Modified molecular matrix model for predicting molecular composition of naphtha＇

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.

New Algebraic Structures from Hermitian One-Matrix Model

Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field Theory （CFT） method. From multi-loop equations of the one-matrix model, we get a more general constraint. It can be expressed in terms of the operator algebras, which is the Virasoro subalgebra with extra parameters. In this sense, we named as generalized Virasoro constraint. We enlarge this algebra with central extension, this is a new kind of algebra, and the usual Virasoro algebra is its subalgebra. And we give a bosonic realization of its subalgebra.

Ripple-based matrix modeling and cross-coupling effect analysis of double-input DC-DC Boost converters

This paper deals with the modeling and cross-coupling effect analysis in double-input Boost converters with multiplex current control. A ripple-based multiplex current controlled matrix model is proposed to restore the system's high-frequency domain dynamics information and resolve the coexistence problem of the sample-and-hold effect in multiplex current controllers, which significantly improves the resolution of the conventional average model. Based on the proposed model, both sub-harmonic and low-frequency oscillations are identified in terms of stability analysis, and the inherent mechanism of these complicated nonlinear dynamic behavior is revealed, which not only illustrates the origin of the oscillations but also points out the dominant factors in diverse types of instability situation. Besides, cross-coupling effect analysis is performed to study the interaction between the input ports with the help of the Gershgorin band, and the mechanism of the special unbalanced oscillation phenomenon is revealed. Furthermore, the sensitivity analysis approach is used to identify the key parameters with respect to the cross-coupling effect, which provides more design-oriented knowledge for practical engineering. In addition, the benefits of the proposed model are further illustrated through a comparative analysis. Finally, these theoretical results are verified by experimental ones. These results are beneficial to the improvement of performance as well as the understanding of the cross-coupling effect of multi-input converters.

Theory-Intelligent Dynamic Matrix Model of Flatness Control for Cold Rolled Strips

In order to increase the precision of flatness control, considering the principle and the measured data of rolling process essence, the theory-intelligent dynamic matrix model of flatness control is established by using theory and in-telligent methods synthetically. The network model for rapidly calculating the theory effective matrix is established by the BP network optimized by the particle swarm algorithm. The network model for rapidly calculating the meas- urement effective matrix is established by the RBF network optimized by the cluster algorithm. The flatness control model can track the practical situation of roiling process by on-line selVlearning. The scheme for flatness control quantity calculation is established by combining the theory control matrix and the measurement control matrix. The simulation result indicates that the establishment of theory-intelligent dynamic matrix model of flatness control with stable control process and high precision supplies a new way and method for studying flatness on-line control model.

Error propagation with R-matrix model fitting

The error propagation features with R-matrix model fitting 7Li, 11B and 17O systems have been researched systematically. Some laws of error propagation have been revealed, an experience formula for describing standard error propagation has been established, and the most possible error range for evaluated standard cross section of 6Li (n, α), 10B (n, α) and 10B (n, α1) has been determined.

Modeling mechanism of a novel fractional grey mode based on matrix analysis

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.

Derived vascular endothelial cells induced by mucoepidermoid carcinoma cells:3-dimensional collagen matrix model

Mucoepidermoid carcinoma undergoes uniquely vigorous angiogenic and neovascularization processes,possibly due to proliferation of vascular endothelial cells(ECs) induced by mucoepidermoid carcinoma cells(MCCs) in their three-dimensional(3D) microenvironment.To date,no studies have dealt with tumor cells and vascular ECs from the same origin of mucoepidermoid carcinoma using the in vitro 3D microenvironment model.In this context,the current research aims to observe neovascularization with mucoepidermoid carcinoma microvascular ECs(MCMECs) conditioned by the microenvironment in the 3D collagen matrix model.We observed the growth of MCMECs purified by immunomagnetic beads and induced by MCCs,and characteristics of tubule-like structures(TLSs) formed by induced MCMECs or non-induced MCMECs.The assessment parameters involved the growth curve,the length,the outer and inner diameters,and the wall thickness of the TLSs,and the cell cycle.Results showed that MCCs induced formation of the TLSs in the 3D collagen matrix model.A statistically significant difference was noted regarding the count of TLSs between the control group and the induction group on the 4th day of culture(t=5.00,P=0.001).The outer and inner diameters(t1=5.549,P1=0.000;t2=10.663,P2=0.000) and lengths(t=18.035,P=0.000) of the TLSs in the induction group were statistically significant larger than those in the control group.The TLSs were formed at the earlier time in the induction group compared with the control group.It is concluded that MCCs promote growth and migration of MCMECs,and formation of the TLSs.The 3D collagen matrix model with MCMECs induced by MCCs in the current research may be a favorable choice for research on pro-angiogenic factors in progression of mucoepidermoid carcinoma.

