Competitive System Research Articles

The Diffusive Lotka–Volterra Competitive Model with Advection Term: Exclusion, Coexistence and Multiplicity

Earlier, the research was mainly focused on the classic diffusive two-species Lotka–Volterra competitive system (without advection). Averill et al. [2017] regarded a diffusive two-species Lotka–Volterra competitive system with advection term (with one species having a combination of random dispersal and biased movement upward along the resource gradient, while the other species adopts purely random dispersal). In this paper, we consider a more general diffusive two-species Lotka–Volterra competitive system with advection term (involving both species with a combination of random dispersal and biased movement upward along their respective resource gradients). By utilizing the theory of monotone dynamical systems, spectral analysis, methods of super- and sub-solutions and some nontrivial analytic skills, we finally obtain a rather deep understanding on the global dynamics. Moreover, our results reveal that the dynamical behavior of the system is very complex: exclusion, coexistence and bistability all may happen depending closely on the interspecific competition intensities. More interestingly, by bifurcation theory, we find that the system always admits multiple coexistence steady states when the interspecific competition intensities are near the critical point.

Multi-scale Information Aggregation for Spoofing Detection

Synthesis artifacts that span scales from small to large are important cues for spoofing detection. However, few spoofing detection models leverage artifacts across different scales together. In this paper, we propose a spoofing detection system built on SincNet and Deep Layer Aggregation (DLA), which leverages speech representations at different levels to distinguish synthetic speech. DLA is totally convolutional with an iterative tree-like structure. The unique topology of DLA makes possible compounding of speech features from convolution layers at different depths, and therefore the local and the global speech representations can be incorporated simultaneously. Moreover, SincNet is employed as the frontend feature extractor to circumvent manual feature extraction and selection. SincNet can learn fine-grained features directly from the input speech waveform, thus making the proposed spoofing detection system end-to-end. The proposed system outperforms the baselines when tested on ASVspoof LA and DF datasets. Notably, our single model surpasses all competing systems in ASVspoof DF competition with an equal error rate (EER) of 13.99%, which demonstrates the importance of multi-scale information aggregation for synthetic speech detection.

The impact of a payer-provider joint venture on healthcare value.

To examine how a novel payer-provider joint venture (JV) between one payer and multiple competitive delivery systems in New Hampshire (NH), which included value-based payment, care management, and non-financial supports, impacted healthcare value and payer and provider group experiences. We conducted a mixed-methods study. We used a quasi-experimental longitudinal difference-in-differences design to examine the impact of the JV (which started in January 2016 and ended in December 2020) on healthcare utilization, quality, and spending, using members in Maine (ME) as a control group. We also analyzed patient uptake of the JV's care management program using routinely collected administrative data and assessed payer and provider group leaders' perspectives about the JV via semi-structured interviews. We used administrative and claims data from 2013 to 2019 in a commercially insured population under 65 years in NH and ME. We also used administrative data on care management eligibility and uptake and conducted semi-structured interviews with payer and provider group leaders affiliated with the JV. The JV was associated with no sustained change in medical utilization, quality, and spending throughout the study period. In the first year of the JV, there was a $142 (95% confidence interval: $41, $243) increase in pharmaceutical spending per member and a 13% (4.4%, 25%) relative increase in days covered for diabetes medications. Only 15% of eligible members engaged in care management, which was a key component of the JV's multi-pronged approach. In a disconnect from the empirical findings, payer and provider group leaders believed that the JV reduced healthcare costs and improved quality. Our findings provide evidence for future payer-provider JVs and demonstrate the importance of having a valid control group when evaluating JVs and value-based payment arrangements.

