Related papers: Deviations in the Franks-Misiurewicz conjecture

This paper is concerned with the well known Jeffreys-Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular,…

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

We prove inversion of adjunction for higher rational singularities.

A completeness theorem is proved involving a system of integro-differential equations with some $\lambda$-depending boundary conditions. Also some sufficient conditions for the root functions to form a Riesz basis are established.

This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1) representation theory, (2) algebraic…

A ``self--similar'' example is constructed that shows that a conjecture of N. U. Arakelyan on the order of decrease of deficiencies of an entire function of finite order is not true.

Let $d\geq 2$ be an integer and let $\omega_1,\cdots ,\omega_d$ be moduli of continuity in a specified class which contains the moduli of H\"{o}lder continuity. Let $f_k$, $k\in\{1,\cdots,d\}$, be $C^{1+\omega_k}$ orientation preserving…

In this paper we analyze the status of some `unbelievable results' presented in the paper `On Some Contradictory Computations in Multi-Dimensional Mathematics' [1] published in Nonlinear Analysis, a journal indexed in the Science Citation…

We prove the log-Brunn-Minkowski conjecture for convex bodies with symmetries to $n$ independent hyperplanes, and discuss the equality case and the uniqueness of the solution of the related case of the logarithmic Minkowski problem. We also…

We recently formulated important Modular Bourgain-Tzafriri Restricted Invertibility Conjectures and Modular Johnson-Lindenstrauss Flattening Conjecture in the Appendix of \textit{[arXiv: 2207.12799.v1]}. For the sake of wide accessibility…

Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains. The counterexample also suggests that Cox's assumptions are insufficient to prove the result even in infinite domains. The same…

The Komlos conjecture in discrepancy theory states that for some constant K and for any m by n matrix A whose columns lie in the unit ball there exists a +/- 1 vector x such that the infinity norm of Ax is bounded above by K. This…

Motivated by problems arising in the relative trace formula and arithmetic invariant theory we prove the existence of rational points on orbits arising from certain infinitesimal symmetric spaces. As an application, we prove analogous…

In this paper, besides a counterexample to Bloch's principle, normality criteria leading to counterexamples to the converse of Bloch's principle in several complex variables are proved. Some Picard-type theorems and their corresponding…

In this paper we investigate the perturbation properties of rational Misiurewicz maps, when the Julia set is the whole sphere (the other case is treated in [1]). In particular, we show that if f is a Misiurewicz map and not a flexible…

We discuss recent versions of the Brunn-Minkowski inequality in the complex setting, and use it to prove the openness conjecture of Demailly and Koll\'ar.

In this paper, we prove a version of the universality theorem for the Hurwitz zeta-function in the case where the parameter is algebraic and irrational. Then we apply the result to show that many of such Hurwitz zeta-functions have…

Under a mild technical assumption, we prove a necessary and sufficient condition for a totally real compacdt set in $\mathbb{C}^n$ to be rationally convex. This generalizes a classical result of Duval-Sibony

We prove a new lower bound for the Frobenius norm of the inverse of an non-negative matrix. This bound is only a modest improvement over previous results, but is sufficient for fully resolving a conjecture of Harwitz and Sloane, commonly…

We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…