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Recently, electroencephalography (EEG) signals have shown great potential for emotion recognition. Nevertheless, multichannel EEG recordings lead to redundant data, computational burden, and hardware complexity. Hence, efficient channel selection, especially single-channel selection, is vital. For this purpose, a technique termed brain rhythm sequencing (BRS) that interprets EEG based on a dominant brain rhythm having the maximum instantaneous power at each 0.2 s timestamp has been proposed. Then, dynamic time warping (DTW) is used for rhythm sequence classification through the similarity measure. After evaluating the rhythm sequences for the emotion recognition task, the representative channel that produces impressive accuracy can be found, which realizes single-channel selection accordingly. In addition, the appropriate time segment for emotion recognition is estimated during the assessments. The results from the music emotion recognition (MER) experiment and three emotional datasets (SEED, DEAP, and MAHNOB) indicate that the classification accuracies achieve 70-82% by single-channel data with a 10 s time length. Such performances are remarkable when considering minimum data sources as the primary concerns. Furthermore, the individual characteristics in emotion recognition are investigated based on the channels and times found. Therefore, this study provides a novel method to solve single-channel selection for emotion recognition.

In 2020, an unexpectedly large outbreak of the coronavirus disease 2019 (COVID-19) epidemic was reported in mainland China. As we known, the epidemic was caused by imported cases in other provinces of China except for Hubei in 2020. In this paper, we developed a differential equation model with tracing isolation strategy with close contacts of newly confirmed cases and discrete time imported cases, to perform assessment and risk analysis for COVID-19 outbreaks in Tianjin and Chongqing city. Firstly, the model behavior without imported cases was given. Then, the real-time regeneration number in Tianjin and Chongqing city revealed a trend of rapidly rising, and then falling fast. Finally, sensitivity analysis demonstrates that the earlier with Wuhan lock-down, the fewer cases in these two cities. One can obtain that the tracing isolation of close contacts of newly confirmed cases could effectively control the spread of the disease. But it is not sensitive for the more contact tracing isolation days on confirmed cases, the fewer cases. Our investigation model could be potentially helpful to provide model building technology for the transmission of COVID-19.

Due to the strong infectivity of COVID-19, it spread all over the world in about three months and thus has been studied from different aspects including its source of infection, pathological characteristics, diagnostic technology and treatment. Yet, the influences of control strategies on the transmission dynamics of COVID-19 are far from being well understood. In order to reveal the mechanisms of disease spread, we present dynamical models to show the propagation of COVID-19 in Wuhan. Based on mathematical analysis and data analysis, we systematically explore the effects of lockdown and medical resources on the COVID-19 transmission in Wuhan. It is found that the later lockdown is adopted by Wuhan, the fewer people will be infected in Wuhan, and nevertheless it will have an impact on other cities in China and even the world. Moreover, the richer the medical resources, the higher the peak of new infection, but the smaller the final scale. These findings well indicate that the control measures taken by the Chinese government are correct and timely.

Since December 2019, an outbreak of a novel coronavirus pneumonia (WHO named COVID-19) swept across China. In Shanxi Province, the cumulative confirmed cases finally reached 133 since the first confirmed case appeared on January 22 2020, and most of which were imported cases from Hubei Province. Reasons for this ongoing surge in Shanxi province, both imported and autochthonous infected cases, are currently unclear and demand urgent investigation. In this paper, we developed a SEIQR difference-equation model of COVID-19 that took into account the transmission with discrete time imported cases, to perform assessment and risk analysis. Our findings suggest that if the lock-down date in Wuhan is earlier, the infectious cases are fewer. Moreover, we reveal the effects of city lock-down date on the final scale of cases: if the date is advanced two days, the cases may decrease one half (67, 95% CI: 66–68); if the date is delayed for two days, the cases may reach about 196 (95% CI: 193–199). Our investigation model could be potentially helpful to study the transmission of COVID-19, in other provinces of China except Hubei. Especially, the method may also be used in countries with the first confirmed case is imported.

