A note on extremal quasi-conformal mappings

An extremal quasi-conformal mapping f of a domain D is said to be of non-landslide type if the set Ef(δ):= {z∈D:|μf(z)|≤||μ|| ∞ -δ} has no interior points for any δ > 0. In this paper,we construct a quasi-conformal mapping f of the unit disc D such that its Teichmu¨ller equivalence class [f] contains infinitely many extremal mappings of non-landslide type. The relation between extremal mappings of non-landslide type and locally extremal mappings is also discussed.

REVISITING A NON-DEGENERACY PROPERTY FOR EXTREMAL MAPPINGS

We extend an earlier result obtained by the author in [7].

Object-Based Burned Area Mapping with Extreme Gradient Boosting Using Sentinel-2 Imagery

The Sentinel-2 satellites are providing an unparalleled wealth of high-resolution remotely sensed information with a short revisit cycle, which is ideal for mapping burned areas both accurately and timely. This paper proposes an automated methodology for mapping burn scars using pairs of Sentinel-2 imagery, exploiting the state-of-the-art eXtreme Gradient Boosting (XGB) machine learning framework. A large database of 64 reference wildfire perimeters in Greece from 2016 to 2019 is used to train the classifier. An empirical methodology for appropriately sampling the training patterns from this database is formulated, which guarantees the effectiveness of the approach and its computational efficiency. A difference (pre-fire minus post-fire) spectral index is used for this purpose, upon which we appropriately identify the clear and fuzzy value ranges. To reduce the data volume, a super-pixel segmentation of the images is also employed, implemented via the QuickShift algorithm. The cross-validation results showcase the effectiveness of the proposed algorithm, with the average commission and omission errors being 9% and 2%, respectively, and the average Matthews correlation coefficient (MCC) equal to 0.93.

The Role of Color Doppler Ultrasound Arterial Mapping for Decision Making in the Treatment of Patients with Lower Extremity Peripheral Arterial Disease

Purpose: To assess the efficacy of color Doppler imaging for decision making in the treatment of patients with lower extremity peripheral arterial disease (PAD) compared to digital subtraction angiography (DSA). Materials and Methods: Color Doppler scan was done on patients suspected for lower limb PAD, a day prior to the DSA which was done by a vascular surgeon. Also, for the patients who were candidates for endovascular intervention based on the color Doppler arterial mapping results, endovascular interventions were performed at the same time if the DSA findings are correlated with the color Doppler map. The grading for evaluated segments was normal, insignificant stenosis (<50%), hemodynamically significant stenosis (≥50%) and occlusion. We yielded the diagnostic efficacy indices of Doppler for detecting arterial stenosis in each 18 different arterial segments below the renal arteries including, infrarenal aorta, common and external iliac, common femoral, superficial femoral (proximal, middle and distal segments), deep femoral, popliteal artery, tibioperoneal trunk, anterior and posterior tibial arteries (proximal, middle and distal segments) and peroneal artery (proximal and distal segments). Then, we yielded the kappa agreement between Doppler and DSA findings considering the grade of stenosis in 18 arterial segments separately. Results: Totally 115 lower extremities (2045 arterial segments) were evaluated in 90 patients [mean age: 60.8 ± 8.9 (range: 47 - 84 years old)] of which 68 (75.6%) were men. The sensitivity of color Doppler for all arterial segments was 90% or higher except for common iliac artery, distal segment of superficial femoral artery and proximal segments of anterior and posterior tibialis and peroneal arteries. However, the specificity was 89% or higher, in all arterial segments. Kappa agreement was 0.72 or higher in all segments (All P-Values 0.001). Conclusion: This study suggests that considering excellent capability of color Doppler sonography in the evaluation of lower extremity arterial disease, color Doppler arterial mapping is sufficient for decision making in the treatment of these patients and can reduce the rate of diagnostic angiography.

Quadrilaterals, extremal quasiconformal extensions and Hamilton sequences

The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrigues many mathematicians. It had been a conjecture for some time that the dilatations Ko（h） and K1（h） of h are equal before Anderson and Hinkkanen disproved this by constructing concrete counterexamples. The independent work of Wu and of Yang completely characterizes the condition for Ko（h） = K1 （h） when h has no substantial boundary point. In this paper, we give a necessary and sufficient condition to determine the equality for h admitting a substantial boundary point.

