由繁入简的合理变换

学生在解答一些题目时,可通过一些合理的变换,让题目由繁入简,进而培养他们不断探究和创新的意识,提高他们的数学素养。

A Multifunctional Chiral Metasurface with Asymmetric Transmission and Linear-Polarization Conversion

In this paper,a multifunctional chiral metasurface is presented to achieve asymmetric transmission(AT)and linear-polarization conversion(LPC).The designed metasurface consists of a cross swords-like shape and two holes in the lower side of the unit cell.In the frequency band from 8.3 GHz to 10.4 GHz,AT is realized with more than 90%efficiency and the same chiral metasurface transforms linear polarized wave into its orthogonal counterpart with high efficiency.For LPC,the polarization conversion ratio(PCR)is greater than 95%.The proposed metasurface is stable against the incident angles of striking electromagnetic(EM)waves up to 60°for both operations of AT and LPC.

Axle-equivalent method of steel-deck pavement

An index system of steel deck pavement design is proposed according to the study and classification of failure types. Furthermore the axle-equivalent equation is presented according to the fatigue principle of pavement structures. Based on indoor experiments and theoretical analysis, this paper studies the stress characteristics of three different axle types which are corresponding with the other three typical pavement structures, and also presents the parameters of each axle＇s equivalent formula. The three axle types include single-axle single-wheel, single-axle double-wheel and double-axle double-wheel. According to analyses of influential factors such as climate, environment, traffic and stress condition, the developed axle equivalent formula and the parameters modified by the field test data can be applied in the design of a new bridge deck pavement and the assessment of an existing bridge deck pavement.

Some Opinions on the Paper “Several Inequalities of Matrix Traces”

In this paper,we find some mistakes in the paper “Several Inequalities of Matrix Traces” which was published in Chinese Quarterly Journal of Mathematics,Vol.10,No.2.

Triangular Au-Ag framework nanostructures prepared by multi-stage replacement and their spectral properties

Triangular Au-Ag framework nanostructures （TFN） were synthesized via a multi-step galvanic replacement reaction （MGRR） of single-crystalline triangular silver nanoplates in a chlorauric acid （HAuCl4） solution at room temperature. The morphological, compositional, and crystal structural changes involved with reaction steps were analyzed by using transmission electron microscopy（TEM）, energy-dispersive X-ray spectrometry （EDX）, and X-ray diffraction. TEM combined with EDX and selected area electron diffraction confirmed the replacement of Ag with Au. The in-plane dipolar surface plasmon resonance （SPR） absorption band of the Ag nanoplates locating initially at around 700 nm gradually redshifted to 1 100 nm via a multi-stage replacement manner after 7 stages. The adding amount of HAuCl4 per stage influenced the average redshift value per stage, thus enabled a fine tuning of the in-plane dipolar band. A proposed formation mechanism of the original Ag nanoplates developing pores while growing Au nanoparticles covering this underlying structure at more reaction steps was confirmed by exploiting surface-enhanced Raman scattering （SERS）.

Equivalent Doping Transformation Method for Predicting Breakdown Voltage and Peak Field at Breakdown of Epitaxial-Diffused Punch-Through Junction

Based on a new semi empirical analytical method, namely equivalent doping transformation, the breakdown voltage and the peak field of the epitaxial diffused punch through junction have been obtained. The basic principle of this method is introduced and a set of breakdown voltage and peak field plots are provided for the optimum design of the low voltage power devices. It shows that the analytical results coincide with the previous numerical simulation well.

Prediction of Breakdown Voltage of Asymmetric Linearly-Graded Junction by Equivalent Doping Profile Transformation Method

This report describes an equivalent doping profile transformation method with which the avalanche breakdown voltage of the asymmetric linearly graded junction was analytically predicted.The maximum breakdown voltage and the different depletion layer extension on the diffused side and substrate side are demonstrated in the report.The report shows the equivalent doping profile method is valid to predict the breakdown voltage of the complex P N junction.The analytical results agree with the experimental breakdown voltage in comparison with the abrupt junction and symmetric linearly graded junction approximations.

Thermodynamics of Cr(Ⅵ) adsorption on strong alkaline anion exchange fiber

Removal of Cr（VI） from aqueous solution by strong alkaline anion exchange fiber （SAAEF） was achieved using batch adsorption experiments. The effect of contact time, initial Cr（VI） concentration and pH was investigated. The results showed that the maximum adsorption capacity of SAAEF was 187.7 mg/g at pH=1.0. The adsorption capacity increased with Cr（VI） concentration but decreased with pH value when pH〉1.0. Adsorption isotherms at various temperatures were obtained. Langmuir, Freundlich, Dubinin-Radushkevich and Temkin models were adopted and the equilibrium data fitted best with the Langmuir isotherm. The constants of these models indicated that the adsorption process involved both chemisorption and physisorption. The values of thermodynamic parameters, including DH, DG and DS, suggested that the adsorption of Cr（VI） on SAAEF was a spontaneous, entropy-driven and endothermic process. Q（iso） was not a constant value, which indicated an inhomogenous energy distribution on SAAEF.

