Dynamics of the coronavirus disease 2019(COVID-19)epidemic in Wuhan City,Hubei Province and China:a second derivative analysis of the cumulative daily diagnosed cases during the first 85 days

Background:Controlling the coronavirus disease 2019(COVID-19)epidemic requires information beyond new and cumulative cases.This study aims to conduct an in-depth analysis by geographic strata:Wuhan City(hereafter referred to as Wuhan)only,Hubei Province(hereafter referred to as Hubei)excluding Wuhan,and China excluding Hubei.Methods:Daily cumulative confirmed COVID-19 cases between December 8,2019(the date of symptom onset based on patients'recall during the investigation),and March 1,2020,from official sources and published studies were analyzed.The second derivative model was used for information extraction.Data analysis was conducted separately for the three strata.Results:A total of 80026 diagnosed COVID-19 cases were reported during the first 85 days of the epidemic,with 49315 cases from Wuhan,17788 from Hubei excluding Wuhan,and 12923 from China excluding Hubei.Analytical results indicate that the COVID-19 epidemic consists of an Acceleration,a Deceleration,and a Stabilization Phase in all three geographic strata,plus a Silent Attack Phase for Wuhan only.Given the reported incubation period of 14 days,effects of the massive anti-epidemic actions were revealed by both the Acceleration and Deceleration Phases.The Acceleration Phase signaled the effect of the intervention to detect the infected;the Deceleration Phase signaled the declines in new infections after the infected were detected,treated and quarantined.Conclusion:Findings of the study provide new evidence to better monitor the epidemic,evaluate its response to intervention,and predict the trend long.In addition to re-evaluating the control of the COVID-19 epidemic in China,this study provided a model for monitoring outbreaks of COVID-19 in different countries across the world.

An inverse problem to estimate an unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid

In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.The implicit numerical method is employed to solve the direct problem.For the inverse problem,we first obtain the fractional sensitivity equation by means of the digamma function,and then we propose an efficient numerical method,that is,the Levenberg-Marquardt algorithm based on a fractional derivative,to estimate the unknown order of a Riemann-Liouville fractional derivative.In order to demonstrate the effectiveness of the proposed numerical method,two cases in which the measurement values contain random measurement error or not are considered.The computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a RiemannLiouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.

Catalytic Kinetic Determination of Micro Amounts of Oxalic Acid by Second-Order Derivative Oscillopolarography

It was found that micro amounts of oxalate showed a very strong catalytic effect on the slow reaction between K 2Cr 2O 7 and Orange Ⅳ in a diluted sulfuric acid medium in a water bath at 70 ℃ . Orange Ⅳ exhibited a sensitive second order derivative polarographic wave at -0 50 V( vs . SCE). This provides the basis for a sensitive and selective catalytic kinetic method for oxalate determination with second order derivative oscillopolarography. The effects of sulphuric acid, K 2Cr 2O 7, and orange Ⅳ concentrations, reaction temperature and reaction time were investigated. A calibration curve of oxalate in the range of 0 1-2 0 μg/mL was obtained by the fixed time procedure. The detection limit was 0 03 μg/ mL. The possible interference from co existing substances or ions was examined. The new method has a high sensitivity and a good selectivity compared to other existing methods for oxalic acid determination. It has been applied to the determination of micro amounts of oxalate in real urine samples with satisfactory results.

A PRELIMINARY STUDY ON THE THEORY OF THE SECOND AND THIRD ORDER DERIVATIVE ADSORPTION CHRONOPOTENTIOMETRY FOR A REVERSIBLE REACTION

The equations of the second and third order derivative curves of time with respect to potential for a reversible process in adsorption chronopotentiometry are derived and experimentally verified.

Color Edge Detection Using Multidirectional Sobel Filter and Fuzzy Fusion

A new model is proposed in this paper on color edge detection that uses the second derivative operators and data fusion mechanism.The secondorder neighborhood shows the connection between the current pixel and the surroundings of this pixel.This connection is for each RGB component color of the input image.Once the image edges are detected for the three primary colors:red,green,and blue,these colors are merged using the combination rule.Then,the final decision is applied to obtain the segmentation.This process allows different data sources to be combined,which is essential to improve the image information quality and have an optimal image segmentation.Finally,the segmentation results of the proposed model are validated.Moreover,the classification accuracy of the tested data is assessed,and a comparison with other current models is conducted.The comparison results show that the proposed model outperforms the existing models in image segmentation.

