Model Coefficients Research Articles

Numerical Prediction of Solid Particle Erosion in Jet Pumps Based on a Calibrated Model

Jet pumps are widely used in petrochemical processes, nuclear cooling, and wastewater treatment due to their simple structure, high reliability, and stable performance under extreme conditions. However, when transporting solid-laden two-phase flows, they face severe erosion problems, leading to reduced efficiency, malfunctions, or even failure. Therefore, optimizing jet pump performance and extending its service life is crucial. In this study, an experimental platform was established to conduct experiments on wall erosion in jet pumps. The CFD-DEM method was used to simulate the solid–liquid two-phase flow in the jet pump, comparing six erosion models for predicting erosion rates. The Grey Wolf Optimization algorithm was applied to calibrate model coefficients. The results indicate that the Neilson erosion model shows the best consistency with the experimental results. The inlet flow rate significantly influenced the erosion rates, while the flow rate ratio had a smaller effect. The particle concentration exhibited a nonlinear relationship with erosion, with diminishing impact beyond a certain threshold. As the factors varied, the erosion distribution tended to be uniform, but high erosion areas remained locally concentrated, indicating intensified localized erosion.

Studies of electron-ion resonant recombination of li-like Si11+ions

Abstract Theoretical investigations of L-shell △n = 0, 1, and 2 (2s → 2p, 3 l ′ , and 4 l ′ ) dielectronic recombination (DR), as well as K-shell △n = 1, 2, and 3 (1s → 2 l ′ , 3 l ′ , and 4 l ′ ) DR of Li-like Si 11+ ions are performed, using the relativistic distorted-wave approach. Detailed resonance energies, resonance strengths, and recombination rate coefficients are calculated including complex configuration mixing, Breit interaction, and QED corrections. Good agreement is achieved between the theoretical rate coefficients and the experimental results. The plasma rate coefficients are also calculated for electron temperatures ranging from 10−1 to 106 eV, and an analytical formula is presented to fit the total plasma rate coefficients for convenient modeling of astrophysical and fusion plasmas.

A Sequential Learning Procedure for Estimating Coefficients in Linear Regression With Applications to Online Sales Examination

ABSTRACTIn this paper, we consider the problem of estimating coefficients in a linear regression model. We propose a sequential learning procedure to determine the sample size for achieving a given small estimation risk, under the widely used Gauss‐Markov setup with independent normal errors. The procedure is proven to enjoy the second‐order efficiency and risk‐efficiency properties, which are validated through Monte Carlo simulation studies. Using e‐commerce data, we implement the procedure to examine the influential factors of online sales.

Realizing the Calculation of a Fully Normalized Associated Legendre Function Based on an FPGA

A large number of fully normalized associated Legendre function (fnALF) calculations are required to compute Earth’s gravity field elements using ultra high-order gravity field coefficient models. In the surveying and mapping industry, researchers typically rely on CPU-based systems for these calculations, which leads to limitations in execution speed and power efficiency. Although modern CPUs improve instruction execution efficiency through instruction-level parallelism, the constraints of a shared memory architecture impose further limitations on the execution speed and power efficiency. This results in exponential increases in computation time as demand rises alongside high power consumption. In this article, we present a new computational implementation of an fnALF based on the ZYNQ platform. We design a task-parallel “pipeline” architecture which converts the original serial logic into a more efficient hardware implementation, and we utilize a redundant calculation layer to handle repetitive coefficient computations separately. The experimental results demonstrate that our system achieved accurate and rapid calculations. Under the only one geocentric residual latitude condition, we measured the computation times for spherical harmonic coefficient degrees of 360, 720, and 1080 to be 0.155922 s, 0.520950 s, and 1.401609 s, respectively. In the case of the multiple geocentric residual latitudes condition, our design generally yielded efficiency gains of over three times those of MATLAB R2020b implementation. Additionally, our calculated results were used to determine the geoid height in the field with an error of less than ±0.1m, confirming the reliability of our computations.

Anand Model Constants of Sn-Ag-Cu Solders: What Do They Actually Mean?

