The swing lemma, due to G. Grätzer for slim semimodular lattices and extended by G. Czédli and G. Grätzer for all planar semimodular lattices, describes the congruence generated by a prime interval in an efficient way. Here we present a new proof...
A prominent achievement of natural language processing (NLP) is its ability to understand and generate meaningful human language. This capability relies on complex feedforward transformer block architectures pre-trained on large language models (LLMs...
Let $R$ be a commutative Noetherian ring, $E$ a non-zero finitely generated $R$-module and $I$ an ideal of $R$. One purpose of this paper is to show that the sequences $\Ass_RE/ \widetilde{I_E^n}$ and $\Ass_R\widetilde{I^n _E}/\widetilde{I^{n+1}_E}$,...
Let $R$ be a commutative Noetherian ring, $M$ a finitely generated $R$-module and $I$ a proper ideal of $R$. In this paper we introduce and analyze some properties of $r(I, M)=\bigcup_{k\geqslant 1} (I^{k+1}M: I^kM)$, {\it the Ratliff-Rush ideal as...
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Autoregressive language models (LMs) generate one token at a time, yet human reasoning operates over higher-level abstractions - sentences, propositions, and concepts. This contrast raises a central question- Can LMs likewise learn to reason over str...
We propose the minimal supersymmetric sterile neutrino model (MSSNM) where the sterile neutrino masses are about 1 eV, while the active neutrino masses and the mixings among the active and sterile neutrinos are generated during late time phase tran...
Sep 30, 2010 · A compiler generates object code files (machine language) from source code. A linker combines these object code files into an executable. Many IDEs invoke them in succession, so you …
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Jul 2, 2025 · Daydreaming, synonymous with mind-wandering or task-unrelated thought (TUT), is technically defined as a shift of attention away from external tasks towards internal, self-generated …
As real-time analysis of the new data become increasingly compelling, more organizations deploy Hybrid Transactional/Analytical Processing (HTAP) systems to support real-time queries on data recently generated by online transaction processing. This p...
In this work we probe the possibility of high-temperature conventional superconductivity in the boron-carbon system, using ab-initio screening. A database of 320 metastable structures with fixed composition (50$\%$/50$\%$) is generated with the Minim...
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We consider controller-stopper problems in which the controlled processes can have jumps. The global filtration is represented by the Brownian filtration, enlarged by the filtration generated by the jump process. We assume that there exists a conditi...
Feb 9, 2026 · GitHub Copilot now supports multiple AI models, each optimized for different workflows, from quick edits to deep debugging to multi-step agentic tasks that generate or modify code across …
Jan 9, 2023 · ChatGPT is a chatbot that uses the GPT-3.5 language model by OpenAI to generate responses to user input. It has been trained on a large dataset of human conversation and is able to …
Radio relics trace shock fronts generated in the intracluster medium (ICM) during cluster mergers. The particle acceleration mechanism at the shock fronts is not yet completely understood. We observed the Toothbrush relic with the Effelsberg and Sard...
Let R be a differential domain finitely generated over a differential field, F, with field of constants, C, of characteristic 0. Let E be the quotient field of R. The paper investigates necessary and sufficient conditions on R's differential ideals...
This note intended to give a counterexample to a question related to the following theorem. Let D be a differential domain finitely generated over a differential field F with algebraically closed field of constants,C, of characteristic 0. If D has...
The paper investigates the converse to the following theorem. Let R be a differential domain R which is finitely generated over a differential field F whose field of constants is algebraically closed of characteristic 0. If R has no proper nonzero...