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Rotation Problem for a Two-Phase Drop
The paper deals with the stability of a uniformly rotating finite mass consisting of two immiscible viscous incompressible fluids with unknown...
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BG Approximations of Multiphysics pH Distributed Systems with Finite Number of Ports
This paper proposes a procedure for the modeling of linear passive devices with distributed parameters as Hamiltonian systems with a finite number of...
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The Definition of the Indices of Oscillation, Rotation, and Wandering of Nonlinear Differential Systems
AbstractThe definitions of the indices of oscillation, rotation and wandering, similar to the Lyapunov exponents and suitable for nonlinear systems...
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Fast norm computation in smooth-degree Abelian number fields
This paper presents a fast method to compute algebraic norms of integral elements of smooth-degree cyclotomic fields, and, more generally,...
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Rauzy Fractals and their Number-Theoretic Applications
In this paper, we construct and study Rauzy partitions of order n for a certain class of Pisot numbers. These partitions are partitions of a torus...
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A Strong Solution of Navier-Stokes Equations with a Rotation Effect for Isentropic Compressible Fluids
We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside...
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Two-valued number pyramids
Number pyramids are common in elementary school mathematics. Trying to express the value of the top block in terms of the values at the base leads to...
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On the Chromatic Number of 2-Dimensional Spheres
In 1976 Simmons conjectured that every coloring of a 2-dimensional sphere of radius strictly greater than 1/2 in three colors has a pair of...
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Time Averages and Periodic Attractors at High Rayleigh Number for Lorenz-like Models
Revisiting the Lorenz ’63 equations in the regime of large of Rayleigh number, we study the occurrence of periodic solutions and quantify...
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Pseudo solutions, rotation sets, and shadowing rotations for monotone recurrence relations
By introducing for monotone recurrence relations pseudo solutions, which are analogues of pseudo orbits of dynamical systems, we show that for...
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On the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with compact center leaves
In this paper we study the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms defined on 3-torus with compact...
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A Formula for the Linking Number in Terms of Isometry Invariants of Straight Line Segments
AbstractThe linking number is usually defined as an isotopy invariant of two non-intersecting closed curves in 3-dimensional space. However, the...
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The Rotation Number Integer Quantization Effect in Braid Groups
V. M. Buchstaber, O. V. Karpov, and S. I. Tertychnyi initiated the study of the rotation number integer quantization effect for a class of dynamical...
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A Multiscale Problem for Viscous Heat-Conducting Fluids in Fast Rotation
In the present paper, we study the combined incompressible and fast rotation limits for the full Navier–Stokes–Fourier system with Coriolis,...
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A Fast Algorithm for Computing the Number of Magic Series
We present a fast algorithm for computing the number of magic series, an enumeration problem of a certain integer partition. Kinnaes showed that the...
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An Almost Optimal Bound on the Number of Intersections of Two Simple Polygons
What is the maximum number of intersections of the boundaries of a simple m -gon and a simple n -gon? This is a basic question in combinatorial...
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Asymptotic limit of fast rotation for the incompressible Navier–Stokes equations in a 3D layer
We consider the initial value problem for the Navier–Stokes equation with the Coriolis force in a three-dimensional infinite layer. We prove the...