T are two fuzzy semi-groups, then a subset μ ⊆ S × T is
known as a relational morphism from S to T , if the conditions are satisfied by the relations as follows: (RM1)
(∀a ∈ S) aμ̸ = ∅; (RM2) (∀a, b ∈ S) (aμ)(bμ) ⊆ (ab)μ. It is known as injective if, in addition: (RM3)
(∀a, b ∈ S) aμ ∩ bμ̸ = ∅ ⇒ aμ = bμ [7]. To showing every relational morphism is a fuzzy sub semi-group of
direct products S × T . We say that S divides T if there exists a fuzzy sub semi-group U of T and a morphism
ψ from U onto S. Thus, S is a quotient of a fuzzy sub semi-group of T . To shows that S divides T if as well
as only if U is a relation morphism injection originating S to T [7,6,4]

A Hybrid VADER-BERT Sentiment Analysis Framework for Real-Time Stock Market Prediction

Ramathulasi Thota, Rajasekharababu M, Srinivasarao P — Fri, 10 Oct 2025 00:05:49 +0000

The stock market, significantly shaped by public sentiment as articulated through various media channels, social networking sites, and financial discussions, demonstrates a vibrant adaptability to the collective perceptions of investors. This research presents an advanced real-time sentiment analysis framework that effectively merges VADER (Valence Aware Dictionary for Sentiment Reasoning) and BERT (Bidirectional Encoder Representations from Transformers), representing a substantial progression compared to prior methodologies. Previous methods, which depend on individual models such as VADER or BERT, are hindered by intrinsic drawbacks: VADER’s rule-based framework struggles to interpret complex textual nuances, whereas BERT’s resource-intensive nature constrains prompt analysis. In contrast, the proposed system leverages VADER’s rapid processing capabilities for succinct, informal texts together with BERT’s sophisticated understanding of intricate financial language. This synthesis allows for the accurate identification of both explicit and implicit sentiment indicators, thus providing a more holistic depiction of market sentiment. Sentiment indices generated from this analysis are systematically correlated with fluctuations in stock prices to assess their predictive value. Additionally, a robust web-based application has been created to support real-time sentiment tracking for selected equities. Empirical assessments confirm that this hybrid framework considerably outperforms the efficacy of conventional single-model systems in terms of both accuracy and speed, establishing a powerful tool for investors and financial researchers.

Analytic Mean Labeling in Certain Classes of Graphs

SIVA SENKAR M, Vijayakumar P — Fri, 17 Oct 2025 17:48:33 +0000

A graph labeling is a mapping, when the map assigns integers to vertices/edges, it is called
vertex/edge labeling and when it assigns to both, it is called total labeling. The idea of mean labeling was
proposed by Somasundaram and Ponraj. An injective function f : V → {t : 0 ≤ t ≤ q} is called a mean
labeling of a graph G(V,E) if for every u, v ∈ V , the edge labels are (f(u)+f(v))/2 whenever f(u) + f(v) is even and (f(u)+f(v)+1)/2 whenever f(u) + f(v) is odd such that edge labels are distinct. The idea of analytic mean
labeling was coined by Tharmaraj and Sarasija and they have proved the existence in the following graphs:
path,cycle, star, Ladder, bistar, fan, comb and the joint sum of two copies of certain graph. The concept
of Analytic even mean labeling is introduced by Sajitha Kumari et., al, and they proved Jewel graph, Jelly
Fish graph, Triangular Book graph, Triangular Book with Book Mark admits analytic even mean labeling.
Motivated by these studies, here we examine the existence of Analytic Mean labeling and Analytic Even Mean
Labeling in the duplicate graphs of ladder, triangular ladder, slant ladder and Zig-Zag ladder graphs.

