Related papers: Integral geometry and Mizel's problem

We consider the so-called Gross-Pitaevskii equations supplemented with non-standard boundary conditions. We prove two mathematical results concerned with the initial value problem for these equations in Zhidkov spaces.

We describe the progress in the last 10 years related to Koszul modules and syzygies of algebraic varieties. Topics discussed include the general theory of Koszul modules and resonance varieties, applications to Chen ranks of K\"ahler and…

We answer a question of Zadrozny.

On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.

We solve the inverse spectral problem for rotationally symmetric manifolds, which include the class of surfaces of revolution, by giving an analytic isomorphism from the space of spectral data onto the space of functions describing the…

In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in order to give a geometric interpretation of the dual Orlicz…

A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the…

In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.

We present some new and recent algorithmic results concerning polynomial system solving over various rings. In particular, we present some of the best recent bounds on: (a) the complexity of calculating the complex dimension of an algebraic…

Bell and Zhang have shown that if $A$ and $B$ are two connected graded algebras finitely generated in degree one that are isomorphic as ungraded algebras, then they are isomorphic as graded algebras. We exploit this result to solve the…

The paper is devoted to some extremal problems, related to convex polygons in the Euclidean plane and their perimeters. We present a number of results that have simple formulations, but rather intricate proofs. Related and still unsolved…

This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.

In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.

We discuss the integrability properties of the Boussinesq equations in the language of geometrical quantities defined on an appropriately chosen coset manifold connected with the $W_{3}$ algebra of Zamolodchikov. We provide a geometrical…

We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.

We consider an open question posed in \cite{Zhu-Baggio-17} on the uniqueness of the solution to a parametric spectral estimation problem.

In this article, we continue to study the geometry of bisections of certain rational elliptic surfaces. As an application, we give examples of Zariski N + 1-plets of degree 2N + 4 whose irreducible components are an irreducible quartic…

We discuss the hypergeometric solutions of the quantized Knizhnik-Zamolodchikov (qKZ) equation at level zero and show that they give all solutions of the qKZ equation. We completely describe linear relations between the hypergeometric…

This work provides a characterization of left and right Zinbiel algebras.Basic identities are established and discussed, showing that Zinbiel algebras are center-symmetric, and therefore Lie-admissible algebras. Their bimodules are given,…

In this work, we prove the existence of integrable solutions for the following generalized mixed-type nonlinear functional integral equation $$x(t)=g\left(t,(Tx)(t)\right)+f\left(t,\int_0^t…