This study reported the inhibitive efficiency a binuclear cobalt complex with the ligand N, N’-bis(salicylidene)-phenylmethanediamine at different concentrations for the corrosion protection of 2024 aluminium alloy substrate. The electrochemical impedance spectroscopy measurements confirmed a high protective performance from 94 to 98
In this paper, we consider a class of the Caputo fractional stochastic differential equations of order alpha is an element of (12, 1]. Our aim is to analyze the continuous dependence of solutions on the fractional order alpha. We first provide explicit estimates for the rate of weak convergence the solutions. We then describe the exact asymptotic behavior of this convergence to show that the rate is optimal. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Despite significant progress in alignment, large language models (LLMs) remain vulnerable to adversarial attacks that elicit harmful behaviors. Activation steering techniques offer a promising inference-time intervention approach, but existing methods suffer from critical limitations: activation addition requires careful coefficient tuning and is sensitive to layer-specific norm variations, while directional ablation provides only binary control. Recent work on Angular Steering introduces continuous control via rotation in a 2D subspace, but its practical implementation violates norm preservation, causing distribution shift and generation collapse, particularly in models below 7B parameters. We propose Selective Steering, which addresses these limitations through two key innovations: (1) a mathematically rigorous norm-preserving rotation formulation that maintains activation distribution integrity, and (2) discriminative layer selection that applies steering only where feature representations exhibit opposite-signed class alignment. Experiments across nine models demonstrate that Selective Steering achieves 5.5x higher attack success rates than prior methods while maintaining zero perplexity violations and approximately 100% capability retention on standard benchmarks. Our approach provides a principled, efficient framework for controllable and stable LLM behavior modification. Code: https://github.com/knoveleng/steering
As large language models (LLMs) become integral to safety-critical applications, ensuring their robustness against adversarial prompts is paramount. However, existing red teaming datasets suffer from inconsistent risk categorizations, limited domain coverage, and outdated evaluations, hindering systematic vulnerability assessments. To address these challenges, we introduce RedBench, a universal dataset aggregating 37 benchmark datasets from leading conferences and repositories, comprising 29,362 samples across attack and refusal prompts. RedBench employs a standardized taxonomy with 22 risk categories and 19 domains, enabling consistent and comprehensive evaluations of LLM vulnerabilities. We provide a detailed analysis of existing datasets, establish baselines for modern LLMs, and open-source the dataset and evaluation code. Our contributions facilitate robust comparisons, foster future research, and promote the development of secure and reliable LLMs for real-world deployment. Code: https://github.com/knoveleng/redeval
We study Kakeya maximal operators associated with horizontal lines in finite Heisenberg groups ℍ_n(𝔽_q). For the operator parameterized only by projective horizontal directions, we show that projection to 𝔽_q^2n reduces the problem to the affine finite field Kakeya maximal operator, and we determine the exact ℓ^u →ℓ^v growth exponent for all n and all 1 ≤ u,v ≤∞. We then introduce a refined-direction operator that also records the central slope of a horizontal line. In ℍ_1(𝔽_q), we prove the sharp ℓ^2 →ℓ^2 estimate M_ℍ_1^rdF_ℓ^2(D_1)≲ q^1/2F_ℓ^2(ℍ_1(𝔽_q)), deduce the exact mixed-norm exponent formula, and obtain lower bounds for horizontal Heisenberg Kakeya sets with prescribed refined directions. The argument is purely Fourier-analytic and does not use the polynomial method. An outlook toward a new approach to the affine Kakeya problem in 𝔽_q^3 will be discussed in this paper.
