The graph of a polynomial function is more than just a pretty curve; it's a treasure map revealing key characteristics of the function it represents. By carefully observing the graph's features, we ...

Julia Kagan is a financial/consumer journalist and former senior editor, personal finance, of Investopedia. Chip Stapleton is a Series 7 and Series 66 license holder, CFA Level 1 exam holder, and ...

ABSTRACT: Brualdi and Goldwasser characterized the Laplacian permanents of trees. In this paper, we study the Laplacian permanents of trees. We characterize some Laplacian permanents of trees. The ...

An audiogram can diagnose your hearing loss and indicate what type of hearing loss you have. It can distinguish your hearing in each ear and whether you have hearing loss on one or both sides. You can ...

While retrieval-augmented generation is effective for simpler queries, advanced reasoning questions require deeper connections between information that exist across documents. They require a knowledge ...

Abstract: In this paper, the design and application of Hermite polynomial graph filter is studied. First, the basics of graph signal processing (GSP) is briefly reviewed and the design problem of ...

The original version of this story appeared in Quanta Magazine. Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a ...

A holy grail of theoretical computer science, with numerous fundamental implications to more applied areas of computing such as operations research and artificial intelligence, is the question of ...