Communications in Mathematics and Applications

A New More General Integral Transform: Sharad Transform and Its Applications

2025-07-01T06:19:00+00:00

In this paper, we are presenting the new broad essential transform called the Sharad transform. Additionally, we demonstrated a few theorems and properties, similar to the linearity property and the convolution theorem. Additionally, we fostered a connection between the new transform and another old useful transform, similar to the Laplace transform, the Sumudu transform, the natural transform, the Elzaki transform, the Abhoodh transform, the Formable transform, and so forth. Here we presume that these transforms are the extraordinary instances of the new broad basic transform, the Sharad transform. This transform is applied to ordinary differential equations and partial differential equations. This transform will be utilised in the future to tackle a lot more the ordinary differential equations, the partial differential equations, integro-differential equations, fractional differential equations, difference equations, differential-difference equations, and so forth.

Multi-Label Classification for Drift Detection in IoT Data Streams

2025-07-01T06:41:30+00:00

With the prevalence of Internet of Things (IoT) systems, data is exponentially growing, resulting in data streams. Data streams are massive, potentially non-stop, and arrive at high speed. These systems process IoT data streams in a non-stationary manner, making them susceptible to concept drift occurrence and class imbalance. Concept drift occurs as a result of the change in the underlying distribution over time, while class imbalance occurs when some class distribution is uneven. This paper proposes an Implicit Drift Detection model with Multi-Label kNN (IDD-MLkNN), aimed at addressing concept drift in multi-label classification for IoT data streams. While the model is applicable across various domains, its performance was specifically assessed using two IoT datasets — Bot_IoT and Edge_IIoTset — associated with intrusion detection systems. Applying the proposed model to oversee IoT network traffic offers practical advantages, potentially reducing the time and expenses of re-examining attack data. The evaluation was conducted for sudden and gradual concept drift scenarios. Experimental results show the superiority of the IDD-MLkNN over other well-known multilabel classification models in different performance measures such as the Subset Accuracy, Accuracy, Hamming Score, and F-measure. However, it was less efficient in terms of Evaluation Time compared to other multi-label classification methods.

Certain Classes of Meromorphically Univalent Functions Associated With Subordinaion and Inclusion Relations

2025-07-09T10:52:51+00:00

In this present paper, we introduce some new classes of Meromorphic function in punctured unit disk involving integral operator. Our concern is to study some useful characteristic properties for the above defined general integral operator with applications of meromorphic function.

Enhancing Classification Accuracy With K-Nearest Neighbors: Optimizing Distance Metrics and Handling Unlabeled Data

2025-07-15T07:11:33+00:00

The K-Nearest Neighbors (K-NN) is a supervised machine learning algorithm, specifically within the realm of classification and regression tasks. It is a simple yet powerful method used for making predictions based on similarities between data points. The fundamental idea behind K-NN is to classify or predict a new data point's label or classify by looking at the labels of its nearest neighbors in the training dataset. This research introduces an adaptive K-NN classification approach that leverages local data characteristics to dynamically adjust neighborhood size and distance metrics. This adaptive K-NN classification approach is thoroughly examined through comparisons with \(k=3\), \(k=5\) and \(k=7\). By adjusting neighborhood size and distance metrics, the study yields nuanced performance insights. Calculated outlier-to-class distances offer valuable adaptability indications. The experimental results showcase its potential to enhance classification accuracy and adaptability in diverse data scenarios. This method contributes to the advancement of K-NN based classification techniques and provides a promising direction for improving the efficiency of data classification tasks in real-world applications.

Exploring Explainable AI (EXAI) – An Emerging Trend in Healthcare Sector

2025-07-15T10:03:14+00:00

Industry 4.0 and COVID-19 drove businesses to adopt AI/ML amid VUCA, advancing toward Industry 5.0. Explainable AI (EXAI) fosters trust in healthcare’s digital shift, enhanced remote care, and chronic-disease management, ushering smarter decisions and better patient outcomes. The authors used snowball sampling via Google Forms, surveying hospitals, practitioners, vendors, and customers on healthcare technology adoption. Data were visualized and analyzed descriptively. Explainable AI (EXAI) shows significant promise in managing NCDs, with ML tools aiding better diagnosis and treatment. Once EXAI is integrated nationwide in healthcare, Indian businesses will pivot, analyzing new challenges, enabling data-driven solutions that enhance well being and innovation.

Results on Invariant Submanifolds of Hyperbolic Kenmotsu Manifolds

2025-07-15T11:04:14+00:00

In this paper, our main focus was on studying the geodesic property of invariant submanifolds of Hyperbolic Kenmotsu manifolds. We also investigated different conditions regarding the second fundamental form \(\pi\) and established its equivalence. These conditions included being 2-semiparallel, pseudoparallel, 2-pseudoparallel, Ricci-generalized pseudoparallel and 2-Ricci-generalized pseudoparallel.

Configuring Generalized Form of Half Companion Sequence of Special Dio-Triples involving Centered Triacontagonal Number

2025-07-15T11:23:35+00:00

In this paper, the generalized half companion sequence of a special Dio-3-tuple covering the centred triacontagonal number of different ranks with different properties are produced. Also, we analyze the extendability of 3-tuples to quadruples for some ranks by performing a suitable algebraic algorithm and various enthralling patterns are presented using MATLAB.

QSPR Analysis of Novel Topological Index Based on Proximity Degree

2025-07-15T18:25:19+00:00

In this article, we define a \(k\)-proximity degree and based on this distance degree, we introduce a novel topological index named Proximity Index \((\PI_k)\). By considering octane and heptane isomers, we have studied QSPR regression analysis to predict the physio-chemical properties and chemical applicability of the index.

On Upper and Lower fsgb-Continuous Multifunctions in Fuzzy Topological Spaces

2025-07-20T17:40:30+00:00

In this study, the weaker forms of fuzzy multifunctions such as upper and lower fsgb-continuous multifunctions are introduced and their properties are examined. Further, the characteristics of upper and lower fsgb-irresolute multifunctions have also been studied.

Fixed Point Theorems for Multiplicative Cyclic \((\alpha,\beta)\)-Convex Contraction of Type-2 in Dislocated Quasi \(b\)-Multiplicative Metric Space and Its Applications

2025-07-22T06:09:27+00:00

The dislocated quasi \(b\)-multiplicative metric space is introduced as an extension of dislocated quasi \(b\)-metric space, which is demonstrated some well-known fixed point theorems and shows fixed point results for a contraction of rational type. Specifically, we generalize the convex contraction to encompass the dislocated quasi \(b\)-multiplicative setting. The results of this study not only contribute to the theoretical foundations of fixed point theory but also offers a new perspective on the applicability of dislocated quasi \(b\)-multiplicative metric spaces.