STEWART PLATFORM MULTIDIMENSIONAL TRACKING CONTROL SYSTEM SYNTHESIS

Context. Creating guaranteed competitive motion control systems for complex multidimensional moving objects, including unstable ones, that operate under random controlled and uncontrolled disturbing factors, with minimal design costs, is one of the main requirements for achieving success in this class devices market. Additionally, to meet modern demands for the accuracy of motion control processes along a specified or programmed trajectory, it is essential to synthesize an optimal control system based on experimental data obtained under conditions closely approximating the real operating mode of the test object. Objective. The research presented in this article aims to synthesize an optimal tracking control system for the Stewart platform’s working surface motion, taking into account its multidimensional dynamic model. Method. The article employs a method of a multidimensional tracking control system structural transformation into an equivalent stabilization system for the motion of a multidimensional control object. It also utilizes an algorithm for synthesizing optimal stabilization systems for dynamic objects, whether stable or not, under stationary random external disturbances. The justified algorithm for synthesizing optimal stochastic stabilization systems is constructed using operations such as addition and multiplication of polynomial and fractional-rational matrices, Wiener factorization, Wiener separation of fractional-rational matrices, and the calculation of dispersion integrals. Results. As a result of the conducted research, the problem of defining the concept of analytical design for a Stewart platform’s optimal motion control system has been formalized. The results include the derived transformation equations from the tracking control system to the equivalent stabilization system of the Stewart platform’s working surface motion. Furthermore, the structure and parameters of the main controller transfer function matrix for of this control system have been determined. Conclusions. The justified use of the analytical design concept for the Stewart platform’s working surface optimal motion control system formalizes and significantly simplifies the solution to the problem of synthesizing complex dynamic systems, applying the developed technology presented in [1]. The obtained structure and parameters of the Stewart platform’s working surface motion control system main controller, which is divided into three components W1, W2, and W3, improve the tracking quality of the program signal vector, account for the cross-connections within the Stewart platform, and increase the accuracy of executing the specified trajectory by increasing the degrees of freedom in choosing the controller structure

Сучасні аспекти формування збірних команд у баскетболі

The main factor in the development of team game sports, including basketball, is the presence of globalization, professionalization and commercialization processes, which significantly affects the performance of national teams in the most important international starts. Changes in the system of competitive basketball activities have led to a significant expansion of the system of international competitions, which requires from coaches a reasonable approach to the formation of national teams as a basis for successful performance in the Games of the Olympics and World Championships. Material and Methods. The study analyzed the competitive performance of 21 men's and 19 women's national basketball teams that participated in the Olympic Games and World Championships from 1936 to 2020. In order to determine the peculiarities of the formation of national teams in basketball, we analyzed the data of 264 players (men and women) who became medalists of the Olympic Games in the period from 1976 to 2024. Results. The results of the study indicate that the main leaders in modern basketball are the USA men's and women's national teams with the highest percentage of winning medals in the Olympics (31.7% and 30.5%) and World Championships (21.0% and 24.6%). The main focus of the formation of the USA national teams for participation in the Olympic Games coaches - the availability of experience in international competitions (the number of Olympic cycles that the athlete spent as a member of the national team) and the age of athletes. Based on the performance of the men's and women's teams, a trend of increasing number of athletes over the age of 32 is identified, where the maximum value for men (5 players) is observed in 2024 and for women (4) in 2016. Conclusions. The analysis of basketball development shows that the use of modern international experience in the rational formation of national teams allowed to establish that the integral component is the age of players, professional experience of participation in international competitions as part of the national team, as well as the universalization of player training. At this stage of basketball development, there is a tendency to increase the age of female athletes who are members of national teams, which provides an effective rotation over several Olympic cycles

Highly effective fluorescence detection of UO22+ ions by an anionic Na/Eu heterometallic metal–organic framework with Lewis basic chelating sites

