This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemi...This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.展开更多
Background:Establishing an appropriate prognostic model for PCa is essential for its effective treatment.Glycolysis is a vital energy-harvesting mechanism for tumors.Developing a prognostic model for PCa based on glyc...Background:Establishing an appropriate prognostic model for PCa is essential for its effective treatment.Glycolysis is a vital energy-harvesting mechanism for tumors.Developing a prognostic model for PCa based on glycolysis-related genes is novel and has great potential.Methods:First,gene expression and clinical data of PCa patients were downloaded from The Cancer Genome Atlas(TCGA)and Gene Expression Omnibus(GEO),and glycolysis-related genes were obtained from the Molecular Signatures Database(MSigDB).Gene enrichment analysis was performed to verify that glycolysis functions were enriched in the genes we obtained,which were used in nonnegative matrix factorization(NMF)to identify clusters.The correlation between clusters and clinical features was discussed,and the differentially expressed genes(DEGs)between the two clusters were investigated.Based on the DEGs,we investigated the biological differences between clusters,including immune cell infiltration,mutation,tumor immune dysfunction and exclusion,immune function,and checkpoint genes.To establish the prognostic model,the genes were filtered based on univariable Cox regression,LASSO,and multivariable Cox regression.Kaplan–Meier analysis and receiver operating characteristic analysis validated the prognostic value of the model.A nomogram of the risk score calculated by the prognostic model and clinical characteristics was constructed to quantitatively estimate the survival probability for PCa patients in the clinical setting.Result:The genes obtained from MSigDB were enriched in glycolysis functions.Two clusters were identified by NMF analysis based on 272 glycolysis-related genes,and a prognostic model based on DEGs between the two clusters was finally established.The prognostic model consisted of LAMPS,SPRN,ATOH1,TANC1,ETV1,TDRD1,KLK14,MESP2,POSTN,CRIP2,NAT1,AKR7A3,PODXL,CARTPT,and PCDHGB2.All sample,training,and test cohorts from The Cancer Genome Atlas(TCGA)and the external validation cohort from GEO showed significant differences between the high-risk and low-risk groups.The area under the ROC curve showed great performance of this prognostic model.Conclusion:A prognostic model based on glycolysis-related genes was established,with great performance and potential significance to the clinical application.展开更多
The degradation of micropollutants in water via ultraviolet(UV)-based advanced oxidation processes(AOPs)is strongly dependent on the water matrix.Various reactive radicals(RRs)formed in UV-AOPs have different reaction...The degradation of micropollutants in water via ultraviolet(UV)-based advanced oxidation processes(AOPs)is strongly dependent on the water matrix.Various reactive radicals(RRs)formed in UV-AOPs have different reaction selectivities toward water matrices and degradation efficiencies for target micropollutants.Hence,process selection and optimization are crucial.This study developed a facilitated prediction method for the photon fluence-based rate constant for micropollutant degradation(K′_(p,MP))in various UV-AOPs by combining model simulation with portable measurement.Portable methods for measuring the scavenging capacities of the principal RRs(RRSCs)involved in UV-AOPs(i.e.,HO^(·),SO_(4)^(·-),and Cl^(·))using a mini-fluidic photoreaction system were proposed.The simulation models consisted of photochemical,quantitative structure–activity relationship,and radical concentration steady-state approximation models.The RRSCs were determined in eight test waters,and a higher RRSC was found to be associated with a more complex water matrix.Then,by taking sulfamethazine,caffeine,and carbamazepine as model micropollutants,the k′_(p,MP) values in various UV-AOPs were predicted and further verified experimentally.A lower k′_(p,MP) was found to be associated with a higher RRSC for a stronger RR competition;for example,k′_(p,MP) values of 130.9 and 332.5 m^(2) einstein^(–1),respectively,were obtained for carbamazepine degradation by UV/H_(2)O_(2) in the raw water(RRSC=9.47×10^(4) s^(-1))and sand-filtered effluent(RRSC=2.87×10^(4) s^(-1))of a drinking water treatment plant.The developed method facilitates process selection and optimization for UV-AOPs,which is essential for increasing the efficiency and cost-effectiveness of water treatment.展开更多
In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on pe...In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.展开更多
To fully display the modeling mechanism of the novelfractional order grey model (FGM (q,1)), this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and...To fully display the modeling mechanism of the novelfractional order grey model (FGM (q,1)), this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and the raw data matrix, whichare consistent with the fractional order accumulative grey model(FAGM (1,1)). Following this, this paper decomposes the accumulativedata difference matrix into the accumulative generationmatrix, the q-order reductive accumulative matrix and the rawdata matrix, and then combines the least square method, findingthat the differential order affects the model parameters only byaffecting the formation of differential sequences. This paper thensummarizes matrix decomposition of some special sequences,such as the sequence generated by the strengthening and weakeningoperators, the jumping sequence, and the non-equidistancesequence. Finally, this paper expresses the influences of the rawdata transformation, the accumulation sequence transformation,and the differential matrix transformation on the model parametersas matrices, and takes the non-equidistance sequence as an exampleto show the modeling mechanism.展开更多
