Equation Methodology Research Articles

Three-dimensional eigensolutions of the unsteady compressible boundary-region equations

A previous paper of the authors (Duck & Stephen, J. Fluid Mech., vol. 917, 2021, A56) considered the effect of three-dimensional, temporally periodic, linear and incompressible disturbances on a Blasius boundary layer, in particular when the disturbance wavelength is both comparable to and longer than the boundary-layer thickness. This previous study revealed that, unlike the two-dimensional counterpart, a mode exists that exhibits regimes of downstream spatial growth. In this paper we extend the analysis to the compressible regime, based on the boundary-region equations methodology. The aforementioned unstable mode is seen to persist into the compressible regime, and is studied using a combination of numerical and asymptotic methods. The paper adopts several approaches. First is a numerical approach in which the spatial development of the disturbances is assessed. This then leads to a consideration of the far-downstream behaviour, using (several) asymptotic limits. Of some note, in addition to unstable modes found in the incompressible case, is the existence of a further class of instability, not found in the incompressible case (which is also analysed asymptotically), corresponding to what amounts to an inviscid instability. The far-downstream analysis enables a (sub-)classification into entropy and non-entropy modes. The former, according to this analysis, are spatially damped, with one caveat, as revealed by our marching procedure, which highlights how spatial development of disturbances can be important.

First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations: Mathematical Framework and Illustrative Application to the Nordheim–Fuchs Reactor Safety Model

First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Neural Ordinary Differential Equations: Mathematical Framework and Illustrative Application to the Nordheim–Fuchs Reactor Safety Model

Modeling Population Dynamics in the Indian Context: A Differential Difference Equation Approach

The study of population dynamics is of paramount importance in comprehending the evolving demographics and socioeconomic structure of a country. The task of modelling population dynamics in the Indian context poses distinct challenges and opportunities owing to the extensive and heterogeneous nature of the country's population. This research paper utilises a differential difference equation (DDE) methodology to comprehensively model population dynamics in India. The study seeks to enhance comprehension of population dynamics by considering various factors, including birth rates, death rates, migration patterns, and seasonal variations. The study employs Delay Differential Equations (DDEs) as a mathematical framework to effectively model the dynamic characteristics of population systems. These equations account for time delays, historical events, and discrete factors that play a significant role in shaping population dynamics, whether it be growth or decline. Numerical techniques, such as Euler's method and the Runge-Kutta method, are utilised in order to solve Delay Differential Equation (DDE) models and effectively simulate the dynamics of populations over a given time period. The evaluation of each method involves a comparative analysis of its accuracy, smoothness, convergence properties, and computational efficiency. The research findings presented in this study enhance our comprehension of population dynamics in India and offer significant insights that can be utilised by policymakers, urban planners, and researchers in the fields of demography, public health, and social sciences. The results have the potential to provide valuable insights for evidence-based decision-making and the development of effective policies aimed at addressing the various challenges and opportunities related to population dynamics in the Indian context.

Effects of mHealth Practice Patterns on Improving Metabolic Syndrome Using the Information-Motivation-Behavioral Skills Model.

Chronic diseases contribute to 68% of global mortality, highlighting the importance of early detection and management of conditions such as metabolic syndrome. Effective lifestyle interventions, particularly through mobile health (mHealth), have shown potential in promoting health and reducing cardiometabolic risk. This study utilized mHealth data from public health centers in South Korea, targeting adults with risk factors for metabolic syndrome. The Intervention-Motivation-Behavioral skills (IMB) theoretical model was applied to categorize participants' practice patterns over time using the Group-Based Trend Model (GBTM). And the Generalized Estimating Equations (GEE) methodology was applied to confirm the effective practice patterns for improving metabolic syndrome. Data were collected over 24 weeks. The dataset encompasses life-log data capable of capturing changes in intervention, self-report surveys, and clinical measurements, all linked to personal identification keys and thereby integrated. Participants demonstrated improved health behaviors, with the healthy eating score increasing from 5.0 to 6.4 and physical activity rates rising from 41.5% to 59%. Health risk factors decreased significantly, with the mean number of risk factors dropping from 2.4 to 1.4. The percentage of subjects with three or more metabolic syndrome components decreased from 42.3% in the initial period to 19.2% in the final period. Practice patterns by IMB components were classified into three categories: continuous type, late decline type, and early decline type. Improvements in health behavior and metabolic syndrome were observed in the continuous type of each IMB component. The mHealth interventions were confirmed to be positively associated with improved health behavior and management of metabolic syndrome in the continuous practice patterns of IMB.