Uranium is a serious radioactive contaminant that can easily migrate into groundwater and surface water, posing a deadly threat to human health. Despite the development of various materials for detecting uranyl ions in water, rational design and synthesis of new uranium sensors with sensitivity, selectivity, and fast response remain challenging. Herein, we demonstrate a novel strategy for obtaining highly sensitive and selective UO22+ sensors by constructing heterometallic metal–organic framework with both an anionic skeleton and abundant chelating sites. Namely, the first anionic Na/Eu heterometallic metal–organic framework (Na/Eu-MOF) based UO22+ sensor is successfully synthesized by using sodium salt and europium salt as reactants, and abundant ether groups were introduced into its porous structure as chelating Lewis basic sites. Beneficial from the synergistic effect between the anionic skeleton and the chelating sites, Na/Eu-MOF achieved rapid, selective adsorption and fluorescence quenching toward uranyl ion. The detection limits of Na/Eu-MOF in deionized and lake water were determined to be 49.7 nM and 113.0 nM, respectively, which are lower than the maximum concentration of 130.0 nM in drinking water proposed by the United States Environmental Protection Agency, indicating potential environmental applications. The detection capability of Na/Eu-MOF is attributed to the combination system of energy competition and interactions between UO22+ ions and Na/Eu-MOF. This work offers a feasible strategy to construct an anionic heterometallic metal–organic framework with chelating sites for uranyl detection in an aqueous solution.

Attack efficiency in first league men’s volleyball for playing positions, according to the value level of the teams

Background and Study Purpose. The attack is a crucial technical element in scoring points in volleyball. This research aims to identify differences in attack efficiency and errors based on the value level of teams in the competitive system, considering different playing positions. Material and Methods. The analysis included 86 attacking players from the rosters of 12 teams in the men’s domestic first league. The distribution by positions was as follows: 37 outside hitters, 19 opposites, and 30 middle blockers. Statisticians from each team recorded the data using Data Volley software during three championship matches. For each player, the following parameters were interpreted: Attack Efficiency (E%), Error% (=), Blocked Attack% (/), Poor% (-), Blocked but Recovered% (!), Positive% (+), and Winning% (#). Attack efficiency was analyzed for each playing position across top teams (positions 1-4 in the final ranking), mid-level teams (positions 5-8), and lower-level teams (positions 9-12). Results. Across all three playing positions, top teams demonstrate higher percentages in attack efficiency, winning executions, and positive outcomes compared to average and lower-level teams. Top and average teams also have lower percentages of errors in attack executions. For the outside hitter position, no statistically significant superiority is observed between top and middle teams for any attack variable, indicating a balance in player performance. In the opposite hitter position, top and middle-level players show higher attack efficiency and direct point scores (Winning). They also have lower poor execution rates, despite the lack of statistical confirmation for superiority in many attack variables. Among all positions, top middle blockers exhibit a clear superiority over low-level teams across all attack variables. Conclusions. The findings of the study highlight the critical role of team value level in influencing attack efficiency and execution quality across different playing positions in volleyball. The results underscore the importance of strategic differentiation in training and game planning. This is especially crucial for teams aiming to optimize their performance. Coaches and trainers should focus on tailored approaches that address the specific strengths and weaknesses of each playing position. They should also consider the overall team value level in their strategies. This approach could lead to improved competitive outcomes and a more effective utilization of player potential across all levels of competition.

Exploring the Relationship between Reward Practices and Employee Engagement among County Governments in North Rift Region, Kenya

County governments in Kenya have not had systematic practices of employee engagement. The few that did adopt these practices did so in an isolated, informal, and uncoordinated manner, which was unlikely to yield any meaningful results. Effective human resource practices can have a significant impact on employee engagement. Low employee engagement can result in various issues, including high employee turnover, low productivity, and reduced organizational effectiveness. This study sought to establish the effect of employee reward practices on employee engagement among selected county governments in the North Rift Region, Kenya. The study was anchored on Human Capital Theory. The target population comprised 10,009 employees working in three North Rift counties comprising of Elgeyo Marakwet, Uasin Gishu, and Nandi Counties. The target population was made up of 2,611 employees from Elgeyo Marakwet County, 3,164 employees from Uasin Gishu County, and 4,234 employees from Nandi County. Cluster and simple random sampling techniques were used to select the 385 employees. The data was collected using structured questionnaires. A pilot study was conducted to examine the validity and reliability of the research instrument. Quantitative data from the closed-ended questions was analyzed using descriptive statistics. The study used descriptive statistics, including mean, frequencies, percentages, and standard deviation, to assess respondents' levels of agreement with the statements in the questionnaire. Furthermore, regression analysis was conducted to establish the relationship between employee reward practices and employee engagement. The results were presented using tables. The findings revealed that the model was significant in explaining the relationship between employee reward practices and engagement (F = 142.299, p = 0.000). The study also found that employee reward practices (B=0.358, p<0.001) had positive and significant effect on employee engagement. Consequently, the study recommends that County governments should focus on revising and strengthening their reward practices to ensure fairness and competitiveness. Additionally, the managements of the three counties should develop competitive and equitable reward systems that recognize and reward employees' contributions effectively. Keywords: Reward Practices, Employee Engagement, Public Sector Motivation, County Governments, North Rift Region

