Model reduction of fractional impedance spectra for time–frequency analysis of batteries, fuel cells, and supercapacitors

Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis is urgently required.The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional-order models to integer-order models and from high-to low-order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process.The following work has been carried out:(i)the model-reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique,respectively;(ii)the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis;(iii)the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured;and(iv)the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium-ion batteries,supercapacitors,and solid oxide fuel cells.In turn,the numerical validation has demonstrated the powerful function of the joint time–frequency analysis.The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time-domain transient analysis and frequency-domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.

Target versus sub-target dose of renin–angiotensin system inhibitors on survival in elderly patients with heart failure with reduced ejection fraction: a systematic review and meta-analysis

BACKGROUND The efficiency of the target versus sub-target dose of renin–angiotensin system inhibitors(RASIs)in elderly patients with heart failure(HF)with reduced ejection fraction(HErEF)remains unclear.METHODS PubMed,Embase,and the Cochrane Central Register of Controlled Trials were searched from database inception through March 2022 for randomized controlled trials(RCTs)and observational studies considering the effect of the target versus sub-target dose of RASIs on survival in elderly patients(≥60 years)with HErEF.The primary outcome was all-cause mortality.The secondary outcomes were cardiac mortality,HF hospitalization,and the composite endpoint of mortality or HF hospitalization.A meta-analysis was conducted to generate combined hazard ratio(HR)and 95%CI.RESULTS Seven studies(two RCTs and five observational studies)enrolling 16,634 patients were included.A pooled analysis suggested that the target versus sub-target dose of RASIs led to lower rates of all-cause mortality(HR=0.92,95%CI:0.87–0.98,I2=21%)and cardiac mortality(HR=0.93,95%CI:0.85–1.00,I2=15%)but not reduced rates of HF hospitalization(HR=0.94,95%CI:0.88–1.01,I2=0)and the composite endpoint(HR=1.03,95%CI:0.91–1.15,I2=51%).However,the target dose of RASIs was associated with a similar primary outcome(HR=0.85,95%CI:0.64–1.14,I2=0)in a subgroup of very elderly patients>75 years of age.CONCLUSIONS Our analysis suggests that the target dose of RASIs has a better survival benefit in elderly patients with HFrEF compared to the sub-target dose of RASIs.However,the sub-target dose of RASIs is associated with a similar mortality rate in very elderly patients>75 years of age.Future high-quality and adequately powered RCTs are warranted.

Multiple grain-size fraction analysis of heavy minerals and the provenance identification of sediments from the abandoned Huanghe River,eastern China

The quantitative analysis of sediment sources in a sink is an important scientific topic and challenge in provenance research.The characteristics of heavy minerals,combined with the geochemical constituents of detrital grains,provide a reliable provenance-tracing approach.We developed a mineral identification method to analyze the multiple grain-size fraction of sediments,from which the elemental geochemistry of hornblende was used to compare the characteristics of sediments from the Huaihe River and Huanghe(Yellow)River in eastern China.Elements that were statistically identified as being able to discriminate sediment provenance were employed to perform a quantitative analysis of the sources of sediments of the abandoned Huanghe River.Results reveal that the Huaihe River is characterized by a high amphibole content of>60%and that the Huanghe and abandoned Huanghe rivers have greater abundances of limonite and carbonate minerals compared with those of the Huaihe River.The contents of trace elements and rare earth elements in hornblende show that the sediments of the abandoned Huanghe River are similar to those of the Huanghe River but different from those of the Huaihe River.Furthermore,chemical mass balance was used to calculate the relative contributions of different provenances of sediment from the abandoned Huanghe River,and nine trace elements of hornblende were identified as discriminators of provenance.Approximately 2%of the hornblende in the abandoned Huanghe River is derived from the Huaihe River and 98%from the Huanghe River.Considering the proportion of hornblende in the total sediment,it is inferred that the contribution of Huaihe River sediment to the abandoned Huanghe River is approximately 0.5%.This study shows that mineral analysis using multiple grain-size fractions(within the wide range of 1Φto 6Φ)with assessment in elemental geochemistry of hornblende can characterize the provenance of fluvial material in coastal zones.

