Related papers: Solutions to a Romanoff type problem
This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is…
Given any closed Riemannian manifold $(M,g)$ we use the Lyapunov-Schmidt finite-dimensional reduction method and the classical Morse and Lusternick-Schnirelmann theories to prove multiplicity results for positive solutions of a subcritical…
The dual Minkowski problem in the two-dimensional plane is studied in this paper. By combining the theoretical analysis and numerical estimation of an integral with parameters, we find the number of solutions to this problem for the…
This paper deals with the use of numerical methods based on random root sampling techniques to solve some theoretical problems arising in the analysis of polynomials. These methods are proved to be practical and give solutions where…
In this paper, we determine all unitary solutions to the Yang-Baxter equation in dimension four. Quantum computation motivates this study. This set of solutions will assist in clarifying the relationship between quantum entanglement and…
This is an expository article presenting various results about the Cheeger problem and its connections with other relevant mathematical problems. In section 2 we synthetically describe three mathematical problems (eigenvalue estimates,…
We provide infinitely many solutions of a Dirichlet problem on balls.
We study the solutions of the inverse problem \[ g(z)=\int f(y) P_T(z,dy) \] for a given $g$, where $(P_t(\cdot,\cdot))_{t \geq 0}$ is the transition function of a given Markov process, $X$, and $T$ is a fixed deterministic time, which is…
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.
We prove the existence of a solution of the Yamabe equation on complete manifolds with finite volume and positive Yamabe invariant. In order to circumvent the standard methods on closed manifolds which heavily rely on global (compact)…
In this paper, we devote our interest to solving the real cubic truncated moment problem. We provide some results that allow to get a complete solution via a minimal representing measure. Some numerical examples are also presented to…
It is well known that many famous Burnside-type problems have positive solutions for PI-groups and PI-algebras. In the present article we also consider various Burnside-type problems for PI-groups and PI-representations of groups.
In this paper, we shall study the existence of weak solutions to Hessian type equations on compact Riemannian manifolds without boundary.
In the summer of 2013 Marcus, Spielman, and Srivastava gave a surprising and beautiful solution to the Kadison--Singer problem. The current presentation is slightly more didactical than other versions that have appeared since; it hopes to…
We present a solution of the generalized Hirzebruch problem on the relations between the Chern numbers of a stably almost complex manifold and the Chern numbers of its virtual Chern submanifolds.
We show that one dimensional non-stationary Schr\"odi-nger equation with a specific choice of potential reduces to the quantum Painlev\'e II equation and the solution of its Riccati form appears as a dominant term of that potential.…
During the Conference on Ulam's Type Stability (Rytro, Poland, 2014), Ioan Rasa recalled his 25-years-old problem concerning some inequality involving the Bernstein polynomials. We offer the complete solution (in positive). As a~tool we use…
We complete the classification of $4\times 4$ regular solutions of the Yang-Baxter equation. Apart from previously known models, we find four new models of non-difference form. All the new models give rise to Hamiltonians and transfer…
In an earlier paper [6] the author wrote the homothetic equations for vacuum solutions in a first order formalism allowing for arbitrary alignment of the dyad. This paper generalises that method to homothetic equations in non-vacuum spaces…
Topological interpretation of the link invariants associated with the Weinstein--Xu classical solutions of the quantum Yang-Baxter equation are provided.