Abstract Finite element simulations are broadly utilized to calculate the thermally induced mechanical deformations of interconnecting solder materials in electronics. The Anand unified viscoplasticity model is a prevalent choice for simulating the mechanical responses of solder joints, comprising nine parameters whose individual effects are not fully addressed in the literature. For this reason, this study examines the influence of each Anand parameter on the mechanical response of leadless Tin-Silver-Copper solder alloys with varying silver content through comprehensive nonlinear finite element simulations. Anand model coefficients for different SAC alloys, including SAC105, SAC205, SAC305, and SAC405, were sourced from existing literature and used to establish a systematic study matrix for each parameter. These coefficients were then integrated into thermomechanical simulations to induce inelastic deformations in the solder interconnections. The response of the solder interconnects is analyzed using equivalent inelastic strains and inelastic strain energy density. Results indicated that specific Anand parameters could skew the solder joint stress-strain response towards brittle behavior, while other parameters could lead to a more ductile response. Through statistical factorial analysis, the significance of each parameter is found to vary considerably, ranging from negligible to highly significant. The findings of this study are crucial for understanding the behavior of different SAC solder configurations and their expected thermal fatigue performance based on Anand creep constants. Furthermore, this paper provides foundational insights into the interpretation of Anand coefficients and their influence on the mechanical response of solder materials, a topic not yet explored in the existing literature.

Shape Mediation Analysis in Alzheimer's Disease Studies.

As a crucial tool in neuroscience, mediation analysis has been developed and widely adopted to elucidate the role of intermediary variables derived from neuroimaging data. Typically, structural equation models (SEMs) are employed to investigate the influences of exposures on outcomes, with model coefficients being interpreted as causal effects. While existing SEMs have proven to be effective tools for mediation analysis involving various neuroimaging-related mediators, limited research has explored scenarios where these mediators are derived from the shape space. In addition, the linear relationship assumption adopted in existing SEMs may lead to substantial efficiency losses and decreased predictive accuracy in real-world applications. To address these challenges, we introduce a novel framework for shape mediation analysis, designed to explore the causal relationships between genetic exposures and clinical outcomes, whether mediated or unmediated by shape-related factors while accounting for potential confounding variables. Within our framework, we apply the square-root velocity function to extract elastic shape representations, which reside within the linear Hilbert space of square-integrable functions. Subsequently, we introduce a two-layer shape regression model to characterize the relationships among neurocognitive outcomes, elastic shape mediators, genetic exposures, and clinical confounders. Both estimation and inference procedures are established for unknown parameters along with the corresponding causal estimands. The asymptotic properties of estimated quantities are investigated as well. Both simulated studies and real-data analyses demonstrate the superior performance of our proposed method in terms of estimation accuracy and robustness when compared to existing approaches for estimating causal estimands.

Risk prediction score for high spinal block in patients undergoing cesarean delivery: a retrospective cohort study.

High spinal block is a serious complication of spinal anesthesia. However, findings regarding its associated risk factors are inconsistent, and no studies have reported a relevant risk prediction score. We aimed to determine the risk prediction score for high spinal block in patients who were induced spinal anesthesia for cesarean delivery. This retrospective cohort study was conducted at a hospital in Southern Thailand between 2019 and 2020. We recorded demographic characteristics, gestational age (GA), hyperbaric bupivacaine dose, sensory block level, pre- and post-procedure blood pressure, and birth weight. High spinal block was defined as a decrease in pinprick sensation > T4. Risk scores, adjusted odds ratios (OR), and 95% confidence intervals (CI) were determined. Risk scores were derived from the coefficients of the final multivariate logistic regression model. The incidence of high spinal block was 22.4% among the 1003 parturients. Our risk prediction tool for high spinal block had a sensitivity and specificity of 76% and 49%, respectively, and was classified into high (> 21), intermediate (15-21), and low (≤ 14) risk groups. The patient-related predictors were a GA < 35weeks (OR [95% CI]: 2.31 [1.13, 4.71], score of 8), height < 150cm (2.21 [1.11, 4.38], score of 8), and post-pregnancy body mass index > 27.5kg/m2 (2.68 [1.33, 5.41], score of 10). The anesthesia-related predictors were a hyperbaric bupivacaine dose > 11mg (2.56 [1.34, 4.87], score of 9) and induction by a first-year resident (1.48 [1.05, 2.09], score of 4). The surgery-related predictors were previous cesarean delivery in labor (1.83 [1.2, 2.78], score of 6) and elective cesarean delivery (2.53 [1.57, 4.07], score of 9) compared to indication by cephalopelvic disproportion. The incidence of intraoperative hypotension was significantly higher in the high-block group than in the control group (46% vs. 25%, p < 0.001). The combination of patient- and anesthesia-related predictors played an important role in the intermediate- and high-risk groups for high sensory spinal block. Addressing the modifiable risk factors-a GA < 35weeks, an optimal dose of bupivacaine, and the experience level of the spinal block performer-could minimize the risk of high spinal block during cesarean delivery.

