Discover a fast and powerful calculus-based method for finding square roots with impressive accuracy. This explanation shows how derivatives and iterative approximation can be used to quickly zero in ...

1 Warwick Mathematics Institute, The University of Warwick, Coventry, United Kingdom 2 School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang, China To ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...

ABSTRACT: In this paper, we establish an SIR reaction-diffusion infectious disease model with saturated incidence rate and vaccination. Firstly, we prove the uniform boundedness of the solution of ...

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Iterative preference optimization methods have shown efficacy in general instruction tuning tasks but yield limited improvements in reasoning tasks. These methods, utilizing preference optimization, ...