New theoretical analysis method for the phase center in the Fresnel region of complex structure antennas

A finite domain time difference （FDTD） and second-derivative combined method is proposed for the evaluation of phase center in the Fresnel region of complex structure millimeter antennas. This method adopts FDTD＇s near to far field transformation to obtain the fields in Fresnel region and then applies the second-derivative method to calculate the phase center. The adoption of FDTD efficiently overcomes the difficulties arising from the existing calculation methods＇ requirements for the radiation analytical formula of some complex antennas, which makes the existing second-derivative method more applicable in engineering. Also, FDTD increases the precision owing to the superposition field calculation from its extrapolation. The correctness of this proposed method is certified with typical examples and the phase center in the Fresnel region of a microwave radiometry calibration corrugate horn antenna is evaluated with the key features.

Smoothness Prior Approach for Spectral Smoothing and Baseline Correction

Smoothness prior approach for spectral smoothing is investigated using Fourier frequency filter analysis.We show that the regularization parameter in penalized least squares could continuously control the bandwidth of low-pass filter.Besides,due to its property of interpolating the missing values automatically and smoothly,a spectral baseline correction algorithm based on the approach is proposed.This algorithm generally comprises spectral peak detection and baseline estimation.First,the spectral peak regions are detected and identified according to the second derivatives.Then,generalized smoothness prior approach combining identification information could estimate the baseline in peak regions.Results with both the simulated and real spectra show accurate baseline-corrected signals with this method.

Hyperuricemia Prediction Using Photoplethysmogram and Arteriograph

Hyperuricemia is an alarming issue that contributes to cardiovascular disease.Uric acid(UA)level was proven to be related to pulse wave velocity,a marker of arterial stiffness.A hyperuricemia prediction method utilizing photoplethysmogram(PPG)and arteriograph by using machine learning(ML)is proposed.From the literature search,there is no available papers found that relates PPG with UA level even though PPG is highly associated with vessel condition.The five phases in this research are data collection,signal preprocessing including denoising and signal quality indexes,features extraction for PPG and SDPPG waveform,statistical analysis for feature selection and classification of UA levels using ML.Adding PPG to the current arteriograph able to reduce cost and increase the prediction performance.PPG and arteriograph data were measured from 113 subjects,and 226 sets of data were collected from the left and right hands of the subjects.The performance of four types of ML,namely,artificial neural network(ANN),linear discriminant analysis(LDA),k-nearest neighbor(kNN),and support vector machine(SVM)in predicting hyperuricemia was compared.From the total of 98 features extracted,16 features of which showed statistical significance for hyper and normouricemia.ANN gives the best performance compared to the other three ML techniques with 91.67%,95.45%,and 94.12%for sensitivity,specificity,and accuracy,respectively.Features from PPG and arteriograph able to be used to predict hyperuricemia accurately and noninvasively.This study is the first to find the relationship of PPG with hyperuricemia.It shows a significant relation between PPG signals and arteriograph data toward the UA level.The proposed method of UA prediction shows its potential for noninvasive preliminary assessment.

具有非线性斜导数边界条件的二阶完全非线性椭圆方程的障碍问题

在自然结构条件下证明了具有非线性斜导数边界条件的二阶完全非线性随圆方程障碍问题Ｗ＾２，∞解的存在性，唯一性和正则性。抗议了Ｓ。Ｌｅｎｈａｒ，Ｐ。Ｌ。Ｌｉｏｎｓ和陈亚浙等人关于Ｄｉｒｉｃｈｌｅｔ边界条件的工作。

Non-Parametric Local Maxima and Minima Finder with Filtering Techniques for Bioprocess