The similarity is a fundamental measure from the homology theory in bioinformatics, and the biological sequence can be classified based on it. However, such an approach has not been utilized for electroencephalography (EEG)-based emotion recognition. To this end, the sequence generated by choosing the dominant brain rhythm owning maximum instantaneous power at each 0.2 s timestamp of the EEG signal has been proposed. Then, to recognize emotional arousal and valence, the similarity measures between pairwise sequences have been performed by dynamic time warping (DTW). After evaluations, the sequence that provides the highest accuracy has been obtained. Thus, the representative channel has been found. Besides, the appropriate time segment for emotion recognition has been estimated. Those findings helpfully exclude redundant data for assessing emotion. Results from the DEAP dataset displayed that the classification accuracies between 72%-75% can be realized by applying the single-channel data with a 5 s length, which is impressive when considering fewer data sources as the primary concern. Hence, the proposed idea would open a new way that uses the similarity measures of sequences for EEG-based emotion recognition.

Brucellosis is one of the worlds major infectious and contagious bacterial disease. In order to study different types of brucellosis transmission models among sheep, we propose a deterministic model to investigate the transmission dynamics of brucellosis with the flock of sheep divided into basic ewes and other sheep. The global dynamical behavior of this model is given: including the basic repro-duction number, the existence and uniqueness of positive equilibrium, the global asymptotic stability of the equilibrium. We prove the uniqueness of positive endemic equilibrium through using proof by contradiction, and the global stability of endemic equilibrium by using Lyapunov function. Especially, we give the specific coefficients of global Lyapunov function, and show the calculation method of these specific coefficients. By running numerical simulations for the cases with the basic reproduction number to demonstrate the global stability of the equilibria and the unique endemic equilibrium, re-spectively. By some sensitivity analysis of the basic reproduction number on parameters, we find that vaccination rate of sheep and seropositive detection rate of recessive infected sheep are very important factor for brucellosis.

An outbreak of rapidly spreading coronavirus established human to human transmission and now became a pandemic across the world. The new confirmed cases of infected individuals of COVID-19 are increasing day by day. Therefore, the prediction of infected individuals has become of utmost important for health care arrangements and to control the spread of COVID-19. In this study, we propose a compartmental epidemic model with intervention strategies such as lockdown, quarantine, and hospitalization. We compute the basic reproduction number (R0), which plays a vital role in mathematical epidemiology. Based on R0, it is revealed that the system has two equilibrium, namely disease-free and endemic. We also demonstrate the non-negativity and boundedness of the solutions, local and global stability of equilibria, transcritical bifurcation to analyze its epidemiological relevance. Furthermore, to validate our system, we fit the cumulative and new daily cases in India. We estimate the model parameters and predict the near future scenario of the disease. The global sensitivity analysis has also been performed to observe the impact of different parameters on R0. We also investigate the dynamics of disease in respect of different situations of lockdown, e.g., complete lockdown, partial lockdown, and no lockdown. Our analysis concludes that if there is partial or no lockdown case, then endemic level would be high. Along with this, the high transmission rate ensures higher level of endemicity. From the short time prediction, we predict that India may face a crucial phase (approx 6000000 infected individuals within 140 days) in near future due to COVID-19. Finally, numerical results show that COVID-19 may be controllable by reducing the contacts and increasing the efficacy of lockdown.

Brucellosis, the most common zoonotic disease worldwide, represents a great threat to animal husbandry with the potential to cause enormous economic losses. Meanwhile, brucellosis is one of the major public-health problems in China, and the number of human brucellosis cases has increased dramatically in recent years. In order to show the main features of brucellosis transmission in China, we give a systematic review on the transmission dynamics of brucellosis including a series of mathematical models and their applications in China. For different situations, dynamical models of brucellosis transmission in single population and multiple populations are devised based on ordinary differential equations. Furthermore, we revealed the spatial-temporal characteristics and effective control measures of brucellosis transmission. The results may provide new perspectives for the prevention and control of other types of zoonoses.

When everyone focuses on 2019 coronavirus disease (COVID-19) in Hubei province, the epidemic in other province cannot be ignored, which also has an impact on the epidemic in the whole country. The most distinctive epidemic characteristic in all regions except Wuhan is that the most of confirmed cases are imported cases from Wuhan, and the propagation chain is relatively clear. Based on detailed contact tracing information of confirmed cases, combined with first-order outbreak response measures, we establish a disease transmission dynamical model to describe the infection propagation chain among the human population. Using Shanxi province as a case, modeling results indicate that the epidemic peak in Shanxi province occurred in February 2. In addition, our model suggests that according to the current development trend, COVID-19 will disappear in February with the final epidemic number of approximately 175 cases. It is verified that the most effective outbreak control measures in Shanxi include home isolation of people, surveillance and isolation of second-generation cases, contact tracing and management of contacts. With the end of the holiday, if the average number of contacts per person per day is less than 6 , it has little impact on the incidence of COVID-19, and even if third- and fourth-generation cases occur, the epidemic will be under control, no later than late March with a finial outbreak size of 220 cases. However, if the average number of contacts per person per day is greater than 6, the number of COVID-19 cases will continue to be reported resulting in another epidemic peak. Through the forecast and evaluation of COVID-19 in Shanxi, it is verified that the model with infection generations is more accurate to describe the spread mode and can be extended to regions with imported cases.

