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the 2 in the denominator, I used the quotient rule and then multiplied the fraction by x to the 1/2, which allowed me to do some factorizing to cancel out the denominator. However, I am left with simp …

The following is an attempt at a proof that $S=(S^\perp)^\perp$ for any $S \subseteq V$. I have reason to believe the conclusion is not true in general but I can not find any errors in this proof. If …

We have seen from history of attempted proofs of Riemann Hypothesis(RH) no matter where / how we start, we always end up at theoretical dead end/ barrier. As there is duality between Zeta zeros and pr …

I need a bit of help finishing this theorem I believe it to be true. First, set $\mathcal{B} = \{A, B, \dots, Z\}$ to be the set of capital letters in base 64, and define $\mathcal{A}_m$ as the set of …

The framework addresses undefined mathematical operations like zero raised to the first power (0^1) and division by zero (1/0) by introducing definitions that include infinity as the inverse of zero. …

I was wondering what is research in mathematics. Can it be considered research only the research in open problems or it can be considered research also the finding of new formulas, new classes of prim …

Let $H$ be a Hilbert space and $D:\mathrm{Dom}(D) \to H$ a densely defined operator on $H$. We further assume that $D$ is closed and self-adjoint. If we further assume that $D$ is positive, then we ca …

I am working on a problem about planar graphs and trying to understand if two statements can both be true at the same time. The problem states that for any planar graph with at least 3 or more vertice …

Here is the textbook, chapter 7, page 300. This lemma seems very of important, and I've spend about 8 hours trying to figure it out, but I'm unable to prove even the weaker version of the lemma (on …

Is this question well posed? If not, can you improve it? If so, what is the solution? I am holding a dinner party for 12 people. Their names are A, B,...L. The seats are numbered: 1, 2, ... 12. The pe …

Is there any difference between the visual boundary of a relatively hyperbolic group and the Bowditch boundary of a relatively hyperbolic group? Visual boundary is generally associated to a CAT(0) spa …

I have an optimization problem and was using a linear programming optimizer to find solutions. However, I find that past a certain size, the problem becomes "infeasible" and has no solutions. So I am …

Consider the collection $\mathcal{C}$ of all maps $f \colon B_1 -\overline{B}_\beta \to \mathbb{C}$ such that $f$ is biholomorphic onto its image. Is this collection $\mathcal{C}$ path-connected? In p …

In the usual sense, Maximum Likelihood Estimation is the common method for Parameter estimation in ARMA(p,q) model. If I am looking to estimate parameters for ARMA(p,q) with Bayesian Inference, how ca …

Every well-ordered set $W$ is isomorphic to a unique ordinal Proof: We start with some well-ordered set $W$. We attempt to construct a bijective map from $W$. Let us consider this class $$\{(x, \alp …