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Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

Computer Modeling in Engineering & Sciences 2024年第3期138卷 2471-2495页

作者： Wimonmas Bamrungsetthapong Pramote Charongrattanasakul division of Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiPathum Thani12110Thailand division of mathematics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology KrungthepBangkok10120Thailand

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull *** control chart developed supports the examination of the mean lifespan variation for a particular product in the process of *** control limit levels are used:the warning control limit,inner control limit,and outer control ***,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control *** control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control ***,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

关键词： Modified DS np chart generalizedmultiple dependent state sampling time truncated life test Weibull distribution average run length average sample size

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Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

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Communications on Applied mathematics and Computation 2024年第2期6卷 1428-1471页

作者： Paula Chen Jerome Darbon Tingwei Meng division of Applied mathematics Brown UniversityProvidenceRIUSA Department of mathematics UCLALos AngelesCAUSA

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high *** this paper,we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the *** also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent ***,we present an efficient,grid-free numerical solver based on our representation formulas,which is shown to scale linearly with the state dimension,and thus,to overcome the curse of *** existing optimization methods and the min-plus technique,we extend our numerical solvers to address more general classes of convex and nonconvex initial *** demonstrate the capabilities of our numerical solvers using implementations on a central processing unit(CPU)and a field-programmable gate array(FPGA).In several cases,our FPGA implementation obtains over a 10 times speedup compared to the CPU,which demonstrates the promising performance boosts FPGAs can *** numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

关键词： Optimal control Hamilton-Jacobi partial differential equations Grid-free numerical methods High dimensions Field-programmable gate arrays(FPGAs)

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An analytical approach for the fractional-order Hepatitis B model using new operator

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International Journal of Biomathematics 2024年第1期17卷 177-198页

作者： Surath Ghosh division of mathematics School of Advanced Sciences Vellore Institute of TechnologyChennaiIndia

In this work,the main goal is to implement Homotopy perturbation transform method(HPTM)involving Katugampola fractional *** an example,a fractional order Hepatitis model is considered to analyze the *** first,the integer order model is converted to fractional order model in Caputo ***,the new operator Katugampola fractional derivative is used to present the *** new such kind of operator is illustrated in Caputo *** is described to get the solution of the proposed model using the new kind of ***,there are some analyses about the new kind of operator to prove the efficiency of the operator.

关键词： Caputo derivative Katugampola fractional derivative homotopy perturbation transform method Hepatitis B model

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Impact of vaccination on the dynamics of COVID-19:A mathematical study using fractional derivatives

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International Journal of Biomathematics 2024年第2期17卷 201-232页

作者： Shraddha Ramdas Bandekar Mini Ghosh C.Rajivganthi division of mathematics School of Advanced Sciences Vellore Institute of TechnologyChennaiIndia

Arrival of a new disease marks a yearlong destruction of human lives and economy in general,and if the disease turns out to be a pandemic the loss is ***-19 is one such pandemic that has claimed millions of lives till *** is a suffering throughout the world due to various factors associated with the pandemic,be it loss of livelihoods because of sudden shutdown of companies and lockdown,or loss of lives due to lack of medical aid and inadequate vaccination *** this study,we develop a six-compartmental epidemiological model incorporating *** motivation behind the study is to analyze the significance of higher vaccination efficacy and higher rate of population getting vaccinated in controlling the rise in infectives and thereby the untimely demise of various *** work begins with an ordinary differential equation model followed by stability analysis of the same,after which a fractional-order derivative model of the same is formulated and the existence of uniformly stable solution for the system is *** addition to this,we present the stability of the equilibria in general for the fractional model *** sensitivity analysis of the basic reproduction number along with its correlation with various parameters is *** addition to this,sensitivity of certain state variables in the fractional model with respect to *** orders as well with respect to different infection rate is exhibited in this *** related to lockdown and usage of face shields are incorporated in the entire study,and importance of these is highlighted in the study as *** major takeaway from the study is that mere vaccination will not sufice in eradication of the *** vaccine efficacy plays a major role along with other intervention included in the *** numerical simulations are carried out in MATLAB software using ode45 and fdel2.

