## 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
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- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
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- AIMS Mathematics

DCDS

In this note, we investigate the localized multifractal spectrum of Birkhoff average in the beta-dynamical system $([0,1], T_{\beta})$ for general $\beta>1$, namely the dimension of the following level sets $$
\Big\{x\in [0,1]: \lim_{n\to \infty}\frac{1}{n}\sum_{j=0}^{n-1}\psi(T^jx)=f(x)\Big\},
$$ where $f$ and $\psi$ are two continuous functions defined on the unit interval $[0,1]$. Instead of a constant function in the classical multifractal cases, the function $f$ here varies with $x$. The method adopted in the proof indicates that the multifractal analysis of Birkhoff average in a general $\beta$-dynamical system can be achieved by approximating the system by its subsystems.

DCDS-B

A proportionally-fair controller with
time delay is considered to control Internet congestion. The time
delay is chosen to be a controllable parameter. To represent the
relation between the delay and congestion analytically, the method
of multiple scales is employed to obtain the periodic solution
arising from the Hopf bifurcation in the congestion control model. A
new control method is proposed by perturbing the delay periodically.
The strength of the perturbation is predicted analytically in order
that the oscillation may disappear gradually. It implies that the
proved control scheme may decrease the possibility of the congestion
derived from the oscillation. The proposed control scheme is
verified by the numerical simulation.

DCDS

We study the limit of vanishing ratio of the electron mass to the
ion mass (zero-electron-mass limit) in the scaled Euler-Poisson
equations. As the first step of this justification, we construct the
uniform global classical solutions in critical Besov spaces with the
aid of ``Shizuta-Kawashima" skew-symmetry. Then we establish
frequency-localization estimates of Strichartz-type for the equation
of acoustics according to the semigroup formulation. Finally, it is
shown that the uniform classical solutions converge towards that of
the incompressible Euler equations (for

*ill-prepared*initial data) in a refined way as the scaled electron-mass tends to zero. In comparison with the classical zero-mach-number limit in [7,23], we obtain different dispersive estimates due to the coupled electric field.
MBE

HIV transmission process involves a long incubation and infection
period, and the transmission rate varies greatly with infection stage. Conse-
quently, modeling analysis based on the assumption of a constant transmission
rate during the entire infection period yields an inaccurate description of HIV
transmission dynamics and long-term projections. Here we develop a general
framework of mathematical modeling that takes into account this heterogeneity
of transmission rate and permits rigorous estimation of important parameters
using a regression analysis of the twenty-year reported HIV infection data in
China. Despite the large variation in this statistical data attributable to the
knowledge of HIV, surveillance efforts, and uncertain events, and although the
reported data counts individuals who might have been infected many years
ago, our analysis shows that the model structured on infection age can assist
us in extracting from this data set very useful information about transmission
trends and about effectiveness of various control measures.

CPAA

In this paper, we study some important properties of positive
solutions for a nonlinear integral system. With the help of the
method of moving planes in an integral form, we show that under
certain integrable conditions, all of positive solutions to this
system are radially symmetric and decreasing with respect to the
origin. Meanwhile, using the regularity lifting lemma, which was
recently introduced by Chen and Li in [1], we obtain the
optimal integrable intervals and sharp asymptotic behaviors for such
positive solutions, which characterize the closeness of system to
some extent.

JIMO

In many real-life scheduling environments, the jobs deteriorate at a certain rate while waiting to be processed. This paper addresses some single-machine scheduling problems with past-sequence-dependent (p-s-d) delivery times and a linear deterioration. The p-s-d delivery time of a job is proportional to the job's waiting time. It is assumed that the deterioration process is reflected in the job
processing times being an increasing function of their starting times. We consider the following objectives: the makespan, total completion time, total weighted completion time, maximum lateness, and total absolute differences in completion times. We seek the optimal schedules for the problems to minimize the makespan and total completion time.
Despite that the computational complexities of the problems to
minimize the total weighted completion time and maximum lateness remain open, we present heuristics and analyze their worst-case performance ratios, and show that some special cases of the problems are polynomially solvable.
We also show that the optimal schedule for the problem to minimize the total absolute differences in completion times is $V$-shaped with respect to the normal job processing times.

CPAA

This paper is a continuation of the paper ([1] ), which is called paper (I) afterward.
In the present paper, which we shall call paper (II), we study the
interfacial instability property of the side interface of a growing disc-like crystal
at the early stage of growth by using
the approach developed in the interfacial wave (IFW) theory of dendritic growth.
Our analysis show that the system allows two types of unstable modes over the
side-interface: (1). The axi-symmetric $(m=0)$ modes. The most
dangerous axi-symmetric mode is the base mode $A_0$, which is
responsible for formation of the axi-symmetric pattern over the
side-interface, anti-symmetric about the central plane of the
disc; (2). The non-axi-symmetric modes,
which are responsible for non-axi-symmetric pattern formation around the
edge of the disc. The growth rates of these non-axi-symmetric
modes are much smaller than the growth rate of the base mode
$A_0$. During the course of disc growth, the unstable $A_0$-mode
merges first. It leads to the formation of anti-symmetric pattern
about the central plane over the side-interface.
Following the onset of unstable base mode
$A_0$, a set of non-axi-symmetric growing modes also appear.
However, due to the smallness of growth rate of these unstable modes,
the non-axi-symmetric pattern
around the edge of the disc becomes observable, only after a
sufficiently long time. Our theoretical predictions are in good
agreement with the available experimental data.

CPAA

This paper is concerned with the global well-posedness and stability
of classical solutions to the Cauchy problem for the multidimensional
full hydrodynamic model in semiconductors on the framework of Besov space.
By using the high- and low- frequency decomposition method, we obtain the
exponential decay of classical solutions (close to equilibrium). Moreover, it is
also shown that the vorticity decays to zero exponentially in the 2D and 3D
space. The work

*weakens*the regularity requirement of the initial data and improves some known results in Sobolev space.
JIMO

In this paper, we firstly propose a technique
named

**Duplicating**, which duplicates machines in batch scheduling environment. Then we discuss several applications of**Duplicating**in solving batch scheduling problems. For the batch scheduling problem on unrelated parallel machines to minimize makespan, we give a $(4 - \frac{2}{B})$- approximation algorithm and a $(2 - \frac{1}{B} + \epsilon)$ algorithm when $m$ is fixed. We also present a $4(2 - \frac{1}{B} + \epsilon)$-competitive algorithm for the on-line scheduling problem on identical machines to minimize total weighted completion time by another technique-$\rho-dual$, which is proposed originally by Hall et al.(1997).
DCDS

This paper deals with non-isentropic hydrodynamic models for
semiconductors with short momentum and energy relaxation times. With
the help of the Maxwell iteration, we construct a new approximation
and show that periodic initial-value problems of certain scaled
non-isentropic hydrodynamic models have unique smooth solutions in a
time interval independent of the two relaxation times. Furthermore,
it is proved that as the two relaxation times both tend to zero, the
smooth solutions converge to solutions of the corresponding
semilinear drift-diffusion models.

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