A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Quantifying the agreement and accuracy characteristics of four satellite-based LULC products for cropland classification in China

Various land use and land cover(LULC)products have been produced over the past decade with the development of remote sensing technology.Despite the differences in LULC classification schemes,there is a lack of research on assessing the accuracy of their application to croplands in a unified framework.Thus,this study evaluated the spatial and area accuracies of cropland classification for four commonly used global LULC products(i.e.,MCD12Q1V6,GlobCover2009,FROM-GLC and GlobeLand30)based on the harmonised FAO criterion,and quantified the relationships between four factors(i.e.,slope,elevation,field size and crop system)and cropland classification agreement.The validation results indicated that MCD12Q1 and GlobeLand30 performed well in cropland classification regarding spatial consistency,with overall accuracies of 94.90 and 93.52%,respectively.The FROMGLC showed the worst performance,with an overall accuracy of 83.17%.Overlaying the cropland generated by the four global LULC products,we found the proportions of complete agreement and disagreement were 15.51 and 44.72% for the cropland classification,respectively.High consistency was mainly observed in the Northeast China Plain,the Huang-Huai-Hai Plain and the northern part of the Middle-lower Yangtze Plain,China.In contrast,low consistency was detected primarily on the eastern edge of the northern and semiarid region,the Yunnan-Guizhou Plateau and southern China.Field size was the most important factor for mapping cropland.For area accuracy,compared with China Statistical Yearbook data at the provincial scale,the accuracies of different products in descending order were:GlobeLand30,FROM-GLC,MCD12Q1,and GlobCover2009.The cropland classification schemes mainly caused large area deviations among the four products,and they also resulted in the different ranks of spatial accuracy and area accuracy among the four products.Our results can provide valuable suggestions for selecting cropland products at the national or provincial scale and help cropland mapping and reconstruction,which is essential for food security and crop management,so they can also contribute to achieving the Sustainable Development Goals issued by the United Nations.

Closed-form steady-state solutions for forced vibration of second-order axially moving systems

Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.

Three-dimensional mixed convection stagnation-point fow past a vertical surface with second-order slip velocity

This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.

Six New Sets of the Non-Elementary Jef-Family-Functions that Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs

In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs.

Influence of initial check, information exchange, final accuracy check, reaction information nursing on the psychology of elderly with lung cancer

BACKGROUND As one of the fatal diseases with high incidence,lung cancer has seriously endangered public health and safety.Elderly patients usually have poor self-care and are more likely to show a series of psychological problems.AIM To investigate the effectiveness of the initial check,information exchange,final accuracy check,reaction(IIFAR)information care model on the mental health status of elderly patients with lung cancer.METHODS This study is a single-centre study.We randomly recruited 60 elderly patients with lung cancer who attended our hospital from January 2021 to January 2022.These elderly patients with lung cancer were randomly divided into two groups,with the control group taking the conventional propaganda and education and the observation group taking the IIFAR information care model based on the conventional care protocol.The differences in psychological distress,anxiety and depression,life quality,fatigue,and the locus of control in psychology were compared between these two groups,and the causes of psychological distress were analyzed.RESULTS After the intervention,Distress Thermometer,Hospital Anxiety and Depression Scale(HADS)for anxiety and the HADS for depression,Revised Piper’s Fatigue Scale,and Chance Health Locus of Control scores were lower in the observation group compared to the pre-intervention period in the same group and were significantly lower in the observation group compared to those of the control group(P<0.05).After the intervention,Quality of Life Questionnaire Core 30(QLQ-C30),Internal Health Locus of Control,and Powerful Others Health Locus of Control scores were significantly higher in the observation and the control groups compared to the pre-intervention period in their same group,and QLQ-C30 scores were significantly higher in the observation group compared to those of the control group(P<0.05).CONCLUSION The IIFAR information care model can help elderly patients with lung cancer by reducing their anxiety and depression,psychological distress,and fatigue,improving their tendencies on the locus of control in psychology,and enhancing their life qualities.

