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The purpose of this paper is to conveniently and accurately design partial knitting knitted fabrics based on matrix transformation.

Using mathematical modeling, the pattern diagram block matrix and process design matrix of partial knitting knitted fabrics are established, and the process knitting diagram with parameter information is generated. Based on the establishment of the mathematical model of the process knitting diagram, a loop deformation method based on three-dimensional (3D) coordinate point matrix transformation is proposed.

The matrix transformation method can provide a suitable deformed loop mode for partial knitting knitted fabrics and helps to generate a 3D modeling diagram conveniently.

This paper proposed a method of design and modeling of partial knitting knitted fabric based on matrix transformation. Taking the 3D modeling effect of conventional partial knitting as an example to test the modeling method, the results show that after matrix transformation, the loop model can realize the rapid transformation and calculation of the coordinates of the control point and generate a 3D modeling diagram.

The purpose of this paper is twofold: to improve the traditional conditional autoregressive Wishart (CAW) and heterogeneous autoregressive (HAR)-CAW model to account for heterogeneous leverage effect and to adjust the high-frequency volatility. The other is to confirm whether CAW-type models that have statistical advantages have economic advantages.

Based on the high-frequency data, this study proposed a new model to describe the volatility process according to the heterogeneous market hypothesis. Thus, the authors acquire needed and credible high-frequency data.

By designing two mean-variance frameworks and considering several economic performance measures, the authors find that compared with five other models based on daily data, CAW-type models, especially LHAR-CAW and HAR-CAW, indeed generate the substantial economic values, and matrix adjustment method significantly improves the three CAW-type performances.

The findings in this study suggest that from the aspect of economics, LHAR-CAW model can more accurately built the dynamic process of return rates and covariance matrix, respectively, and the matrix adjustment can reduce bias of realized volatility as covariance matrix estimator of return rates, and greatly improves the performance of unadjusted CAW-type models.

Compared with traditional low-frequency models, investors should allocate assets according to the LHAR-CAW model so as to get more economic values.

This study proposes LHAR-CAW model with the matrix adjustment, to account for heterogeneous leverage effect and empirically show their economic advantage. The new model and the new bias adjustment approach are pioneering and promote the evolution of financial econometrics based on high-frequency data.

In this “Info-plosion” era, recommendation systems (or recommenders) play a significant role in finding interesting items in the surge of online digital activity and e-commerce. The purpose of this paper is to model users' preference evolution to recommend potential items which users may be interested in.

A novel recommendation system, namely evolution-learning recommendation (ELR), is developed to precisely predict user interest for making recommendations. Differing from prior related methods, the authors integrate the matrix factorization (MF) and recurrent neural network (RNN) to effectively describe the variation of user preferences over time.

A novel cumulative factorization technique is proposed to efficiently decompose a rating matrix for discovering latent user preferences. Compared to traditional MF-based methods, the cumulative MF could reduce the utilization of computation resources. Furthermore, the authors depict the significance of long- and short-term effects in the memory cell of RNN for evolution patterns. With the context awareness, a learning model, V-LSTM, is developed to dynamically capture the evolution pattern of user interests. By using a well-trained learning model, the authors predict future user preferences and recommend related items.

Based on the relations among users and items for recommendation, the authors introduce a novel concept, virtual communication, to effectively learn and estimate the correlation among users and items. By incorporating the discovered latent features of users and items in an evolved manner, the proposed ELR model could promote “right” things to “right” users at the “right” time. In addition, several extensive experiments are performed on real datasets and are discussed. Empirical results show that ELR significantly outperforms the prior recommendation models. The proposed ELR exhibits great generalization and robustness in real datasets, including e-commerce, industrial retail and streaming service, with all discussed metrics.

Process mining provides a new means to improve processes in a variety of application domains. The purpose of this paper is to abstract a process model and then use the discovered models from process mining to make useful optimization via predictions.

The paper divides the process model into a combination of “pair-adjacent activities” and “pair-adjacent persons” in the event logs. First, two new handover process models based on adjacency matrix are proposed. Second, by adding the stage, frequency, and time for every activity or person into the matrix, another two new handover prediction process models based on stage adjacency matrix are further proposed. Third, compute the conditional probability from every stage to next stage through the frequency. Finally, use real data to analyze and demonstrate the practicality and effectiveness of the proposed handover optimization process.

