Related papers: Open Problems in Analysis of Boolean Functions
In the paper, some lower bounds for polygamma functions are refined.
In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.
In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
Similarly to noises, Boolean algebras of sigma-fields can be black. A noise may be treated as a homomorphism from a Boolean algebra of regular open sets to a Boolean algebra of sigma-fields. Spectral sets are useful also in this framework.
This is the second volume of a textbook for a two-semester course in mathematical analysis. This second volume is about analysis of multi-variable functions. The topics covered include Euclidean spaces, convergence of sequences, open sets…
In this paper, we derive more on $\alpha^{m}$-continuous functions and $\alpha^{m}$-irresolute functions with $\alpha^{m}$-open maps and $\alpha^{m}$-closed maps in topological spaces also we introduce $I_{\alpha^{m}}(A)$ and…
Open problems from the 15th Annual ACM Symposium on Computational Geometry.
Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the…
In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
We set new dual problems for the weighted spaces of holomorphic functions of one variable in domains on the complex plane, namely: nontriviallity of a given space, description of zero sets, description of (non-)uniqueness sets, the…
We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de…
This is a collection of open problems from workshop "Differential Geometry, Billiards, and Geometric Optics" at CIRM on October 4-8, 2021.
Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function…
These open problems were presented in the Problem Sessions held during the Tianyuan Workshop on Computability Theory and Descriptive Set Theory, June 16-20, 2025. The problems are organized into sections named after their contributors, in…
We formulate several open questions related to enumerative combinatorics, which arise in the spectral analysis of Hill operators with trigonometric polynomial potentials.
Given a relational specification between Boolean inputs and outputs, the goal of Boolean functional synthesis is to synthesize each output as a function of the inputs such that the specification is met. In this paper, we first show that…
Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.
The nonlinearity of a Boolean function is a key property in deciding its suitability for cryptographic purposes, e.g. as a combining function in stream ciphers, and so the nonlinearity computation is an important problem for applications.…