Urea breath test for Helicobacter pylori infection in adult dyspeptic patients: A meta-analysis of diagnostic test accuracy

BACKGROUND Helicobacter pylori(H.pylori)infection has been well-established as a significant risk factor for several gastrointestinal disorders.The urea breath test(UBT)has emerged as a leading non-invasive method for detecting H.pylori.Despite numerous studies confirming its substantial accuracy,the reliability of UBT results is often compromised by inherent limitations.These findings underscore the need for a rigorous statistical synthesis to clarify and reconcile the diagnostic accuracy of the UBT for the diagnosis of H.pylori infection.AIM To determine and compare the diagnostic accuracy of 13C-UBT and 14C-UBT for H.pylori infection in adult patients with dyspepsia.METHODS We conducted an independent search of the PubMed/MEDLINE,EMBASE,and Cochrane Central databases until April 2022.Our search included diagnostic accuracy studies that evaluated at least one of the index tests(^(13)C-UBT or ^(14)C-UBT)against a reference standard.We used the QUADAS-2 tool to assess the methodo-logical quality of the studies.We utilized the bivariate random-effects model to calculate sensitivity,specificity,positive and negative test likelihood ratios(LR+and LR-),as well as the diagnostic odds ratio(DOR),and their 95%confidence intervals.We conducted subgroup analyses based on urea dosing,time after urea administration,and assessment technique.To investigate a possible threshold effect,we conducted Spearman correlation analysis,and we generated summary receiver operating characteristic(SROC)curves to assess heterogeneity.Finally,we visually inspected a funnel plot and used Egger’s test to evaluate publication bias.endorsing both as reliable diagnostic tools in clinical practice.CONCLUSION In summary,our study has demonstrated that ^(13)C-UBT has been found to outperform the ^(14)C-UBT,making it the preferred diagnostic approach.Additionally,our results emphasize the significance of carefully considering urea dosage,assessment timing,and measurement techniques for both tests to enhance diagnostic precision.Nevertheless,it is crucial for researchers and clinicians to evaluate the strengths and limitations of our findings before implementing them in practice.

Diagnostic Accuracy of Computerized Bowel Sound Analysis with Non-Invasive Devices for Irritable Bowel Syndrome:A Systematic Review and Meta-Analysis

Objective To assess the diagnostic accuracy of bowel sound analysis for irritable bowel syndrome(IBS)with a systematic review and meta-analysis.Methods We searched MEDLINE,Embase,the Cochrane Library,Web of Science,and IEEE Xplore databases until September 2023.Cross-sectional and case-control studies on diagnostic accuracy of bowel sound analysis for IBS were identified.We estimated the pooled sensitivity,specificity,positive likelihood ratio,negative likeli-hood ratio,and diagnostic odds ratio with a 95% confidence interval(CI),and plotted a summary receiver operat-ing characteristic curve and evaluated the area under the curve.Results Four studies were included.The pooled diagnostic sensitivity,specificity,positive likelihood ratio,nega-tive likelihood ratio,and diagnostic odds ratio were 0.94(95%CI,0.87‒0.97),0.89(95%CI,0.81‒0.94),8.43(95%CI,4.81‒14.78),0.07(95%CI,0.03‒0.15),and 118.86(95%CI,44.18‒319.75),respectively,with an area under the curve of 0.97(95%CI,0.95‒0.98).Conclusions Computerized bowel sound analysis is a promising tool for IBS.However,limited high-quality data make the results'validity and applicability questionable.There is a need for more diagnostic test accuracy studies and better wearable devices for monitoring and analysis of IBS.

Second-Order MaxEnt Predictive Modelling Methodology. I: Deterministically Incorporated Computational Model (2nd-BERRU-PMD)

This work presents a comprehensive second-order predictive modeling (PM) methodology designated by the acronym 2nd-BERRU-PMD. The attribute “2nd” indicates that this methodology incorporates second-order uncertainties (means and covariances) and second-order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best- Estimate Results with Reduced Uncertainties” and the last letter (“D”) in the acronym indicates “deterministic,” referring to the deterministic inclusion of the computational model responses. The 2nd-BERRU-PMD methodology is fundamentally based on the maximum entropy (MaxEnt) principle. This principle is in contradistinction to the fundamental principle that underlies the extant data assimilation and/or adjustment procedures which minimize in a least-square sense a subjective user-defined functional which is meant to represent the discrepancies between measured and computed model responses. It is shown that the 2nd-BERRU-PMD methodology generalizes and extends current data assimilation and/or data adjustment procedures while overcoming the fundamental limitations of these procedures. In the accompanying work (Part II), the alternative framework for developing the “second- order MaxEnt predictive modelling methodology” is presented by incorporating probabilistically (as opposed to “deterministically”) the computed model responses.