Agency conflicts, product market competition and investment efficiency: new evidence from emerging market

PurposeThis study examines the influence of product market competition on investment inefficiency of Indian firms in context of agency problems. Additionally, this study also investigates whether intense competition is a substitute for or complementary to corporate governance in reducing investment inefficiency of firms.Design/methodology/approachUtilizing the residuals extracted from Biddle et al. (2009) investment model, investment inefficiency, overinvestment and underinvestment are measured for 506 non-financial Indian listed firms with 6,998 firm-year observations from 2009 to 2022. Product market competition is measured using various proxies such as the Herfindahl–Hirschman index, top-four firm concentration ratio, total number of firms in industry, industry market size, weighted average of entry costs and research and development (R&D) to sales ratio. Firms' internal governance is measured using a newly corporate governance index developed with 65 new governance stipulations. Several pooled ordinary least squares (OLS) panel regressions were estimated involving investment inefficiency of firms, product market competition, governance index and firm-specific variables. Endogeneity issues were addressed through two-stage least squares. Robustness checks were also conducted using a two-step system generalized method of moments (GMM).FindingsThe main finding of the study indicates that heightened product market competition reduces investment inefficiency, overinvestment and underinvestment among the selected Indian firms suggesting that firms facing intense competition are less prone to invest below or above optimal levels. This is primarily because in highly competitive industries, managers face greater liquidation risks, prompting more efficient capital investment decisions. The results also indicate that robust corporate governance significantly mitigates investment inefficiencies in non-competitive industries compared to competitive ones suggesting heightened competition reduces managerial slack, resulting in diminished benefits from good governance in competitive settings. Overall results indicate a substitution effect between corporate governance and competition in reducing investment inefficiency, with robustness across various empirical specifications, industry classifications and alternative competition and inefficiency measures.Practical implicationsThe evidence from this work emphasizes the pivotal roles of market competitiveness and corporate governance in shaping investment efficiency. Regulators must closely monitor monopolistic behaviors to safeguard stakeholder interests, enhance investment efficiency and foster value creation. Recognizing the positive impact of market competition, firms should prioritize initiatives to promote industrial openness and intensify competition while strengthening market mechanisms. Policymakers should consider implementing competition-centric governance policies, such as deregulation and antitrust laws, to stimulate market competition. These measures can mitigate governance-related costs and promote a competitive marketplace.Originality/valueThis study provides fresh evidence concerning the effects of product market competition on investment efficiency of Indian firms under new governance norms, an unexplored area in India as most of the existing work has primarily examined the association between competition and investment levels. To best of our knowledge, this is one of the earliest studies demonstrating the substitution effects of competitiveness and governance systems on lowering investment inefficiency suggesting a significant influence of corporate governance in non-competitive industries. Finally, this study contributes to the field of methodology by developing a new firm-specific governance index based on 65 governance indicators.

DEVELOPING A COMPETITIVE REWARD SYSTEM TO ATTRACT QUALIFIED TEACHERS

The quality of education plays an important role in determining educational outcomes, as competent and dedicated educators are able to provide effective teaching, motivate students, and help them reach their full potential. However, in many countries, including Indonesia, there are still challenges in attracting and retaining quality educators. Therefore, it is important for educational institutions to formulate a reward system that is not only financially competitive, but also includes non-financial aspects that can improve the satisfaction and motivation of educators. This study employs a descriptive qualitative approach. Data collection was conducted through a literature review, focusing on relevant written sources such as books, journal articles, research reports, theses, and dissertations. Data analysis was conducted using triangulation to compare and confirm information from various sources, providing a more comprehensive and reliable understanding of the topic being studied. The results show that the development of a competitive reward system is critical to attracting quality educators, who are key to improving the quality of educational education. Education institutions can create an atmosphere that supports the improvement of teaching quality and education as a whole by implementing a balanced reward system and considering feedback from educators.

