Mathematics and Computer Science: Research Updates Vol. 10

Evaluation of Spanning Tree of a Network with Pentagonal Neutrosopic Fuzzy Number

Satyajit Sahu — 2026-04-16

Classical fuzzy sets and models may not adequately capture complicated, ambiguous, and uncertain real-life problems. Neutrosophic logic and neutrosophic sets theory are well-known theories for handling these types of several problems. In this work, we present a novel method that uses single-valued pentagonal neutrosophic integers as edge lengths to evaluate the smallest spanning tree of an undirected connected neutrosophic weighted graph. A new matrix-based algorithm for constructing the minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph is proposed. The suggested algorithm is compared with existing approaches, and a numerical example is provided for illustration. Highlight the key contributions of this study, including the algorithm’s compatibility with MATLAB and its improved ability to manage uncertainty compared to traditional approaches.

Coefficient Bounds for New Subclasses of Bi-Univalent Functions Involving the S\(\breve{a}\)l\(\breve{a}\)gean Deferential Operator and Fekete–Szeg\(\ddot{o}\) Inequalities

A. Naik — 2026-04-16

The study of bi-univalent functions has attracted considerable attention in geometric function theory due to its importance in coefficient problems and related applications. Motivated by recent developments in differential operators, this paper introduces two new subclasses of bi-univalent functions belonging to the family Σ in the open unit disk using the S˘al˘agean differential operator. For these subclasses, upper bounds for the initial coefficients |b2| and |b3| are obtained. The results extend and unify several earlier findings in the literature. In addition, a Fekete-Szeg¨o type inequality is established for the newly defined subclasses. The proposed framework provides a useful basis for further investigations, including higher-order coefficient estimates, Hankel determinants, and related problems.

Dom-Forcing Sets in Graphs and Its Relationships with Domination and Zero Forcing Number

P. Susanth — 2026-04-16

A dominating set D_f ⊆ V (G) of a graph G is called a dom-forcing set if it also constitutes a zero forcing set. The minimum cardinality of such a set is defined as the dom-forcing number of G, denoted by Fd(G). This paper initiates a systematic study of the dom-forcing number and examines its relationship with classical graph parameters such as the domination number and the zero forcing number. We determine the exact values of dom-forcing number for several wellknown classes of graphs, including paths, cycles, coconut tree graphs, diamond snake graphs, triangular snake graphs, hypercubes, the Petersen graph, pineapple graphs, complete graphs, complete bipartite graphs, wheel graphs, and helm graphs. Further, we characterize classes of graphs for which the dom-forcing
number coincides with either the domination number or the zero forcing number. In addition, the dom-forcing number of the splitting graph of a given graph is investigated, and relevant bounds and structural properties are established. These results contribute to a deeper understanding of the interplay between domination and zero forcing processes in graphs.

Early Malware Detection Using Information-Theoretic Signals: A Survey from Entropy to Compression

Kabeya Tshiseba Cedric — 2026-04-16

Malware remains one of the most critical threats in the digital ecosystem, targeting both mobile and desktop platforms. Malware continues to evolve in ways that reduce the effectiveness of signature matching and evade analysis environments, creating demand for early detection methods that can flag suspicious binaries before behaviour is observed. Early malware detection is, therefore, a race against time, where the advantage often lies with the attacker. This chapter surveys information-theoretic approaches for early malware detection, focusing on the progression from classical uncertainty measures to algorithmic notions of complexity.

A structured literature-gathering process was employed, covering entropy-based analysis, compression-based approximations of algorithmic complexity, and compression-distance similarity measures. The study first examines Shannon entropy as a lightweight indicator of packing, encryption, and obfuscation, and explains how entropy computed over whole files, executable sections, or sliding windows can localise anomalous regions in portable executable binaries. It then explores algorithmic complexity through the lens of Kolmogorov complexity, outlining practical approximations using general-purpose compression. Compression-based measures enable the estimation of structural regularities in binaries that are not captured by frequency statistics alone. Building on this, normalised compression distance (NCD) is introduced as a featureless similarity measure for clustering and nearest-neighbor detection.

Findings highlight how entropy, compressibility, and compression-based similarity can be combined into hybrid pipelines that support triage, prioritisation, and explainable inspection, while also noting key limitations. High entropy is not unique to malware and can arise in legitimate packed installers, multimedia resources, or encrypted payloads, leading to false alarms if used in isolation. Section-wise and sliding-window entropy analysis provide better localisation of suspicious regions, improving interpretability compared to whole-file entropy approaches. Compression-based methods can be computationally demanding and sensitive to file size, compressor choice, and adversarial manipulation. NCD enables featureless similarity detection and effective malware family clustering, but faces scalability challenges due to pairwise comparisons. Hybrid pipelines combining entropy, compression, and structural features provide improved precision and reduced false positives, making them more suitable for real-world deployment.

By synthesising these techniques and their practical considerations, this article provides guidance for designing robust early-warning detectors and for integrating information-theoretic signals with complementary static and learning-based components in operational settings. The transition from Shannon entropy, a statistical measure of disorder, to Kolmogorov complexity, an algorithmic measure of information, represents a deeper analytical framework for malware detection. While entropy remains valuable for fast screening, integrating algorithmic information theory opens pathways toward more adaptive and generalised detection systems.