FGFs and their receptors (FGFRs) are critical for many biologic processes, including angiogenesis, wound healing and tissue regeneration. Aberrations in FGFR signaling are common in cancer, making FGFRs a promising target in antitumor studies. To date, many FGFR inhibitors are being detected in clinical studies, and resistance to some inhibitors has emerged. Understanding the mechanisms of resistance is a fundamental step for further implementation of targeted therapies. In this review, we will describe the basic knowledge regarding FGF/FGFR signaling and categorize the clinical FGFR inhibitors. The mechanisms of resistance to FGFR inhibitors and corresponding strategies of overcoming drug resistance will also be discussed.

Cholera, as an endemic disease around the world, has generated great threat to human society and caused enormous morbidity and mortality with weak surveillance system. In this paper, we propose a mathematical model to describe the transmission of Cholera. Moreover, basic reproduction number and the global dynamics of the dynamical model are obtained. Then we apply our model to characterize the transmission process of Cholera in China. It was found that, in order to avoid its outbreak in China, it may be better to increase immunization coverage rate and make effort to improve environmental management especially for drinking water. Our results may provide some new insights for elimination of Cholera.

The survival of pathogens outside the host in the environment is an important factor for some diseases transmission. Environment-to-individuals is an indirect mode of transmission, which also plays a role in the dynamics of some disease. In this paper, we proposed a general multi-group epidemic model with nonlinear direct and indirect transmission incidence rates, nonlinear pathogen shedding rates, and common environmental contamination for indirect transmission. Under the certain assumptions, the basic reproduction number of the model is identified. We proved the global stability of the equilibria by using global Lyapunov functions with the specific coefficients and graph-theoretical approach theorem, which are determined by the basic reproduction number. The main result of our model is that we give the specific coefficients of global Lyapunov functions. From the discussion of our model, we conclude that our model contains earlier cholera models, brucellosis models, and other general disease multi-group models as special cases.

In China, foot-and-mouth disease (FMD) serotype O remains prevalent, and its main host is pigs. Infected but undiscovered pigs can carry foot-and-mouth disease virus (FMDV) for a longtime. And, the virus can spread among farms through pig trade. Although individual vaccination at least 2 times a year and monthly monitoring disease and culling all individual in same group for pigs are adopted vigorously in China, the epidemic remains prevalent. Therefore, in this paper, based on these propagation characteristics and control measures of the epidemic in China, we take the pig farms as research individuals, the trade among farms as transmission routes to establish a dynamic model with nonlinear incidence. In addition, we use this model to assess the impact of trade and transport of pigs among farms on the spread of foot-and-mouth disease virus (FMDV), and to assess the effect of the immunization, monitoring and culling adopted presently in China on the control of the epidemic. By the dynamical analysis of the model, it is found that there will appear backward branching under some conditions, which means that there are two spreading thresholds for the disease, and the disease development trend is also related to the current epidemic situation. Besides, we give the threshold conditions of key parameters to control the spread of FMD. By carrying out data fitting and parameter estimation, we confirm the model rationality, and give four evaluation indexes: the basic reproduction number R0 of FMD serotype O in China, the value of the infected farms at the equilibria, annual probability of a susceptible farm being infected and annual transmission intensity of an infected farm. By carrying out the sensitivity analysis of key parameters on four evaluation indexes, the effect of parameters on the spread of the disease can be intuitively observed. All these can provide a theoretical basis for understanding of the trading-based transmission mechanism, control and prevention of foot-and-mouth disease in pigs in China.

A general mathematical model for schistosomiasis is formulated that incorporates the miracidia and cercariae dynamics, since parasites play an important role in the transmission dynamics of schistosomiasis. Under the biologically motivated assumptions, the basic reproduction number R 0 is defined and shown to give a sharp threshold that determines whether or not the disease dies out. By using Lyapunov functions, we conclude that if R 0 1 , then the disease-free equilibrium is globally asymptotically stable, and schistosomiasis dies out; if R 0 > 1 , then the disease-free equilibrium is unstable, a unique endemic equilibrium is globally asymptotically stable, and schistosomiasis persists at a positive level.