Kinetic adsorption studies of methylene blue and crystal violet dyes removal in single and competitive systems using lemon peels/activated carbon/alginate composite

Kinetic adsorption studies of methylene blue and crystal violet dyes removal in single and competitive systems using lemon peels/activated carbon/alginate composite

Wave Speeds for a Time-Periodic Bistable Three-Species Lattice Competition System

In this paper, we consider propagation direction (which can be used to predict which species will occupy the habitat or win the competition eventually) of a bistable wave for a three-species time-periodic lattice competition system with bistable nonlinearity, aiming to address an open problem. As a first step, by transforming the competition system to a cooperative one, we study the asymptotic behavior for the bistable wave profile and then prove the uniqueness of the bistable wave speed. Secondly, we utilize comparison principle and build up two couples of upper and lower solutions to judge the sign of the bistable wave speed which partially provides the answer to the open problem. As an application, we reduce the time-periodic system to a space–time homogeneous system, we obtain the corresponding criteria and carry out numerical simulations to illustrate the availability of our results. Moreover, an interesting phenomenon we have found is that the two weak competitors can wipe out the strong competitor under some circumstances.

Distributed Bipartite Consensus of Multi-Agent Systems via Disturbance Rejection Control Strategy

This work aims to focus on analyzing the consensus control problem in cooperative–competitive networks in the occurrence of external disturbances. The primary motive of this work is to employ the equivalent input-disturbance estimation technique to compensate for the impact of external disturbances in the considered multi-agent system. In particular, a suitable low-pass filter is implemented to enhance the accuracy of disturbance estimation performance. In addition, a specific signed, connected, and structurally balanced undirected communication graph with positive and negative edge weights is considered to express the cooperation–competition communication among neighboring agents. The cooperative–competitive multi-agent system reaches its final state with same magnitude and in opposite direction under the considered structurally balanced graph. By utilizing the properties of Lyapunov stability theory and graph theory, the adequate conditions assuring the bipartite consensus of the examined multi-agent system are established as linear matrix inequalities. An illustrative example is delivered at the end to check the efficacy of the designed control scheme.

Legal regulation of education in Ukraine. Part 6: Features of admission to higher education in Ukraine

This article examines the legal issues of regulating the access of citizens of Ukraine to higher education of the third educational and scientific degree (doctor of philosophy) in the paradigm of international acts, the Constitution of Ukraine, the Laws of Ukraine, and Resolutions of the Cabinet of Ministers of Ukraine in the field of education. This is related to the existence of certain legal conflicts in the education sector, which arose as a result of the ambiguity and imperfection of the legislation of Ukraine on education, which the Ministry of Education and Science of Ukraine uses to illegally restrict the access of citizens of Ukraine to higher education of the third educational and scientific degree. Taking into account the requirements of the Constitution of Ukraine, the Universal Declaration of Human Rights of the United Nations, and the Convention for the Protection of Human Rights and Fundamental Freedoms, the article presents the results of a study of the peculiarities of the application of the provisions of the relevant legislative acts in the field of education (with all changes and additions introduced as of September 1, 2024), namely the Law of Ukraine “On Education” (dated September 5, 2017, under No. 2145-VIII), the Law of Ukraine “On Higher Education” (dated July 1, 2014, under No. 1556- VII) and the “Procedure for Training Candidates for Higher Education Degrees of Doctor of Philosophy and Doctor of Sciences in institutions of higher education (scientific institutions)”, approved by Resolution No. 261 of the Cabinet of Ministers of Ukraine (dated March 23, 2016). At the same time, the research is mainly focused on the peculiarities of applying the above­mentioned legislative acts to determine the differences in the conditions of access to free and paid education and the established legitimacy and feasibility of certain elements of such conditions. Principally this concerns the introduction by the State of Ukraine of unified professional exams and other tests (with the use of external independent evaluation) as a condition for access to the next stage of tests, namely, entrance exams and other tests for admission to study introduced by higher education institutions of Ukraine. That is, the legality of establishing a two-level system of competitions and entrance tests for those who wish to obtain a higher education of the third educational and scientific degree (doctor of philosophy) on a paid basis (i.e., at their own expense or the expense of non-state grants and scholarships) is being considered. The article is the sixth one within the cycle of studies in which the peculiarities of access of Ukrainian citizens to higher education in martial law conditions are addressed.