Efficient Data Preprocessing for Extractive Question Answering Models

Sivakumar S, Meenakshi S P — Sat, 01 Nov 2025 18:40:21 +0000

abstract: Thisstudypresentsasystematicapproachtobuildingadomain-specificquestion-answering(QA)
dataset fromIndianLokSabhaparliamentaryproceedings,withaprimaryfocusonmeticulousdataprepro
cessing.Parliamentarytranscriptsareoftenlengthy,noisy,andunstructured,posingsignificantchallengesfor
downstreamnatural languageprocessing(NLP)tasks.Toaddressthis,wedesignedacomprehensiveprepro
cessingpipelineinvolvingcleaning,segmentation,annotation,normalization,andtokenizationtoconvertraw
transcriptsintostructured,high-qualityQA-readydata.Eachstepwastailoredtothelinguisticandstructural
characteristicsofparliamentarytext. Experimentalevaluationthroughanablationstudydemonstratedthat
ourpreprocessingpipeline ledtoasignificantperformance improvementof9.4%inExactMatch(EM)and
8.5%inF1scorewhenusedtotrainaBERT-basedQAmodel.Additionally,weconductedbiasanalysisand
comparedourdataset’sperformancewithstandardbenchmarks tovalidate itsqualityandrelevance. This
workunderscoresthatrobustpreprocessingisfoundationaltocreatingreliable,domain-adaptedQAdatasets
forextractivemodels

An Efficient CNN-Based Deep Learning Model with Ada-Belief Optimizer for Heart Disease Prediction

Sat, 01 Nov 2025 18:44:08 +0000

Heart arrest remains a leading cause for loss of life worldwide, demanding accurate and early prediction to enable timely mediate and minimize healthcare burdens. However, clinical environments often suffer from data noise, missing values, and variability across sources, which significantly degrade the potential of traditional machine learning models. To tackle these constraints, this paper proposes a Deep Ensemble Learning framework for robust heart failure prediction in noisy clinical settings. The proposed model integrates multiple deep learning architectures something like CNNs, LSTMs, and Transformer-based models through a weighted ensemble mechanism to enhance generalization and resilience to noise. Using Ada-Belief optimizer, the system obtained an accuracy of 98 percent after training. Clinical data from publicly available datasets are augmented with synthetic noise to test the model’s robustness. Comparative results indicate that the deep ensemble method significantly overtakes individual models and conventional ensemble practices in terms of accuracy (98.45), sensitivity (99.41), and F1-score (99.81). Furthermore, explainability tools like SHAP are employed to interpret model predictions, ensuring clinical relevance and trust. The findings suggest that deep ensemble learning is a promising avenue for reliable and interpretable heart failure prediction in real-world, noisy healthcare environments.

Antisymmetric Gravitational Lorentz Force Tensor Predicts Gravitational Force Theory

Ather Qayyum, Naveed Hussain, Hassnain Abdullah Hussain — Sat, 01 Nov 2025 18:51:48 +0000

Three-dimensional gravitational Lorentz force m [g + (gt×ω)] predicts antisymmetric gravitational Lorentz force (GLF) tensor G^ whose components are Newton’s gravitational force mg and gravitational Coriolis force m(gt×ω) in the language of standard electrodynamics. It obeys principle of relativity, conservation law and symmetry. The model consists of gravitational force equations, gravitational force Maxwell’s equations, conservation law, wave equation of Newtonian gravitational force and wave equation of gravitational Coriolis force. The framework of dual of GLF tensor *G^ possesses the same results. Matrix method and Einstein’s summation convention method (ESCM) both are valid. The transformation of GLF laws in noninertial coordinate metric based on single transformation law (STL) for 4-vectors and tensors tells us about the existence of zero-point gravitational energy, gravitational torque, zero-point gravitational Maxwell’s equations as gravitational power and force. Conservation law by matrix method gives zero but by ESM predicts 7D wave of gravitational energy accompanied by classical conservation law. This framework reduces to its classical limit when extra terms are subjected to zero. This model will provide simple representation of gravitation physics for ready applications not only in daily life but also in the study of astrophysics and cosmology.