Tensor Landmark Analysis With Application to ADNI data

ABSTRACTRecent advancements in data collection have facilitated the use of multidimensional arrays, also known as tensors, in prediction of health outcomes. In this article, we introduce a tensor landmark model for predicting survival outcomes using multiple longitudinal biomarkers as tensor covariates through CANDECOMP/PARAFAC (CP) decomposition. An iteratively reweighted least squares estimation is adopted for components of the tensor coefficients in the landmark model. We also present empirical results of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) for right‐censored data to select the CP rank. Simulations and Alzheimer's disease neuroimaging initiative (ADNI) data analysis demonstrate that our proposed model accurately estimates survival coefficients and predicts survival probabilities. The implementation code can be found online (https://github.com/sparkqkr/TensorCoxReg).

Automatic segmentation and visualization of cortical and marrow bone in mandibular condyle on CBCT: a preliminary exploration of clinical application.

To develop a deep learning-based automatic segmentation method for cortex and marrow in mandibular condyle on cone-beam computed tomography (CBCT) images and explore its clinical application. 825 condyles of 490 CBCT images from 3 centers of Stomatology hospitalaffliated to Zhejiang University School of Medicinewere collected. A deep learning model was developed for simultaneous segmentation of cortex and marrow in mandibular condyle. It included a region of interest extraction network and a segmentation network based on 3D U-net, with modifications made to improve the segmentation boundaries. To evaluate its clinical potential, the model's segmentation efficiency and accuracy were compared with those of both junior and senior oral and maxillofacial radiologists. Additionally, the model's ability to assist junior radiologists in diagnosis through visualization and quantitative analysis of the generated 3D model was also assessed. The Dice similarity coefficient of the deep learning model was 0.901 (cortex), 0.969 (marrow), and 0.982 (entire condyle). Hausdorff distance was 0.755mm (cortex), 0.826mm (marrow), and 0.760mm (entire condyle). The model outperformed radiologists across all segmentation metrics, completing the task in merely 15.06s. With the assistance of visualization and quantitative analysis generated from the model's segmentation, the diagnostic accuracy of junior radiologists significantly improved. The proposed deep learning-based model achieved accurate and efficient segmentation for mandibular condylar cortex and marrow. It possessed capability to generate precise 3D models, facilitating visual quantitative measurement and aiding in the diagnosis of condylar bony changes. This model holds potential for clinical applications in orthognathic surgery, orthodontic treatment, and other TMJ-related interventions.

A novel friction coefficient model parameters identification method for needle-tissue insertion procedure

Abstract In endoscopic liver vascular insertion surgeries, during the process of angiographic operation, the success of vascular staining depends on precise needle insertion control which heavily relies on experienced surgeons. Endoscopic vascular insertion surgical navigation system shows the potential to improve position precision, however it relies on needle-tissue interaction model and parameter identification to provide essential information for improving needle insertion accuracy, in which the friction coefficient is important parameters but difficult to determine. In this paper, a novel needle-tissue friction coefficient identification method was proposed with unknown tissue Young's modulus under endoscopic liver surgery scenarios. A modified friction coefficient model was proposed including the adhesion and elastic friction component to describe needle-tissue dynamic interaction process which can predict the friction coefficient more precisely. The proposed parameter estimation method based on the modified friction model can simultaneously estimate friction coefficient and Young's modulus. The proposed method was demonstrated by the friction coefficient measurement experiment. The results showed that the friction coefficient model prediction results agreed well with expected value. The proposed method can be applied to provide essential tissue-needle interactive information to improve needle insertion precision in the endoscopic liver vascular insertion surgery scenarios.