Uniform Convergence of Extremal Polynomials When Domains Have Corners and Special Cusps on the Boundary

We study the approximation properties of the extremal polynomials in Ap?norm and C?norm. We prove estimates for the rate of such convergence of the sequence of the extremal polynomials on domains with corners and special cusps.

Extremely hidden multi-stability in a class of two-dimensional maps with a cosine memristor

We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction,bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multistability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially,this work can be used for some real applications in secure communication, such as data and image encryptions.

New Finite Difference Mapped WENO Schemes with Increasingly High Order of Accuracy

In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbolic conservation laws.For the purpose of designing increasingly high-order finite difference WENO schemes,the equal-sized stencils are becoming more and more wider.The more we use wider candidate stencils,the bigger the probability of discontinuities lies in all stencils.Therefore,one innovation of these new WENO schemes is to introduce a new splitting stencil methodology to divide some fourpoint or five-point stencils into several smaller three-point stencils.By the usage of this new methodology in high-order spatial reconstruction procedure,we get different degree polynomials defined on these unequal-sized stencils,and calculate the linear weights,smoothness indicators,and nonlinear weights as specified in Jiang and Shu(J.Comput.Phys.126:202228,1996).Since the difference between the nonlinear weights and the linear weights is too big to keep the optimal order of accuracy in smooth regions,another crucial innovation is to present the new mapping functions which are used to obtain the mapped nonlinear weights and decrease the difference quantity between the mapped nonlinear weights and the linear weights,so as to keep the optimal order of accuracy in smooth regions.These new MWENO schemes can also be applied to compute some extreme examples,such as the double rarefaction wave problem,the Sedov blast wave problem,and the Leblanc problem with a normal CFL number.Extensive numerical results are provided to illustrate the good performance of the new finite difference MWENO schemes.

矩形上全组合偏差的极值问题

根据Kalaj在圆环上给出的全组合偏差定义,给出了矩形上全组合偏差和组合偏差的定义.同时,在从矩形到矩形上并保持端点的所有同胚映射类中,分别考虑了组合偏差和全组合偏差的极值问题,利用面积长度方法和均值不等式证明了仿射映射为此两类极值问题的唯一解.该结果推广了相关文献的结果.

基于Adaboost-INGO-HKELM的变压器故障辨识

针对目前变压器故障诊断准确率低的问题,提出一种多策略集成模型。首先通过等度量映射(isometric mapping, Isomap)对高维非线性不可分的变压器故障数据进行降维处理。其次,利用混合核极限学习机(hybrid kernel based extreme learning machine, HKELM)进行训练学习,考虑到HKELM模型易受参数影响,所以利用北方苍鹰优化算法(northern goshawk optimization, NGO)对其参数进行寻优。但由于NGO收敛速度较慢,易陷入局部最优,引入切比雪夫混沌映射、择优学习、自适应t分布联合策略对其进行改进。同时为了提高模型整体的准确率,通过结合Adaboost集成算法,构建Adaboost-INGO-HKELM变压器故障辨识模型。最后,将提出的Adaboost-INGO-HKELM模型与未进行降维处理的INGO-HKELM模型、Isomap-INGO-KELM模型、Adaboost-Isomap-GWO-SVM等7种模型的测试准确率进行对比。提出的Adaboost-INGO-HKELM模型的准确率可达96%,均高于其他模型,验证了该模型对变压器故障辨识具有很好的效果。

基于物候与极端气候信息的耕地土壤有机碳空间分布预测研究

土壤有机碳(Soil Organic Carbon,SOC)作为陆地生态系统中最大的碳库,在农田土壤质量和作物产量方面发挥着重要作用。准确预测耕地SOC的空间分布对于制定农业管理措施至关重要。在数字土壤制图(Digital Soil Mapping,DSM)框架下,选择有效的环境协变量是提高SOC空间预测精度的重要方法。以往遥感指数和气候变量通常使用某个时段或时点的(平均)值作为输入变量,而很少有研究将时间特性和事件用于土壤有机碳预测。因此,引入物候变量、极端气候变量弥补部分损失的地物信息和气候特征,探讨其对研究区耕地SOC空间变异的响应特性及预测SOC空间分布的可行性。以江西省上高县为研究区域,采用随机森林模型,选取遥感数据、DEM衍生变量、物候参数、气候特征因子等作为环境协变量引入模型中,并用普通克里格(Ordinary Kriging,OK)对模型结果进行残差修正,最后对比不同类型变量组合下模型的预测效果及预测精度。结果表明,时序变量、物候变量及极端气候变量能够改善模型的预测性能,并且残差作为误差项还能进一步提升模型的精度。结合时序变量、物候变量、极端气候变量、地形变量和残差的组合拥有最高的预测精度,相较于地形变量、遥感变量和气候变量的组合,将R2、MAE和RMSE提升了90.00%、58.95%和57.14%。变量贡献率分析显示,SU、a3和TXx是影响研究区耕地SOC分布的重要变量。因此,物候变量和极端气候变量具有较好的应用前景,未来还需验证极端气候变量作为环境变量在不同土地利用、大尺度研究区下预测土壤属性的有效性。