Second-Order MaxEnt Predictive Modelling Methodology. II: Probabilistically Incorporated Computational Model (2nd-BERRU-PMP)

This work presents a comprehensive second-order predictive modeling (PM) methodology based on the maximum entropy (MaxEnt) principle for obtaining best-estimate mean values and correlations for model responses and parameters. This methodology is designated by the acronym 2nd-BERRU-PMP, where the attribute “2nd” indicates that this methodology incorporates second- order uncertainties (means and covariances) and second (and higher) order sensitivities of computed model responses to model parameters. The acronym BERRU stands for “Best-Estimate Results with Reduced Uncertainties” and the last letter (“P”) in the acronym indicates “probabilistic,” referring to the MaxEnt probabilistic inclusion of the computational model responses. This is in contradistinction to the 2nd-BERRU-PMD methodology, which deterministically combines the computed model responses with the experimental information, as presented in the accompanying work (Part I). Although both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies yield expressions that include second (and higher) order sensitivities of responses to model parameters, the respective expressions for the predicted responses, for the calibrated predicted parameters and for their predicted uncertainties (covariances), are not identical to each other. Nevertheless, the results predicted by both the 2nd-BERRU-PMP and the 2nd-BERRU-PMD methodologies encompass, as particular cases, the results produced by the extant data assimilation and data adjustment procedures, which rely on the minimization, in a least-square sense, of a user-defined functional meant to represent the discrepancies between measured and computed model responses.

Accuracy of FreeStyle Libre flash glucose monitoring in patients with type 2 diabetes who migrated from highlands to plains

BACKGROUND The FreeStyle Libre flash glucose monitoring(FGM)system entered the Chinese market in 2017 to complement the self-monitoring of blood glucose.Due to its increased usage in clinics,the number of studies investigating its accuracy has increased.However,its accuracy has not been investigated in highland populations in China.AIM To evaluate measurements recorded using the FreeStyle Libre FGM system compared with capillary blood glucose measured using the enzyme electrode method in patients with type 2 diabetes(T2D)who had migrated within 3 mo from highlands to plains.METHODS Overall,68 patients with T2D,selected from those who had recently migrated from highlands to plains(within 3 mo),were hospitalized at the Department of Endocrinology from August to October 2017 and underwent continuous glucose monitoring(CGM)with the FreeStyle Libre FGM system for 14 d.Throughout the study period,fingertip capillary blood glucose was measured daily using the enzyme electrode method(Super GL,China),and blood glucose levels were read from the scanning probe during fasting and 2 h after all three meals.Moreover,the time interval between reading the data from the scanning probe and collecting fingertip capillary blood was controlled to<5 min.The accuracy of the FGM system was evaluated according to the CGM guidelines.Subsequently,the factors influencing the mean absolute relative difference(MARD)of this system were analyzed by a multiple linear regression method.RESULTS Pearson’s correlation analysis showed that the fingertip and scanned glucose levels were positively correlated(R=0.86,P=0.00).The aggregated MARD of scanned glucose was 14.28±13.40%.Parker's error analysis showed that 99.30%of the data pairs were located in areas A and B.According to the probe wear time of the FreeStyle Libre FGM system,MARD_(1 d) and MARD_(2-14 d) were 16.55%and 14.35%,respectively(t=1.23,P=0.22).Multiple stepwise regression analysis showed that MARD did not correlate with blood glucose when the largest amplitude of glycemic excursion(LAGE)was<5.80 mmol/L but negatively correlated with blood glucose when the LAGE was≥5.80 mmol/L.CONCLUSION The FreeStyle Libre FGM system has good accuracy in patients with T2D who had recently migrated from highlands to plains.This system might be ideal for avoiding the effects of high hematocrit on blood glucose monitoring in populations that recently migrated to plains.MARD is mainly influenced by glucose levels and fluctuations,and the accuracy of the system is higher when the blood glucose fluctuation is small.In case of higher blood glucose level fluctuations,deviation in the scanned glucose levels is the highest at extremely low blood glucose levels.

