A methodized short‐cut to conics

It is my firm belief that mathematics is methodology. The briefer is the method, the more effective it is in treating problems. The novel methodized treatment in this article features all the concepts of conics relating to transformation between coordinate systems and standard forms with graphic illustrations.

Denote O’ as the centre of an ellipse or a hyperbola or the vertex of a parabola and F as a focus of a conic. Let O'F=cu, u=[cosθ, sinθ], v = [‐sinθ, cosθ] and P(x,y), then the transformation x’ = u.O'P, y‘ = v.O'P which leads to the standard form for each conic relative to x’ — O'—y‘

The theorem on normal projection in this article is very important in analytic geometry and especially useful for problems involving conies when a directrix or an axis is given.     

福建省能源消费、劳动力与经济增长结构突变单位根检验及多变量因果关系分析

尝试运用最新发展的自回归分布滞后模型(ARDL)对福建省1978-2009年能源消费、劳动力和经济增长三者的因果关系进行检验和分析.常规单位根检验认为能源消费、劳动力和经济增长是一阶单整,I(1);而Zivot & Andrews(ZA)内生性结构突变单位根检验发现三个序列为带有结构突变的趋势平稳过程.ARDL边界检验和格兰杰因果检验结果表明能源消费、劳动力和经济增长间存在稳定的长期均衡关系,表现为从经济增长、劳动力到能源消费的长期因果关系;而在短期因果关系上,表现为经济增长到能源消费单向因果关系,以及经济增长与劳动力之间的双向因果关系.研究同时对福建省经济增长和能源保护战略提出了政策建议.     

Crystal Structure Determination of Thallium Carbodiimide,Tl2NCN

Orange‐red single crystals of thallium carbodiimide, Tl₂NCN, have been grown from an aqueous solution of cyanamide and thallium carbonate under strongly basic conditions. Tl₂NCN crystallizes in space group with a = 5.338(1), b = 6.626(2), c = 9.645(3) Å, α = 98.765(4)°, β = 98.685(4)°, γ = 113.178(4)°, and Z = 3; the structure can be considered a strongly distorted anti‐CdI₂ type. One finds two crystallographically different and irregular [NCN]Tl₆ octahedra in which the Tl–N distances of the three‐coordinate monovalent thallium ions lie between 2.52 and 2.72Å. The two symmetry‐inequivalent NCN^2? units adopt the carbodiimide shape, and the course of its molar volume as a function of the monovalent counter cation is analyzed.     

Function projective lag synchronization of fractional-order chaotic systems

Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.     

The effect of physical back-diffusion of 13CO2 tracer on the coupling between photosynthesis and soil CO2 efflux in grassland

Pulse labelling experiments provide a common tool to study short-term processes in the plant–soil system and investigate below-ground carbon allocation as well as the coupling of soil CO₂ efflux to photosynthesis. During the first hours after pulse labelling, the measured isotopic signal of soil CO₂ efflux is a combination of both physical tracer diffusion into and out of the soil as well as biological tracer release via root and microbial respiration. Neglecting physical back-diffusion can lead to misinterpretation regarding time lags between photosynthesis and soil CO₂ efflux in grassland or any ecosystem type where the above-ground plant parts cannot be labelled in gas-tight chambers separated from the soil. We studied the effects of physical ¹³CO₂ tracer back-diffusion in pulse labelling experiments in grassland, focusing on the isotopic signature of soil CO₂ efflux. Having accounted for back-diffusion, the estimated time lag for first tracer appearance in soil CO₂ efflux changed from 0 to 1.81±0.56 h (mean±SD) and the time lag for maximum tracer appearance from 2.67±0.39 to 9.63±3.32 h (mean±SD). Thus, time lags were considerably longer when physical tracer diffusion was considered. Using these time lags after accounting for physical back-diffusion, high nocturnal soil CO₂ efflux rates could be related to daytime rates of gross primary productivity (R²=0.84). Moreover, pronounced diurnal patterns in the δ¹³C of soil CO₂ efflux were found during the decline of the tracer over 3 weeks. Possible mechanisms include diurnal changes in the relative contributions of autotrophic and heterotrophic soil respiration as well as their respective δ¹³C values. Thus, after accounting for physical back-diffusion, we were able to quantify biological time lags in the coupling of photosynthesis and soil CO₂ efflux in grassland at the diurnal time scale.     

Finite‐Time lag synchronization of delayed neural networks via periodically intermittent control

The problem of finite‐time lag synchronization of delayed neural networks via periodically intermittent control is studied. In two sections, based on the same finite‐time stability theory and using the same sliding mode control, by designing a periodically intermittent feedback controller and adjusting periodically intermittent control strengths with the updated laws, we achieve the finite‐time lag synchronization between two time delayed networks. In addition, we ensure that the trajectory of the error system converges to a chosen sliding surface within finite time and keeps it on forever. Finally, two examples are presented to verify the effectiveness of the analytical results obtained here. © 2015 Wiley Periodicals, Inc. Complexity 21: 211–219, 2016     

稳定律吸引场中学生化的Hanson Russo型增量定理

该文通过建立关于部分和学生化增量的大偏差不等式, 在稳定律吸引场中证得了学生化的Hanson Russo型增量定理.     

肋板结构受压构件的剪力滞效应分析

建立了肋板结构受压构件考虑剪力滞效应时的微分方程,并以该微分方程的解作为位移插值函数,得到了较为精确的有限段单元刚度矩阵,数值算例证明本方法具有好的精度,且具有一维有限元法的便利和广泛适应性。     

MCMCINLA Estimation of Missing Data and Its Application to Public Health Development in China in the Post-Epidemic Era

Medical data are often missing during epidemiological surveys and clinical trials. In this paper, we propose the MCMCINLA estimation method to account for missing data. We introduce a new latent class into the spatial lag model (SLM) and use a conditional autoregressive specification (CAR) spatial model-based approach to impute missing values, making the model fit into the integrated nested Laplace approximation (INLA) framework. Combining the advantages of both the Markov chain Monte Carlo (MCMC) and INLA frameworks, the MCMCINLA algorithm is used to implement imputation of the missing data and fit the model to derive estimates of the parameters from the posterior margins. Finally, the economic data and the hemorrhagic fever with renal syndrome (HFRS) disease data of mainland China from 2016–2018 are used as examples to explore the development of public health in China in the post-epidemic era. The results show that compared with expectation maximization (EM) and full information maximum likelihood estimation (FIML), the predicted values of the missing data obtained using our method are closer to the true values, and the spatial distribution of HFRS in China can be inferred from the imputation results with a southern-heavy and northern-light distribution. It can provide some references for the development of public health in China in the post-epidemic era.