Detection of Bahasa Cyberbullying Speech Using Large-scale N-Gram Machine Learning Models with Increased Document-Terms Probability

Sat, 01 Nov 2025 18:55:45 +0000

A rising number of bullying incidents, whether between people or groups (cyberbullying), can be attributed to the proliferation of social media technologies and sharing websites. One difficulty in identifying cyberbullying in Bahasa is that words can have more than one meaning when combined with another, making them ambiguous or even negative. In this article, we look at how to increase the probability value of document-terms in a machine learning model to achieve high classification accuracy in the detection of Bahasa cyberbullying, which features a wide range of meanings, word spellings, and meaning shifts on social networking platforms. In addition, a language model with sequential sequences of n-words to capture patterns and statistics in the text data (Large-scale N-Gram) is applied throughout the detection phase to categorize texts based on the cyberbullying corpus created during training and testing. Our research shows that the accuracy of Indonesian cyberbullying detection may be greatly enhanced by collecting trends and boosting the probability value of document-terms.

Modelling drug resistance and insecticide e ects in infectious disease transmission with saturated incidence for control interventions

Sat, 01 Nov 2025 18:58:40 +0000

The burden of vector-borne infections is a complex interplay of biological, environmental,
and social factors. Dengue infection constitutes a substantial and multifaceted threat to
both human health and the socio-economic aspects of impoverished regions. In order to address
these challenges, a thorough comprehension of the complex dengue dynamics is necessary. In this
study, we construct an epidemic model for dengue with saturated incidence in the framework of
Caputo-Fabrizio derivative with drug resistance. Boundedness and positivity of the solution of
the suggested model are examined. The endemic indicator, denoted by R0, is computed using the
next-generation matrix technique. It is demonstrated that for R0 < 1, the system’s infection-free
steady-state is locally asymptotically stable. The fixed-point theorem is then used to examine the
existence and uniqueness of the proposed system’s solution. The time series analysis of the model
has been presented to illustrate the influence of several parameters on the dengue infection system.
The role of memory index has been conceptualized through numerical findings. Our findings
anticipate the pivotal scenario within the system pertinent to the control and prevention of dengue.

A Study of Selective English Language Lab Activities towards Honing Soft Skills by Using Analytical Hierarchy Method

Sat, 01 Nov 2025 19:01:34 +0000

TheFourthIndustrialRevolutionischaracterizedbytheseamless integrationofdigital tech
nologiesintoindustrialoperationsandsystems.Thetwenty-firstcenturyisawitnesstounparalleledadvance
mentsindatagenerationandconnectivity, sophisticatedanalytics,andincreasinglyseamlesshuman-machine
interaction. Theprofessionalarenahassignificantlybeenreshapedasthere isaccelerationinadoptingnew
technologies,drivenbytheneedtoremainrelevantinthecurrentcompetitiveglobalmarket.Foranengineer
inggraduate, thedigital shift inthe industryhasheightenedtheneedtobeequippedwiththetechnological
competencysincetheyarerequirednotonlytounderstandtraditionalengineeringprinciplesbutalsotopos
sesstheaptitudetoworkwithemergingtechnologieswhichinturnenablesthemtoinnovate, solvecomplex
problemswitheaseandcollaborateeffectivelyindigitallyintegratedplatforms. However, theemployability
andsustenance inthe industry,fightingalloddsarenotguaranteedonlybyacquiringthehardskills.Tech
nicalcompetenceoncecomplementedbytheessentialsoftskillscanensureholisticprofessionalgrowthforan
engineeringgraduateresultingintoenhancedworkefficiencyandsustainedrelevance. TheEnglishlanguage
labsinengineeringcollegesacrossIndiacancatertotheseneedsbyeffectivedesigningofvariouslabactivities
suchasdebates, groupdiscussions, roleplays, powerpointpresentations just tonameafew. Inthis study
theauthorsadoptedtheAnalyticalHierarchyProcess(AHP)asadecision-makingtool toassessthe impact
ofdifferent labactivitiesandidentifythemost in-demandsoftskill inthecurrentprofessional landscape.