PCA-Kriging-Based Oscillating Jet Actuator Optimization and Wing Separation Flow Control

In order to improve the separation control effect of an oscillating jet, the external flow field of the actuators and the wing wake are obtained via hot-wire measurements to optimize the actuator and achieve wing separation flow control. The optimization objectives are to improve the sweeping uniformity and range of the jet. In the present study, the PCA method is used for the modal decomposition of the velocity distribution. The modal-based actuator evaluation parameters are proposed, and the kriging surrogate models of the modal coefficients (principal components) on the actuator parameters are established. The multi-objective genetic algorithm was utilized to complete the optimization of the actuator, and the effect of flow separation control on the wing was verified. The results show that three patterns exist in the time-averaged velocity distribution of the external flow field: unimodal, broad and bimodal, from unimodal to bimodal, the degree of the jet sweeping uniformity gradually decreases, and the sweeping range gradually increases. The pattern of the velocity distribution modals affects the degree of jet sweeping uniformity, while the distance of the modal peaks affects the jet sweeping range. The two evaluation parameters are negatively correlated: insufficient sweeping range or poor sweeping uniformity of the jet are not conducive to wing separation flow control, and the two must be coordinated to achieve the optimal control effect.

The Effect of Ellipsoidal Particle Surface Roughness on Drag and Heat Transfer Coefficients Using Particle-Resolved Direct Numerical Simulation

The purpose of this study is to estimate the effect of roughness layer thickness on the heat transfer and drag coefficients of ellipsoidal particles. Using an OpenFOAM-based particle-resolved direct numerical simulation (PR-DNS) method, we calculated the drag coefficient and Nusselt number for an isolated axisymmetric nonspherical particle with a rough surface in a uniform flow. The PR-DNS results indicate that the drag coefficient varies linearly with the effective roughness Sef at different angles, which can be expressed as CD=kSef−1+CD0. The changes in k are consistent with the Happel and Brenner equation. Furthermore, the influence of roughness on the heat transfer efficiency factor can be represented by Ef=Sef−65. The models for the drag coefficient and Nusselt number are valid within the ranges 1.25≤Ar≤2.5,1≤Sef≤2, and 10≤Rep≤200, thereby extending the applicability of the equations developed for smooth particles. These newly developed correlations for the drag coefficient and Nusselt number can be utilized for non-isothermal flows of particle mixtures containing materials with various rough-surfaced ellipsoids.

A revised elastic-plastic contact model of cycloidal pinwheel based on length scale

This study explores the relationship between surface roughness and characteristic scale through theoretical analyses and experimental data. Considering the concavity and convexity of cycloidal gear tooth profile curvatures, a curved surface contact coefficient model suitable for both inner and outer contacts, with either equal or unequal curvatures, has been developed. Moreover, a fractal contact model is constructed for cycloidal pinwheels. This model considers scale correlation and analyzes the influence of microscopic parameters on the elastic-plastic critical grade and the behavior of the contact area. Additionally, the influence of the micro-convex body frequency index on surface contact performance is explored to provide theoretical insights for improving the elastic contact ratio and reducing wear on contact surfaces.

Explicit and explainable artificial intelligent model for prediction of CO2 molecular diffusion coefficient in heavy crude oils and bitumen

Optimizing CO2 injection for enhanced oil recovery (EOR) requires a precise estimation of the CO2-diffusivity coefficient in porous media. This study developed a predictive model for the molecular diffusivity coefficient of CO2 in bitumen and heavy crude oils using a Bayesian regularized artificial neural network. The unique contributions of the developed model compared to existing models include: First, a simple and accurate mathematical correlation between inputs and CO2-diffusivity has been presented, making it easy to use particularly for individuals with limited understanding of machine learning. Secondly, the time it takes the model to make a prediction (its inference latency) has been established and the model has been physically validated using trend analysis. Fourthly, independent datasets were used to test for the model generalizability.The model was evaluated using 260 data points from the literature, with 70 % for training and 30 % for testing. Key performance metrics were calculated, including root mean square error (RMSE = 0.03), and coefficient of determination (R2 = 0.996). Furthermore, an outlier detection analysis using the statistical leverage approach demonstrated that the data used was of high quality. A relevancy factor analysis revealed that pressure had the greatest impact on CO2 diffusivity, followed by temperature, while CO2 mass fraction had the least impact. The developed model operates within a temperature range of 295 K – 363 K and a pressure range of 1 MPa – 8MPa. Overall, the outcomes of this study contribute to the efficient prediction of CO2 diffusivity in heavy crude oil and bitumen.