关键词： Caputo fractional derivative basic reproduction number stability analysis sensitivityanalysis vaccination

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Second-order error analysis of the averaged L1 scheme L1 for time-fractional initial-value and subdiffusion problems

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Science China mathematics 2024年第7期67卷 1641-1664页

作者： Jinye Shen Fanhai Zeng Martin Stynes School of mathematics Southwestern University of Finance and EconomicsChengdu611130China School of mathematics Shandong UniversityJinan250100China Applied and Computational mathematics division Beijing Computational Science Research CenterBeijing100193China

Fractional initial-value problems(IVPs) and time-fractional initial-boundary value problems(IBVPs), each with a Caputo temporal derivative of order α ∈(0, 1), are considered. An averaged variant of the well-known L1 scheme is proved to be O(N^(-2)) convergent for IVPs on suitably graded meshes with N points, thereby improving the O(N^(-(2-α))) convergence rate of the standard L1 scheme. The analysis relies on a delicate decomposition of the temporal truncation error that yields a sharp dependence of the order of convergence on the degree of mesh grading used. This averaged L1 scheme can be combined with a finite difference or piecewise linear finite element discretization in space for IBVPs, and under a restriction on the temporal mesh width, one gets again O(N^(-2)) convergence in time, together with O(h^(2)) convergence in space,where h is the spatial mesh width. Numerical experiments support our results.

关键词： time-fractional subdiffusion averaged L1 scheme

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New approach for particle size and shape analysis of iron-based oxygen carriers at multiple oxidation states

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Particuology 2024年第7期90卷 493-503页

作者： Victor Purnomo Marcelo Dal Belo Takehara Robin Faust Lidiya Abdisa Ejjeta Henrik Leion division of Energy and Materials Department of Chemistry and Chemical EngineeringChalmers University of TechnologyGöteborg 41258Sweden division of Energy Science Department of Engineering Sciences and MathematicsLuleåUniversity of TechnologyLuleå97187Sweden

One of the crucial issues in the chemical looping technology lies in its bed material:the oxygen *** size analysis of an oxygen carrier is important since in a fluidized bed the material can only work well within a specific size *** the favorable size ranges for oxygen carrier materials have already been reported,none of the published studies has analyzed the particle size and shape of oxygen carriers in ***,the effect of oxygen carriers'oxidation degree on such properties has not been considered *** study aimed to report the particle size and shape analysis of five iron-based oxygen carriers,one natural ore,one synthetic material,and three residue products,at different oxidation degrees using dynamic image analysis(DIA).The oxygen carriers were prepared at different mass conversion degrees in a fluidized bed batch *** size distribution,sphericity,and aspect ratio of the oxygen carrier particles were examined experimentally using a Camsizer *** results show that the DIA method was successfully able to analyze the particle size and shape of our oxygen carriers with satisfying accuracy for *** oxidation state of the investigated materials seems to only affect the particle size and shape of oxygen carriers to a minor ***,exposures to redox cycles in a fluidized bed reactor may alter the particle size and shape of most oxygen carriers.

关键词： Oxygen carrier Size and shape analysis Dynamic image analysis Oxidation state Fluidized bed Chemical looping

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Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators

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Science China mathematics 2024年第2期67卷 237-252页

作者： Hong-Lin Liao Tao Tang Tao Zhou School of mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China SUSTech International Center for mathematics Shenzhen 518055China NCMIS&LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The positive definiteness of real quadratic forms with convolution structures plays an important rolein stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysistool to handle discrete convolution kernels resulting from variable-step approximations for convolution *** precisely, for a class of discrete convolution kernels relevant to variable-step L1-type time discretizations, weshow that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Ourproof is based on an elementary constructing strategy by using the properties of discrete orthogonal convolutionkernels and discrete complementary convolution kernels. To our knowledge, this is the first general result onsimple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using theunified theory, we obtain the stability for some simple nonuniform time-stepping schemes straightforwardly.

关键词： discrete convolution kernels positive definiteness variable time-stepping orthogonal convolution kernels complementary convolution kernels

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Efficient Finite Difference WENO Scheme for Hyperbolic Systems withNon-conservativeProducts

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Communications on Applied mathematics and Computation 2024年第2期6卷 907-962页

作者： Dinshaw S.Balsara Deepak Bhoriya Chi-Wang Shu Harish Kumar Physics Department University of Notre DameNotre DameUSA ACMS Department University of Notre DameNotre DameUSA division of Applied mathematics Brown UniversityProvidenceUSA Department of mathematics Indian Institute of TechnologyDelhiIndia

Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation *** multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable *** makes them quite attractive for several science and engineering ***,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative *** this paper,we perform such an extension which improves the domain of the applicability of such *** extension is carried out by writing the scheme in fluctuation *** use the HLLI Riemann solver of Dumbser and Balsara(***.304:275-319,2016)as a building block for carrying out this *** of the use of an HLL building block,the resulting scheme has a proper supersonic *** use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the *** new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present *** conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied *** examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional *** Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the *** some

关键词： Hyperbolic PDEs Numerical schemes Non-conservative products Stiff source terms Finite difference WENO

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Traveling wave solutions of the nonlinear Gilson-Pickering equation in crystal lattice theory

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Journal of Ocean Engineering and Science 2024年第1期9卷 40-49页

作者： A.T.Nguyen O.Nikan Z.Avazzadeh division of Applied mathematics Science and Technology Advanced InstituteVan Lang UniversityHo Chi Minh CityVietnam Faculty of Technology Van Lang UniversityHo Chi Minh CityVietnam School of mathematics Iran University of Science and TechnologyNarmakTehranIran Department of Applied mathematics Xi’an Jiaotong-Liverpool UniversitySuzhou 215123China

This paper focuses on obtaining the traveling wave solutions of the nonlinear Gilson-Pickering equa-tion(GPE),which describes the prorogation of waves in crystal lattice theory and plasma *** solution of the GPE is approximated via the finite difference technique and the localized meshless radial basis function generated finite *** association of the technique results in a meshless approach that does not require linearizing the nonlinear *** the first step,the PDE is converted to a system of nonlinear ODEs with the help of the radial *** the second step,a high-order ODE solver is adopted to discretize the nonlinear ODE *** global collocation techniques pose a considerable computationl burden due to the calculation of the dense algebraic *** proposed method approx-imates differential operators over the local support domain,leading to sparse differentiation matrices and decreasing the computational *** results and comparisons are provided to confirm the efficiency and accuracy of the method.

关键词： Nonlinear Gilson–Pickering equation Soliton wave solutions Meshless technique RBF LRBF-FD Optimal shape parameter

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Flow Injection Analysis Technique for Online Preconcentration of Lead Ions in Airborne Particulate Matter Using Imprinted Polymer as the Sorbent

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Journal of Analysis and Testing 2024年第2期8卷 180-190页

作者： Muhammad Bachri Amran Novita Ambarsari Muhammad Ali Zulfikar Asri Indrawati Rusnadi Rusnadi Saipul Hamdi Analytical Chemistry division Faculty of Mathematics and Natural SciencesInstitut Teknologi BandungBandung 40132Indonesia Research Center for Climate and Atmosphere National Research and Innovation AgencyBandung 40135Indonesia

This work reported a simple and sensitive flow injection analysis(FIA)technique coupled with a Flame Atomic Absorption Spectrophotometer(FAAS)for online preconcentration of lead(Ⅱ)ions in the airborne particulate matter samples(PM_(2.5))using ion-imprinted polymers as adsorbent packed in minicolumn.A bulk polymerization method was chosen to synthesize the polymer based on a ternary complex of lead ions with 4-2-pyridilazo resorcinol and 4-vinyl pyridine with methacrylic acid as a functional *** optimum pH for sorption was 6,and other variables for the FIA system were optimized,including breakthrough volume,eluent concentration,and eluent *** optimum conditions were reached with a breakthrough volume of 4.45 mL,calculated as a dynamic retention capacity of 5.20 mg/g of Pb(II)40 mg/L,with a 1.5 mL/min flow *** eluent used for the FIA system was 0.5 mL HNO_(3)of 3 mol/***,precision,and limits of detection of the FIA system were determined before being applied to preconcentration and analysis of lead ions in PM_(2.5)*** precision of the method was determined to be 3.09%by calculating the coefficients of the *** of the method in the concentration range of 50-1000μg/L gave a coefficient correlation of 0.9925,showing a good response,and the limit of detection of the system was 5.11μg/L,better than that of the FAAS *** of the FIA system were evaluated and showed good results with an enrichment factor of more than 20 times higher and a concentration efficiency of 11.65 min^(-1)with a consumptive index of 4.5 *** and analysis of the PM_(2.5)samples in Bandung City showed the concentrations of Pb(II)were 26.67μg/L and 33.3μg/L with the accuracy of the method for each sample of104.75%and 107.86%.

关键词： Flow injection analysis Lead(II)ions Imprinted polymer Particulate matter

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