Preparation and ionic conductivity of composite polymer electrolytes based on hyperbranched star polymer

Hyperbranched star polymer HBPS-(PPEGMA) _x was synthesized by atom transfer radical polymerization (ATRP) using hyperbranched polystyrene (HBPS) as macroinitiator and poly(ethylene glycol) methyl ether methacrylate (PEGMA) as monomer. The structure of the prepared hyperbranched star polymer was characterized by ¹H NMR, ATR-FTIR, and GPC. Polymer electrolytes based on HBPS-(PPEGMA) _x , lithium salt, and/or nano-TiO₂ were prepared. The influences of lithium salt concentration and type, nano-TiO₂ content, and size on ionic conductivity of the obtained polymer electrolytes were investigated. The results showed that the low crystallinity of the prepared polymer electrolyte was caused by the interaction between lithium salt and polymer. The addition of TiO₂ into HBPS-(PPEGMA) _x /LiTFSI improved the ionic conductivity at low temperature. The prepared composite polymer electrolyte showed the highest ionic conductivity of 9?×?10^?5 S cm^?1 at 30 °C when the content of TiO₂ was 15 wt% and the size of TiO₂ was 20 nm.     

Hyperbolic Schrödinger equation

Clifford algebra corresponds to Minkwoski space. The coupling between real object particles and light quantums can be discussed by Minkowski space’s directional strangeness. We introduce Galilei transfomation and Schr?dinger equation into Minkowski space and give a geometrical explanation for classical quantum theory.     

Time Domain Impedance Boundary Conditions for a Slip Mean FlowBoundary

In modeling the physical condition of an impedance boundary, the assumption of either particle displacement continuity (PDC) or particle normal velocity continuity (PVC) at the interface between the acoustic treatment and the adjacent fluid needs to be used. Although it is well accepted that the impedance boundary condition derived from the PDC is the appropriate impedance boundary condition when there is a slip mean flow at the liner surface, the time domain impedance boundary condition is however unstable due to the Kelvin‐Helmholtz instability associated with the ”vortex sheet.” In this paper, an effective time domain impedance boundary condition for a slip mean flow boundary is proposed and validated. Several relevant issues related to the PDC and PVC are discussed. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Highly efficient photoluminescence of Er2SiO5 films grown by reactive magnetron sputtering method

E₂SiO₅ thin films were fabricated on Si substrate by reactive magnetron sputtering method with subsequent annealing treatment. The morphology properties of as-deposited films have been studied by scanning electron microscope. The fraction of erbium is estimated to be 23.5 at% based on Rutherford backscattering measurement in as-deposited Er-Si-O film. X-ray diffraction measurement revealed that Er₂SiO₅ crystalline structure was formed as sample treated at 1100 °C for 1 h in O₂ atmosphere. Through proper thermal treatment, the 1.53 μm Er³⁺-related emission intensity can be enhanced by a factor of 50 with respect to the sample annealed at 800 °C. Analysis of pump-power dependence of Er³⁺ PL intensity indicated that the upconversion phenomenon could be neglected even under a high photon flux of 10²¹(photons/cm²/sec). Temperature-dependent photoluminescence (PL) of Er₂SiO₅ was studied and showed a weak thermal quenching factor of 2. Highly efficienct photoluminescence of Er₂SiO₅ films has been demonstrated with Er³⁺ concentration of 10²²/cm³, and it opens a promising way towards future Si-based light source for Si photonics.     

Recurrence relations for semilocal convergence of a fifth-order method in Banach spaces

In this paper, we study the semilocal convergence for a fifth-order method for solving nonlinear equations in Banach spaces. The semilocal convergence of this method is established by using recurrence relations. We prove an existence-uniqueness theorem and give a priori error bounds which demonstrates the R-order of the method. As compared with the Jarratt method in Hernández and Salanova (Southwest J Pure Appl Math 1:29–40, 1999) and the Multi-super-Halley method in Wang et al. (Numer Algorithms 56:497–516, 2011), the differentiability conditions of the convergence of the method in this paper are mild and the R-order is improved. Finally, we give some numerical applications to demonstrate our approach.     