Typically extrema filtration techniques are based on non-parametric properties such as magnitude of prominences and the widths at half prominence, which cannot be used with data that possess a dynamic nature. In this work, an extrema identification that is totally independent of derivative-based approaches and independent of quantitative attributes is introduced. For three consecutive positive terms arranged in a line, the ratio (R) of the sum of the maximum and minimum to the sum of the three terms is always 2/n, where n is the number of terms and 2/3 ≤ R ≤ 1 when n = 3. R > 2/3 implies that one term is away from the other two terms. Applying suitable modifications for the above stated hypothesis, the method was developed and the method is capable of identifying peaks and valleys in any signal. Furthermore, three techniques were developed for filtering non-dominating, sharp, gradual, low and high extrema. Especially, all the developed methods are non-parametric and suitable for analyzing processes that have dynamic nature such as biogas data. The methods were evaluated using automatically collected biogas data. Results showed that the extrema identification method was capable of identifying local extrema with 0% error. Furthermore, the non-parametric filtering techniques were able to distinguish dominating, flat, sharp, high, and low extrema in the biogas data with high robustness.

Stable and Accurate Second-Order Formulation of the Shifted Wave Equation

High order finite difference approximations are derived for a one-dimensional model of the shifted wave equation written in second-order form. Thedomain is discretized using fully compatible summation by parts operators and theboundary conditions are imposed using a penalty method, leading to fully explicittime integration. This discretization yields a strictly stable and efficient scheme. Theanalysis is verified by numerical simulations in one-dimension. The present study isthe first step towards a strictly stable simulation of the second-order formulation ofEinstein’s equations in three spatial dimensions.

Influence of Fly Ash Addition on the Hydration of Portland Cement

Influence of fly ash addition on the hydrationof Portland cement clinker,particularly at the initial stage,has been studied on the basis of measured data obtained. Fly ash,considering its active components,was added as a partial replacement of Portland cement at different water/cementitious ratios. The hydration heat was measured in a controlled environmental room of 20 ℃. Both non-evaporable water content and mineral phase were investigated. Data indicate that the amount of fly ash involved in hydration reaction is little at initial stage while it becomes more after 7 d hydration. As hydration reaction is a continuous process,chemical stress results in the disruption of stable structure on the surface of fly ash consisting of Ca,O,Si,Al,C,etc. Additionally,surface of glass beads begins to lose smooth and reacts to blend in with the paste.

Analysis and discrimination of ten different sponges by multi-step infrared spectroscopy

In this study,a convenient method using multi-step infrared spectroscopy,including Fourier transform infrared spectroscopy（FT-IR）,second derivative infrared spectroscopy（SD-IR） and two-dimensional correlation infrared spectroscopy（2DCOS-IR）,was employed to analyze and discriminate ten marine sponges from two classes collected from the Xisha Islands in the South China Sea.Each sponge had an exclusive macroscopic fingerprint.From the IR spectra,it was noted that the main ingredient of calcareous sponges was calcium carbonate,but that of demosponges was proteins.For sponges from the same genus or having highly similar chemical profile（IR spectral profile）,SD-IR and 2DCOS-IR were applied to successfully reveal the tiny differences.It was demonstrated that the multi-step infrared spectroscopy was a feasible and objective approach for marine sponge identification.

A STUDY ON DEFORMATIONS OF RAY AND ITS RELEVANT FACTORS

In this paper,the effects of first and second meridional derivative(i.e.h_s~,d^2f/dy^2,″)of the Coriolis parameter,Westerly profile and topography structure on ray routes are qualitatively analysed by use of a sim- plified mathematical model.The analysis indicates that the second derivatives of the above relevant factors play an important role in the formation of great circle route.A profile of west wind similar to the real atmosphere may result in a“sine wave pattern”of ray.The effects of west wind shear,β factor and the slope of topography on the scale of radius of great circle,critical latitude of rays ard the amplitude of wave train of teleconnection aro also discussed.Additionally,the characters of critical velocity profile for meridionally trapped wave are men- tioned.

Low Dimensional Cohomology of Hom-Lie Algebras and q-deformed W(2, 2) Algebra

This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W（2, 2） algebra. We show that the q-deformed W（2, 2） algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspondence between the equivalence classes of one-dimensional central extensions of a Hom-Lie algebra and its second cohomology group, leading us to determine the second cohomology group of the q-deformed W（2, 2） algebra. In addition, we generalize some results of derivations of finitely generated Lie algebras with values in graded modules to Hom-Lie algebras.As application, we compute all αk-derivations and in particular the first cohomology group of the q-deformed W（2, 2） algebra.