ON TECHNOLOGICAL PR OBLEMS OF FABRICATION OF RELIEF DESIGNS BY ISOMETRIC TRANSFORMATION OF THIN SHEET

Some problems connect ed with production of new light-weight filler type are considered for sandwich layers. Constructively, the filler is the folded structure that can be developed on a plane. This feature makes it possible to produce the filler by isometric t ransformation of thin sheet through local bending without material stretching.Th e main difficulty is that the bending must be carried out along all lines of com plex-shaped marking-out at a time. The problem of shaping can be solved by use of the original shaping device that can be transformed in operation. The herein -presented technology of production makes it possible to fabricate parts with d eep relief using a wide gamut of different materials even as the thin-sheet met al alloys and paper.

Darboux Transformations for Space-Like Isothermic Surfaces in R^m,1

In this paper,by using the G_(m,1)~(1,1)-system,we study Darboux transformations for space-like isothermic surfaces in Minkowski space R~(m,1),where G_(m,1)~(1,1)=O(m+1,2)/O(m,1)×O(1,1).

Study on inhomogeneous cooling behavior of extruded profile with unequal and large thicknesses during quenching using thermo-mechanical coupling model

The interfacial heat transfer coefficient between hot profile surface and cooling water was determined by using inverse heat conduction model combined with end quenching experiment. Then, a Deform-3 D thermo-mechanical coupling model for simulating the on-line water quenching of extruded profile with unequal and large thicknesses was developed. The temperature field, residual stress field and distortion of profile during quenching were investigated systematically. The results show that heat transfer coefficient increases as water flow rate increases. The peak heat transfer coefficient with higher water flow rates appears at lower interface temperatures. The temperature distribution across the cross-section of profile during quenching is severe nonuniform and the maximum temperature difference is 300 ℃ at quenching time of 3.49 s. The temperature difference through the thickness of different parts of profile first increases sharply to a maximum value, and then gradually decreases. The temperature gradient increases obviously with the increase of thickness of parts. After quenching, there exist large residual stresses on the inner side of joints of profile and the two ends of part with thickness of 10 mm. The profile presents a twisting-type distortion across the cross-section under non-uniform cooling and the maximum twisting angle during quenching is 2.78°.

Ammonia nitrogen removal from aqueous solution using zeolite modified by microwave-sodium acetate

The characteristics of the zeolite modified by microwave and sodium acetate and its sorption of ammonia-nitrogen from simulated water sample were investigated.The results show that the modified zeolite by microwave-sodium acetate(SMMZ)has a high sorption efficiency and removal performance.The ammonia-nitrogen removal rate of SMMZ reaches 92.90%.The surface of SMMZ becomes loose and some pores appear,the specific surface area,total pore volume and average pore diameter increase after modification.Compared to the natural zeolite,SMMZ has a more concentrated pore size distribution in the range of 0-10 nm.The cation exchange capacity(CEC)of SMMZ is higher than that of the natural zeolite.And the ammonia nitrogen removal rate is consistent with the change of CEC.The SMMZ possesses rapid sorption and slow balance characteristics and ammonia-nitrogen sorption is consistent with both Langmuir adsorption isotherm model and Freundlich adsorption isotherm model.The adsorption kinetics of ammonia-nitrogen follows the pseudo-second order kinetic model.

Solving Non-Isospectral mKdV Equation and Sine-Gordon Equation Hierarchies with Self-Consistent Sources via Inverse Scattering Transform

N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources andthe hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scatteringtransform.

An explicit representation and computation for the outer inverse

First,an explicit representation A(2)T,S=(GA+E)^-1G of the outer invers A(2)T,S for a matrix A∈Cm×n with the prescribed range T and null space S is derived,which is simpler than A(2)T,S=(GA+E)^-1G-V(UV)-2UG proposed by Ji in 2005.Next,a new algorithm for computing the outer inverse A(2)T,S based on the improved representation A(2)T,S=(GA+E)^-1G through elementary operations on an appropriate partitioned matrix GAInIn0 is proposed and investigated.Then,the computational complexity of the introduced algorithm is also analyzed in detail.Finally,two numerical examples are shown to illustrate that this method is correct.

