Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

Convex analysis plays a fundamental role in mathematics. In this paper, we extend the concept of convexity to vector-valued functions in Banach lattices. We introduce the notion of “order convexity” ...

Abstract: Some basic t-norms defined on [0, 1] are well known in many study areas and applications. However, more general extension of them into vector forms can be used in a lot of new ...

Cryptographic hash functions secure data by providing a unique fixed-length output for each input. These functions are essential in blockchain for data integrity and secure transactions. Understanding ...

THIS work of Prof. Einar Hille is one of the important mathematical books of the century ; it should be read seriously by every mathematician. The subject of semi-groups is one of great and growing ...

Suppose I have a vector-valued function f(x) = y, where x and y are both vectors of some length (same or different length). f could be evaluated over a regular grid of x values, producing a set of y ...

Lipids are fatty compounds that perform a range of essential functions in the body. Phospholipids, steroids, and triglycerides are examples of lipids. Although lipids play an essential role in the ...

This paper covers the concept of a conservative vector field, and its application in vector physics and Newtonian mechanics. Conservative vector fields are defined as the gradient of a scalar-valued ...

Tools like Semantic Kernel, TypeChat, and LangChain make it possible to build applications around generative AI technologies like Azure OpenAI. That’s because they allow you to put constraints around ...