A SCATTERING MATRIX MODEL OF SEMICONDUCTOR SUPERLATTICES IN MULTIDIMENSIONAL WAVE-VECTOR SPACE AND ITS DIFFUSION LIMIT

The authors first establish a quantum microscopic scattering matrix model in multidimen-sional wave-vector space, which relates the phase space density of each superlattice cell withthat of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (SphericalHarmonics Expansion)-type model of diffusion equations for the particle number density in theposition-energy space is obtained. The crucial features of diffusion constants on retaining thememory of the quantum scattering characteristics of the superlattice elementary cell (like e.g.transmission resonances) are shown in order. Two examples are treated with the analyticallycomputation of the diffusion constants.

A Study Regarding Solution of a Knowledge Model Based on the Containing-Type Error Matrix Equation

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.

Unsupervised Multi-Level Non-Negative Matrix Factorization Model: Binary Data Case

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.

Model Reduction via Reducibility Matrix

In this work, a new model reduction technique is introduced. The proposed technique is derived using the matrix reducibility concept. The eigenvalues of the reduced model are preserved; that is, the reduced model eigenvalues are a subset of the full order model eigenvalues. This preservation of the eigenvalues makes the mathematical model closer to the physical model. Finally, the outcomes of this method are fully illustrated using simulations of two numeric

IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

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.

A New Quantum Number Triangular Array That Defines the Internal Organization of Valence Quarks, the Hadron Quark Model, and the CKM Matrix

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, vF. 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 nbem. 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, nbem equal to 1;the strange and down quarks with nbem equal to 2;and the up quark with nbem 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 nbem 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 nbem 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, nbem, is an important discovery that generates a new proto-valence quark triangle that secondarily generates the composite quark model and the CKM matrix.

Simplified prediction model for elastic modulus of particulate reinforced metal matrix composites

Some structural parameters of the metal matrix composite, including particulate shape and distribution do not influence the elastic modulus. A prediction model for the elastic modulus of particulate reinforced metal matrix Al composite was developed and improved. Expressions of rigidity and flexibility of the rule of mixing were proposed. A five-zone model for elasticity performance calculation of the composite was proposed. The five-zone model is thought to be able to reflect the effects of the MMC interface on elastic modulus of the composite. The model overcomes limitations of the currently-understood rigidity and flexibility of the rule of mixing. The original idea of a five-zone model is to propose particulate/interface interactive zone and matrix/interface interactive zone. By integrating organically with the law of mixing, the new model is found to be capable of predicting the engineering elastic constants of the MMC composite.

Tool life modeling for evaluating the effects of cutting speed and reinforcements on the machining of particle reinforced metal matrix composites

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.

Simplification and improvement of prediction model for elastic modulus of particulate reinforced metal matrix composite

In this paper, we proposed a five-zone model to predict the elastic modulus of particulate reinforced metal matrix composite. We simplified the calculation by ignoring structural parameters including particulate shape, arrangement pattern and dimensional variance mode which have no obvious influence on the elastic modulus of a composite, and improved the precision of the method by stressing the interaction of interfaces with pariculates and maxtrix of the composite. The five- zone model can reflect effects of interface modulus on elastic modulus of composite. It overcomes limitations of expressions of rigidity mixed law and flexibility mixed law. The original idea of five zone model is to put forward the particulate/interface interactive zone and matrix/interface interactive zone. By organically integrating the rigidity mixed law and flexibility mixed law, the model can predict the engineering elastic constant of a composite effectively.

Finite element model for arch bridge vibration dynamics considering effect of suspender length adjustment on geometry stiffness matrix

In this paper, we established a finite element (FEM) model to analyze the dynamic characteristics of arch bridges. In this model, the effects of adjustment to the length of a suspender on its geometry stiffness matrix are stressed. The FEM equations of mechanics characteristics, natural frequency and main mode are set up based on the first order matrix perturbation theory. Applicantion of the proposed model to analyze a real arch bridge proved the improvement in the simulation precision of dynamical characteristics of the arch bridge by considering the effects of suspender length variation.

Mechanical Behaviour Modelling of an Mg-Stabilized Zirconia Reinforced TRIP-Matrix-Composite under Cold Working Conditions

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.

Modeling One Dimensional Two-Cell Model with Tumor Interaction Using Krylov Subspace Methods

A brain tumor occurs when abnormal cells grow, sometimes very rapidly, into an abnormal mass of tissue. The tumor can infect normal tissue, so there is an interaction between healthy and infected cell. The aim of this paper is to propose some efficient and accurate numerical methods for the computational solution of one-dimensional continuous basic models for the growth and control of brain tumors. After computing the analytical solution, we construct approximations of the solution to the problem using a standard second order finite difference method for space discretization and the Crank-Nicolson method for time discretization. Then, we investigate the convergence behavior of Conjugate gradient and generalized minimum residual as Krylov subspace methods to solve the tridiagonal toeplitz matrix system derived.