The process model can be extended with information to predict what will actually happen, how possible to reach the next activity, who will do this activity, and the corresponding probability if there are several people executing the same activity, etc.

The contribution of this paper is to predict what will actually happen, how possible it is to reach the following activities or persons in the next stage, how soon to reach the following activities or persons by calculating all the possible interval time via different traces, who will do this activity, and the corresponding probability if there are several people executing the same activity, etc.

The purpose of this paper is to investigate the stress distribution in shape memory alloy (SMA) composite due to phase transformations in the fiber in view of the applied boundary conditions on the matrix.

A consistent homogenization of a SMA wire‐reinforced polymer composite volume element undergoing quasi‐static deformation was performed and SMA wire‐matrix interface behaviour was presented. For the SMA wire, a one‐dimensional phenomenological constitutive model was used. Eshelby's inclusion theory was employed for homogenization. A strain averaging approach was reviewed in which the average strain was substituted back to obtain the expressions for the effective stiffness, the inelastic strain, and the average stresses in the constituent phases. In order to study the stress distribution in SMA composite and constituent phases (fiber and matrix) as a consequence of the SMA wire‐matrix interface effect, interfacial stress model was derived. Interfacial axial and shear stress distribution is characterized for forward and reverse phase transformations. Finally, the thermomechanical behaviours were computed by applying strain energy approach incorporating the interface effects.

The results presented show that due to the difference between the shear modulus of matrix and SMA wire, and because of the strain non‐uniformity at the SMA wire‐matrix interface, shear stress is developed within the matrix under the axial loading of the representative volume element (RVE). The shear stress increases more rapidly as the SMA wire radius is increased but not with increase in the length. However, the axial stress does not increase much with increase in the SMA wire radius and length. Further, the average stress equation of the RVE at the SMA wire‐matrix interface is effectively addressed. The modeling approach is successfully validated extensively for different geometric and volumetric parameters for different loading conditions. It is evident that the interface effect of SMA wire composites is SMA stiffness dominated due to the fact that the geometric parameters do not influence much the stresses as compared to the change in SMA wire stiffness.

The approach is based on modeling the fiber matrix interface effect using homogenization scheme. Further, the strain energy approach is applied to compute the stress‐strain response. This indicates the importance of modeling the SMA wire‐matrix interface effect, and in particular, the energy exchange between the constituent phases. The results have been compared for different geometric parameters as well as volume fractions of the constituent phases under different loading conditions.

The purpose of this paper is to attempt to integrate manufacturing system analysis to obtain system‐wide optimized solutions and to increase the level of comprehensiveness of the manufacturing system modelling and to develop method of characterization of manufacturing systems based on its structure.

Elements constituting the manufacturing plant and the interactions between them have been identified through a literature survey and have been represented by graph‐based model. The matrix models and the variable permanent function models are developed for carrying out decomposition, characterization and the total analysis.

Structural patterns and combination sets of subsystems interacting in various ways have been recognized as capabilities of manufacturing system in different performance dimensions. The permanent function of the manufacturing system matrix has been proposed as a systematic technique for structural analysis of manufacturing system. Also, the terms of permanent multinomial characterize the manufacturing systems uniquely and are highly useful for computational storage, retrieval, communication as well as analysis of the structural information of manufacturing system.

The structure‐based characterization technique developed has the potential of aiding the ongoing research activities in the field of benchmarking, and business process reengineering. The graph theory‐based methodology will serve as a framework to develop composite performance measures building on the performance measures of the individual elements of the manufacturing system graph in various dimensions.

Through the use of proposed methodology, a manufacturing manager will be able to make better informed decisions towards organizational efforts of improving the productivity and speed. For aiding several decisions, different “what‐if” scenarios may be generated with several structural modifications.

This graph theory‐based methodology is a novel mechanism to seamlessly integrate manufacturing system giving way to system wide optimization. The paper is an attempt to address the need for comprehensive and integrated analysis of the manufacturing system.

A multi-physics process model is developed to analyze reactive melt infiltration (RMI) fabrication of ceramic-matrix composite (CMC) materials and components. The paper aims to discuss this issue.