New Configurations of the Fuzzy Fractional Differential Boussinesq Model with Application in Ocean Engineering and Their Analysis in Statistical Theory

The fractional-order Boussinesq equations(FBSQe)are investigated in this work to see if they can effectively improve the situation where the shallow water equation cannot directly handle the dispersion wave.The fuzzy forms of analytical FBSQe solutions are first derived using the Adomian decomposition method.It also occurs on the sea floor as opposed to at the functionality.A set of dynamical partial differential equations(PDEs)in this article exemplify an unconfined aquifer flow implication.Thismethodology can accurately simulate climatological intrinsic waves,so the ripples are spread across a large demographic zone.The Aboodh transform merged with the mechanism of Adomian decomposition is implemented to obtain the fuzzified FBSQe in R,R^(n) and(2nth)-order involving generalized Hukuhara differentiability.According to the system parameter,we classify the qualitative features of the Aboodh transform in the fuzzified Caputo and Atangana-Baleanu-Caputo fractional derivative formulations,which are addressed in detail.The illustrations depict a comparison analysis between the both fractional operators under gH-differentiability,as well as the appropriate attributes for the fractional-order and unpredictability factorsσ∈[0,1].A statistical experiment is conducted between the findings of both fractional derivatives to prevent changing the hypothesis after the results are known.Based on the suggested analyses,hydrodynamic technicians,as irrigation or aquifer quality experts,may be capable of obtaining an appropriate storage intensity amount,including an unpredictability threshold.

Time series analysis-based seasonal autoregressive fractionally integrated moving average to estimate hepatitis B and C epidemics in China

BACKGROUND Hepatitis B(HB)and hepatitis C(HC)place the largest burden in China,and a goal of eliminating them as a major public health threat by 2030 has been set.Making more informed and accurate forecasts of their spread is essential for developing effective strategies,heightening the requirement for early warning to deal with such a major public health threat.AIM To monitor HB and HC epidemics by the design of a paradigmatic seasonal autoregressive fractionally integrated moving average(SARFIMA)for projections into 2030,and to compare the effectiveness with the seasonal autoregressive integrated moving average(SARIMA).METHODS Monthly HB and HC incidence cases in China were obtained from January 2004 to June 2023.Descriptive analysis and the Hodrick-Prescott method were employed to identify trends and seasonality.Two periods(from January 2004 to June 2022 and from January 2004 to December 2015,respectively)were used as the training sets to develop both models,while the remaining periods served as the test sets to evaluate the forecasting accuracy.RESULTS There were incidents of 23400874 HB cases and 3590867 HC cases from January 2004 to June 2023.Overall,HB remained steady[average annual percentage change(AAPC)=0.44,95%confidence interval(95%CI):-0.94-1.84]while HC was increasing(AAPC=8.91,95%CI:6.98-10.88),and both had a peak in March and a trough in February.In the 12-step-ahead HB forecast,the mean absolute deviation(15211.94),root mean square error(18762.94),mean absolute percentage error(0.17),mean error rate(0.15),and root mean square percentage error(0.25)under the best SARFIMA(3,0,0)(0,0.449,2)12 were smaller than those under the best SARIMA(3,0,0)(0,1,2)12(16867.71,20775.12,0.19,0.17,and 0.27,respectively).Similar results were also observed for the 90-step-ahead HB,12-step-ahead HC,and 90-step-ahead HC forecasts.The predicted HB incidents totaled 9865400(95%CI:7508093-12222709)cases and HC totaled 1659485(95%CI:856681-2462290)cases during 2023-2030.CONCLUSION Under current interventions,China faces enormous challenges to eliminate HB and HC epidemics by 2030,and effective strategies must be reinforced.The integration of SARFIMA into public health for the management of HB and HC epidemics can potentially result in more informed and efficient interventions,surpassing the capabilities of SARIMA.

MULTIFRACTAL ANALYSIS OF THE CONVERGENCE EXPONENT IN CONTINUED FRACTIONS

Let x∈(0,1)be a real number with continued fraction expansion[a_(1)(x),a_(2)(x),a_(3)(x),⋯].This paper is concerned with the multifractal spectrum of the convergence exponent of{a_(n)(x)}_(n≥1) defined by τ(x):=inf{s≥0:∑n≥1an^(-s)(x)<∞}.

Fractional Envelope Analysis for Rolling Element Bearing Weak Fault Feature Extraction

The bearing weak fault feature extraction is crucial to mechanical fault diagnosis and machine condition monitoring.Envelope analysis based on Hilbert transform has been widely used in bearing fault feature extraction. A generalization of the Hilbert transform, the fractional Hilbert transform is defined in the frequency domain, it is based upon the modification of spatial filter with a fractional parameter, and it can be used to construct a new kind of fractional analytic signal. By performing spectrum analysis on the fractional envelope signal, the fractional envelope spectrum can be obtained. When weak faults occur in a bearing, some of the characteristic frequencies will clearly appear in the fractional envelope spectrum. These characteristic frequencies can be used for bearing weak fault feature extraction.The effectiveness of the proposed method is verified through simulation signal and experiment data.

