Related papers: Another counterexample to Zygmund's conjecture

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

We use non-perturbative U-duality symmetries of type II strings to construct new vacuum solutions. In some ways this generalizes the F-theory vacuum constructions. We find the possibilities of new vacuum constructions are very limited.…

We give a short proof of Belaga's result on bounds to perigees of $(3x+d)$-cycles of a given oddlength. We also reformulate the Collatz cycle conjecture which is rather a algorithmic problem into a purely arithmetic problem.

A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…

To verify the universal validity of the "two-sided" monotonicity condition introduced in [8], we will apply it to include more classical examples. The present paper selects the $L^{p}$ convergence case for this purpose. Furthermore, Theorem…

In this article, a new construction of derived equivalences is given. It relates different endomorphism rings and more generally cohomological endomorphism rings - including higher extensions - of objects in triangulated categories. These…

This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.

In this paper we use computational methods to disprove a conjecture by Alaoglu and Erd\H{o}s regarding the superabundant numbers.

Motivated by Alladi's recent multi-dimensional generalization of Sylvester's classical identity, we provide a simple combinatorial proof of an overpartition analogue, which contains extra parameters tracking the numbers of overlined parts…

We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.

Through the use of a nonstandard version of Frostman's lemma, the notion of Hausdorff dimension is formulated in nonstandard euclidean space of arbitrary dimension. This allows for a nonstandard proof of the Kakeya conjecture in two…

In 1979, Herzog put forward the following conjecture: if two simple groups have the same number of involutions, then they are of the same order. We give a counterexample to this conjecture.

In this note a simple extension of the complex algebra to higher dimension is proposed. Using the postulated algebra a two dimensional Dirac equation is formulated and its solution is calculated. It is found that there is a sub-algebra…

A classical proof of Pisier's construction of a polynomially bounded operator not similar to a contraction is given.

We prove the Hardy-Littlewood theorem in two dimensions for functions whose Fourier coefficients obey general monotonicity conditions and, importantly, are not necessarily positive. The sharpness of the result is given by a counterexample,…

In the present note we give a new proof of a result due to Wiseman and Wilson which establishes an analogue of the Sylvester-Gallai theorem valid for curves of degree two. The main ingredients of the proof come from algebraic geometry.…

We look at an old conjecture of A. Tarski on cardinal arithmetic and show that if a counterexample exists, then there exists one of length omega_1 + omega .

We give a proof of the Kodaira vanishing theorem on smooth complex surfaces using geometric stability conditions. Likewise, we give a new proof of a result of Xie characterizing the counterexamples of the Kodaira vanishing theorem in…

We prove that the set of accumulation points of thresholds in dimension three is equal to the set of thresholds in dimension two, excluding one.

The finitistic dimension conjecture is closely connected to the symmetry of the finitistic dimension. Recent work indicates that such connection extends to one of its upper bounds, the delooping level. In this paper, we show that the same…