Background Parkinson’s disease (PD) is one of the most common neurodegenerative diseases, neuropathologically characterized by misfolded protein aggregation, called Lewy bodies and Lewy neurites. PD is a slow-progressive disease with colonic dysfunction appearing in the prodromal stage and lasting throughout the course of the disease. Methods In order to study PD pathology in the colon, we examined the age-dependent morphological and pathological changes in the colon of a PD mouse model expressing human wildtype α-synuclein (α-syn) fused with the green fluorescent protein (GFP), under the endogenous mouse α-syn promoter. Results We observed an age-dependent progressive expression and accumulation of α-syn-GFP in the enteric neurons of Meissner’s (submucosal) and Auerbach’s (myenteric) plexuses of the colon. Additionally, the phosphorylation of α-syn at serine 129 also increased with age and the aggregation of α-syn-GFP coincided with the appearance of motor deficits at 9 months of age. Furthermore, α-syn (-GFP) distinctly co-localized with different subtypes of neurons, as identified by immunohistochemical labeling of vasoactive intestinal peptide (VIP), neuronal nitric oxide synthase (nNOS), and calretinin. Conclusions Our results show the development of α-syn pathology in the enteric neurons of the colon in a PD mouse model, which coincide with the appearance of motor deficits. Our mouse model possesses the potential and uniqueness for studying PD gastrointestinal dysfunction. Electronic supplementary material The online version of this article (10.1186/s40035-018-0118-8) contains supplementary material, which is available to authorized users.

Based on the double member model of wall-frame structure and the corresponding transfer matrix method, the concept of frequent impedance of rigid foundation is introduced so that SSI can be taken into account. This method is more convenient and efficient compared to finite element method because of fewer structural parameters and faster calculation speed. Necessary structure parameters include 7 parameters of each storey, geometry size and total mass of foundation and elastic parameters of site soil. Totally 39 examples were calculated for 13 values of foundation mass and 3 kinds of soil, which are compared to the result of fix bottom model of upper structure. Results show that SSI does not always deduce a decrease of seismic response. Sometimes SSI may increases structural displacement evidently. The simplified method would provide structure designers an efficient tool to understand seismic behavior of wall-frame structures with various foundation and site soil.

Tuberculosis (TB), an air-borne infectious disease, is a major public-health problem in China. The reported number of the active tuberculosis cases is about one million each year. The morbidity data for 2005–2012 reflect that the difference in morbidity based on age group is significant, thus the role of age-structure on the transmission of TB needs to be further developed. In this work, based on the reported data and the observed morbidity characteristics, we propose a susceptible-exposed-infectious-recovered (SEIR) epidemic model with age groupings, involving three categories: children, the middle-aged, and senior to investigate the role of age on the transmission of tuberculosis in Mainland China from 2005 to 2016. Then, we evaluated the parameters by the Least Square method and simulated the model and it had good alignment with the reported infected TB data in Mainland China. Furthermore, we estimated the basic reproduction number R0 of 1.7858, with an obtained 95% confidence interval for R0 of (1.7752, 1.7963) by Latin hypercube sampling, and we completed a sensitivity analysis of R0 in terms of some parameters. Our study demonstrates that diverse age groups have different effects on TB. Two effective measures were found that would help reach the goals of theWorld Health Organization (WHO) End TB Strategy: an increase in the recovery rate and the reduction in the infectious rate of the senior age group.

Brucellosis, the most common zoonotic disease worldwide, represents a great threat to animal husbandry with the potential to cause enormous economic losses. Brucellosis has become a major public health problem in China, and the number of human brucellosis cases has increased dramatically in recent years. In order to evaluate different intervention strategies to curb brucellosis transmission in China, a novel mathematical model with a general indirect transmission incidence rate was presented. By comparing the results of three models using national human disease data and 11 provinces with high case numbers, the best fitted model with standard incidence was used to investigate the potential for future outbreaks. Estimated basic reproduction numbers were highly heterogeneous, varying widely among provinces. The local basic reproduction numbers of provinces with an obvious increase in incidence were much larger than the average for the country as a whole, suggesting that environment-to-individual transmission was more common than individual-to-individual transmission. We concluded that brucellosis can be controlled through increasing animal vaccination rates, environment disinfection frequency, or elimination rates of infected animals. Our finding suggests that a combination of animal vaccination, environment disinfection, and elimination of infected animals will be necessary to ensure cost-effective control for brucellosis.