Clinical study on improving the diagnostic accuracy of adult elbow joint cartilage injury by multisequence magnetic resonance imaging

BACKGROUND Due to frequent and high-risk sports activities,the elbow joint is susceptible to injury,especially to cartilage tissue,which can cause pain,limited movement and even loss of joint function.AIM To evaluate magnetic resonance imaging(MRI)multisequence imaging for improving the diagnostic accuracy of adult elbow cartilage injury.METHODS A total of 60 patients diagnosed with elbow cartilage injury in our hospital from January 2020 to December 2021 were enrolled in this retrospective study.We analyzed the accuracy of conventional MRI sequences(T1-weighted imaging,T2-weighted imaging,proton density weighted imaging,and T2 star weighted image)and Three-Dimensional Coronary Imaging by Spiral Scanning(3D-CISS)in the diagnosis of elbow cartilage injury.Arthroscopy was used as the gold standard to evaluate the diagnostic effect of single and combination sequences in different injury degrees and the consistency with arthroscopy.RESULTS The diagnostic accuracy of 3D-CISS sequence was 89.34%±4.98%,the sensitivity was 90%,and the specificity was 88.33%,which showed the best performance among all sequences(P<0.05).The combined application of the whole sequence had the highest accuracy in all sequence combinations,the accuracy of mild injury was 91.30%,the accuracy of moderate injury was 96.15%,and the accuracy of severe injury was 93.33%(P<0.05).Compared with arthroscopy,the combination of all MRI sequences had the highest consistency of 91.67%,and the kappa value reached 0.890(P<0.001).CONCLUSION Combination of 3D-CISS and each sequence had significant advantages in improving MRI diagnostic accuracy of elbow cartilage injuries in adults.Multisequence MRI is recommended to ensure the best diagnosis and treatment.

Numerical Investigation of Thermal Behavior of CNC Machine Tool and Its Effects on Dimensional Accuracy of Machined Parts

The dimensional accuracy of machined parts is strongly influenced by the thermal behavior of machine tools (MT). Minimizing this influence represents a key objective for any modern manufacturing industry. Thermally induced positioning error compensation remains the most effective and practical method in this context. However, the efficiency of the compensation process depends on the quality of the model used to predict the thermal errors. The model should consistently reflect the relationships between temperature distribution in the MT structure and thermally induced positioning errors. A judicious choice of the number and location of temperature sensitive points to represent heat distribution is a key factor for robust thermal error modeling. Therefore, in this paper, the temperature sensitive points are selected following a structured thermomechanical analysis carried out to evaluate the effects of various temperature gradients on MT structure deformation intensity. The MT thermal behavior is first modeled using finite element method and validated by various experimentally measured temperature fields using temperature sensors and thermal imaging. MT Thermal behavior validation shows a maximum error of less than 10% when comparing the numerical estimations with the experimental results even under changing operation conditions. The numerical model is used through several series of simulations carried out using varied working condition to explore possible relationships between temperature distribution and thermal deformation characteristics to select the most appropriate temperature sensitive points that will be considered for building an empirical prediction model for thermal errors as function of MT thermal state. Validation tests achieved using an artificial neural network based simplified model confirmed the efficiency of the proposed temperature sensitive points allowing the prediction of the thermally induced errors with an accuracy greater than 90%.

Second-Order MaxEnt Predictive Modelling Methodology. III: Illustrative Application to a Reactor Physics Benchmark

