相关论文: A quest for 5-point condition a la Alexandrov

This article discusses the search procedure for the Poincar\'e recurrences to classify solutions on an attractor of a fourth-order nonlinear dynamical system using a previously developed high-precision numerical method. For the resulting…

We briefly review the various contexts within which one might address the issue of ``why'' the dimensionless constants of Nature have the particular values that they are observed to have. Both the general historical trend, in physics, of…

We present a short proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies.

In the present paper, we consider several valid notions of orientability of Alexandov spaces and prove that all such conditions are equivalent. Further, we give topological and geometric applications of the orientability. In particular, a…

This paper explores the cubic-quintic Schr\"odinger equation in the entire Euclidean space. Our objectives are twofold: first, to advance the understanding of unresolved issues related to this equation, which are well known in the…

We study the orbits and manifolds near the equilibrium points of a rotating asteroid. The linearised equations of motion relative to the equilibrium points in the gravitational field of a rotating asteroid, the characteristic equation and…

In this paper we show a Zariski pair of sextics which is not a degeneration of the original example given by Zariski. This is the first example of this kind known. The two curves of the pair have a trivial Alexander polynomial. The…

In this paper we present some linear algebra behind quadratic parts of quadratically flat complex points of codimension two real submanifold in a complex manifold. Assuming some extra nondegenericity and using the result of Hong, complete…

The hypothesis is discussed that our universe is really 5--dimensional with a nonzero cosmological constant that produces a large negative curvature. In this scenario, the observable flat 4--dimensional universe is identified with the…

The condition for adiabatic approximation are of basic importance for the applications of the adiabatic theorem. The traditional quantitative condition was found to be necessary but not sufficient, but we do not know its physical meaning…

A perfect Euler cuboid is a rectangular parallelepiped with integer edges and integer face diagonals whose space diagonal is also integer. Such cuboids are not yet discovered and their non-existence is also not proved. Perfect Euler cuboids…

In this paper, we mainly consider the problem of spherical distribution of 5 points, that is, how to configure 5 points on a sphere such that the mutual distance sum attains the maximum. It is conjectured that the sum of distances is…

The theory of Chebyshev (uniform) approximation for univariate polynomial and piecewise polynomial functions has been studied for decades. The optimality conditions are based on the notion of alternating sequence. However, the extension the…

The Aharonov-Casher problem in the presence of a Lorentz-violating background nonminimally coupled to a spinor and a gauge field is examined. Using an approach based on the self-adjoint extension method, an expression for the bound state…

In this paper we give a new formulation of an abstract control problem in terms of a Grushin problem, so that we will reformulate all notions of controllability, observability and stability in a new form that gives readers an easy…

A conjecture connecting Lyapunov exponents of coupled map lattices and the node theorem is presented. It is based on the analogy between the linear stability analysis of extended chaotic states and the Schr\"odinger problem for a particle…

Using a method developped in [1] and [2], we prove the existence of weak non trivial solutions to fourth order elliptic equations with singularities and with critical Sobolev growth.

A classical Theorem of Alexandrov states that the map associating its boundary to a convex polyhdedron of the 3-dimensional Euclidean space is a bijection from the set of convex polyhdedron up to congruence to the set of isometry classes of…

Multivariable Alexander invariants of algebraic links calculated in terms of algebro-geometric invariants (polytopes and ideals of quasiadjunction). The relations with log-canonical divisors, the multiplier ideals and a semicontinuity…

There is some evidence that the Universe is presently undergoing accelerating expansion. This has restored some credit to the scenarios with a non-vanishing cosmological constant. From the point of view of a theory of fundamental…