Gradient estimate and a Liouville theorem for a pp-Laplacian evolution equation with a gradient nonlinearity

In this paper, we establish a local gradient estimate for a $p$-Lpalacian equation with a fast growing gradient nonlinearity. With this estimate, we can prove a parabolic Liouville theorem for ancient solutions satisfying some growth restriction near infinity

Well-posedness and gradient blow-up estimate near the boundary for a Hamilton-Jacobi equation with degenerate diffusion

This paper is concerned with weak solutions of the degenerate viscous Hamilton-Jacobi equation $$\partial_t u-\Delta_p u=|\nabla u|^q,$$ with Dirichlet boundary conditions in a bounded domain $\Omega\subset\mathbb{R}^N$, where $p>2$ and $q>p-1$. With the goal of studying the gradient blow-up phenomenon for this problem, we first establish local well-posedness with blow-up alternative in $W^{1, \infty}$ norm. We then obtain a precise gradient estimate involving the distance to the boundary. It shows in particular that the gradient blow-up can take place only on the boundary. A regularizing effect for $u_t$ is also obtained.Comment: 20 pages 1 figur

Comments on `Irreversibility in Response to Forces Acting on Graphene Sheets'

In the letter "Phys. Rev. Lett 104, 196804 (2010)" the compression-relaxation mechanism (CRM) for a graphene sheet (GS) was reported to be irreversible and resulted in static ripples on GS, such that for T <Tc the free-energy of the rippled GS is smaller than that of roughened GS. We will point out several technical difficulties, such as the use of the relation Delta A= for the free energy calculations and the definition of the rough state, with their simulations. We show that (at T <Tc) their introduced rough state suffer boundary stress, thus is a rippled state and their obtained inequality A_{ripple}<A_{rough} is no longer valid. Therefore the introduced mechanism is reversible. Furthermore, from theoretical point of view for an infinitely slow rate of CRM, the relation Delta A= (in common non-equilibrium simulations) is allowed. In this case authors of Ref. [1] must report the used infinitely small rate and justify how it is in practice valid. We show Delta A for the system that was used in [1]

Comparative evaluation of various GPS-free localization algorithm for wireless sensor networks

Wireless Sensor Networks (WSN) are tremendously being used in different environments to perform various monitoring tasks such as search, rescue, disaster relief, target tracking and a number of tasks in smart environments. For example wireless sensors nodes can be designed to detect the ground vibrations generated by silent footsteps of a burglar and trigger an alarm. In many difficult and complex tasks, node localization is very important and critical step to fulfill the purpose of WSN. This project was conducted on the basis of localization of sensor nodes in the scope of GPS-free localizations schemes. We firstly investigated the current localization techniques in wireless scenario for the aim of designing a GPS-free localization scheme based on the local coordinate system formation. A multidimensional scaling method based on dynamic curvilinear belt structure and cooperative localization method was used in this project. Then a simulation result and comparison were carried in MATLAB. The vast majority of current materials on spot discovery in WSNs reflect some beacon nodes with known place. Their spots are then used to look for the positions connected with other normal sensor nodes. Manual rating and configuration means of obtaining spot don't scale and are also error-prone, and equipping sensors with GPS is normally expensive and rule isn't followed in indoor and urban environment. As such, sensor sites can therefore gain from a selfsetting up method where nodes cooperate with each other, estimate nearby distances on their neighbors, and converge to some consistent organize system containing only translation freedom. Dis

Bribes for Faster Delivery

The paper models the practice of charging bribes for faster delivery of essential services in third world countries. It then examines the possibility of curbing corruption by supervision, and secondly, by introducing competition among delivery agents. It is argued that a supervisory solution eludes the problem because no hard evidence of the reduction of corruption can be established for this type of offenses. It is also shown that using more than one supplier cannot eliminate the practice, and the bribe paying part of the market attains a determinate proportion as the number of suppliers increases. However the bribe rate and average waiting time come down at a diminishing rate with increase in the number of suppliers, and this property can be used to determine an optimal number of suppliers.third world; queues; corruption; bribes; optimal mechanism