This work illustrates the innovative results obtained by applying the recently developed the 2nd-order predictive modeling methodology called “2nd- BERRU-PM”, where the acronym BERRU denotes “best-estimate results with reduced uncertainties” and “PM” denotes “predictive modeling.” The physical system selected for this illustrative application is a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. This benchmark is modeled using the neutron transport Boltzmann equation (involving 21,976 uncertain parameters), the solution of which is representative of “large-scale computations.” The results obtained in this work confirm the fact that the 2nd-BERRU-PM methodology predicts best-estimate results that fall in between the corresponding computed and measured values, while reducing the predicted standard deviations of the predicted results to values smaller than either the experimentally measured or the computed values of the respective standard deviations. The obtained results also indicate that 2nd-order response sensitivities must always be included to quantify the need for including (or not) the 3rd- and/or 4th-order sensitivities. When the parameters are known with high precision, the contributions of the higher-order sensitivities diminish with increasing order, so that the inclusion of the 1st- and 2nd-order sensitivities may suffice for obtaining accurate predicted best- estimate response values and best-estimate standard deviations. On the other hand, when the parameters’ standard deviations are sufficiently large to approach (or be outside of) the radius of convergence of the multivariate Taylor-series which represents the response in the phase-space of model parameters, the contributions stemming from the 3rd- and even 4th-order sensitivities are necessary to ensure consistency between the computed and measured response. In such cases, the use of only the 1st-order sensitivities erroneously indicates that the computed results are inconsistent with the respective measured response. Ongoing research aims at extending the 2nd-BERRU-PM methodology to fourth-order, thus enabling the computation of third-order response correlations (skewness) and fourth-order response correlations (kurtosis).

A HIGH ACCURACY DIFFERENCE SCHEME FOR THE SINGULAR PERTURBATION PROBLEM OF THE SECOND-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM

In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.

Further Analysis of Machine Tool Dimensional Accuracy and Thermal Stability under Varying Floor Temperature

Machining is as old as humanity, and changes in temperature in both the machine’s internal and external environments can be of great concern as they affect the machine’s thermal stability and, thus, the machine’s dimensional accuracy. This paper is a continuation of our earlier work, which aimed to analyze the effect of the internal temperature of a machine tool as the machine is put into operation and vary the external temperature, the machine floor temperature. Some experiments are carried out under controlled conditions to study how machine tool components get heated up and how this heating up affects the machine’s accuracy due to thermally induced deviations. Additionally, another angle is added by varying the machine floor temperature. The parameters mentioned above are explored in line with the overall thermal stability of the machine tool and its dimensional accuracy. A Robodrill CNC machine tool is used. The CNC was first soaked with thermal energy by gradually raising the machine floor temperature to a certain level before putting the machine in operation. The machine was monitored, and analytical methods were deplored to evaluate thermal stability. Secondly, the machine was run idle for some time under raised floor temperature before it was put into operation. Data was also collected and analyzed. It is observed that machine thermal stability can be achieved in several ways depending on how the above parameters are joggled. This paper, in conclusion, reinforces the idea of machine tool warm-up process in conjunction with a carefully analyzed and established machine floor temperature variation for the approximation of the machine tool’s thermally stability to map the long-time behavior of the machine tool.

Study on the Accuracy of Serum Prealbumin Level in Predicting the Prognosis of Patients with Critical Respiratory Illness

Objective: To analyze the accuracy of serum prealbumin levels in predicting the prognosis of patients with critical respiratory illness. Methods: Fifty patients with critical respiratory illness admitted to our hospital from October 2022 to September 2023 were selected and divided into an observation group and a control group after condition assessment, with 25 cases in each group. The results of cholinesterase (ChE), prealbumin (PALB), albumin (ALB), aspartate aminotransferase (AST), total protein (TP), and forced expiratory volume (FEV1)/Predicted (Pred) of the two groups were measured. Results: The ChE levels of the observation group were lower than those of the control group, while the PALB and ALB levels of the observation group were higher than those of the control group (P < 0.05). The AST, TP, and FEV1 /Pred levels of the observation group were higher than those in the control group (P < 0.05). Conclusion: Serum PALB levels can be used as the main indicator for prognosis in critically ill respiratory patients.

Second-Order Raman Scattering from n- and p-Type 4H-SiC

The results of second-order Raman-scattering experiments on n- and p-type 4H-SiC are presented,covering the acoustic and the optical overtone spectral regions.Some of the observed structures in the spectra are assigned to particular phonon branches and the points in the Brillouin zone from which the scattering originates.There exists a doublet at 626/636cm -1 with energy difference about 10cm -1 in both n- and p-type 4H-SiC,which is similar to the doublet structure with the same energy difference founded in hexagonal GaN,ZnO, and AlN.The cutoff frequency at 1926cm -1 of the second-order Raman is not the overtone of the A 1(LO) peak of the n-type doping 4H-SiC,but that of the undoping one.The second-order Raman spectrum of 4H-SiC can hardly be affected by doping species or doping density.

Anti-periodic solutions to a class of second-order evolution equations

In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.