Graphene has been extensively explored to enhance functional and mechanical properties of metalmatrix nanocomposites for wide-range applications due to their superior mechanical,electrical and thermal properties.This ...Graphene has been extensively explored to enhance functional and mechanical properties of metalmatrix nanocomposites for wide-range applications due to their superior mechanical,electrical and thermal properties.This article discusses recent advances of key mechanisms,synthesis,manufacture,modelling and applications of graphene metal matrix nanocomposites.The main strengthening mechanisms include load transfer,Orowan cycle,thermal mismatch,and refinement strengthening.Synthesis technologies are discussed including some conventional methods(such as liquid metallurgy,powdermetallurgy,thermal spraying and deposition technology)and some advanced processing methods(such as molecular-level mixing and friction stir processing).Analytical modelling(including phenomenological models,semi-empirical models,homogenization models,and self-consistent model)and numerical simulations(including finite elements method,finite difference method,and boundary element method)have been discussed for understanding the interface bonding and performance characteristics between graphene and different metal matrices(Al,Cu,Mg,Ni).Key challenges in applying graphene as a reinforcing component for the metal matrix composites and the potential solutions as well as prospectives of future development and opportunities are highlighted.展开更多
To reduce the torque ripple in motors resulting from the use of conventional direct torque control(DTC),a model predictive control(MPC)-based DTC strategy for a direct matrix converter-fed induction motor is proposed ...To reduce the torque ripple in motors resulting from the use of conventional direct torque control(DTC),a model predictive control(MPC)-based DTC strategy for a direct matrix converter-fed induction motor is proposed in this paper.Two new look-up tables are proposed,these are derived on the basis of the control of the electromagnetic torque and stator flux using all the feasible voltage vectors and their associated switching states.Finite control set model predictive control(FCS-MPC)has then been adopted to select the optimal switching state that minimizes the cost function related to the electromagnetic torque.Finally,the experimental results are shown to verify the reduced torque ripple performance of the proposed MPC-based DTC method.展开更多
An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to swit...An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to switch from bad to good status. A matrix based on error logic is used to express current status u, expectant status u1 and transformation matrix T. It is u, u1, and T that are used to build error matrix equation T (u)= u1. This allows us to find a method whereby bad status “u” changes to good status “u1” by solving the equation. The conversion method that transform from current to expectant status can be obtained from the transformation matrix T. On this basis, this paper proposes a new kind of error matrix equation named “containing-type error matrix equation”. This equation is more suitable for analyzing the realistic question. The method of solving, existence and form of solution for this type of equation have been presented in this paper. This research provides a potential useful new technique for decision analysis.展开更多
Purpose: The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants, including the quarks, are associated with partial harmonic fractional exponents, , of a fundamental freq...Purpose: The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants, including the quarks, are associated with partial harmonic fractional exponents, , of a fundamental frequency, v<sub>F</sub>. The model has shown that the properties of the quarks are based on a progression of prime number composites. They also fall on three separate power law lines related to integer factors of the Y-intercept, , of a fundamental electromagnetic line which is scaled by the Rydberg constant, R and Planck’s constant. The quark lines are scaled by the quantum number factors {1, 2, 3}, and their Y-intercepts are referred to as n<sub>bem</sub>. The goal is to present a new proto-quark model in a six-quark inverted triangular array that defines the global organization of the valence quarks, which determines the hadronic quantum numbers, the standard hadron quark model, and the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Methods: The charm, bottom, top quarks are associated with power law line Y-intercept, n<sub>bem</sub> equal to 1;the strange and down quarks with n<sub>bem</sub> equal to 2;and the up quark with n<sub>bem</sub> equal to 3. An inverted equilateral triangular array with three rows arranged from upper row (triangle base) to bottom row (triangle vertex), is associated respectively with n<sub>bem</sub> numbers 