David is a best-selling author, speaker and trainer. He is also CEO of IPD, a world-class marketing agency based in Tampa, Florida. The only thing that’s certain in marketing is this: Nothing is ...

Joshua Kristian McCoy is a freelance writer and film critic from the United States. He is a lifelong film buff, a voting member of the Georgia Film Critics Association, a tournament-winning Smash Bros ...

Two weeks ago, a modest-looking paper was uploaded to the arXiv preprint server with the unassuming title “On the invariant subspace problem in Hilbert spaces”. The paper is just 13 pages long and its ...

Nathan Brownlowe does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond ...

Abstract: This article discusses the invariant subspaces that are restricted to be external direct sums. Some existence conditions are presented that facilitate finding such invariant subspaces. This ...

Direct marketing—a marketing term that some have characterized as a tired or outdated form of marketing—is having its moment in the sun again. Have you spoken to a Gen-Z or Millennial marketer (like ...

In 50 years of searching, mathematicians found only one example of a “subspace design” that fit their criteria. A new proof reveals that there are infinitely more out there. In the fall of 2017, ...

Direct indexing is having a moment. The option that was once exclusive to high-net-worth investors is moving downstream—and quickly. In 2022, Fidelity expanded its direct-index offerings to retail ...

The most powerful formula in physics starts with a slender S, the symbol for a sort of sum known as an integral. Further along comes a second S, representing a quantity known as action. Together, ...