基于ISOMAP-ELM的软测量建模及化工应用

针对化工生产反应过程复杂，难以直接建立对应的机理模型，提出了一种基于ISOMAP—ELM的软测量模型。将等距离映射与极限学习机结合，通过等距离映射对输入数据进行降维，消除输入数据的共线性，在低维空间提取更具代表性的特征分量，最后对特征分量采用极限学习机训练，以此建立软测量模型。验证结果表明，所提出算法与传统的基于ELM以及基于欧式距离降维的MDS—ELM模型相比，具有更高的预测精度，模型的均方误差仅为0．28，软测量模型的命中率达到94％，对化工生产具有一定的指导意义。

青藏高原及周边地区极端降水天气事件及其基于自组织特征映射方法的天气背景分型

利用2008—2014年中国自动站与CMORPH降水产品融合资料和NCEP再分析资料,基于自组织特征映射方法对青藏高原及周边地区的6 h极端降水天气进行了统计分析。发现6 h极端降水的高值和高频次主要分布在青藏高原西南部和东南部,以及东南侧的四川盆地和南侧沿喜马拉雅山至横断山脉一带。6 h极端降水在高原西南部多发生在14时(北京时,下同),在东南部多发生在20时,而在四川盆地和南侧主要发生在08时。采用自组织特征映射方法将2008—2014年高原及周边地区6 h分辨率的天气背景分为5类,类型I至类型V体现了从夏季—春秋—冬季的渐变,6 h极端降水天气事件发生比率依类递减。高原上总的极端降水主要来自类型I的高原极端降水,类型II及以下的高原极端降水落区逐类缩减并趋于沿冈底斯山零散分布。对比各类型的天气背景发现,高原上类型II及以下的动力强迫较类型I逐渐增强,但是暖心、湿度和对流有效位能等有利热力条件却依类明显缩减,使得高原极端降水落区依类迅速缩减。有利热力条件的分布与大范围极端降水的落区有很好的对应关系,热力条件减弱后,动力条件的增强及其与高原复杂地形的相互作用是导致零散极端降水的重要原因。四川盆地和高原南侧的对流有效位能明显高于高原内,高原在周边的强迫抬升易于触发对流不稳定,释放较高的对流有效位能,形成较强和较频繁的极端降水天气事件。

基于差分进化改进混合核极限学习机的指纹定位

针对极限学习机(extreme learning machine,ELM)指纹定位泛化性能弱、鲁棒性差等问题,提出一种改进的差分进化算法优化混合核极限学习机的指纹定位方法。该方法利用改进型的Logistic混沌映射提高差分进化算法全局搜索的能力,同时利用动态控制参数法避免差分进化算法陷入局部最优,然后通过改进差分进化算法自适应调整混合核极限学习机的参数,提高训练效率。在线阶段,利用混合核函数提高极限学习机的学习性能和泛化性能,并引入L1惩罚函数防止过拟合。其泛化能力相较于单一核极限学习机提升明显。该方法有92%的测试点定位误差小于0.5 m,平均误差相较于加权K近邻法(weighted Knearest neighbor,WKNN)降低了32.6%。

煤与瓦斯突出的L-Isomap-KELM模型

煤与瓦斯突出预测是一个复杂多因素的、非线性的高维问题,传统的预测方法存在预测精度不高,预测速度慢等不足。针对上述问题,提出了将地标等距特征映射(Landmarks Isometric Mapping,L-Isomap)理论与核极端学习机(Kernel Extreme Learning Machine,KELM)相结合应用到煤与瓦斯突出预测中的新方法。首先,采用L-Isomap进行非线性降维,完成特征提取;然后,用KELM来融合煤与瓦斯突出风险与致突因素组成的特征向量之间的非线性关系,建立煤与瓦斯突出预测的L-Isomap-KELM模型,并将其与极端学习机(ELM)预测模型相比。仿真结果表明:L-Isomap-KELM预测模型能够达到97.31%的准确率,并且运算速度快,还具有很好的泛化能力。