Brucellosis is one of the major public health problems in China, since there is a very large number of cattle and sheep. While the mixed feeding between cattle and sheep in public farm is one of the most typical characteristics in brucellosis outbreak regions, which has a large influence on the spreading of brucellosis. In this paper, we propose a multi-group SEIRV dynamical model with bidirectional mixed cross infection between cattle and sheep, and aim to investigate the influence of cross infection of mixed feeding on the brucellosis transmission. Firstly, we obtain the basic reproduction number R 0 , confirm the uniform existence and unique positive equilibrium of dynamic model when R 0 > 1 and prove the global stability of endemic equilibrium when R 0 > 1 . In addition, sensitivity analysis of the infectious herds with different system in term of some parameter values are given. It is found that if there exists the bidirectional of mixed cross infection between cattle and sheep, the disease cannot disappear even though R 01 1 and R 02 1 . These findings have important implication for brucellosis control: if we want to eliminate the brucellosis, firstly we should take measures to remove mixed cross infection, i.e., to prohibit mixed feeding.

Streptococcosis is one of the major infectious and contagious bacterial diseases for swine farm in southern China. The influence of various control measures on the outbreaks and transmission ofS. suisis not currently known. In this study, in order to explore effective control and prevention measures we studied a deterministic dynamic model with stage structure forS. suis. The basic reproduction numberℛ0is identified and global dynamics are completely determined byℛ0. It shows that ifℛ0<1, the disease-free equilibrium is globally stable and the disease dies out, whereas ifℛ0>1, there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. The model simulations well agree with new clinical cases and the basic reproduction number of this model is about 1.1333. Some sensitivity analyses ofℛ0in terms of the model parameters are given. Our study demonstrates that combination of vaccination and disinfection of the environment are the useful control strategy forS. suis.

Smoothed finite element method (S-FEM) based on triangular elements has recently been widely used for solving solid mechanics problems. In this paper, a novel [Formula: see text]S-FEM using quadrilateral elements ([Formula: see text]SFEM-Q4) is proposed to obtain ultra-accurate solutions in the displacement and strain energy for solid mechanics problems. This method combines node-based S-FEM (NS-FEM), edge-based S-FEM (ES-FEM) and cell-based S-FEM (CS-FEM) equipped with a scale factor [Formula: see text] that controls contribution from each of these three different S-FEM models. This novel combination makes the best use of the upper bound property of the NS-FEM and the lower bound property of the CS-FEM (with 4 or more sub-smoothing domains for each element), and establishes a continuous strain-energy function of a scale factor [Formula: see text] for obtaining close-to-exact solutions. Our [Formula: see text]SFEM-Q4 also ensures the variational consistence and the compatibility of the displacement field, and hence guarantees to reproduce linear field exactly. Various solid mechanics problems are presented to validate the stability, effectiveness and ultra-accuracy of the proposed method.

Smoothed finite element method (S-FEM) is a new general numerical method which has been applied to solve various practical engineering problems. It combines standard finite element method (FEM) and meshfree techniques based on the weaken-weak (W2) formulation. This project, for the first time, develops a preprocessor software package SFEM-Pre for creating types of two-dimensional (2D) and three-dimensional (3D) S-FEM models following strictly the S-FEM theory. Because the software architecture of our 3D processor is the same as our 2D preprocessor, we will mainly introduce the 2D preprocessor in terms of software design for easier description, but the examples will include both 2D and 3D cases to fully demonstrate and validate the whole preprocessor of S-FEM. Our 2D preprocessor package is equipped with a graphical user interface (GUI) for easy use, and with a connectivity database for efficient computation. Schemes are developed for not only automatically meshes the problem domains using our GUI, but also accepts various geometry files made available from some existing commercial software packages, such as ABAQUS®and HyperMesh®. In order to improve the efficiency of our preprocessor, a parallel triangulation mesh generator has also been developed based on the advancing front technique (AFT) to create triangular meshes for complex geometry, and at the same time to create six types of connectivity needed for various S-FEM models. In addition, a database is implemented in our code to record all these connectivity to avoid duplicated calculation. Finally, intensive numerical experiments are conducted to validate the efficiency, accuracy and stability of our preprocessor codes. It is shown that with our preprocessor, an S-FEM can be created automatically without much human intervention for geometry of arbitrary complexity.

