Fusion frames and distributed processing

Let {W_i}_iI be a (redundant) sequence of subspaces of a Hilbert space each being endowed with a weight v_i, and let be the closed linear span of the W_is, a composite Hilbert space. {(W_i,v_i)}_iI is called a fusion frame provided it satisfies a certain property which controls the weighted overlaps of the subspaces. These systems contain conventional frames as a special case, however they reach far “beyond frame theory.” In case each subspace W_i is equipped with a spanning frame system {f_ij}_jJi, we refer to {(W_i,v_i,{f_ij}_jJi)}_iI as a fusion frame system. The focus of this article is on computational issues of fusion frame reconstructions, unique properties of fusion frames important for applications with particular focus on those superior to conventional frames, and on centralized reconstruction versus distributed reconstructions and their numerical differences. The weighted and distributed processing technique described in this article is not only a natural fit to distributed processing systems such as sensor networks, but also an efficient scheme for parallel processing of very large frame systems. Another important component of this article is an extensive study of the robustness of fusion frame systems.     

Numerical Simulation Study on Flow Laws and Heat Transfer of Gas Hydrate in the Spiral Flow Pipeline with Long Twisted Band

The natural gas hydrate plugging problems in the mixed pipeline are becoming more and more serious. The hydrate plugging has gradually become an important problem to ensure the safety of pipeline operation. The deposition and heat transfer characteristics of natural gas hydrate particles in the spiral flow pipeline have been studied. The DPM model (discrete phase model) was used to simulate the motion of solid particles, which was used to simulate the complex spiral flow characteristics of hydrate in the pipeline with a long twisted band. The deposition and heat transfer characteristics of gas hydrate particles in the spiral flow pipeline were studied. The velocity distribution, pressure drop distribution, heat transfer characteristics, and particle settling characteristics in the pipeline were investigated. The numerical results showed that compared with the straight flow without a long twisted band, two obvious eddies are formed in the flow field with a long twisted band, and the velocities are maximum at the center of the vortices. Along the direction of the pipeline, the two vortices move toward the pipe wall from near the twisted band, which can effectively carry the hydrate particles deposited on the wall. With the same Reynolds number, the twisted rate was greater, the spiral strength was weaker, the tangential velocity was smaller, and the pressure drop was smaller. Therefore, the pressure loss can be reduced as much as possible with effect of the spiral flow. In a straight light flow, the Nusselt number is in a parabolic shape with the opening downwards. At the center of the pipe, the Nusselt number gradually decreased toward the pipe wall at the maximum, and at the near wall, the attenuation gradient of the Nu number was large. For spiral flow, the curve presented by the Nusselt number was a trough at the center of the pipe and a peak at 1/2 of the pipe diameter. With the reduction of twist rate, the Nusselt number becomes larger. Therefore, the spiral flow can make the temperature distribution more even and prevent the large temperature difference, resulting in the mass formation of hydrate particles in the pipeline wall. Spiral flow has a good carrying effect. Under the same condition, the spiral flow carried hydrate particles at a distance about 3–4 times farther than that of the straight flow.     

Characterization of lipid bilayer formation in aligned nanoporous aluminum oxide nanotube arrays

Aligning lipid bilayers in nanoporous anodized aluminum oxide (AAO) is a new method to help study membrane proteins by electron paramagnetic resonance (EPR) and solid-state nuclear magnetic resonance (NMR) spectroscopic methods. The ability to maintain hydration, sample stability, and compartmentalization over long periods of time, and to easily change solvent composition are major advantages of this new method. To date, 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC) has been the only phospholipid used for membrane protein studies with AAO substrates. The different properties of lipids with varying chain lengths require modified sample preparation procedures to achieve well formed bilayers within the lining of the AAO substrates. For the first time, the current study presents a simple methodology to incorporate large quantities of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC), DMPC, and 1,2-dipalmitoyl-3-sn-phosphatidylcholine (DPPC) phospholipids inside AAO substrate nanopores of varying sizes. (2)H and (31)P solid-state NMR were used to confirm the alignment of each lipid and compare the efficiency of alignment. This study is the first step in standardizing the use of AAO substrates as a tool in NMR and EPR and will be useful for future structural studies of membrane proteins. Additionally, the solid-state NMR data suggest possible applications of nanoporous aluminum oxide in future vesicle fusion studies.     

