math papers | Gist.Science

Graded L1-2-3 time stepping and adaptive tension splines for two-dimensional time-fractional reaction–diffusion equations

This paper proposes a high-order numerical method for two-dimensional time-fractional reaction–diffusion equations by introducing an adaptive tension spline spatial operator that selects optimal parameters based on local solution modes and a stable L1-2-3 time-stepping scheme on graded meshes, thereby achieving a temporal convergence order of approximately $4-\alpha$ while correcting misconceptions regarding fourth-order accuracy in existing non-polynomial spline literature.

Binod Kumar, Rishikesh Kumar, {Mani Bhushan Kumar, Deo Aryan2026-09-08

🔢 mathematics

An Improvement-Path Framework and an Exact Algorithm for Single-Machine Scheduling with Release Times

This paper proposes a novel improvement-path framework and an exact iterative repair algorithm that, by modeling machine idle time as negative waiting time to simplify the problem structure and characterizing queue discontinuity as the sole obstacle to improvement, guarantees finding a globally optimal schedule for the NP-hard single-machine scheduling problem with release times in finite time.

Xiaoyang Duan, Peixin Zhao2026-09-08

🔢 mathematics

Dynamic Savings with Adaptive Adjustment in the Solow–Swan Model: Bistability and Escape from a Poverty Trap

This paper extends the Solow–Swan model by introducing an adaptive, capital-dependent savings rate to create a two-dimensional dynamical system that exhibits bistability and poverty traps, demonstrating how temporary public investment can strategically push an economy across a separatrix to escape low-capital equilibria.

Jorge Zazueta, Leobardo Plata2026-09-07

🔢 mathematics

Completion-Shock Queues: Departure-Induced Invalidation and Endogenous Service Correlation

This paper analyzes a single-server FCFS queue where job completions trigger probabilistic shocks that invalidate waiting jobs, requiring remediation, and derives exact stability conditions, stationary distributions, and heavy-traffic penalties to quantify the impact of such endogenous service correlations on system performance.

Igor Kleiner2026-09-07

🔢 mathematics

A Tensor Greedy Double-Block Extended Kaczmarz Method for Inconsistent Tensor Linear Systems under the t-product

This paper proposes the Tensor Greedy Double Block Extended Kaczmarz (TGDBEK) method, a novel iterative algorithm that dynamically selects active tensor slices based on residual norms to efficiently solve large-scale inconsistent tensor linear systems under the t-product, demonstrating superior convergence and performance over existing state-of-the-art solvers in both synthetic benchmarks and real-world image deblurring applications.

Jérémie Mabiala, Lionel Tondji2026-09-07

🔢 mathematics

Optimal second-order convergence of the shifted fractional trapezoidal rule for subdiffusion at the Crank--Nicolson point

This paper establishes that the shifted fractional trapezoidal rule with the Crank–Nicolson parameter (θ = 1/2) achieves optimal second-order convergence for subdiffusion problems with smooth initial data by proving that the apparent singularity at the Nyquist frequency is removable and deriving error estimates via a modified Laplace-transform analysis.

Baoli Yin, Guoyu Zhang, Yang Liu, Hong Li2026-09-07

🔢 mathematics

Robustness of Double-Word Addition Algorithms under Overlapping Inputs

This paper establishes the robustness and error bounds of double-word addition algorithms when input components overlap, demonstrating that Fast2Sum remains exact under specific conditions and showing that a simplified multiplication–addition kernel on AVX-512 hardware achieves significant throughput gains with minimal impact on accuracy.

Yuanyuan Yang, Xinyu Lyu, Sida He, Xiliang Lu, Ji Qi, Zhihao Li2026-09-07

🔢 mathematics

Formal Concept Analysis with Three Types of Negation

This paper proposes FCACOI, an extension of Formal Concept Analysis that integrates contradictory, opposite, and intermediary negations to enable robust attribute implication reasoning grounded in the LCOI+PLCOI logic and to facilitate attribute reduction for handling complex negation semantics.

Zhenghua Pan2026-09-07

🔢 mathematics

Development and Rasch Validation of a Mathematical Communication Skills Test for Indonesian Elementary School Students

This study developed and validated a 25-item multiple-choice test for assessing mathematical communication skills among Indonesian elementary students, demonstrating through Rasch analysis that the instrument possesses strong psychometric properties, including high reliability, unidimensionality, and fairness across gender and grade levels.

Ahmad Rustam, Zibar L. Chairan Parisu, Hesti Hesti, Nisraeni Nisraeni, Deni Iriyadi2026-09-04

🔢 mathematics

A New Parametric Kernel Function Based on an Archimedean Copula Generator with Application to Primal-Dual Interior-Point Methods

This paper introduces a new parametric kernel function for primal-dual interior-point methods in linear optimization, derived from the Archimedean Clayton copula generator, which achieves the optimal $O(\sqrt{n} \log n \log(n/\varepsilon))$ iteration bound for large-update methods and demonstrates superior or tied-best performance across all tested instances compared to 54 competing kernel configurations.

Bachir Bounibane, Hamza Bounibane2026-09-04✓ Author reviewed ⓘ

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