Adaptive synchronization and anti-synchronization of Julia sets generated by the competitive model

In this paper, we study the fractal behaviour of a competitive model that describes the interaction of plankton allelopathy. This paper aims to establish synchronization and anti-synchronization of Julia sets of two competitive systems with some different parameters by using an adaptive control strategy. Firstly, a discrete version of the competitive model is obtained, and then the Julia set of the discrete version is generated by using the escape-time algorithm. Adaptive controllers and parameter update laws for unknown parameters are designed to achieve synchronization and anti-synchronization of Julia sets. Furthermore, we can determine unknown parameters of the competitive system by using this adaptive control technique. Here, the adaptive synchronization and anti-synchronization of Julia sets are accomplished by its trajectories synchronization and anti-synchronization due to the close relation of trajectories of the system with the Julia set of the system. Numerical simulations are carried out to validate several key theoretical results as well as the efficacy and accuracy of the applied methodologies. Moreover, with the help of this analysis, we can study other models of a similar type.

Adsorption sites and interactions of pigments in molasses-based distillery effluent on starch-based composites: Ternary competitive adsorption and theoretical calculations

The pigment present in molasses-based distillery effluent constitutes a primary factor influencing its degradation. Adsorption is an effective approach to eliminate pigment from wastewater. In this study, a cationic cassava starch (CCS) magnetic composite (CCS@Fe3O4) was prepared and used as adsorbents for the removal of undesirable pigments. The adsorption behaviors of caffeic acid (CA), gallic acid (GA), and melanoidin (ME) on CCS@Fe3O4 in the wastewater were investigated using single and ternary competitive adsorption systems. The equilibrium adsorption capacities of CA, GA, and ME on CCS@Fe3O4 were 197.04, 195.55, and 623.97 mg/g at the optimized conditions (0.3 mg/mL CCS@Fe3O4 dosage, temperature of 38 °C, and pH of 7). The adsorption kinetic model showed that chemisorption accounted for most of the adsorption of CA, GA, and ME on CCS@Fe3O4. The adsorption mechanisms of pigments on CCS@Fe3O4 were explored at the molecular level through quantum chemical calculations. The electrostatic potentials (ESP), average local ionisation energy (ALIE), and Fukui indices calculation indicated that the quaternary ammonium group in CCS@Fe3O4 was more susceptible to electrophilic reactions. The CC and benzene rings in CA and GA, and the COO- in ME, represent sites of attack for quaternary ammonium during adsorption. Furthermore, the competitive adsorption results, adsorption energy, and electron transfer data demonstrated that the adsorption capacity of CCS@Fe3O4 for pigments followed the order ME>GA>CA. Overall, the competitive adsorption mechanisms of CA, GA, and ME on CCS@Fe3O4 were unveiled, with quantum chemical calculations offering crucial insights into the adsorption process.

A novel differential chaos shift keying system based on joint time slot and code index of carrier phase modulation

This paper proposes a novel differential chaos shift keying (DCSK) system that utilizes carrier phase modulation in combination with time slot and code index modulation, referred to as CP-TCIM-DCSK system, to achieve high data rate transmission. In the proposed CP-TCIM-DCSK system, the carrier modulated by the carrier phase is used to transmit the information-bearing signal. In addition to physically transmitted information bits, extra information bits are conveyed through time slot and Walsh code modulation, as well as carrier phase modulation, making full use of the benefits of multidimensional modulation. To successfully estimate carrier phase bits and code index bits, an effective joint detection algorithm for carrier phase and code index tailored for the CP-TCIM-DCSK system is introduced. The theoretical Bit Error Rate (BER) expressions for the CP-TCIM-DCSK scheme are derived for both Additive White Gaussian Noise (AWGN) and multipath Rayleigh fading channels. Furthermore, a comparison of data rates, energy efficiency, and complexity between the CP-TCIM-DCSK system and the most advanced systems in the same category at present is conducted. The results validate the accuracy of theoretical analysis through simulation and demonstrate that the proposed scheme outperforms its competitive systems in terms of BER performance.