Quantification of Methane Fluxes from Hydrocarbon Seeps to the Ocean and Atmosphere:Development of an in situ and Online Gas Flux Measuring System

Natural hydrocarbon seeps in the marine environment are important contributors to greenhouse gases in the atmosphere. Such gases include methane, which plays a significant role in global carbon cycling and climate change. To accurately quantify the methane flux from hydrocarbon seeps on the seafloor, a specialized in situ and online gas flux measuring(GFM) device was designed to obtain high-resolution time course gas fluxes using the process of equal volume exchange. The device consists of a 1.0-m diameter, 0.9-m tall, inverted conical tent and a GFM instrument that contains a solenoid valve, level transducer, and gas collection chamber. Rising gas bubbles from seeps were measured by laboratory-calibrated GFM instruments attached to the top of the tent. According to the experimental data, the optimal anti-shake time interval was 5 s. The measurement range of the device was 0–15 L min^(-1), and the relative error was ± 1.0%. The device was initially deployed at an active seep site in the Lingtou Promontory seep field in South China Sea. The amount of gas released from a single gas vent was 30.5 m^3 during the measurement period, and the gas flow rate ranged from 22 to 72 Lh^(-1), depending on tidal period, and was strongly negatively correlated with water depth. The measurement results strongly suggest that oceanic tides and swells had a significant forcing effect on gas flux. Low flow rates were associated with high tides and vice versa. The changes in gas volume escaping from the seafloor seeps could be attributed to the hydrostatic pressure induced by water depth. Our findings suggest that in the marine environment, especially in the shallow shelf area, sea level variation may play an important role in controlling methane release into the ocean. Such releases probably also affect atmospheric methane levels.

The Principle Describing Possible Combinations ofSingularities in Deformations of a Fixed Singularity

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ACTIVITY ATTACK ON REDUCED VARIANTS OF RIJNDAEL

The famous Square attacks against the Rijndael algorithm have taken advantage of the change of the balance of some bytes. Further study shows that the change of activity always happens before the change of balance, which builds the foundation for a new activity attack presented in this paper. In the activity attack, the round in which the activity changes is executed in an equivalent form to avoid the obstructive restriction of the subkeys of that round.The existence of the birthday paradox guarantees much fewer plaintexts necessary for activity attacks comparing with that for corresponding Square attacks. But no benefit may result from the new attacks performed independently because the activity attacks guess four instead of one key byte once. Only when both the balance property and the activity property are exploited at the same time can much better performance be obtained. The better performance in the simulation shows that the consuming time and chosen plaintexts necessary are both reduced to one tenth of those of the corresponding Square attacks. So the activity attacks could be viewed as an efficient supplement to the Square attacks.

Reaction pathway and kinetics of CdO nanoparticles prepared from CdCO_3 precursor using thermal decomposition method

The non-isothermal kinetics of CdO nanoparticles prepared from CdCO3 precursor using thermal decomposition method was investigated. A model-fitting Malek approach and a model-free advanced isoconversional method of Vyazovkin were applied to the analysis of the DSC and TGA data. The results showed that CdO nanoparticles prepared from CdCO3 followed an autocatalytic reaction. Sestak–Berggren model could favorably describe the studied reaction process. Moreover, the apparent activation energy of CdCO3 decomposition was calculated to be (119.19±9.97) kJ/mol and the explicit rate equation form of CdCO3 decomposition was established.

Invariants for a Class of Nongeneric Three-Qubit States

We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations are presented for a class of non-generic three-qubit mixed states. It is shown that two such states in this class are locally equivalent if and only if all these invariants have equal values for them.

Study on Multi-stream Heat Exchanger Network Synthesis with Parallel Genetic/Simulated Annealing Algorithm

The multi-stream heat exchanger network synthesis (HENS) problem can be formulated as a mixed integer nonlinear programming model according to Yee et al. Its nonconvexity nature leads to existence of more than one optimum and computational difficulty for traditional algorithms to find the global optimum. Compared with deterministic algorithms, evolutionary computation provides a promising approach to tackle this problem. In this paper, a mathematical model of multi-stream heat exchangers network synthesis problem is setup. Different from the assumption of isothermal mixing of stream splits and thus linearity constraints of Yee et al., non-isothermal mixing is supported. As a consequence, nonlinear constraints are resulted and nonconvexity of the objective function is added. To solve the mathematical model, an algorithm named GA/SA (parallel genetic/simulated annealing algorithm) is detailed for application to the multi-stream heat exchanger network synthesis problem. The performance of the proposed approach is demonstrated with three examples and the obtained solutions indicate the presented approach is effective for multi-stream HENS.