1, 2, and 3. The novelty of our perspective thus defines a new global valence quark organization which supersedes the Standard hadron composite quark model. The quarks are ordered via relative mass, partial fractions, and n<sub>bem</sub> quantum number. The top row of our inverted triangle includes the c, b, and t quarks from left to right;the middle row depicts the d and s quarks;and the bottom row, the up quark. Results: Our array depicts a quantum generator of the global organization of the valence quarks defining the composite quark model. The vertices of the triangular array are the up quarks, the midpoints are the down quarks. All weak transitions are from a corner to a midpoint or vice versa. The standard 3 by 3 CKM matrix is generated from the new quark triangle with each up type quark (u, c, and t) transforming to each down type (d, s, and b), with their experimental flavor transition magnitudes given. Conclusion: A new quark quantum number, n<sub>bem</sub>, is an important discovery that generates a new proto-valence quark triangle that secondarily generates the composite quark model and the CKM matrix.展开更多
The modified shear lag model proposed recently was applied to calculate thermal residual stresses and subsequent stress distributions under tensile and compressive loadings. The expressions for the elastic moduli and ...The modified shear lag model proposed recently was applied to calculate thermal residual stresses and subsequent stress distributions under tensile and compressive loadings. The expressions for the elastic moduli and the yield strengths under tensile and compressive loadings were derived which take account of thermal residual stresses. The asymmetries in the elastic modulus and the yield strength were interpreted using the derived expressions and the obtained results of the stress calculations. The model predictions have exhibited good agreements with the experimental results and also with the other theoretical predictions展开更多
To improve the naphtha composition prediction model based on molecular type homologous series matrix(MTHS), this paper puts forward a novel molecular matrix to characterize the naphtha composition and the normal distr...To improve the naphtha composition prediction model based on molecular type homologous series matrix(MTHS), this paper puts forward a novel molecular matrix to characterize the naphtha composition and the normal distribution hypothesis to better describe the molecular composition distribution within each homologous series of the molecular matrix. Through prediction calculation of eight groups of naphtha samples and eight groups of gasoline samples, it is verified that the normal distribution hypothesis is more applicable than gamma distribution hypothesis for the prediction model. According to the prediction results of the samples,the restrain range of normal distribution parameters during model computing process is summarized. With the bulk properties of naphtha samples and the value range of distribution parameters as input conditions, this study utilizes the improved novel molecular matrix to predict the composition of naphtha samples. As the results show, the novel molecular matrix can predict more detailed composition information of naphtha and improve prediction accuracy with less unknown parameters.展开更多
The expressions of matrix construction by using the singular value decomposition (SVD) are applied to the physics parameter identification of dynamic model. Then, based upon to the characteristics of a kind of matrix ...The expressions of matrix construction by using the singular value decomposition (SVD) are applied to the physics parameter identification of dynamic model. Then, based upon to the characteristics of a kind of matrix construction method, the orders of the parameter identification model can be reduced. After reducing, the mathematics and physics correspondence relations between the subsystem and the original system are distinct. the condensation errors can be avoided. The numerical example shows the benefit of the presented methodology.展开更多
In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic ...In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.展开更多
The wear of cutting tools in the machining of 2024Al alloy composites reinforced with Al2O3 particles using varying sizes and volume fractions of particles up to 23.3vol% was investigated by a turning process using co...The wear of cutting tools in the machining of 2024Al alloy composites reinforced with Al2O3 particles using varying sizes and volume fractions of particles up to 23.3vol% was investigated by a turning process using coated carbide tools K10 and TP30 at different cut- ting speeds. Machining tests were performed with a plan of experiments based on the Taguchi method. The tool life model was developed in terms of cutting speed, size, and volume fraction of particles by multiple linear regressions. The analysis of variance (ANOVA) was also employed to carry out the effects of these parameters on the cutting tool life. The test results show that the tool life decreases with the increase of cutting speed for both cutting tools K10 and TP30, and the tool life of the K10 tool is significantly longer than that of the TP30 tool. For the tool life, cutting speed is found to be the most effective factor followed by particle content and particle size, respectively. The predicted tool life of cutting tools is found to be in very good agreement with the experimentally observed ones.展开更多