Within this model, the following key physical phenomena governing this process are accounted for: capillary and gravity-driven unsaturated flow of the molten silicon into the SiC/SiC CMC preform; chemical reactions between the silicon melt and carbon (either the one produced by the polymer-binder pyrolysis or the one residing within the dried matrix slurry); thermal-energy transfer and source/sink phenomena accompanying reactive-flow infiltration; volumetric changes accompanying chemical reactions of the molten silicon with the SiC preform and cooling of the as-fabricated CMC component to room temperature; development of residual stresses within, and thermal distortions of, the as-fabricated CMC component; and grain-microstructure development within the SiC matrix during RMI.

The model is validated, at the material level, by comparing its predictions with the experimental and modeling results available in the open literature. The model is subsequently applied to simulate RMI fabrication of a prototypical gas-turbine engine hot-section component, i.e. a shroud. The latter portion of the work revealed the utility of the present computational approach to model fabrication of complex-geometry CMC components via the RMI process.

To the authors’ knowledge, the present work constitutes the first reported attempt to apply a multi-physics RMI process model to a gas-turbine CMC component.

The purpose of this paper is to overcome the shortcomings of existing multivariate grey incidence models that cannot analyze the similarity of behavior matrixes.

First, the feasibility of using gradient to measure the similarity of continuous functions is analyzed theoretically and intuitively. Then, a grey incidence degree is constructed for multivariable continuous functions. The model employs the gradient to measure the local similarity, as incidence coefficient function, of two functions, and combines local similarity into global similarity, as grey incidence degree by double integral. Third, the gradient incidence degree model for behavior matrix is proposed by discretizing the continuous models. Furthermore, the properties and satisfaction of grey incidence atom of the proposed model are research, respectively. Finally, a financial case is studied to examine the validity of the model.

The proposed model satisfies properties of invariance under mean value transformation, multiple transformation and linear transformation, which proves it is a model constructed from similarity perspective. Meanwhile, the case study shows that proposed model performs effectively.

The method proposed in the paper could be used in financial multivariable time series clustering, personalized recommendation in e-commerce, etc., when the behavior matrixes need to be analyzed from trend similarity perspective.

It will promote the accuracy of multivariate grey incidence model.

The purpose is to reduce round-off errors in numerical simulations. In the numerical simulation, different kinds of errors may be created during analysis. Round-off error is one of the sources of errors. In numerical analysis, sometimes handling numerical errors is challenging. However, by applying appropriate algorithms, these errors are manageable and can be reduced. In this study, five novel topological algorithms were proposed in setting up a structural flexibility matrix, and five different examples were used in applying the proposed algorithms. In doing so round-off errors were reduced remarkably.

Five new algorithms were proposed in order to optimize the conditioning of structural matrices. Along with decreasing the size and duration of analyses, minimizing analytical errors is a critical factor in the optimal computer analysis of skeletal structures. Appropriate matrices with a greater number of zeros (sparse), a well structure and a well condition are advantageous for this objective. As a result, a problem of optimization with various goals will be addressed. This study seeks to minimize analytical errors such as rounding errors in skeletal structural flexibility matrixes via the use of more consistent and appropriate mathematical methods. These errors become more pronounced in particular designs with ill-suited flexibility matrixes; structures with varying stiffness are a frequent example of this. Due to the usage of weak elements, the flexibility matrix has a large number of non-diagonal terms, resulting in analytical errors. In numerical analysis, the ill-condition of a matrix may be resolved by moving or substituting rows; this study examined the definition and execution of these modifications prior to creating the flexibility matrix. Simple topological and algebraic features have been mostly utilized in this study to find fundamental cycle bases with particular characteristics. In conclusion, appropriately conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.

(1) Five new algorithms were proposed in order to optimize the conditioning of structural flexibility matrices. (2) A JAVA programming language was written for all five algorithms and a friendly GUI software tool is developed to visualize sub-optimal cycle bases. (3) Topological and algebraic features of the structures were utilized in this study.

This is a multi-objective optimization problem which means that sparsity and well conditioning of a matrix cannot be optimized simultaneously. In conclusion, well-conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.

Engineers always finding mathematical modeling of real-world problems and make them as simple as possible. In doing so, lots of errors will be created and these errors could cause the mathematical models useless. Applying decent algorithms could make the mathematical model as precise as possible.

Errors in numerical simulations should reduce due to the fact that they are toxic for real-world applications and problems.

This is an original research. This paper proposes five novel topological mathematical algorithms in order to optimize the structural flexibility matrix.