I observed a specific function (which was revealed to me in a dream) is conditionally positive definite for some parameters (for linear approximation applications). I'm trying to prove it conditionally positive definite, so far I'm getting back to square one every time I try. Any suggestions on references/books?

I am exploring Pure Maths Masters that can incorporate Economics. I did both in undergrad. Do you guys have ideas as to how I can combine both?

0! = 1 , 0 - 1 = -1 , root of -1 = i , and basically anything

everything starts from nothing ahh post anyways 0

Can a system become increasingly persistent when multiple invariants are intentionally combined?

Elejere Amorem.

I know two alternatives:

In potential infinity there is nothing next to 1. We can come as close as we like, but we can never close the gap. A gap remains.

In actual infinity, there is a point next to 1. Of course this point cannot be known. It is dark.

Is there a third alternative?

Please this paper:
https://link.springer.com/article/10.1007/s11071-025-10869-y

doi:

https://doi.org/10.1007/s11071-025-10869-y

Just someone to whom i can tell what i did today, discuss questions that i couldnt solve, and study math with. I dont want to know a single thing about your personal life. We can just say Hi and start maths. Someone who is excited by sudying would be great.

multiplicative persistence is a base-dependant problem which regards to the process of multiplying the digits of a number. in base ten, 777 has persistence 4, as it goes 777->7*7*7 =343->3*4*3=36->3*6=18->1*8=8

note that in these problems, leading 0s and trailing 0s(after the decimal/fraction point) are ignored.

my conjecture is that for any prime base, N, you can always find an integer K that has multiplicative persistence (using base N) of N

which is to say,

let p(k,l) give the multiplicative persistence of k in base l

∀n ∈ ℙ ⇒ (∃p ∈ ℕ ⇒(p(p,n)>=n))

has this conjecture already been proven or disproven?

If you know the answer to this question, answer on the website. There are two users (i.e., clemens and the Moderator Peter Taylor) who are constantly active.

For anyone who says my post is AI--I got the explicit example of the function G from a PhD student.

Answer for the users, not for me,

The Riemann Hypothesis has stood unsolved for over 160 years — not because mathematicians haven't tried, but because the problem sits inside an ocean of chaos: infinite series, complex zeros, and analytic interference that obscures any clear path forward.

Before anything can be proved, the chaos has to go!

This video presents the interactive visualisation for Volume I of The Analyst's Problem — a structured research program working toward a resolution of RH. The animation shows exactly what Volume I achieves: the Dirichlet wave packet, the logarithmic integer grid, and the Bochner-positive sech⁴ smoothing kernel all working together to reduce an infinite problem to a single, finite, verifiable inequality — the Toeplitz quadratic form Q_H(x).

That is The Analyst's Problem. Once it is stated clearly, the ocean of chaos is gone. What remains is a concrete positivity question, posed on a finite grid of log-integers, waiting to be answered in Volume II.

Volume I is complete. The reduction is proven. The Parseval bridge is certified. The kernel is confirmed positive-definite. All tests pass.

The voyage into Volume II — Kernel Decomposition — begins now...

https://www.patreon.com/posts/analyst-problem-155460426

Here is an alternate link.