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Dynamics of a stochastic ratio-dependent predator-prey model
In this paper, we consider a stochastic ratio-dependent predator-prey model. We firstly prove the existence, uniqueness and positivity of the solutions. Then, the boundedness of moments of population are studied. Finally, we sho ... Read More >
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Perron Spectratopes and the Real Nonnegative Inverse Eigenvalue Problem
Call an $n$-by-$n$ invertible matrix $S$ a \emph{Perron similarity} if there is a real non-scalar diagonal matrix $D$ such that $S D S^{-1}$ is entrywise nonnegative. We give two characterizations of Perron similarities and stud ... Read More >
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Convergence Implications via Dual Flow Method
Given a one-dimensional stochastic differential equation, one can associate to this equation a stochastic flow on $[0,+\infty )$, which has an absorbing barrier at zero. Then one can define its dual stochastic flow. In \cite{AW} ... Read More >
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Characterizations of compact sets in fuzzy sets spaces with $L_p$ metric
In this paper, we present characterizations of totally bounded sets, relatively compact sets and compact sets in the fuzzy sets spaces $F_B(\mathbb{R}^m)$ and $F_B(\mathbb{R}^m)^p$ equipped with $L_p$ metric, where $F_B(\mathbb{ ... Read More >
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Modules of the toroidal Lie algebra $\widehat{\widehat{\mathfrak{sl}}}_{2}$
Highest weight modules of the double affine Lie algebra $\widehat{\widehat{\mathfrak{sl}}}_{2}$ are studied under a new triangular decomposition. Singular vectors of Verma modules are determined using a similar condition with ho ... Read More >
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Strong solutions to the compressible Navier-Stokes-Vlasov-Fokker-Planck equation ...
A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The model consists of the Vlasov-Fokker-Planck equation for the particles (disperse phase) coupled with the compressible Navier-Stokes eq ... Read More >
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Shy shadows of infinite-dimensional partially hyperbolic invariant sets
Let $\mathcal{R}$ be a strongly compact $C^2$ map defined in an open subset of an infinite-dimensional Banach space such that the image of its derivative $D_F \mathcal{R}$ is dense for every $F$. Let $\Omega$ be a compact, forwa ... Read More >
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Translates of Polynomials
Let f = 0 be a hypersurface in n-dimensional affine space over a field k. We consider the pencil of hypersurfaces f- c = 0 with c varying over k. Read More >
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Generalized Uniformly Optimal Methods for Nonlinear Programming
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a loca ... Read More >
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Semiclassical analysis and symmetry reduction II. Equivariant quantum ergodicity ...
We study the ergodic properties of Schr\"odinger operators on a compact connected Riemannian manifold $M$ without boundary in case that the underlying Hamiltonian system possesses certain symmetries. More precisely, let $M$ carr ... Read More >