Purification and Structural Analysis of a Selective Toxin Fraction Produced by the Plant Pathogen Setosphaeria turcica

Thirteen fractions from the pathogenic plant fungus Setosphaeria turcica race 1 were separated and collected using high performance liquid chromatography （HPLC）. Their toxic activities were assayed through leaf puncturing on corn differentials （OH43, OH43Ht1, OH43Ht2, and OH43HtN）, and the results revealed that eight fractions were toxic and fraction 6 was specifically toxic to OH43Ht1, which could be taken as a gene-selective toxin fraction. Fraction 6 was finely purified via HPLC and condensed by freeze desiccation. Its chemical structure was analyzed with EI-MS, IR, HMBC, ^1H-NMR, and two-dimensional NMR. The results suggested that fraction 6 contained an unsaturated double bond, carbonyl and methylene groups with molecular weight of 142.

Solid fraction evolution characteristics of semi-solid A356 alloy and in-situ A356–TiB_2 composites investigated by differential thermal analysis

The key factor in semi-solid metal processing is the solid fraction at the forming temperature because it affects the microstructure and mechanical properties of the thixoformed components. Though an enormous amount of data exists on the solid fraction-temperature re- lationship in A356 alloy, information regarding the solid fraction evolution characteristics of A356-TiB2 composites is scarce. The present article establishes the temperature-solid fraction correlation in A356 alloy and A356-xTiB2 （x = 2.5wt% and 5wt%） composites using dif- ferential thermal analysis （DTA）. The DTA results indicate that the solidification characteristics of the composites exhibited a variation of 2℃ and 3℃ in liquidus temperatures and a variation of 3℃ and 5℃ in solidus temperatures with respect to the base alloy. Moreover, the eutectic growth temperature and the solid fraction（fs） vs. temperature characteristics of the composites were found to be higher than those of the base alloy. The investigation revealed that in-situ formed TiB2 particles in the molten metal introduced more nucleation sites and reduced undercooling.

Imaging Analysis by Means of Fractional Fourier Transform

Starting from the diffraction imaging process,we have discussed the relationship between optical imaging system and fractional Fourier transform, and proposed a specific system which can form an inverse amplified image of input function.

Dynamic analysis of a new chaotic system with fractional order and its generalized projective synchronization

Based on the stability theory of the fractional order system, the dynamic behaviours of a new fractional order system are investigated theoretically. The lowest order we found to have chaos in the new three-dimensional system is 2.46, and the period routes to chaos in the new fractional order system are also found. The effectiveness of our analysis results is further verified by numerical simulations and positive largest Lyapunov exponent. Furthermore, a nonlinear feedback controller is designed to achieve the generalized projective synchronization of the fractional order chaotic system, and its validity is proved by Laplace transformation theory.

Modeling and Dynamic Analysis of Fractional-Order Buck Converter in Continuous Conduction Mode

According to the fact that the actual inductor and actual capacitor are fractional, the mathematical and state-space averaging models of fractional order Buck converters in continuous conduction mode(CCM) are constructed by using fractional calculus theory. Firstly, the parameter conditions that ensure that the converter working in CCM is given and transfer functions are derived. Also, the inductor current and the output voltage are analyzed. Then the difference between the mathematical model and the circuit model are analyzed, and the effect of fractional order is studied by comparing the integer order with fractional order model. Finally, the dynamic behavior of the current-controlled Buck converter is investigated. Simulation experiments are achieved via the use of Matlab/Simulink. The experimental results verify the correctness of theoretical analysis, the order should be taken as a significant parameter. When the order is taken as a bifurcation parameter, the dynamic behavior of the converter will be affected and bifurcation points will be changed as order varies.

Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19in Nigeria Using Atangana-Baleanu Operator

We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.

GC/MS Analysis of Organic Compounds in Hot Water-Extractable Fraction from Shenfu Coal

Shenfu Coal was extracted with hot pure water and slurry was isolated. The concentrated benzene-soluble fraction (CBSF) was analyzed with GC/MS and four types of organic compounds (OCs) were detected: HACOCs,DTEs,DMDT and LCAs. The amount of benzyl benzoate which is the most abundant OC was calculated by an inter-nal standard method with an indicated amount of BP. The broken hydrogen bonds and ether bonds were responsible for the extraction of OCs from the coal .DTEs,DMDT and LCAs are essentially insoluble in water,whereas they are soluble,probably owing to intermolecular interaction of OCs with HACOCs.