SPATIAL ESTIMATION OF SOIL EROSION USING GEOSPATIAL TECHNIQUE – A CASE STUDY OF JANJEVA RIVER CATCHMENT (KOSOVO)

The aim of the study is to analyse the spatial estimation of soil erosion in a small size river catchment of Janjeva (Kosovo). Soil erosion is becoming a serious threat and its spatial estimation is crucial for soil resource protection and management. The Revised Universal Soil Loss Equation (RUSLE) methodology integrated with GIS techniques was applied to estimate the annual erosion rate. Different datasets including open-source data were used to find main components of soil erosion. The results show different soil erosion classes depending on lithological settings, landforms, climate conditions, soil properties, land cover and soil conservation practices. By calculating RUSLE parameters for Janjeva River catchment (84 km²), we found out that mean annual erosion rate is 1 t·ha-¹·yr-¹. Erosion rate class <5 t·ha-¹·yr-¹ dominates the catchment’s area with 92.5%, while other classes have 7.5% of catchments total area. Highest rates of soil erosion are found in volcanic rocks, steep slopes and soils without conservation practices. Soils located in western part of the catchment with adequate conservation practice have minimum erosion rate.

Challenges in Numerical Solutions of Higher-Dimensional Differential Equations

Differential equations constitute a fundamental tool in modeling various natural phenomena across scientific disciplines such as physics, engineering, and finance. We provide an overview of fractional differential equations, focusing on the computational requirements associated with their numerical solutions from a computer science perspective. We analyze the computational intricacies concerning First-Order Linear ODE, First-Order Nonlinear ODE, Second-Order Linear ODE, Second-Order Nonlinear ODE, Heat Equation (PDE), and Wave Equation (PDE). This comparative assessment delves into the computational demands of solving these equations using differential equation methodologies. While analytical solutions provide deep insights, obtaining numerical solutions, particularly in higher dimensions, remains a persistent challenge. Finite difference methods commonly employed for numerical solutions, In higher-dimensional problems, traditional numerical methods face challenges stemming from an exponential surge in grid points and the consequent demand for substantially decreased time step sizes. This paper explores the challenges posed by higher-dimensional differential equations in numerical solutions. It highlights the infeasibility of finite difference methods in such scenarios and emphasizes the need for innovative numerical techniques capable of efficiently handling the complexities of higher-dimensional differential equations. Overcoming these challenges is crucial for advancing our understanding and modeling capabilities in complex real-world systems governed by differential equations. Continued research efforts strive to develop novel numerical methodologies capable of addressing these challenges, aiming to broaden the scope of solvable higher-dimensional differential equations and expand their application across diverse scientific domains.

A randomized operator splitting scheme inspired by stochastic optimization methods

In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given time step does not necessarily use all the parts of the split operator. This is in contrast to deterministic splitting schemes which always use every part at least once, and often several times. As a result, the computational cost can be significantly decreased in comparison to such methods. We rigorously define a randomized operator splitting scheme in an abstract setting and provide an error analysis where we prove that the temporal convergence order of the scheme is at least 1/2. We illustrate the theory by numerical experiments on both linear and quasilinear diffusion problems, using a randomized domain decomposition approach. We conclude that choosing the randomization in certain ways may improve the order to 1. This is as accurate as applying e.g. backward (implicit) Euler to the full problem, without splitting.