Unexpected phase transformation from VO2(R) to VO2(A) during hydrothermal treatment in the V2O5�CH2C2O4�CH2O system

Vanadium dioxide (VO₂) was directly synthesized via the reduction of V₂O₅ with oxalic acid adopting two different types of hydrothermal processes in the temperature ranging from 180 to 260 °C. The products were characterized by X-ray diffraction, field-emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), and X-ray photoelectron spectroscopy (XPS). In all these processes, the VO₂(B) phase was first formed at a relative lower temperature or the initial stage at higher temperature and then it transformed to the VO₂(R) phase with the increase of temperature. The building-block-stacking mechanism was proposed to elucidate the transformation from VO₂(B) nano-plates to snowflake-like VO₂(R) powders. During this transformation, no trace of the VO₂(A) phase was observed when one-step hydrothermal treatment method was used, whereas some part of the branches of the snowflake-like VO₂(R) particles transformed to metastable VO₂(A) nanofibers in the autoclave during cooling process when the two-step hydrothermal treatment method was conducted. The reason for this transformation can be contributed to the defects formed during the stacking process.     

Improved structural stability and electrochemical performance of Na<Subscript>3</Subscript>V<Subscript>2</Subscript> (PO<Subscript>4</Subscript>)<Subscript>3</Subscript> cathode material by Cr doping

Cr-doped sodium vanadium phosphate (NVP) in the form of Na₃V_2-xCr_x(PO₄)₃ (x = 0, 0.02, 0.04, 0.08, 0.10) is synthesized via a facile sol-gel route as cathode materials for sodium ion batteries. The structure and morphology of these materials are systematically characterized by x-ray diffraction (XRD), Fourier-infrared spectra (FT-IR), and scanning electron microscope (SEM). XRD analysis reveals that with the increasing amount of Cr, the crystallographic parameters show a descending trend. Electrochemical tests show that the cycle stability and the specific capacity of the sodium ion batteries can be significantly improved by doping Cr into NVP. Among all the Cr-doped cathode materials, Na₃V_1.92Cr_0.08(PO₄)₃ achieves the highest capacity of 112.2 mAh g^?1 and the capacity retention is 97.2 % after 50 cycles. Electrochemical impedance spectroscopy measurements demonstrate that Cr doping is an effective method to reduce the contact resistance of interparticles by suppressing irreversible phase transformation at low sodium contents.     

Optimal Information Update for Energy Harvesting Sensor with Reliable Backup Energy

The timely delivery of status information collected from sensors is critical in many real-time applications, e.g., monitoring and control. In this paper, we consider a scenario where a wireless sensor sends updates to the destination over an erasure channel with the supply of harvested energy and reliable backup energy. We adopt the metric age of information (AoI) to measure the timeliness of the received updates at the destination. We aim to find the optimal information updating policy that minimizes the time-average weighted sum of the AoI and the reliable backup energy cost. First, when all the environmental statistics are assumed to be known, the optimal information updating policy exists and is proved to have a threshold structure. Based on this special structure, an algorithm for efficiently computing the optimal policy is proposed. Then, for the unknown environment, a learning-based algorithm is employed to find a near-optimal policy. The simulation results verify the correctness of the theoretical derivation and the effectiveness of the proposed method.     

Global bifurcations in a disturbed Hamiltonian vector field approaching A 3:1 resonant Poincaré map (I)

In this paper, we use a qualitative method to study global and local bifurcations in a disturbed Hamiltonian vector field approaching a Poincaré map in the 3:1 resonant case. We give explicit calculation formulas to determine bifurcation parameters and draw various bifurcations and phase portraits in the phase plane.The project supported by the National Natural Science Foundation of China.     

Periodic solutions of the higher-dimensional non-autonomous systems

In this paper, the new existence theorem, unique theorem of periodic solution of the periodic system

and new stationary oscillation theorem of the periodic system

are derived by using functional analysis method, algebraic method and the new estimated formulas of solution of the homogenous linear system. Our results extend and improve some main results related to references. In addition, these criteria are of great interest in many applications such as computation.     

The Theory of Multiresolution Analysis Frames and Applications to Filter Banks

The notion of a frame multiresolution analysis (FMRA) is formulated. An FMRA is a natural extension to affine frames of the classical notion of a multiresolution analysis (MRA). The associated theory of FMRAs is more complex than that of MRAs. A basic result of the theory is a characterization of frames of integer translates of a function φ in terms of the discontinuities and zero sets of a computable periodization of the Fourier transform of φ. There are subband coding filter banks associated with each FMRA. Mathematically, these filter banks can be used to construct new frames for finite energy signals. As with MRAs, the FMRA filter banks provide perfect reconstruction of all finite energy signals in any one of the successive approximation subspacesV_jdefining the FMRA. In contrast with MRAs, the perfect reconstruction filter bank associated with an FMRA can be narrow band. Because of this feature, in signal processing FMRA filter banks achieve quantization noise reduction simultaneously with reconstruction of a given narrow-band signal.