In this work, a three-dimensional (3D) nonlinear smoothed finite element method (S-FEM) solver is developed for large deformation problems. Node-based and face-based S-FEM using automatically generable four-noded tetrahedral elements (NS-FEM-Te4 and FS-FEM-Te4) are adopted to find the solution bounds in strain energy. The lower bound solutions are obtained using FEM-Te4 and FS-FEM-Te4, while the upper bound solutions are obtained using NS-FEM-Te4. A combined [Formula: see text]S-FEM-Te4 with a scaling factor [Formula: see text] that controls the combination is constructed to find nearly exact solutions for the nonlinear solids mechanics problems through adjusting [Formula: see text]. This is achieved using the property that a successive change of scaling factor [Formula: see text] can make the model transform from “overly-stiff” to “overly-soft”. Considering the properties of FS-FEM and NS-FEM, a selective FS/NS-FEM-TE4 is also used to solve 3D nonlinear large deformation problems, which produces a lower bound in strain energy. Hyperelastic Mooney–Rivlin and Ogden materials are both used in this study. Numerical examples reveal that S-FEM-Te4 is an effective method for obtaining solution bounds together with the standard FEM, and the FS-FEM-Te4, NS-FEM-Te4 and selective FS/NS-FEM-TE4 are robust with the high accuracy and computational efficiency for large deformation nonlinear problems.

In the paper, the smoothed finite element method (S-FEM) based on linear triangular elements is used to solve 2D solid contact problems for functionally graded materials. Both conforming and nonconforming contacts algorithms are developed using modified Coulomb friction contact models including tangential strength and normal adhesion. Based on the smoothed Galerkin weak form, the system stiffness matrices are created using the formulation procedures of node-based S-FEM (NS-FEM) and edge-based S-FEM (ES-FEM), and the contact interface equations are discretized by contact point-pairs. Then these discretized system equations are converted into a form of linear complementarity problems (LCPs), which can be further solved efficiently using the Lemke method. The singular value decomposition method is used to deal with the singularity of the stiffness matrices in the procedure constructing the standard LCP, which can greatly improve the stability and accuracy of the numerical results. Numerical examples are presented to investigate the effects of the various parameters of functionally graded materials and comparisons have been made with reference solutions and the standard FEM. The numerical results demonstrate that the strain energy solutions of ES-FEM have higher convergence rate and accuracy compared with that of NS-FEM and FEM for functionally graded materials through the present contact analysis approach.

This paper aims to provide an insight on the mechanism for the fast convergence of multigrid (MG) V-cycle algorithms. With this goal, the Fourier transform analysis is implemented to compute quantitatively the frequency spectrum of components of the residual resulted from the MG iterations. MG method has been extensively employed to solve large-scale systems of algebraic equations. Hence, one needs to understand its fast convergence property and scalability mechanism before applying MG method to a system equation, which affects the computational efficiency directly. In a first step, a number of novel features of the MG algorithm are studied, including the relationships among the iteration numbers needed for converged solutions, condition number of the system matrix and the grid-spacing in this paper. In a second step, the complexity of the MG method is researched, and various numerical experiments have been conducted in solving algebraic equations of models in finite element method for both heat transfer problems and solid mechanics problems. It is found that if the number of iterations in different grids is fixed, the optimal iteration mode is determined according to the attenuation of the high-frequency and low-frequency components of the residual. Our results also show that the complexity of the MG method is close to [Formula: see text], meaning that it is a close-to-linear scalable solver, which echoes the findings given by other literature. This study has revealed an important insight that the linear scalability is achieved by mitigating the negative effects (stagnation in convergence) of the large condition number of the system matrix created on the finest grid, using a sequence of coarser grids with smaller and smaller condition numbers.

We study the pionic transition from Y(4260) to Z c(3900), where Y(4260) and Z c(3900) are regarded as the weakly bound states of D $\bar{D}_{1}$ (2420) + H.c. and D $\bar{D}^{\ast}$ + H.c., respectively. The partial width of Y(4260) $ \rightarrow$ Z c(3900) $\pi$ is estimated to be of the order of MeV with the wave functions of the bound states, where the wave functions are simulated by the simple harmonic oscillator wave functions with equivalent root-mean-square radii.

An effective potential in a meson-meson system is discussed based on the SU(3) chiral constituent quark model, and the analytic form of the potential is explicitly given. In addition, the effective potential is employed to study the bound state problem of $\omega\phi$, which is related to the new resonance of $f_0(1810)$ observed in BESII very recently., Comment: 7 pages, 4 figures