Multi-agent deployment in 3-D via reaction–diffusion system with radially-varying reaction

This paper considers the problem of the deployment of a set of agents distributed on a disk-shaped grid onto three-dimensional (3-D) profiles, by using a continuum approximation (valid in the limit for a large number of agents) and then a control methodology for partial differential equations (PDEs). The agents’ collective behavior is modeled by a pair of radially-varying diffusion–reaction PDEs in polar coordinates, whose state determines the agents’ position. Having a radially-varying reaction coefficient not only increases the challenge of kernel equations becoming singular in radius, but also brings more potential deployment manifolds. To stabilize and increase the convergence of the deployment, a boundary controller and a boundary observer are designed by combining an infinite-dimensional backstepping approach with a Fourier series decomposition technique, thus driving all agents to the desired profile. A key feature of the presented result is that the desired profile only needs to be known by the leaders, with the followers only needing to follow a simple control strategy which requires only the measurement of its current position and communication with its neighbors as defined by the multi-agent system topology. The method provides closed-loop exponential stability with any prescribed convergence rate in the L2 norm. Simulation tests are shown to prove the effectiveness of the proposed algorithm.

Personal factors as determinants of the risk rating for SME investment

ABSTRACT What variables indicate whether a small or medium enterprise (SME) applying for financing from a development bank is a good loan candidate? Structural equation modeling applied to a set of variables can provide the necessary insights. This paper analyzes 407 SMEs that applied for development loans in Pichincha Province, Ecuador. Rather than specific economic/financial quantitative variables often used in credit scoring models, we employed qualitative variables to study creditworthiness. The structural equation methodology can verify whether a client is creditworthy based on company management, product characteristics, and contextual market aspects. Another key contribution is the finding that an entrepreneur's personal/professional traits are the primary determinant for granting this type of loan. The results have theoretical and practical implications that could enhance the limited empirical research in this field to date.

Financial Literacy of Workers in the Tourism Industry in Mexico in 2023: a Structural Equations Approach

This paper attempts to examine the level of financial knowledge of workers in the tourism industry in Mexico through the Structural Equations Methodology (SEM). The type of sampling is non-probabilistic by self-determination. A questionnaire is applied to 500 workers, in 2023, from Mexican companies in the tourism sector considering the following 7 issues: investment, savings, credit, insurance, pensions, expenses and budgets. The SEM allows bring to light the financial knowledge that the surveyed workers have about these issues. Based on a factor structure obtained from the confirmatory analysis, which presents good goodness of fit, structural adjustment, and parsimony, the main findings are: 1) in terms of credit, workers give importance to the requirements requested by financial institutions and consider that they are easy to interpret and comply with, 2) in terms of retirement fund accounts, workers feel confident in institutions that manage their retirement savings and are clear about commissions, 3) in terms of savings, workers perceive that bank accounts have been adapted to their needs since banks have become very flexible in terms of requirements for opening and initial amounts with clear and complete account information, 4) in terms of investment, workers hardly acquire bank promissory notes, and 5) regarding life insurance, workers express the ease that exists to contract insurance, although the cost is limited. The results obtained have practical implications for the tourism sector to continue promoting the habit of saving and the use of financial services and products to which the worker can have access, since this financial knowledge translates into more organized employees in their financial affairs.

High-order finite element method for atomic structure calculations

We introduce featom, an open source code that implements a high-order finite element solver for the radial Schrödinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or exponential, and the convergence can be systematically controlled by increasing the number and/or polynomial order of the finite element basis functions. The Dirac equation is solved using a squared Hamiltonian approach to eliminate spurious states. To address the slow convergence of the κ=±1 states due to divergent derivatives at the origin, we incorporate known asymptotic forms into the solutions. We achieve a high level of accuracy (10−8 Hartree) for total energies and eigenvalues of heavy atoms such as uranium in both Schrödinger and Dirac Kohn-Sham solutions. We provide detailed convergence studies and computational parameters required to attain commonly required accuracies. Finally, we compare our results with known analytic results as well as the results of other methods. In particular, we calculate benchmark results for atomic numbers (Z) from 1 to 92, verifying current benchmarks. We demonstrate significant speedup compared to the state-of-the-art shooting solver dftatom. An efficient, modular Fortran 2008 implementation, is provided under an open source, permissive license, including examples and tests, wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines. Program summaryProgram Title: featomCPC Library link to program files:https://doi.org/10.17632/962fzmm7f7.1Licensing provisions: MITProgramming language: Fortran with command-line interfacesNature of problem: Solution of the Schrödinger, Dirac, and Kohn–Sham equations of density functional theory for isolated atoms.Solution method: A high-order finite element method is used to assemble a generalized eigenproblem that is then solved for eigenvalues and orbitals. The Poisson equation is solved using the finite element method also. Self-consistent field equations are solved using Pulay mixing.Additional comments including restrictions and unusual features: Our solution methodology for the Dirac equation does not suffer from spurious states. We maintain high accuracy even for κ=±1 states. Unlike other methods, our approach is not limited to Coulombic or self-consistent potentials and can handle non-uniform meshes, including exponential meshes.Restrictions: Spherical symmetry.

