Related papers: The stabilized symplectic embedding problem for po…
In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems…
The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier-Stokes equations. We develop a separation of variables representation for this equation in polar…
The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the otherwise smooth surface of such a…
The hallmark feature of polymorphic systems is their ability to assemble into many possible structures at the same thermodynamic state. Designer polymorphic materials can in principle be engineered via programmable self-assembly, but the…
We prove that a very general cubic fourfold containing a plane can be embedded into a holomorphic symplectic eightfold as a Lagrangian submanifold. We construct the desired holomorphic symplectic eightfold as a moduli space of Bridgeland…
Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity…
A venerable problem in combinatorics and geometry asks whether a given incidence relation may be realized by a configuration of points and lines. The classic version of this would ask for algebraic lines over some field or possibly real…
Problems of stabilization of the unstable cycle of one-dimensional complex dynamical system are briefly discussed. These questions reduced to the problem of description of the ranges of polynomials $q(z) = q_1z + q_2z^2 +\dots + q_nz^n$…
A graph is called (generically) rigid in $\mathbb{R}^d$ if, for any choice of sufficiently generic edge lengths, it can be embedded in $\mathbb{R}^d$ in a finite number of distinct ways, modulo rigid transformations. Here we deal with the…
This paper is dedicated to the study of the stability of multiplicities of group representations.
In this paper we study a generalized symplectic fixed point problem, first considered by J. Moser in \cite{M}, from the point of view of some relatively recently discovered symplectic rigidity phenomena. This problem has interesting…
We study the problem of stabilization for the acoustic system with a spatially distributed damping. Imposing various hypotheses on the structural properties of the damping term, we identify either exponential or polynomial decay of…
New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…
Occurring in protoplanetary discs composed of dust and gas, streaming instabilities are a favoured mechanism to drive the formation of planetesimals. The Polydispserse Streaming Instability is a generalisation of the Streaming Instability…
Stationary differential systems with polynomial right sides are considered. Necessary and sufficient conditions are formulated when a given domain is a domain of asymptotic stability and the origin of coordinates is either focus or center.…
We initiate the study of stability of solutions of the 2D inviscid incompressible porous medium equation (IPM). We begin by classifying all stationary solutions of the inviscid IPM under mild conditions. We then prove some linear stability…
We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…
We compute the stable cohomology of moduli spaces of hyperelliptic curves of a fixed genus embedded on a fixed Hirzebruch surface. We also describe these moduli spaces of embedded hyperelliptic curves in terms of moduli spaces of pointed…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…