Can you chip in? This year we’ve reached an extraordinary milestone: 1 trillion web pages preserved on the Wayback Machine. This makes us the largest public repository of internet history ever ...

Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, United States ...

Integrating human values after model training using Learning-based algorithms requires fine-tuning LLMs, which requires more computational power and is time-consuming. Additionally, it generates ...

ABSTRACT: In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the ...

Abstract: In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of ...

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The Pythagorean Theorem—discovered by the Greek mathematician Pythagoras in the 6th century BCE—is a cornerstone of mathematics. Simply stated as a 2 + b 2 = c 2, the theorem posits that the sum of ...