Related papers: Crux's Crux's crux

The paper studies the problem of prescribing positive cross curvature on the three-dimensional sphere. We produce several existence results and an example of non-uniqueness, disproving a conjecture of Hamilton's.

Using Bombieri-Iwaniec method, we establish an improvement on both Gauss's Circle Problem and Dirichlet's Divisor Problem. More precisely, we derive a new estimate for the first spacing problem and combine it with Huxley's results on the…

In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting…

We resolve the longstanding open problem concerning the computational complexity of Max Cut on interval graphs by showing that it is NP-complete.

Several open problems in algebraic logic are solved.

The existence and uniqueness of a solution to a generalized Blasius equation with asymptotic boundary conditions are proved. A new numerical approximation method is proposed.

A newly-generalized problem from a problem initially thought for the Mathematical Olympiad and the methods to solve it.

We show that an inequality related to Newton's inequality provides one more relation between skewness and kurtosis. This also gives simple and alternative proofs of the bounds for skewness and kurtosis.

In this work we provide explicit calculations that support the conclusions stated in Phys. Rev. Lett. 111, 039102 (2013) (comment), regarding recent literature on transverse polarization. We also compare and contrast two methods of deriving…

We analyze the three point Pick interpolation problem on the bidisk

In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…

Open problems from the 15th Annual ACM Symposium on Computational Geometry.

Author of this article created for the first time the method for finding solutions of the Minkowski problem for closed surfaces in Riemannian space.

We have found some new solutions of both rational and trigonometric types by rewriting Yang-Baxter equation as a triple product equation in a vector space of matrices.

Corrigendum : An inverse problem in corrosion detection:stability estimates, J. Inv. Ill-posed Problems 12 (4) (2004), 349-367.

This paper presents a few additions to commutant lifting theory. An operator interpolation problem is introduced and shown to be equivalent to the relaxed commutant lifting problem. Using this connection a description of all solutions of…

A new solvable many-body problem of goldfish type is introduced and the behavior of its solutions is tersely discussed.

A class of generalized Schr\"{o}dinger elliptic problems involving concave-convex and other types of nonlinearities is studied. A reasonable overview about the set of solutions is provided when the parameters involved in the equation assume…

An open problem concerning Riemann sums, posed by O. Furdui, is considered.

We provide an alternative proof that Crosscaps are diffeomorphically stable.