Necessary optimality conditions and regularity results for state and adjoint state of nonlinear control problems

For optimal control problems of nonlinear evolution equations of first order we derive regularity properties for the corresponding adjoint states where the proof is based on the necessary optimal conditions and smoothness properites of the optimal states. These results are used for the characterization of the optimal solution and the corresponding adjoint state of the periodic three-dimensionel NAVIER-STOKES system.     

Regularity of weak solutions to rate‐independent systems in one‐dimension

We show that under some appropriate assumptions, every weak solution (e.g. energetic solution) to a given rate‐independent system is of class SBV, or has finite jumps, or is even piecewise C¹. Our assumption is essentially imposed on the energy functional, but not convexity is required.     

非化学专业无机及分析化学“讲练考”教学模式改革

This article discussed "teaching-practice-test" teaching mode with teaching practical experience and content matching.Results showed that this mode highlighted the proportion of practice and problem-solving in the process of learning; improved students' ability to solve problems using professional and disciplinary knowledge; changed learning styles from cramming way to autonomous learning step by step and trained students' creativity.     

Design and characterization of guided mode resonance filters with the improved structure for facile fabrication

In this study, a guided mode resonance filter with the improved structure for facile fabrication is designed; the properties of the designed filters are simulated by rigorous coupled wave analysis. It is found that the resonance wavelength and spectral linewidth are slightly increased with the increasing of the grating thickness, and seldom changed with the thickness of the grating filling factor, as the parameter error of the grating thickness and the grating filling factor are deviated from the designed value by ±10%, respectively, which are very favorable for simplifying preparation process of the GMR filter.     

An Investigation into the Migration of Segments in Crosslinked Fluorinated Polyimide Adhesive

Crosslinked fluorinated polyimides (CFPI) were successfully synthesized to study and explore the effect of cross-linkage on the migration of fluorinated segments and on the adhesion strength. Characterization by dynamic thermomechanical analysis (DMA) and thermo gravimetric analysis (TGA) confirmed good thermal properties of CFPI. X-ray photoelectron spectroscopy (XPS) results showed that the ratio of fluorinated component (6FDA-ODA) concentration of the surface to the bulk decreased with the crosslink density. The water contact angle of CFPI was lower than that of non-crosslinked fluorinated polyimide, indicating that the migration of fluorinated groups to the surface was reduced by the presence of cross-linkage. Therefore, CFPI, with no fluorine segregation on the surface, exhibited excellent wetting of adherent surfaces and adhesion strength, which was proved by lap shear strength (LSS) measurements and scanning electron microscopy.     

Syntheses and structures of M–Na (M=Zn,Mn) coordination polymers in which ligands and Na ions exhibit complex coordination modes

The novel heteronuclear complexes [Na₂Zn(dipic)₂(H₂O)] _n (1) and [Na₂Mn(dipic)₂(H₂O)₂] _n (2) (H₂dipic?=?pyridine-2,6-dicarboxylic acid) were synthesized and characterized by single-crystal X-ray diffraction, analysis, IR spectroscopy and thermogravimetric analysis. Complex 1 consists of infinite 2D double layers, which are further attached into a 3D network through π–π stacking. All sodium ions are 3-coordinate. Complex 2 has an intricate 3D structure, in which two sodium ions are differently involved in forming polymeric coordination units, and are 3- and 7-coordinate, respectively. Dipic anions act as multidentate ligands showing novel and unprecedented bridging coordination modes. One ligand coordinates to three metal ions and with five bonds; the other coordinates five metal ions with nine bonds.     

Reflective mode of deformed-helix ferroelectric liquid crystal cells for sensing applications

We present a detailed theoretical and experimental study of the reflectance response of a deformed-helix ferroelectric (DHF) liquid crystal (LC) cell to an applied voltage under cross-polarisers. Using a model based on the effective dielectric tensor approximation, we derive simple analytical formulas to design a LC cell with maximum modulation depth and optimal linearity of the electro-optical response intensity versus the electric field. Our experimental results show that the cell works at frequencies up to 10 kHz and exhibits excellent linearity, with a total harmonic distortion as low as ?70 dB. These findings suggest that DHF-LCs can be exploited to develop simple and accurate optical sensors.     

A variational approach to second-order approximability of sliding mode control systems

We consider robustness properties of second-order methods for the sliding mode control of nonlinear ordinary differential equations. A new approach is presented based on the theory of well-posed optimization problems. It is shown that the convergence of the real states of the control system to the ideal one is intimately related to Tykhonov well-posedness of suitably defined dynamic optimization problems.     

Material growth and device fabrication of terahertz quantum-cascade laser based on bound-to-continuum structure

The terahertz quantum-cascade laser （THz QCL） based on bound-to-continuum structure is demonstrated. The X-ray diffraction measurement of the material shows a high crystalline quality of the active region. A THz QCL device was fabricated with semi-insulating surface-plasmon waveguide. The test device is lasing at about 3 THz and operating up to 60 K. It shows a single frequency property under different drive currents and temperatures. At 9 K, the maximum output power is greater than 2 mW with a threshold current density of 159 A/cm2.