Nonlinear wavelet estimation of regression function with random desigm

The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov spaceB ³ _p,q is proved under quite general assumpations. The adaptive nonlinear wavelet estimator with near-optimal convergence rate in a wide range of smoothness function classes is also constructed. The properties of the nonlinear wavelet estimator given for random design regression and only with bounded third order moment of the error can be compared with those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error. Project supported by Doctoral Programme Foundation, the National Natural Science Foundation of China (Grant No. 19871003) and Natural Science Fundation of Heilongjiang Province, China.     

All-silicon chiral metasurfaces and wavefront shaping assisted by interference

The usage of full-color imaging in digital pathology produces significant results. Compared with a grayscale image or a pseudocolor image containing contrast information, a full-color image can identify and detect the target object better with color texture information. Fourier ptychographic microscopy(FPM) is a high-throughput computational imaging technique that breaks the tradeoff between high resolution(HR) and a large field of view. It also eliminates the artifacts of scanning and stitching in digital pathology and improves its imaging efficiency. However, the conventional full-color digital pathology based on FPM is still time-consuming because of the repeated experiments with tri-wavelengths. A color transfer FPM approach termed "CFPM" was reported. The color texture information of a low-resolution full-color pathologic image is directly transferred to the HR grayscale FPM image captured by only a single wavelength. Both of the color space of FPM based on the standard CIE-XYZ color model and the display based on the standard RGB color space were established. Different FPM colorization schemes were analyzed and compared with 30 biological samples. Three types of evaluation approaches were provided, including the root-mean-square error(RMSE), the difference maps, and the image histogram cosine similarity. The average RMSE values of the conventional method and CFPM compared with the ground truth were 5.3% and 5.7%, respectively. Therefore, the reconstruction time is significantly reduced by 2/3 with the sacrifice of precision of only 0.4%. The CFPM method is also compatible with advanced fast FPM approaches to further reduce computation time.     

A Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks

Why heavily parameterized neural networks(NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our linear frequency principle(LFP) model accounts for a key dynamical feature of NNs: they learn low frequencies first, irrespective of microscopic details. Theory based on our LFP model shows that low frequency dominance of target functions is the key condition for the non-overfitting of NNs and is verified by experiments. Furthermore,through an ideal two-layer NN, we unravel how detailed microscopic NN training dynamics statistically gives rise to an LFP model with quantitative prediction power.     

Global well‐posedness of the compressible Euler with damping in Besov spaces

In this paper, we consider the Cauchy problems for compressible Euler equations with damping. In terms of the Littlewood–Paley decomposition and Bony's para‐product formula, we prove the global existence, uniqueness and asymptotic behavior of the solution in the critical Besov space comparing with previous results. Copyright © 2012 John Wiley & Sons, Ltd.     

A Cross‐Cultural Lesson Comparison on Teaching the Connection Between Multiplication and Division

This study compared one lesson across four U.S. “traditional” textbook series, two U.S. reform‐based textbook series, and one Chinese mathematics textbook series in teaching the connection between multiplication and division. The results showed the differences across U.S. and Chinese lessons in both the teaching and the practice parts of the lesson across three dimensions (i.e., problem schemata, response requirement, and algebra readiness). In particular, the Chinese lesson's penetrating analysis or explanation of the topic is reflected in its deliberately constructed examples and wide range of problems (pertaining to problem types and difficulty levels) present in the teaching and practice sections of the lesson. None of analyzed U.S. lessons are comparable with the Chinese lesson with respect to the breadth and depth in teaching the topic. A deliberate emphasis, both arithmetically and algebraically, on problem schema acquisition as found in the Chinese lesson represents a promotion of symbolic or higher order of conceptual understanding. The findings are discussed within the context of teaching big ideas through problem schemata acquisition and the importance of symbolic level of conceptual understanding.