WEAK-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS

The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.

Bound State Description of Particles from a Quantum Field Theory of Fermions and Bosons, Compatible with Relativity

Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected.

Energy equalizing routing for fast data gathering in wireless sensor networks

Energy saving and fast responding of data gathering are two crucial factors for the performance of wireless sensor networks. A dynamic tree based energy equalizing routing scheme （DTEER） was proposed to make an effort to gather data along with low energy consumption and low time delay. DTEER introduces a dynamic multi-hop route selecting scheme based on weight-value and height-value to form a dynamic tree and a mechanism similar to token passing to elect the root of the tree. DTEER can simply and rapidly organize all the nodes with low overhead and is robust enough to the topology changes. When compared with power-efficient gathering in sensor information systems （PEGASIS） and the hybrid, energy- efficient, distributed clustering approach （HEED）, the simulation results show that DTEER achieves its intention of consuming less energy, equalizing the energy consumption of all the nodes, alleviating the data gathering delay, as well as extending the network lifetime perfectly.

Energy Equality and Uniqueness of Weak Solutions to MHD Equations in L~∞(O,T;L^n(Ω))

In this paper, we study the energy equality and the uniqueness of weak solutions to the MHD equations in the critical space L∞（0, T; L^n（Ω）. We prove that if the velocity u belongs to the critical space L∞（0, T; L^n（Ω）, the energy equality holds. On the basis of the energy equality, we further prove that the weak solution to the MHD equations is unique.

Discrete-frequency Convergence of Iterative Learning Control for Linear Time-invariant systems with Higher-order Relative Degree

In this paper, a discrete-frequency technique is developed for analyzing sufficiency and necessity of monotone convergence of a proportional higher-order-derivative iterative learning control scheme for a class of linear time-invariant systems with higher-order relative degree. The technique composes of two steps. The first step is to expand the iterative control signals, its driven outputs and the relevant signals as complex-form Fourier series and then to deduce the properties of the Fourier coefficients. The second step is to analyze the sufficiency and necessity of monotone convergence of the proposed proportional higher-order-derivative iterative learning control scheme by assessing the tracking errors in the forms of Paserval s energy modes. Numerical simulations are illustrated to exhibit the validity and the effectiveness.

Extension Problems Related to the Higher Order Fractional Laplacian

Caffarelli and Silvestre [Comm. Part. Diff. Eqs., 32, 1245-1260 （2007）] characterized the fractional Laplacian （-△）s as an operator maps Dirichlet boundary condition to Neumann condition via the harmonic extension problem to the upper half space for 0 〈 s 〈 1. In this paper, we extend this result to all s 〉 0. We also give a new proof to the dissipative a priori estimate of quasi-geostrophic equations in the framework of Lp norm using the Caffarelli-Silvestre＇s extension technique.