TOOLS FOR EFFECTIVE CAREER DEVELOPMENT MANAGEMENT

In today’s environment, managing employees’ career development is becoming a key factor for the success and sustainable development of organizations, especially small and medium-sized enterprises (SMEs). The purpose of this article is to investigate current approaches to career management in SMEs and provide practical recommendations based on theoretical research and empirical evidence. The novelty of the study lies in the integrated approach to analyzing career management practices using both quantitative and qualitative methods. This allows for a deeper understanding of the impact of career development on employee motivation and retention in a resource-constrained and highly competitive environment. The research methodology includes reviewing existing literature and analyzing case studies from different industries to identify best practices and success stories. The use of mixed research methods, such as surveys and in-depth interviews, provides a more comprehensive view of current practices and their impact on employees. The results of the study show that career development management is critical to improve employee motivation and retention, which is particularly relevant for SMEs. Pay attention to aspects such as training and development, performance appraisal systems, reward systems and their impact on employee motivation. Training and development help to improve employees’ skills and adaptability to changes in the market, while appraisal systems such as 360-degree feedback and regular evaluations help to identify achievements and areas for improvement, forming individual development plans. A fair and competitive compensation system motivates employees and promotes employee retention. The author’s personal contribution is the design and implementation of an integrated research methodology that combines quantitative and qualitative methods, which provided comprehensive data and offered practical recommendations for SMEs. The article also discusses the factors that influence employee retention and the creation of a positive corporate culture, which contributes to their long-term professional growth and enhances companies’ competitiveness in the market. In an environment of rapid change and globalization, SMEs must pay special attention to human capital development to maintain competitiveness and achieve sustainable growth. The article provides recommendations for the implementation of effective career management programs and examples of successful practices from different sectors.

Existence of forced waves and gap formations for a Lotka-Volterra competition system with nonlocal dispersal in a time periodic shift habitat

This paper is devoted to the study of a class of time periodic Lotka-Volterra competition system with nonlocal dispersal and shifting habitats. By using some known results of the periodic KPP model and employing the iterative techniques, we prove that there exist two positive numbers $c_{0}(d_{1})$ and $c_{0}(d_{2})$ such that the system admits a forced wave provided that the forcing speed $c\in(-c_{0}(d_{2}),c_{0}(d_{1}))$. In addition, based on the theoretical results, we show that the gap formations exist for $c>c_{0}(d_{1})$ and $c<-c_{0}(d_{2})$.

Implementation of socio-economic variables in risk adjustment systems: A quantitative analysis using the example of Germany

At least in Western Europe, competitive social health insurance systems have implemented systems of morbidity-based risk adjustment to establish a level playing field for insurers. However, insured persons with specific socio-economic characteristics are still underfunded, leaving incentives for risk selection. In Germany, there is an ongoing debate about (re)implementing socio-economic variables to reduce this undercompensation. This study analyses whether the following four socio-economic groups are systematically under- or over‐compensated under the present risk equalization system in Germany: insured persons with co‐payment exemption (1), recipients of basic income support for unemployment (2), of benefits of social long-term care-insurance (3) and insured persons with reduced earning capacity (4). On this basis, several attempts of incorporating these variables into the German risk adjustment system, allowing a better fit for the socio-economically disadvantaged groups, are examined. With a data set of about 9.2 million insured persons, the performance of the modifications is demonstrated for the German system. The disparate outcomes of the various models in different dimensions necessitate the consideration of trade-offs and their incorporation into the implementation of a model designed to mitigate the undercompensation of the affected insured groups.