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A Block Hybrid Method for Third- and Fourth-Order Nonlinear Boundary Value Problems

This study proposes a stable and accurate unified block hybrid method for solving third- and fourth-order nonlinear boundary value problems that overcomes the ill-conditioning limitations of spectral collocation methods by partitioning the domain into blocks and recovering lower-order derivatives through successive integration, thereby achieving high convergence orders with significantly lower condition numbers.

Mpho Mendy Nefale, Olumuyiwa Otegbeye, Shina Daniel Oloniiju2026-07-02

🔢 mathematics

A Randomized Bracketing Method for Derivative-Free Root Finding with Uniform Spacing Contraction

This paper introduces and analyzes a randomized, derivative-free root-finding method that preserves bracketing by sampling multiple interior points to contract the search interval, proving its convergence properties and demonstrating its effectiveness as a robust, tunable alternative for expensive or parallelizable black-box function evaluations.

Dinesh Kumar, Sudesh K. Srivastav2026-07-01

🔢 mathematics

An Empirical Spectral-Domination Relationship Discovered Through Symbolic Regression

Using machine learning-guided symbolic regression on a diverse dataset of 3,429 graphs, this study identifies a high-accuracy empirical formula relating the domination number and spectral radius of graphs, while explicitly characterizing the extremal cases where the relationship fails.

Rayyan2026-07-01

🔢 mathematics

Verification-domain profiles for a posteriori scalarisation certificates in finite multi-objective optimisation

This paper introduces a scale-invariant verification-domain profile to quantify the robustness of positive scalarisation certificates in finite multi-objective optimisation, establishing a theoretical trichotomy for certifiability and providing efficient row-generation algorithms that achieve exact classification and budget agreements across diverse problem instances.

Antonio Clim2026-07-01

🔢 mathematics

Long-Wave Instability in Confined Pedestrian Flow: A Reduced Dynamical-Systems Framework

This paper presents a one-dimensional reduced dynamical-systems model within the Payne-Whitham and optimal-velocity framework to derive a stability condition for dense pedestrian flow in confined geometries, identifying how density, relaxation time, velocity sensitivity, and width jointly determine the onset of long-wave stop-and-go instabilities.

Tayfun Er2026-06-29

🔢 mathematics

Critical Thinking Activation During Limits Problem Solving Mediated by Symbolab: An Instrumental Genesis Perspective

This qualitative study examines how first-year business students activate Facione's six critical thinking skills while solving calculus limits problems using Symbolab, revealing a "CT-neutral zone" of mechanical input during early instrumental genesis and identifying distinct evaluation subtypes and cross-stage patterns that bridge critical thinking theory with instrumental genesis processes.

Enrique Ceballos-Alexis2026-06-29

🔢 mathematics

Graph-Theoretic Computation of Degree-Based Topological Indices for Hepatocellular Carcinoma Therapeutics: A Mathematical QSPR Framework for Physicochemical Property Prediction

This study establishes a rigorous graph-theoretic framework for predicting the physicochemical properties of five Hepatocellular Carcinoma therapeutics by demonstrating that six degree-based topological indices, particularly the Yemen Index, exhibit statistically significant correlations with Surface Tension through linear regression analysis.

S. Ranjitham, O. V. Shanmuga Sundaram, G. Priyadharsini, A. Saravanan2026-06-26

🔢 mathematics

Existence of non-coexisting steady-state solutions for a class of reaction-diffusion competition systems

This paper investigates a reaction-diffusion competition system based on the Shigesada-Kawasaki-Teramoto model to establish exact parameter ranges ensuring the existence of only non-coexisting steady-state solutions, demonstrating that the impact of cross-diffusion on these solutions depends on the intensity of interspecific competition.

Xinyu Tian, Ningning Zhu2026-06-25

🔢 mathematics

Sharp Boundedness and Stability Estimates for Pseudodifferential Operators Associated with Fractional Hankel--Clifford Transforms

This paper establishes sharp operator-norm and composition bounds for pseudodifferential operators associated with the fractional Hankel–Clifford transform via a closed-form evaluation of a geometric moment integral, and applies these results to derive a stability estimate for a singular Bessel-type Cauchy problem while identifying the specific obstruction to a four-parameter extension.

Balasaheb B. Waphare2026-06-25

🔢 mathematics

Stability and Bifurcation Routes in a Delayed Quadratic Map with Recursive Filtered Memory

This study analytically and numerically characterizes the stability and bifurcation routes of a delayed quadratic map with recursive filtered memory, demonstrating how delay and memory parameters govern fold, flip, and conditional complex-pair transitions within a three-dimensional polynomial framework.

Hafidh Khoerul Fata, Yosephus Decupertino Sumanto, Robertus Heri Soelistyo Utomo2026-06-25

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