Extending the Scope of Instrumental Variable Methods

Abstract Since Philip Wright’s (1928) proposal of the linear instrumental variables (IV) estimator the scope of application of IV models has greatly expanded. There are now nonlinear IV models in use with both additive and nonadditive latent variables, employing both semiparametric and nonparametric specifications. A notable feature of Wright’s linear IV estimator is that it is applicable to incomplete models that leave the genesis of endogenous explanatory variables unspecified. On the other hand, inversion of the linear model enables the value of unobservable heterogeneity to be expressed as a function of observable variables. Only recently has the application of incomplete IV models been extended to cases in which this inversion produces a non-singleton set of values of unobservable variables. This situation arises in many models such as those featuring discrete choice, counts, or censored outcomes, or when there are multiple sources of heterogeneity as in random coefficient models, or when economic considerations result in inequality restrictions on values taken by observed and unobserved variables. This paper provides an introduction to the methods set out for analyzing such generalized instrumental variable (GIV) models in Chesher and Rosen (2017). An illustrative example is provided in which an outcome is determined by a random coefficients linear model with an endogenous explanatory variable and instrumental variable exclusion and independence restrictions.

Diffuse radio sky models using large-scale shapelets

Sky models used in radio interferometric data-processing primarily consist of compact and discrete radio sources. When there is a need to model large-scale diffuse structure such as the Galaxy, specialized source models are sought after for the sake of simplicity and computational efficiency. We propose the use of shapelet basis functions for modeling the large-scale diffuse structure in various radio interferometric data-processing pipelines. The conventional source model construction using shapelet basis functions is restricted to using images of smaller size due to limitations in computational resources such as memory. We propose a novel shapelet decomposition method to lift this restriction, enabling the use of images of millions of pixels (as well as a wide spectral bandwidth) for building models of large-scale diffuse structure. Furthermore, the application of direction-dependent errors onto diffuse sky models is an expensive operation that is often performed as a convolution. We propose using some specific properties of shapelet basis functions to apply these direction-dependent errors as a product of the model coefficients, which avoids the need for convolution. We provide results based on simulations and real observations. In order to measure the efficacy of our proposed method in modeling large-scale diffuse structure, we considered the direction-dependent calibration of simulated as well as real LOFAR observations that have a significant number of diffuse large-scale structure. The results show that by including large-scale shapelet models of the diffuse sky, we are able to overcome a major problem of existing calibration techniques, which do not model this large-scale diffuse structure, that is, the suppression of this large-scale diffuse structure because the model is incomplete.

External Validation of an Electronic Health Record-Based Diagnostic Model for Histological Acute Tubulointerstitial Nephritis.

Accurate diagnosis of acute tubulointerstitial nephritis (AIN) often requires a kidney biopsy. We previously developed a diagnostic statistical model for predicting biopsy-confirmed AIN by combining four laboratory tests after evaluating over 150 potential predictors from the electronic health record. Here, we validate this diagnostic model in two biopsy-based cohorts at Johns Hopkins Hospital (JHH) and Yale, which were geographically and temporally distinct from the development cohort, respectively. We analyzed patients who underwent kidney biopsy at JHH and Yale University (2019-2023). We assessed discrimination (AUC) and calibration using previously derived model coefficients and recalibrated the model using an intercept correction factor that accounted for differences in baseline prevalence of AIN between development and validation cohorts. We included 1982 participants: 1454 at JHH and 528 at Yale. JHH (5%) and Yale (17%) had lower proportions of biopsies with AIN than the development set (23%). The AUC was 0.73 (0.66-0.79) at JHH and 0.73 (0.67-0.78) at Yale, similar to the development set (0.73 (0.64-0.81)). Calibration was imperfect in validation cohorts, particularly at JHH, but improved with application of an intercept correction factor. The model increased AUC of clinicians' prebiopsy suspicion for AIN by 0.10 to 0.77 (0.71-0.82). An AIN diagnostic model retained discrimination in two validation cohorts but needed recalibration to account for local AIN prevalence. The model improved clinicians' ability to predict AIN.

Understanding and Predicting Ligand Efficacy in the μ-Opioid Receptor through Quantitative Dynamical Analysis of Complex Structures.