Associations between self-perceptions of aging and social functioning in older adults: An analysis based on health and retirement study data

ObjectivesSelf-perception of aging (SPA) and social functioning are two important variables in the process of healthy aging, but the relationship between them is still unclear. This study aimed to explore the association between SPA and social functioning in older adults. MethodsWe conducted a longitudinal study utilizing data from the Health and Retirement Study. The sample comprised individuals aged 50 and above. Socio-demographic, psychosocial, and lifestyle information of study participants was systematically collected at baseline (2012 and 2014) and during follow-up four years later (2016 and 2018). SPA was measured using a scale assessing individuals' attitudes toward their aging process. Social functioning was evaluated through 22 questions, reflecting individuals' abilities to engage in and perform various roles and tasks in their daily lives. Multilevel modeling was employed to analyze the relationship between SPA and social functioning. Differences in social functioning changes among various SPA groups were assessed through the Generalized Estimating Equations methodology. ResultsThe study included 8,454 participants with an average age of 68.3 years (SD = 9.92). The multilevel model revealed a significant correlation between SPA and social functioning (β = 0.131; P < 0.001). This relationship persisted after adjusting the model (β = 0.088; P < 0.001). Generalized Estimating Equations indicated noteworthy differences in social functioning changes among distinct SPA groups (P = 0.034). DiscussionPositive SPA is associated with the healthy social functioning of older adults. Healthcare providers could target modifiable aspects of SPA to enhance the social function of older adults and promote successful aging.

Development of three UV-spectroscopic methods for simultaneous estimation of raloxifene and aspirin in pharmaceutical dosage form: Whiteness and greenness assessment with application of ComplexGAPI, AGREE, and RGB

This study evaluates three spectrophotometric techniques for quantifying a binary combination of raloxifene and aspirin in terms of whiteness and greenness. Application of green and white analytical chemistry has gained widespread acceptance in the analytical community. The whiteness and greenness of the assessment were evaluated using three approaches: Complex green analytical procedure index, Analytical GREEnness calculator and Red Green Blue additive model. The technique (I) uses the simultaneous equation methodology for raloxifene at 285 nm and aspirin at 222 nm, respectively. Method (II) includes the area under the curve operating at (280–290) nm and (217–227) nm for raloxifene and aspirin, respectively. Method (III) operates using the first derivative method for raloxifene at 269 nm and aspirin at 216 nm. The linearity range was 2–14 µg/ml for three methods. P-Values were found satisfactory at a 95 % level of confidence. These techniques were intended for the binary mixture analysis in investigational formulations with high recoveries. The developed methods were validated according to ICH guidelines. These developed methods have been utilized in routine analysis to simultaneously determine raloxifene and aspirin without pre-extraction.

Proton Activation in the Presence of a Weak Acid Facilitated by Second Coordination Sphere Effects in Iron Porphyrins**