In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-know...In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient.展开更多
In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathema...In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics,namely,susceptible(S),infected(I),treatment(T),and recovered(R).The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points.To indicate the usefulness of this method,we employ it in some cases.For error analysis of the method,the residual of the solutions is reviewed.The reported examples show that the method is reasonably efficient and accurate.展开更多
We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free ferm...We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.展开更多
Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization pr...Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization problem. Usually, the rank of base matrix needs to be assumed. In this paper, we propose an unsupervised multi-level non-negative matrix factorization model to extract the hidden data structure and seek the rank of base matrix. From machine learning point of view, the learning result depends on its prior knowledge. In our unsupervised multi-level model, we construct a three-level data structure for non-negative matrix factorization algorithm. Such a construction could apply more prior knowledge to the algorithm and obtain a better approximation of real data structure. The final bases selection is achieved through L2-norm optimization. We implement our experiment via binary datasets. The results demonstrate that our approach is able to retrieve the hidden structure of data, thus determine the correct rank of base matrix.展开更多
In the present work, a new method to predict the stress-strain curves for three-phase materials has been developed. It was applied using the example of an Mg-stabilized zirconia reinforced TRIP-matrix-composite. The c...In the present work, a new method to predict the stress-strain curves for three-phase materials has been developed. It was applied using the example of an Mg-stabilized zirconia reinforced TRIP-matrix-composite. The content of the ceramic phase was varied between 5% and 20%, whereas the particle size of the ceramic was selected to be 30 to 50 μm. The method is a further development of mixture rule for multiphase materials with more than two microstructure components. The prediction results were compared with the original method of mixture rule and with the IsoE-method. It is shown that the new method significantly improves the convergence compared to the standard method for mixture rule, even though it does not reach the accuracy of IsoE-method. Furthermore, there is an improvement of predicted convergence for large values of the total stress. Finally, a working map was designed for a quick graphical definition of the objective functions.展开更多
基金the support of Prince Sultan University for paying the article processing charges(APC)of this publication.
文摘This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.
基金supported by the Public Health Research Project in Futian District,Shenzhen(Grant Nos.FTWS2020026,FTWS2021073).
文摘Background:Establishing an appropriate prognostic model for PCa is essential for its effective treatment.Glycolysis is a vital energy-harvesting mechanism for tumors.Developing a prognostic model for PCa based on glycolysis-related genes is novel and has great potential.Methods:First,gene expression and clinical data of PCa patients were downloaded from The Cancer Genome Atlas(TCGA)and Gene Expression Omnibus(GEO),and glycolysis-related genes were obtained from the Molecular Signatures Database(MSigDB).Gene enrichment analysis was performed to verify that glycolysis functions were enriched in the genes we obtained,which were used in nonnegative matrix factorization(NMF)to identify clusters.The correlation between clusters and clinical features was discussed,and the differentially expressed genes(DEGs)between the two clusters were investigated.Based on the DEGs,we investigated the biological differences between clusters,including immune cell infiltration,mutation,tumor immune dysfunction and exclusion,immune function,and checkpoint genes.To establish the prognostic model,the genes were filtered based on univariable Cox regression,LASSO,and multivariable Cox regression.Kaplan–Meier analysis and receiver operating characteristic analysis validated the prognostic value of the model.A nomogram of the risk score calculated by the prognostic model and clinical characteristics was constructed to quantitatively estimate the survival probability for PCa patients in the clinical setting.Result:The genes obtained from MSigDB were enriched in glycolysis functions.Two clusters were identified by NMF analysis based on 272 glycolysis-related genes,and a prognostic model based on DEGs between the two clusters was finally established.The prognostic model consisted of LAMPS,SPRN,ATOH1,TANC1,ETV1,TDRD1,KLK14,MESP2,POSTN,CRIP2,NAT1,AKR7A3,PODXL,CARTPT,and PCDHGB2.All sample,training,and test cohorts from The Cancer Genome Atlas(TCGA)and the external validation cohort from GEO showed significant differences between the high-risk and low-risk groups.The area under the ROC curve showed great performance of this prognostic model.Conclusion:A prognostic model based on glycolysis-related genes was established,with great performance and potential significance to the clinical application.
