Multiple solutions for superlinear elliptic systems of Hamiltonian type
Rumei Zhang Jin Chen Fukun Zhao
This paper is concerned with the following periodic Hamiltonian elliptic system

$\-\Delta \varphi+V(x)\varphi=G_\psi(x,\varphi,\psi)$ in $\mathbb{R}^N,$
$\-\Delta \psi+V(x)\psi=G_\varphi(x,\varphi,\psi)$ in $\mathbb{R}^N,$
$\varphi(x)\to 0$ and $\psi(x)\to0$ as $|x|\to\infty.$

Assuming the potential $V$ is periodic and $0$ lies in a gap of $\sigma(-\Delta+V)$, $G(x,\eta)$ is periodic in $x$ and superquadratic in $\eta=(\varphi,\psi)$, existence and multiplicity of solutions are obtained via variational approach.
keywords: strongly indefinite functionals. Hamiltonian elliptic system variational methods
Grasping force based manipulation for multifingered hand-arm Robot using neural networks
Chun-Hsu Ko Jing-Kun Chen
Multifingered hand-arm robots play an important role in dynamic manipulation tasks. They can grasp and move various shaped objects. It is important to plan the motion of the arm and appropriately control the grasping forces for the multifingered hand-arm robots. In this paper, we perform the grasping force based manipulation of the multifingered hand-arm robot by using neural networks. The motion parameters are analyzed and planned with the constraint of the multi-arms kinematics. The optimal grasping force problem is recast as the second-order cone program. The semismooth Newton method with the Fischer-Burmeister function is then used to efficiently solve the second-order cone program. The neural network manipulation system is obtained via the fitting of the data that are generated from the optimal manipulation simulations. The simulations of optimal grasping manipulation are performed to demonstrate the effectiveness of the proposed approach.
keywords: second-order cone program Robots grasping force neural networks.
Modeling and control of local outbreaks of West Nile virus in the United States
Jing Chen Jicai Huang John C. Beier Robert Stephen Cantrell Chris Cosner Douglas O. Fuller Guoyan Zhang Shigui Ruan
West Nile virus (WNV) was first detected in the United States (U.S.) during an outbreak in New York City in 1999 with 62 human cases including seven deaths. In 2001, the first human case in Florida was identified, and in Texas and California it was 2002 and 2004, respectively. WNV has now been spread to almost all states in the US. In 2015, the Center for Disease Control and Prevention (CDC) reported 2,175 human cases, including 146 deaths, from 45 states. WNV is maintained in a cycle between mosquitoes and animal hosts in which birds are the predominant and preferred reservoirs while most mammals, including humans, are considered dead-end hosts, as they do not appear to develop high enough titers of WNV in the blood to infect mosquitoes. In this article, we propose a deterministic model by including interactions among mosquitoes, birds, and humans to study the local transmission dynamics of WNV. To validate the model, it is used to simulate the WNV human data of infected cases and accumulative deaths from 1999 to 2013 in the states of New York, Florida, Texas, and California as reported to the CDC. These simulations demonstrate that the epidemic of WNV in New York, Texas, and California (and thus in the U.S.) has not reached its equilibrium yet and may be expected to get worse if the current control strategies are not enhanced. Mathematical and numerical analyses of the model are carried out to understand the transmission dynamics of WNV and explore effective control measures for the local outbreaks of the disease. Our studies suggest that the larval mosquito control measure should be taken as early as possible in a season to control the mosquito population size and the adult mosquito control measure is necessary to prevent the transmission of WNV from mosquitoes to birds and humans.
keywords: sensitive analysis transmission dynamics. West Nile virus mathematical modeling basic reproduction number
A result on Hardy-Sobolev critical elliptic equations with boundary singularities
Jinhui Chen Haitao Yang
In this note, a Hardy-Sobolev critical elliptic equation with boundary singularities and sublinear perturbation is studied. We obtain a result on the existence of classical solution and the multiplicity of weak solutions by making use of sub-super solutions and variational methods.
keywords: Hardy-Sobolev critical exponent sublinear perturbation. boundary singularity
Modeling and analyzing the transmission dynamics of visceral leishmaniasis
Lan Zou Jing Chen Shigui Ruan

In this paper, we develop a mathematical model to study the transmission dynamics of visceral leishmaniasis. Three populations: dogs, sandflies and humans, are considered in the model. Based on recent studies, we include vertical transmission of dogs in the spread of the disease. We also investigate the impact of asymptomatic humans and dogs as secondary reservoirs of the parasites. The basic reproduction number and sensitivity analysis show that the control of dog-sandfly transmission is more important for the elimination of the disease. Vaccination of susceptible dogs, treatment of infective dogs, as well as control of vertical transmission in dogs are effective prevention and control measures for visceral leishmaniasis.

keywords: Visceral leishmaniasis mathematical modeling reservoir vertical transmission basic reproduction number

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