AbstractThe catalytic activity of two iron‐based porphyrin complexes containing pyridine‐functionalized second coordination spheres, referred to as Py2XPFe and CuPy2XPFe, have been investigated for the hydrogen evolution reaction (HER) and compared with the unsubstituted analog TMPFe in acetonitrile. The CuPy2XPFe incorporates a second metal center within the pyridine residues and represents a heterodinuclear system, while the structurally analogous Py2XPFe lacks an additional metal in the second coordination sphere. Both the Py2XFe and CuPy2XPFe complexes are observed to activate the weak acid, acetic acid (AcOH) at the FeII/I couple rather than at the more energy intensive FeI/0 couple observed for the unfunctionalized TMPFe complex at low acid concentrations. The ability of the monometallic Py2XPFe to activate the weak proton source at the FeII/I couple manifests as an ECEC(E)′ type electrochemical mechanism, rather than an EECC(E)′ type mechanism as observed for TMPFe. The CuPy2XPFe displays improved reactivity compared with the Py2XPFe and TMPFe under the same substrate conditions, however the mechanistic nuances into bimetallic CuPy2XPFe system are currently unclear. The concentration of AcOH was incrementally increased and the rate constants of the initial protonation step i. e. formation of a hydridic species (k1,app), as well as of the protonation of the hydridic species to produce dihydrogen (kglobal) were calculated using the Foot‐of‐the‐wave and plateau current rate equation methodologies, respectively. The kinetic analysis indicates that the activation of protons through the ECEC(E)′ type mechanism for the Py2XPFe results in a system in which k1,app&lt; kglobal. As both the monometallic Py2XPFe and bimetallic CuPy2XPFe activate the AcOH at less cathodic potentials than TMPFe under identical conditions, the overpotentials (ηTOF/2) for these complexes are thus dramatically lower. The reactivity difference of the Py2XPFe when compared to non‐substituted iron porphyrin analogs is due to the hanging group's influence, which is believed to either act as hydrogen bond promoters for the active site or aids to stabilize a catalytic intermediate species during catalysis.

Progress update on inclusion of atmospheric profiling for sonic boom propagation through turbulence

Research continues in the field of sonic boom propagation to aid international efforts in technical standards of civil supersonic aircraft, and simulation is necessary to validate the data produced by up-and-coming demonstration aircraft. Turbulence is important when considering how sonic booms propagate; their effects can be heard at the ground as demonstrated through the SonicBAT project. Current efforts are being made to improve the turbulent sonic boom propagation code KZKFourier to increase accuracy and robustness. This presentation will serve as progress update on including atmospheric profiling in KZKFourier. Previous versions did not have this feature. The inclusion of atmospheric profiling in KZKFourier will allow for quantities such as humidity, density, and temperature to vary within the atmospheric boundary layer. The presentation will discuss both the analytical inclusion of profiling on the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation methodology and its implementation in the C + + code. [Work supported by the FAA through ASCENT Project 57 under the supervision of Sandy Liu. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the FAA.]

A sharp immersed method for 2D flow-body interactions using the vorticity-velocity Navier-Stokes equations

Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by hydrodynamic forces. However, for the vorticity-velocity form of the Navier-Stokes equations, existing immersed geometry discretizations for two-way coupled problems only achieve first order spatial accuracy near solid boundaries. Here we introduce a sharp-interface approach based on the immersed interface method to handle the one- and two-way coupling between an incompressible flow and one or more rigid bodies using the 2D vorticity-velocity Navier-Stokes equations. Our main contributions are three-fold. First, we develop and analyze a moving boundary treatment for sharp immersed methods that can be applied to PDEs with implicitly defined boundary conditions, such as those commonly imposed on the vorticity field. Second, we develop a two-way coupling methodology for the vorticity-velocity Navier-Stokes equations based on control-volume momentum balance that does not require the pressure field. Third, we show through extensive testing and validation that our resulting flow-body solver reaches second-order accuracy for most practical scenarios, and provides significant efficiency benefits compared to a representative first-order approach.

Sustainable entrepreneurial ecosystems: interdependencies of infrastructure and capital and the effects of local culture

PurposeSustainable entrepreneurial ecosystem research is an emerging trend within the entrepreneurship domain. Drawing from resource dependency theory, this study examines the interdependent nature of sustainable entrepreneurial ecosystem factors and the mediating role of local culture as it relates to entrepreneurial action. The authors collected data from 12 entrepreneurial ecosystems in Australia and developed a model of the interdependencies of sustainable entrepreneurial ecosystem factors.Design/methodology/approachThe data were collected through an e-survey of Small and Medium Entreprise (SME) owners in New South Wales, Australia. The authors applied partial least squares structural equation methodology to assess the structural models, validate the outer models and examine the inner model.FindingsThe findings reinforce empirical support for sustainable entrepreneurial ecosystems. The environment where sustainable entrepreneurial ecosystems are evolved influences their functionality. Further, entrepreneurial culture mediates the relationship with other ecosystem factors. The theoretical and practical implications are discussed.Originality/valueThis study focuses on understanding the interdependent nature of sustainable ecosystem factors. The authors identified entrepreneurial culture as a mediator to business support services, educational institutional support and financial capital availability with business and social networks.