基金supported by the National Natural Science Foundation of China(52222002)Bureau of International Cooperation of Chinese Academy of Sciences(032GJHZ2022035MI)State Key Laboratory of Environmental Aquatic Chemistry(23Z01ESPCR).
文摘The degradation of micropollutants in water via ultraviolet(UV)-based advanced oxidation processes(AOPs)is strongly dependent on the water matrix.Various reactive radicals(RRs)formed in UV-AOPs have different reaction selectivities toward water matrices and degradation efficiencies for target micropollutants.Hence,process selection and optimization are crucial.This study developed a facilitated prediction method for the photon fluence-based rate constant for micropollutant degradation(K′_(p,MP))in various UV-AOPs by combining model simulation with portable measurement.Portable methods for measuring the scavenging capacities of the principal RRs(RRSCs)involved in UV-AOPs(i.e.,HO^(·),SO_(4)^(·-),and Cl^(·))using a mini-fluidic photoreaction system were proposed.The simulation models consisted of photochemical,quantitative structure–activity relationship,and radical concentration steady-state approximation models.The RRSCs were determined in eight test waters,and a higher RRSC was found to be associated with a more complex water matrix.Then,by taking sulfamethazine,caffeine,and carbamazepine as model micropollutants,the k′_(p,MP) values in various UV-AOPs were predicted and further verified experimentally.A lower k′_(p,MP) was found to be associated with a higher RRSC for a stronger RR competition;for example,k′_(p,MP) values of 130.9 and 332.5 m^(2) einstein^(–1),respectively,were obtained for carbamazepine degradation by UV/H_(2)O_(2) in the raw water(RRSC=9.47×10^(4) s^(-1))and sand-filtered effluent(RRSC=2.87×10^(4) s^(-1))of a drinking water treatment plant.The developed method facilitates process selection and optimization for UV-AOPs,which is essential for increasing the efficiency and cost-effectiveness of water treatment.
文摘In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.
基金supported by the National Natural Science Foundation of China(5147915151279149+2 种基金71540027)the China Postdoctoral Science Foundation Special Foundation Project(2013T607552012M521487)
文摘To fully display the modeling mechanism of the novelfractional order grey model (FGM (q,1)), this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and the raw data matrix, whichare consistent with the fractional order accumulative grey model(FAGM (1,1)). Following this, this paper decomposes the accumulativedata difference matrix into the accumulative generationmatrix, the q-order reductive accumulative matrix and the rawdata matrix, and then combines the least square method, findingthat the differential order affects the model parameters only byaffecting the formation of differential sequences. This paper thensummarizes matrix decomposition of some special sequences,such as the sequence generated by the strengthening and weakeningoperators, the jumping sequence, and the non-equidistancesequence. Finally, this paper expresses the influences of the rawdata transformation, the accumulation sequence transformation,and the differential matrix transformation on the model parametersas matrices, and takes the non-equidistance sequence as an exampleto show the modeling mechanism.
基金The authors would like to acknowledge the financial supports from Xi'an Science Research Project of China(No.2020KJRC0089)Shaanxi Coal Industry Group United Fund of China(No.2019JLM-2)+4 种基金National Natural Science Foundation of China,China(No.51901192)Key Research and Development Projects of Shaanxi Province(No.2019GY-164)Science and Technology Project of Weiyang District of Xi'an City(No.201857)Shaanxi Youth Star Program of Science and Technology(No.2020KJXX-061)as well as Newton Mobility Grant(No.IE161019)through Royal Society and the National Natural Science Foundation of China.
文摘Graphene has been extensively explored to enhance functional and mechanical properties of metalmatrix nanocomposites for wide-range applications due to their superior mechanical,electrical and thermal properties.This article discusses recent advances of key mechanisms,synthesis,manufacture,modelling and applications of graphene metal matrix nanocomposites.The main strengthening mechanisms include load transfer,Orowan cycle,thermal mismatch,and refinement strengthening.Synthesis technologies are discussed including some conventional methods(such as liquid metallurgy,powdermetallurgy,thermal spraying and deposition technology)and some advanced processing methods(such as molecular-level mixing and friction stir processing).Analytical modelling(including phenomenological models,semi-empirical models,homogenization models,and self-consistent model)and numerical simulations(including finite elements method,finite difference method,and boundary element method)have been discussed for understanding the interface bonding and performance characteristics between graphene and different metal matrices(Al,Cu,Mg,Ni).Key challenges in applying graphene as a reinforcing component for the metal matrix composites and the potential solutions as well as prospectives of future development and opportunities are highlighted.