Moiré Effect in Planar and Cylindrical Objects

Vladimir Saveljev — 2026-04-16

Background: The moiré effect occurs when viewing through grids with periodically modulated transmittance/reflectivity.

Aim: To analyse the moiré effect systematically in flat and cylindrical objects, as well as in their combinations.

Study Design: The theory is based on projections. Experiments were conducted with models of cylinders and other objects.

Methodology: The occurrence of the moiré effect is classified by the position of the grid wavevector relative to the base.

Results: The moiré cases are presented systematically and uniformly. Analytical formulas for the moiré magnification coefficient are analysed. The typical difference between experimental data and theory was 2-5%. Patterns of functions in combined objects are described. A general, systematic picture of the moiré effect is presented.

Conclusion: The experiments confirm the theory. The results can be used for nanoparticles, minimization and measurement.

The Concept of Tripolar Fuzzy Bi-ideal of a Near Ring: An Introduction

Rakshita Deshmukh — 2026-04-16

The notion of a near ring was introduced by Dickson in 1905. Fuzzy ideals in near rings were studied by Zaid. A tripolar fuzzy set is a generalization of fuzzy set, intuitionistic fuzzy set, and bipolar fuzzy set. In this paper, the concept of tripolar fuzzy bi ideal of a near ring, which is a generalisation of tripolar fuzzy set, fuzzy bi ideal of a near ring. The intent was to study few properties of it.

Coincidence Angles and Rational Structures in the Square Lattice

Rosalio G. Artes Jr. — 2026-04-16

Aims: The aim of this work is to take a closer look at how the square lattice \(\mathbb{Z}^2\) behaves under rotation, with particular attention to coincidence angles and their connection to rational slopes.

Study Design: The study is theoretical and builds on standard ideas from lattice theory, basic geometry, and elementary number theory.

Place and Duration of Study: Since the work is purely theoretical, it is not associated with a specific location or experimental time period.

Methodology: The approach begins by constructing a family of coincidence angles using pairs of lattice points that are symmetric with respect to the line y = x. Their behavior is then examined using direct algebraic arguments together with simple trigonometric identities. Lattice directions are grouped into equivalence classes, which makes it possible to relate them naturally to rational numbers. The density result is obtained by relying on the well-known density of rational numbers in \(\mathbb{R}\).

Results: The analysis shows that each rational value determines a corresponding lattice direction and an associated coincidence angle. A simple expression for the coincidence span is obtained, and it is further shown that these angles are dense in the interval (0, \(\frac{\pi}{2}\)).

Conclusion: Taken together, these results point to a clear connection between lattice geometry, rotation, and number-theoretic ideas. The framework developed here provides a straightforward way to understand coincidence site lattices and may also be useful in contexts where lattice orientation plays a role, such as in crystallographic studies.

Queuing Networks under Server Failures and Customer Abandonment: Performance Evaluation with Corrective Maintenance and Feedback

Finyori Fayama — 2026-04-16

Queuing systems (QS) are well-suited to the study of objects in which the same type of activity is regularly repeated. Researchers quite often use queuing theory apparatus to describe and analyse micro logistic systems. Using probabilistic models, it is also possible to estimate the capacity, the probability of system overflow, and the loss probability (refuse to service an incoming request), i.e., the most significant system operation risks (Bychkov et al., 2021). Queuing systems with heterogeneous servers, customer feedback and abandonment have several applications, including manufacturing systems, computer systems, telecommunications systems, etc. Several recent studies have dealt with queue models with heterogeneous servers, feedback and customer abandonment. The aim of this work is to evaluate the performance of M/M/K (K > 2) multiserver queuing networks with intermittently accessible servers, failed servers, corrective maintenance, feedback and client dropouts. Using the Geometric Matrix Method (GMM), we obtained the equilibrium equations of the system, and solving them by substitution enabled us to obtain the steady-state probabilities. Using these probabilities, we obtained measures of system performance. In a second step, we extended the M/M/2 model to include avariable number of servers M/M/K (K > 2) model). As this model is more complex to analyze numerically, we used the algorithmic method. Firstly, we used the PSO algorithm to minimize operational costs by dynamically adjusting the arrival rate λ, the service rate μ and the number of servers K. Secondly, we used the PSO algorithm to minimize the average waiting time and the abandonment rate in order to maximize customer satisfaction. This will benefit both the operator and the customer. The minimum total operational cost is 273.54, and the optimal values of the arrival rate, service level and number of servers to achieve this minimum cost are 10, 10 and 2, respectively. The average number of customers in the queue, as well as the average waiting time, is zero. Using the R software, the optimal values for the arrival rate λ, the service level λ, the number of servers K, the minimum total cost C, the minimum average wait time (Wq) and the minimum abandonment rate (R) were obtained. As the number of servers increases, it becomes difficult to study
the model using numerical methods. We therefore used an algorithmic method to evaluate the system’s performance. The study recommended making an extension to the M/G/K model, i.e., by considering general service distributions (G) instead of the exponential distribution (M). Further research also intends to explore other potential extensions, such as priority queues or different maintenance strategies.