Applying RUSLE for soil erosion estimation in Romania under current and future climate scenarios

Soil erosion is one of the main land degradation processes, often enhanced by unsuitable human activities. In the context of global climate change, soil erosion also exhibits quantitative and qualitative changes induced by the temporally dynamic erosion factors, namely rainfall erosivity and land use. Our study attempts to forecast the evolution of soil erosion rates under climate change scenarios over the Romanian territory. Firstly, we apply the Revised Universal Soil Loss Equation (RUSLE) methodology to achieve a spatial model of soil erosion for the current climate conditions. Secondly, we use projections of rainfall erosivity to derive soil erosion models for two future climate change scenarios (Representative Concentration Pathway - RCP 4.5 and 8.5) and two periods of time (2041–2060, 2061–2080). Thirdly, we compute the differences between future projected and current erosion rates to identify spatial patterns of soil erosion evolution. The results show that, under the influence of rainfall erosivity dynamics, soil erosion tends to increase during the next decades. Overall, an enhancement of soil erosion rates on 84–90% of the country is expected to take place. Most of the erosion rates will increase slightly, with <1 t ha−1 yr−1, from an overall average of 2.94 t ha−1 yr−1, at present, to 3.67 (2061–2080, RCP 8.5) – 3.74 (2041–2060, RCP 8.5) t ha−1 yr−1 at country level. Locally, the erosion rates may increase with >5–10 t ha−1 yr−1 on areas estimated to cumulate >8000 km2. The most affected areas will be the soils situated in hilly and plateau regions, leading to an enhancement of their fertility degradation.

Pro-environmental behavior of learners using CADMIACA model

This research provides clear perspective with broad spectrum on the pro-environmental behavior (PEB) of learners. It sought to determine the level of awareness, attitudes, intention, motivation, environmental social interaction, environmental education and green behavior of learners, and the significant relationship and significant difference among the variables. The researcher utilized the descriptive-qualitative survey method; through the use of a questionnaire backed up with Key Informant Interview (KII) and triangulated by Focus Group Discussion (FGD). CADMIACA, the model of this research, are from the theories of Comprehensive Action Determination Model (CADM) Motivational, Interpersonal ones (MI) and the Action Competence Approach (ACA). For the empirically causal relationship among variables, structural equation methodology (SEM) was initiated. The study included 384 learners from junior and senior high school of NDDU-IBED Lagao, General Santos City, school year 2017-2018. Overall, there is no significant difference on the PEB of junior and senior high school learners; they had a moderate energy-saving behavior and high level of environmental education. On the other hand, there is a significant difference in the attitude and global warming of students. Another study is recommended, using other respondents from a subdivision or barangay to determine whether social status might affect the totality of PEB of an individual.

Cash flow management and its effect on firm performance: Empirical evidence on non-financial firms of China.

The main purpose of this research is to investigate the impact of changes in cash flow measures and metrics on firm financial performance. The study uses generalized estimating equations (GEEs) methodology to analyze longitudinal data for sample of 20288 listed Chinese non-financial firms from the period 2018:q2-2020:q1. The main advantage of GEEs method over other estimation techniques is its ability to robustly estimate the variances of regression coefficients for data samples that display high correlation between repeated measurements. The findings of study show that the decline in cash flow measures and metrics bring significant positive improvements in the financial performance of firms. The empirical evidence suggests that performance improvement levers (i.e. cash flow measures and metrics) are more pronounced in low leverage firms, suggesting that changes in cash flow measures and metrics bring more positive changes in low leverage firms' financial performance relatively to high leveraged firms. The results hold after mitigating endogeneity based on dynamic panel system generalized method of moments (GMM) and sensitivity analysis considering the robustness of main findings. The paper makes significant contribution to the literature related to cash flow management and working capital management. Since, this paper is among few to empirically study, how cash flow measures and metrics are related to firm performance from dynamic stand point especially from the context of Chinese non-financial firms.