矩形上一类全组合偏差极值问题

给出矩形上组合偏差及全组合偏差的新定义,研究了从矩形到矩形上保持端点对应的所有同胚映射在这两类偏差中的极值问题。运用Euler-Lagrange方程、面积长度法和均值不等式证明,并得到这两类极值问题的解为仿射映射,推广了唐茹月在矩形上组合偏差函数极值问题的解是仿射拉伸变换的结果。

基于改进秃鹰算法优化极限学习机的谐波发射水平估计

针对目前电力系统谐波发射水平难以直接测量的问题,提出了一种基于改进秃鹰算法(improved bald eagle search,IBES)优化极限学习机(extreme learning machine,ELM)的谐波发射水平估计方法。首先,在传统秃鹰搜索算法中引入Tent混沌映射和柯西变异算子,利用IBES算法对ELM模型的输入权重和阈值进行寻优。其次,输入公共连接点(point of common coupling,PCC)处谐波电压和谐波电流,代入IBES-ELM模型,估计用户侧和系统侧谐波发射水平。最后进行仿真和工程实例分析,并与其他算法的估计结果进行对比。结果表明,所提IBES-ELM方法估计精度优于长短期记忆网络(long short-term memory,LSTM)、卷积神经网络(convolution neural network,CNN)、反向传播神经网络(back propagation neural network,BP)和CNN-LSTM算法模型,验证了该方法的有效性和稳定性。

基于改进非洲秃鹫算法优化极限学习机的船舶运动预测

针对船舶运动预测模型精度不高而造成预测结果误差大的问题,提出一种利用改进非洲秃鹫优化算法(IAVOA)优化模型参数的极限学习机(ELM)预测模型,对船舶运动状况进行预测。在初始化种群时引入Circle混沌映射,增加种群的多样性;加入自适应算子,调整两类秃鹫对其他秃鹫的指引作用,提升算法的收敛速度和解的质量。利用IAVOA优化的ELM模型对船模水池试验运动数据进行预测,并采用均方根误差和平均绝对误差评判该预测模型,与现有其他启发式算法优化ELM模型比较,所提出的IAVOA-ELM具有更优的预测精度和泛化能力。

Geochemical Mapping:With Special Emphasis on Analytical Requirements

More than 40 national and regional geochemical mapping projects in the world carried out from 1973 to 1988 do not conform to common standards. In particular they have many analytical deficiencies. In the period 1988 to 1992, the International Geochemical Mapping project （Project 259 of UNESCO＇s IGCP Program） prepared recommendations designed to standardize geochemical mapping methods. The analytical requirements are an essential component of the overall recommendations. They included the following： 71 elements should be analyzed in future mapping projects; the detection limits of trace and ultratrace elements must be lower than the corresponding crustal abundances; and the Chinese GSD and Canadian STSD standard sample series should be used for the correlation of global data. A proposal was also made to collect 5000 composite samples, at very low sampling densities to cover the whole Earth＇s land surface. In 1997 an IUGS Working Group on Global Geochemical Baselines was formed to continue the work which began with IGCP 259. From 1997 up to now, new progress has been made especially in China and FOREGS countries under the aegis of this working group, including the study of suitable sampling media, development of a multi-element analytical system, new proficiency test for selection of competent laboratories and role of wide-spaced mapping in mineral exploration. One of the major problems awaiting solution has been the inability of many laboratories to meet the IGCP recommendations to generate high quality geochemical maps. Fortunately several laboratories in China and Europe have demonstrated an ability to meet the requirements and they will be well placed to render technical assistance to other countries.

On the extremal sets of extremal quasiconformal mappings

The properties of the extremal sets of extremal quasiconformal mappings are discussed. It is proved that if an extremal Beltrami coefficientμ(z) is not uniquely extremal, then there exists an extremal Beltrami coefficient v(z) in its equivalent class and a compact subset E ( ) △ with positive measure such that the essential upper bound of ν(z) on E is less than the norm of [μ].