A New Scheme of the ARA Transform for Solving Fractional-Order Waves-Like Equations Involving Variable Coefficients

The goal of this research is to develop a new,simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations(PDEs)with variable coefficient.ARA-transform is a robust and highly flexible generalization that unifies several existing transforms.The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion.The process of finding approximations for dynamical fractional-order PDEs is challenging,but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern and then determining the series coefficients by employing the residual component and the limit at infinity concepts.This approach is effective and useful for solving a massive class of fractional-order PDEs.Five appealing implementations are taken into consideration to demonstrate the effectiveness of the projected technique in creating solitary series findings for the governing equations with variable coefficients.Additionally,several visualizations are drawn for different fractional-order values.Besides that,the estimated findings by the proposed technique are in close agreement with the exact outcomes.Finally,statistical analyses further validate the efficacy,dependability and steady interconnectivity of the suggested ARA-residue power series approach.

Study on Fractional Separation and GC-MS Analysis of Flash Coal Tar Pyrolysed at Low Temperatures

The composition of low temperature pyrolysis coal tar has an effect on its further processing and reasomble utlization In this paper, the compeition or coal tars produced from both low temperature pyroysis in a fluidized bed aud flash pyrolysis with solid heat carrier have been investigated by the methch of fractional seperation and Gas Chromatography-Mass Spectrometry (GC-MS)- It is observed that the degree of coalification maceral and secondary reaction temperature (freeboard temperature in a fluidized bed) have some iufluence on the composition of coal tars- The main compoundes are phenol cresols,xylenols, naphthalene, alkylnaphthalenes, antbraceue, phenanthrene,acenaphthylene, fluoren, indene and so

Stability Analysis, Chaos Control of Fractional Order Vallis and El-Nino Systems and Their Synchronization

In this article the authors have studied the stability analysis and chaos control of the fractional order Vallis and El-Nino systems. The chaos control of these systems is studied using nonlinear control method with the help of a new lemma for Caputo derivative and Lyapunov stability theory.The synchronization between the systems for different fractional order cases and numerical simulation through graphical plots for different particular cases clearly exhibit that the method is easy to implement and reliable for synchronization of fractional order chaotic systems. The comparison of time of synchronization when the systems pair approaches from standard order to fractional order is the key feature of the article.

The Homotopy Analysis Method for Approximating of Giving Up Smoking Model in Fractional Order

In this paper, we consider the giving up smoking model. First, we present the giving up smoking model in fractional order. Then the homotopy analysis method (HAM) is employed to compute an approximate and analytical solution of the model in fractional order. The obtained results are compaired with those obtained by forth order Runge-Kutta method and nonstandard numerical method in the integer case. Finally, we present some numerical results.

Fractional Analysis of Dynamical Novel COVID-19 by Semi-Analytical Technique

This study employs a semi-analytical approach,called Optimal Homotopy Asymptotic Method(OHAM),to analyze a coronavirus(COVID-19)transmission model of fractional order.The proposed method employs Caputo’s fractional derivatives and Reimann-Liouville fractional integral sense to solve the underlying model.To the best of our knowledge,this work presents the first application of an optimal homotopy asymptotic scheme for better estimation of the future dynamics of the COVID-19 pandemic.Our proposed fractional-order scheme for the parameterized model is based on the available number of infected cases from January 21 to January 28,2020,in Wuhan City of China.For the considered real-time data,the basic reproduction number is R0≈2.48293 that is quite high.The proposed fractional-order scheme for solving the COVID-19 fractional-order model possesses some salient features like producing closed-form semi-analytical solutions,fast convergence and non-dependence on the discretization of the domain.Several graphical presentations have demonstrated the dynamical behaviors of subpopulations involved in the underlying fractional COVID-19 model.The successful application of the scheme presented in this work reveals new horizons of its application to several other fractional-order epidemiological models.

Homotopy Analysis Method for a Conservative Nonlinear Oscillator with Fractional Power

In this paper, the homotopy analysis method is applied to deduce the periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to u1/3. By introducing the auxiliary linear operator and the initial guess of solution, the homotopy analysis solving is set up. By choosing the suitable convergence-control parameter, the accurate high-order approximations of solution and frequency for the whole range of initial amplitudes can easily be obtained. Comparison of the results obtained using this method with those obtained by different methods reveals that the former is more accurate, effective and convenient for these types of nonlinear oscillators.