## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

DCDS-B

We show that for a very general and natural class of curvature functions (for example the curvature quotients
$(\sigma_n/\sigma_l)^{\frac{1}{n-l}}$) the problem of finding a complete spacelike strictly convex hypersurface
in de Sitter space satisfying
$f(\kappa)=\sigma \in (1,\infty)$ with a prescribed compact future asymptotic boundary $\Gamma$ at infinity
has at least one smooth solution (if $l=1$ or $l=2$ there is uniqueness). This is the exact analogue of the asymptotic plateau problem in Hyperbolic space
and is in fact a precise dual problem. By using this duality we obtain for free the existence of strictly convex solutions to the asymptotic Plateau problem for $\sigma_l=\sigma,\,1 \leq l < n$ in both de Sitter and Hyperbolic space.

JIMO

In this paper, one introduces the second-order weak composed contingent
epiderivative of set-valued maps, and discusses some of its properties. Then,
by virtue of the second-order weak composed contingent
epiderivative, necessary optimality
conditions and sufficient optimality conditions are obtained for set-valued optimization problems. As
consequences, recent existing results are derived. Several examples are provided to show the main results
obtained.

DCDS-S

In this paper, we investigate the blow-up criteria of smooth solutions and the regularity of weak solutions to the micropolar fluid
equations in three dimensions. We obtain that if
$ \nabla_{h}u,\nabla_{h}\omega\in L^{1}(0,T;\dot{B}^{0}_{\infty,\infty})$
or
$ \nabla_{h}u,\nabla_{h}\omega\in L^{\frac{8}{3}}(0,T;\dot{B}^{-1}_{\infty,\infty})$ then
the solution $(u,\omega)$ can be extended smoothly beyond $t=T$.

DCDS-B

This work is concerned with permanence and ergodicity of stochastic Gilpin-Ayala models involve continuous states as well as discrete events.
A distinct feature is that the Gilpin-Ayala parameter and its corresponding perturbation parameter are
allowed to be varying randomly in accordance with a random switching process.
Necessary and sufficient
conditions of the stochastic permanence and extinction are established,
which are much weaker than the previous results. The existence of the unique stationary distribution is also established. Our approach treats much wider class of systems,
uses much weaker conditions, and substantially generalizes previous results.
It is shown that
regime switching can suppress the impermanence.
Furthermore,
several examples and simulations
are given to illustrate our main results.

BDIA

It is usually true that adding explanatory variables into a probability model increases association degree yet risks losing statistical reliability. In this article, we propose an approach to merge classes within the categorical explanatory variables before the addition so as to keep the statistical reliability while increase the predictive power step by step.

keywords:
Association
,
categorical data
,
category merging
,
statistical reliability
,
predictive power

JIMO

This paper is concerned with the stability for a parametric symmetric vector equilibrium problem. A parametric gap function for the parametric symmetric vector equilibrium problem is introduced and investigated. By virtue of this function, we establish the sufficient and necessary conditions for the Hausdorff lower semicontinuity of solution mapping to a parametric symmetric vector equilibrium problem. The results presented in this paper generalize and improve the corresponding results in the recent literature.

DCDS-S

This paper is concerned with
the initial-boundary value problem for the three-dimensional compressible liquid crystal flows. The system consists of the Navier-Stokes equations describing the evolution of a compressible viscous fluid coupled with various
kinematic transport equations for the heat flow of harmonic maps into $\mathbb{S}^2$.
Assuming the initial density has vacuum and the initial data satisfies a natural compatibility condition, the existence and
uniqueness is established for the local strong solution with
large initial data and also for the global strong solution with
initial data being close to an equilibrium state. The existence result is proved via the local well-posedness and uniform estimates for a proper linearized system with convective terms.

DCDS

In this paper, we consider a non-autonomous stochastic
Lotka-Volterra competitive system $ dx_i (t) = x_i(t)$[($b_i(t)$-$\sum_{j=1}^{n} a_{ij}(t)x_j(t))$$dt$$+
\sigma_i(t) d B_i(t)]$, where $B_i(t)$($i=1 ,\ 2,\cdots,\ n$) are
independent standard Brownian motions. Some dynamical properties are
discussed and the sufficient conditions for the existence of global
positive solutions, stochastic permanence, extinction as well as
global attractivity are obtained. In addition, the limit of the
average in time of the sample paths of solutions is estimated.

CPAA

In this paper,
using spectral decimation, we prove that the ``hot spots"
conjecture holds on higher dimensional Sierpinski gaskets.

IPI

In this paper we consider several inverse boundary value problems
with partial data on an infinite slab. We prove the unique
determination results of the coefficients for the Schrödinger
equation and the conductivity equation when the corresponding
Dirichlet and Neumann data are given either on the different
boundary hyperplanes of the slab or on the same single hyperplane.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]