Let b >= 2 be an integer. In this paper, we study the rep digits in base b that can be expressed as sums or products of Fibonacci, Pell, balancing and Jacobsthal numbers. The proofs of our main theorems use lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker-Davenport reduction method.
Large language models (LLMs) possess vast knowledge acquired from extensive training corpora, but they often cannot remove specific pieces of information when needed, which makes it hard to handle privacy, bias mitigation, and knowledge correction. Traditional model unlearning approaches require computationally expensive fine-tuning or direct weight editing, making them impractical for real-world deployment. In this work, we introduce LoRA-based Unlearning with Negative Examples (LUNE), a lightweight framework that performs negative-only unlearning by updating only low-rank adapters while freezing the backbone, thereby localizing edits and avoiding disruptive global changes. Leveraging Low-Rank Adaptation (LoRA), LUNE targets intermediate representations to suppress (or replace) requested knowledge with an order-of-magnitude lower compute and memory than full fine-tuning or direct weight editing. Extensive experiments on multiple factual unlearning tasks show that LUNE: (I) achieves effectiveness comparable to full fine-tuning and memory-editing methods, and (II) reduces computational cost by about an order of magnitude.
Experimental evaluation demonstrates strong performance, achieving an F1 score of 0.92 for worker detection and 0.93 for personal protective equipment (PPE) classification. The integrated hazard-zone monitoring module further enables spatial safety enforcement, achieving a frame-level detection accuracy of 92
This study systematically evaluates the bioelectrochemical treatment performance of dual-chamber microbial fuel cells using low-cost anion exchange, cation exchange and bipolar membranes under fed-batch operation with low-strength municipal wastewater. Each unit was assembled using carbon felt electrodes, fed with raw wastewater, and activated sludge from an oxidation ditch of a municipal wastewater treatment plant as the anodic substrate. System performance was assessed over multiple cycles by monitoring changes in chemical oxygen demand (COD), total nitrogen, phosphorus, and ammonia concentrations including electrical output, pH shifts, and polarity stability. The results revealed distinct performance profiles for each membrane type. The CEM system supported high removal of COD, TN, and ammonia (65-85 +/- 2 %) but exhibited limited phosphorus reduction (20 +/- 2 %). In contrast, the AEM achieved excellent phosphorus removal (95 +/- 2 %) alongside strong COD reduction, although nitrogen and ammonia removal were comparatively lower. BPM systems exhibited lower COD removal (typically <65 %) but achieved moderate and stable reductions in TN, ammonia, and phosphorus, while producing electrical output consistently higher than AEM and at intermediate levels relative to CEM. Analysis of power generation further confirmed this trend, with CEM delivering the highest output (1.3 mW/m(2)), BPM providing moderate performance (1.13 mW/m(2)), and AEM producing the lowest (0.82 mW/ m(2)). The results reveal how membrane ion selectivity shapes the relationship between nutrient removal and energy production, underscoring the need to match membrane type to specific treatment goals for successful MFC deployment from laboratory scale to industrial wastewater applications.
The existence of a new spin-zero particle with a mass below the electroweak scale is predicted by several theoretical models. Searches for resonant production of photon pairs at the LHC are able to probe these models. We present a search for a narrow resonance produced through gluon fusion that decays into a pair of photons with an invariant mass between 10 and 70 GeV, using a proton-proton collision dataset from the CMS experiment. This dataset, corresponding to an integrated luminosity of 54.4 fb − 1 , was recorded in 2018 at a center-of-mass energy of 13 TeV using a newly introduced diphoton trigger that enabled exploration of the low-mass diphoton spectrum. No significant excess above the expected background is observed. Upper limits are set on the product of the gluon fusion production cross section and the branching fraction of the diphoton decay of a narrow resonance. An interpretation of these limits within an effective field theory framework for axionlike particles is also provided.