The μ-opioid receptor (MOR) is a G-protein coupled receptor involved in nociception and the primary target of opioid drugs. Understanding the relationships among the ligand structure, receptor dynamics, and efficacy in activating MOR is crucial for drug discovery and development. Here, we use coarse-grained normal-mode analysis to predict ligand-induced changes in receptor dynamics with the Quantitative Dynamics Activity Relationship (QDAR) DynaSig-ML methodology, training a LASSO regression model on the entropic signatures (ESs) computed from ligand-receptor complexes. We train and validate the methodology using a data set of 179 MOR ligands with experimentally measured efficacies split into strictly chemically different cross-validation sets. By analyzing the coefficients of the ES LASSO model, we identified key residues involved in MOR activation, several of which have mutational data supporting their role in MOR activation. Additionally, we explored a contact-only LASSO model based on ligand-protein interactions. While the model showed predictive power, it failed at predicting efficacy for ligands with low structural similarity to the training set, emphasizing the importance of receptor dynamics for predicting ligand-induced receptor activation. Moreover, the low computational cost of our approach, at 3 CPU s per ligand-receptor complex, opens the door to its application in large-scale virtual screening contexts. Our work contributes to a better understanding of dynamics-function relationships in the μ-opioid receptor and provides a framework for predicting ligand efficacy based on ligand-induced changes in receptor dynamics.

Study on characteristics and prediction of the pressure drag of the swept strut under supersonic wide-range conditions

In this paper, the numerical simulation of the swept strut ramjet combustor was carried out under wide-range conditions (Ma3 = 1.8 ∼ 5.0), and the pressure drag characteristics of the swept strut were discussed. The results show that the pressure drag characteristics of the swept strut are related to the Mach number of the combustor inlet and the swept angle of the strut. The decreased boundary of the strut pressure drag coefficient gradually advances with the decrease of the Mach number of the combustor inlet. When Ma3 = 1.8 ∼ 2.0, the pressure drag reduction boundary is α = 15°. When Ma3 = 2.2 ∼ 2.8, the pressure drag reduction boundary is α = 45°. When Ma3 = 3.0 ∼ 4.0, the pressure drag reduction boundary is α = 60°. When Ma3 = 5.0, the pressure drag reduction boundary is α = 65°. In addition, with the decrease of the Mach number of the combustor inlet, the pressure drag reduction performance benefit brought by increasing the swept angle of the strut will gradually increase. Furthermore, a pressure drag coefficient prediction model suitable for wide-range conditions and multiple configurations of swept struts was proposed based on deep learning. The prediction model consists of two parts in series, which includes the prediction model of the surface pressure coefficient of the swept strut based on multilayer perceptron (MLP) and the prediction model of the pressure drag coefficient of the swept strut based on convolutional neural network (CNN). To improve the prediction accuracy of the MLP model, new training samples were added based on the ensemble-based uncertainty quantification, and the improved MLP model was obtained by retraining. The results show that both the two prediction models have high prediction accuracy under the effect of multiple complex flow characteristics on the strut. The results of this study are helpful to provide a reference for the aerodynamic drag reduction design of the strut in the wide-speed supersonic combustor.

Analysis of The Impact of Factors Affecting the Recovery of Small and Medium Enterprises in Vietnam with the Goal of Sustainable Development in the Context of Economic Crisis

Objective: The article analyzes the impact of various factors on the profitability of small and medium-sized enterprises (SMEs) in Vietnam amidst an economic crisis, using a dataset of Vietnamese SMEs from 2016 to 2018 across different provinces nationwide. Method: Employing panel data regression techniques in two forms: Fixed Effects (FE) and Random Effects (RE) models to estimate the impact of factors on enterprise profitability. Results and Discussion: Through estimating the two models on the article's dataset, the RE model shows that the coefficients of the explanatory variables in the model are statistically significant, whereas the FE model's coefficients are not. The estimation results from the RE model indicate that all variables including equity value, number of foreign workers, number of sectors the enterprise operates in the dummy variable for state support, average labour cost, and the dummy variable for the main operating sector of the enterprise affect the profitability of the enterprise. The RE model results suggest that the most significant factors impacting enterprise profitability are the business sector and state support. We need to have policies that create favorable conditions for businesses to achieve sustainable development goals (SDG). Conclusions: Results from the estimated model show that the most important factors affecting business profits are the business sector and state support. The state and businesses need to take measures to innovate activities to help businesses develop sustainably during the economic crisis.