Magnetohydrodynamic Stokes flow of couple stress fluid past a viscous liquid drop in a porous medium

Sivaprasad Jammula, Phani Kumar Meduri — Sat, 01 Nov 2025 19:06:19 +0000

This article analyzes the steady flow of couple stress fluid past a viscous liquid droplet embedded in a porous medium under the influence of a magnetic field, employing a no-slip condition. The Stokes and Brinkman equations examine the flow dynamics within and around the liquid drop. The influence of an external magnetic field on fluid flow is characterized by Lorentz’s force in the transverse direction. Analytical expressions for stream functions and drag force on a liquid drop are derived. The analysis yields specific cases, such as viscous fluid flow past a viscous liquid drop and a solid sphere, with results in strong agreement with established literature. Graphical analysis illustrates the relationship among the coefficient of drag, couple stress parameter, and Hartmann number. At low couple stress parameter values, strong couple stress effects result in higher drag. The drag also increases with the rising Hartmann number. Streamline patterns are analyzed about different couple stress parameters and Hartmann numbers.

Bilingual Handwritten Indian Language Translation

Sat, 01 Nov 2025 19:09:28 +0000

This paper presents a deep learning-based system for translating handwritten Sanskrit text into English. The system addresses key challenges posed by Sanskrit, including complex grammar, flexible sentence structure, and varied handwriting styles. The pipeline begins with image preprocessing to enhance handwritten text clarity, followed by Optical Character Recognition (OCR) to convert the images into machine-readable Sanskrit text. A Sequence-to-Sequence (Seq2Seq) model using Long Short-Term Memory (LSTM) networks,

enhanced with an attention mechanism, then translates the text into English. The attention mechanism enables the model to focus on relevant parts of the input during translation. Translation quality is evaluated using standard metrics such as ROUGE, Precision, Recall, and F1 score. Experimental results demonstrate the model’s effectiveness in producing accurate translations. This work contributes to machine translation for low-resource languages and supports the preservation and accessibility of ancient cultural texts.

A Feedforward Neural Network Approach to Solving Systems of Linear Equations

Rashad Al-Jawfi — Sat, 01 Nov 2025 19:14:38 +0000

This paper proposes a neural network-based framework for solving systems of linear equations of the form $\mathbf{A}\mathbf{x} = \mathbf{b}$. The method reformulates the problem as a residual minimization task and employs a feedforward neural network to learn the mapping from input matrix-vector pairs to solution vectors. The network is trained using synthetic data and optimized via gradient descent using residual-based loss. Experimental results demonstrate that the model achieves high accuracy for well-conditioned systems with dimensions up to $n = 20$, producing residual errors below $10^{-4}$ in most cases. Comparative analysis against classical numerical solvers shows that while traditional methods remain superior for ill-conditioned systems, the neural approach offers notable advantages in inference speed, generalization, and suitability for parallel or real-time deployment. Limitations and future enhancements—including scalability, noise robustness, and hybridization—are also discussed.

Extended Vertex Odd Mean Labeling in Certain Graphs

Komalamba Kandikuppa, Vijay Kumar Perumal — Sat, 01 Nov 2025 19:19:43 +0000

Mean labeling was introduced and studied in some graphs by Somasundaram and Ponraj [8].
It is defined as an injective function f : V → { x : 0 ≤ x ≤ q} and the edge labels for each edge uv is allotted
from {{x : 1 ≤ x ≤ q} by the induced function f∗ as the mean value of f(u) and f(v) whenever f(u) + f(v)
is even and [f(u) + f(v) + 1]/2 wheneverf(u) + f(v) is odd. The idea of odd mean labeling was introduced
by K. Manickam and M. Marudai [3]. It is a mean graph with vertex set V = {x : 0 ≤ x ≤ 2q − 1} and edge
set E = {2x − 1 : 1 ≤ x ≤ q}. N. Revathi introduced Vertex Odd Mean and Even Mean Labeling and proved
that Umbrella graph, Mangolian tent and K1 + Cn graphs admit these labeling [5].
Motivated by the above studies, here in this paper, we prove the existence of extended vertex odd mean
labeling in the duplicate graphs of path, comb, twig, star and bistar graphs.

COMPUTING DOUBLE DOMINATION NUMBER OF DOUBLE GRAPH OF SOME REGULAR GRAPHS

Udhayashree R, Rajeswari R — Sat, 01 Nov 2025 19:23:30 +0000

A graph in which every vertex has the same valency or degree is known as a regular graph.
The double graph D(G) of a regular graph is constructed by duplicating each vertex and connecting the
corresponding duplicates iff the original vertices are adjacent. This process creates a motivating and composite
graph structure, raising questions about the domination properties of D(G). In this paper we focus on the
double domination of double graph of some regular graphs which is constructed using an algorithm (Llama
New, 2016). The double domination number of regular graphs on even and odd order are determined.

