Related papers: On the WALA conjecture, Alberti representations an…
Some explanations to Kaldi's PLDA implementation to make formula derivation easier to catch.
Using numerical, theoretical and general methods, we construct evaluation formulas for the Jacobi $\theta$ functions. Some of our results are conjectures, but are verified numerically.
We give a geometric proof of a conjecture of W. Fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for GL(r).
In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…
We prove the Invariant Subspace Conjecture for separable Hilbert spaces.
An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.
We prove a variation of Gronwall's lemma.
We prove an improved form of an expectation of Polya and discuss several related questions
In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.
In this note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show…
A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.
We show that the $\theta=\infty$ conjecture implies the Riemann hypothesis.
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
We show that the Jacobian conjecture of the two dimensional case is true.
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
We give a proof of some small weight and level cases of Serre's conjecture.
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
In this Note, we start off with the primary representation of e and from there present an elementary short proof for the Wallis formula for $\pi$.
We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.
One of the variants to proof the generalized Ito-Wentzell's formula is introduced and examined in this paper. The relationship between different representations of the generalized Ito-Wentzell's formula/ is considered.