基金This work was supported in part by the Hunan Provincial Key Laboratory of Power Electronics Equipment and Grid under Grant 2018TP1001in part by the National Natural Science Foundation of China under Grant 61903382,51807206,61933011+1 种基金in part by the Major Project of Changzhutan Self-Dependent Innovation Demonstration Area under Grant 2018XK2002in part by the Natural Science Foundation of Hunan Province,China under Grant 2020JJ5722 and 2020JJ5753.
文摘To reduce the torque ripple in motors resulting from the use of conventional direct torque control(DTC),a model predictive control(MPC)-based DTC strategy for a direct matrix converter-fed induction motor is proposed in this paper.Two new look-up tables are proposed,these are derived on the basis of the control of the electromagnetic torque and stator flux using all the feasible voltage vectors and their associated switching states.Finite control set model predictive control(FCS-MPC)has then been adopted to select the optimal switching state that minimizes the cost function related to the electromagnetic torque.Finally,the experimental results are shown to verify the reduced torque ripple performance of the proposed MPC-based DTC method.
文摘An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to switch from bad to good status. A matrix based on error logic is used to express current status u, expectant status u1 and transformation matrix T. It is u, u1, and T that are used to build error matrix equation T (u)= u1. This allows us to find a method whereby bad status “u” changes to good status “u1” by solving the equation. The conversion method that transform from current to expectant status can be obtained from the transformation matrix T. On this basis, this paper proposes a new kind of error matrix equation named “containing-type error matrix equation”. This equation is more suitable for analyzing the realistic question. The method of solving, existence and form of solution for this type of equation have been presented in this paper. This research provides a potential useful new technique for decision analysis.
文摘Purpose: The Harmonic Neutron Hypothesis, HNH, has demonstrated that many of the fundamental physical constants, including the quarks, are associated with partial harmonic fractional exponents, , of a fundamental frequency, v<sub>F</sub>. The model has shown that the properties of the quarks are based on a progression of prime number composites. They also fall on three separate power law lines related to integer factors of the Y-intercept, , of a fundamental electromagnetic line which is scaled by the Rydberg constant, R and Planck’s constant. The quark lines are scaled by the quantum number factors {1, 2, 3}, and their Y-intercepts are referred to as n<sub>bem</sub>. The goal is to present a new proto-quark model in a six-quark inverted triangular array that defines the global organization of the valence quarks, which determines the hadronic quantum numbers, the standard hadron quark model, and the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Methods: The charm, bottom, top quarks are associated with power law line Y-intercept, n<sub>bem</sub> equal to 1;the strange and down quarks with n<sub>bem</sub> equal to 2;and the up quark with n<sub>bem</sub> equal to 3. An inverted equilateral triangular array with three rows arranged from upper row (triangle base) to bottom row (triangle vertex), is associated respectively with n<sub>bem</sub> numbers 1, 2, and 3. The novelty of our perspective thus defines a new global valence quark organization which supersedes the Standard hadron composite quark model. The quarks are ordered via relative mass, partial fractions, and n<sub>bem</sub> quantum number. The top row of our inverted triangle includes the c, b, and t quarks from left to right;the middle row depicts the d and s quarks;and the bottom row, the up quark. Results: Our array depicts a quantum generator of the global organization of the valence quarks defining the composite quark model. The vertices of the triangular array are the up quarks, the midpoints are the down quarks. All weak transitions are from a corner to a midpoint or vice versa. The standard 3 by 3 CKM matrix is generated from the new quark triangle with each up type quark (u, c, and t) transforming to each down type (d, s, and b), with their experimental flavor transition magnitudes given. Conclusion: A new quark quantum number, n<sub>bem</sub>, is an important discovery that generates a new proto-valence quark triangle that secondarily generates the composite quark model and the CKM matrix.