The Investigation of Torsional Waves Propagation in a Sandwiched and Initially Stressed Dry Sandy Gibson Poroelastic Dissipative Isotropic Solid

CHANDAVATH BALU, Modem Ramesh, Biragoni Radhika, Perati Malla Reddy — Sat, 01 Nov 2025 19:31:19 +0000

In this paper, torsional waves in sandwiched solids are investigated in the framework of Biot’s incremental theory. The solid consists of dry sandy Gibson poroelastic dissipative isotropic cylindrical solid sandwiched between two heterogeneous isotropic poroelastic cylindrical solids, all are initially stressed. The solutions for the problems of torsional waves in upper heterogeneous poroelastic cylindrical solid, dry sandy Gibson poroelastic cylindrical middle solid, and lower heterogeneous poroelastic cylindrical solids are presented. The solution of the problem reduced to that of Whittaker’s differential equation. Frequency equation is obtained from the boundary conditions of displacement components and stresses which are assumed to be continuous at the interfaces between upper solid and middle, and middle solid and lower solid. The solid under consideration is dissipative, the frequency equation is implicit and complex valued. Employing the values in the frequency equation, the frequency and attenuation coefficient against heterogeneous parameter at fixed sandy parameter, gravity parameter and initial stress are computed. The values are computed using the bisection method implemented in MATLAB. Wave characteristics namely, frequency and attenuation coefficient are computed against heterogeneity at fixed initial stresses, Sandy parameter, gravity parameter, and numerical results are presented in graphs.

A Hybrid CNN–BiLSTM Frame work for Heart Disease Detection

Sat, 01 Nov 2025 20:13:29 +0000

Heart disease continues to rank among the primary causes of death globally, emphasizing the need for precise and user-friendly prediction algorithms. We propose a novel hybrid deep learning model in this study for forecasting heart disease from structured clinical data by combining CNNs along Bidirectional Long Short-Term Memory (BiLSTM) networks. Second-degree polynomial feature expansion or normalization for numerical stability is used to improve the model’s capacity to represent intricate relationships. We also use the Synthetic Minority Oversampling Technique (SMOTE) to handle class imbalance and reformat tabular data into a pseudo-sequential style in order to take advantage of sequence modeling. Our CNN–BiLSTM model achieves 98% accuracy and a 0.98 F1-score, which is a considerable improvement over the baseline machine learning classifiers, such as Decision Trees, Naive Bayes, and Logistic Regression. These results demonstrate how beneficial it is to combine local pattern extraction with temporal modeling to obtain more accurate disease prediction.

INDIVIDUAL COMPONENT FAILURE'S ROLE IN AN IMPERFECT ONE-OUT-OF-THREE COLD AND WARM STANDBY SYSTEM

Hussein Asker, Layla Hendi, Mohammed Shakir Mahdi ZABIBA — Sat, 01 Nov 2025 20:25:36 +0000

This study investigates the reliability and failure behavior of a non-repairable one-out-of-three standby system incorporating both cold and warm redundancy under imperfect switching conditions. Motivated by real-world challenges in hospital emergency power systems, the model includes three critical components: the primary power grid, a cold standby generator, and a warm standby UPS, along with a fillable switching mechanism. A continuous-time Markov chain (CTMC) framework is constructed to evaluate system dynamics, where each component is subject to exponentially distributed failures. System performance is quantified via key reliability metrics, including the reliability function , the failure probability , hazard rate , mean time to failure (MTTF), and steady-state probabilities. Numerical solutions are derived through matrix exponential computations and linear system solvers in MATLAB (R2023b). Results indicate that reliability degrades exponentially with time, the hazard rate stabilises around a constant value, and the system has an expected operational lifespan of approximately 43.19 hours. The steady-state analysis reveals that certain operational states dominate prior to system failure, providing valuable insights for redundancy planning and component prioritisation in critical systems.