文摘The modified shear lag model proposed recently was applied to calculate thermal residual stresses and subsequent stress distributions under tensile and compressive loadings. The expressions for the elastic moduli and the yield strengths under tensile and compressive loadings were derived which take account of thermal residual stresses. The asymmetries in the elastic modulus and the yield strength were interpreted using the derived expressions and the obtained results of the stress calculations. The model predictions have exhibited good agreements with the experimental results and also with the other theoretical predictions
基金Supported by the National Natural Science Foundation of China(U1462206)
文摘To improve the naphtha composition prediction model based on molecular type homologous series matrix(MTHS), this paper puts forward a novel molecular matrix to characterize the naphtha composition and the normal distribution hypothesis to better describe the molecular composition distribution within each homologous series of the molecular matrix. Through prediction calculation of eight groups of naphtha samples and eight groups of gasoline samples, it is verified that the normal distribution hypothesis is more applicable than gamma distribution hypothesis for the prediction model. According to the prediction results of the samples,the restrain range of normal distribution parameters during model computing process is summarized. With the bulk properties of naphtha samples and the value range of distribution parameters as input conditions, this study utilizes the improved novel molecular matrix to predict the composition of naphtha samples. As the results show, the novel molecular matrix can predict more detailed composition information of naphtha and improve prediction accuracy with less unknown parameters.
文摘The expressions of matrix construction by using the singular value decomposition (SVD) are applied to the physics parameter identification of dynamic model. Then, based upon to the characteristics of a kind of matrix construction method, the orders of the parameter identification model can be reduced. After reducing, the mathematics and physics correspondence relations between the subsystem and the original system are distinct. the condensation errors can be avoided. The numerical example shows the benefit of the presented methodology.
基金supported by the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (0506011200702)National Natural Science Foundation of China+2 种基金Tian Yuan Special Foundation (10926059)Foundation of Zhejiang Educational Committee (Y200803920)Scientific Research Foundation of Hangzhou Dianzi University(KYS025608094)
文摘In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.
文摘The wear of cutting tools in the machining of 2024Al alloy composites reinforced with Al2O3 particles using varying sizes and volume fractions of particles up to 23.3vol% was investigated by a turning process using coated carbide tools K10 and TP30 at different cut- ting speeds. Machining tests were performed with a plan of experiments based on the Taguchi method. The tool life model was developed in terms of cutting speed, size, and volume fraction of particles by multiple linear regressions. The analysis of variance (ANOVA) was also employed to carry out the effects of these parameters on the cutting tool life. The test results show that the tool life decreases with the increase of cutting speed for both cutting tools K10 and TP30, and the tool life of the K10 tool is significantly longer than that of the TP30 tool. For the tool life, cutting speed is found to be the most effective factor followed by particle content and particle size, respectively. The predicted tool life of cutting tools is found to be in very good agreement with the experimentally observed ones.
基金Project supported by National Natural Science Foundation of China (Grant No .10271074)
文摘In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient.
文摘In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics,namely,susceptible(S),infected(I),treatment(T),and recovered(R).The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points.To indicate the usefulness of this method,we employ it in some cases.For error analysis of the method,the residual of the solutions is reviewed.The reported examples show that the method is reasonably efficient and accurate.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB30000000)the National Natural Science Foundation of China(Grant Nos.11774398 and T2121001)。
文摘We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.
文摘Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization problem. Usually, the rank of base matrix needs to be assumed. In this paper, we propose an unsupervised multi-level non-negative matrix factorization model to extract the hidden data structure and seek the rank of base matrix. From machine learning point of view, the learning result depends on its prior knowledge. In our unsupervised multi-level model, we construct a three-level data structure for non-negative matrix factorization algorithm. Such a construction could apply more prior knowledge to the algorithm and obtain a better approximation of real data structure. The final bases selection is achieved through L2-norm optimization. We implement our experiment via binary datasets. The results demonstrate that our approach is able to retrieve the hidden structure of data, thus determine the correct rank of base matrix.
文摘In the present work, a new method to predict the stress-strain curves for three-phase materials has been developed. It was applied using the example of an Mg-stabilized zirconia reinforced TRIP-matrix-composite. The content of the ceramic phase was varied between 5% and 20%, whereas the particle size of the ceramic was selected to be 30 to 50 μm. The method is a further development of mixture rule for multiphase materials with more than two microstructure components. The prediction results were compared with the original method of mixture rule and with the IsoE-method. It is shown that the new method significantly improves the convergence compared to the standard method for mixture rule, even though it does not reach the accuracy of IsoE-method. Furthermore, there is an improvement of predicted convergence for large values of the total stress. Finally, a working map was designed for a quick graphical definition of the objective functions.