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This paper aims to address the issue of model discontinuity typically encountered in traditional Denavit-Hartenberg (DH) models. To achieve this, we propose the use of a local Product of Exponentials (POE) approach. Additionally, a modified calibration model is presented which takes into account both kinematic errors and high-order joint-dependent kinematic errors. Both kinematic errors and high-order joint-dependent kinematic errors are analyzed to modify the model.

Robot positioning accuracy is critically important in high-speed and heavy-load manufacturing applications. One essential problem encountered in calibration of series robot is that the traditional methods only consider fitting kinematic errors, while ignoring joint-dependent kinematic errors.

Laguerre polynomials are chosen to fitting kinematic errors and high-order joint-dependent kinematic errors which can avoid the Runge phenomenon of curve fitting to a great extent. Levenberg–Marquard algorithm, which is insensitive to overparameterization and can effectively deal with redundant parameters, is used to quickly calibrate the modified model. Experiments on an EFFORT ER50 robot are implemented to validate the efficiency of the proposed method; compared with the Chebyshev polynomial calibration methods, the positioning accuracy is improved from 0.2301 to 0.2224 mm.

The results demonstrate the substantial improvement in the absolute positioning accuracy achieved by the proposed calibration methods on an industrial serial robot.

In this study, a dynamic contracting model is developed between a venture capitalist (VC) and an entrepreneur (EN) to explore the influence of asymmetric beliefs regarding output-relevant parameters, agency conflicts and complementarity on the VC's posterior beliefs through the EN's unobservable effort choices to influence the optimal dynamic contract.

The authors construct the contracting model by incorporating the VC's effort, which is ignored in most studies. Using backward induction and a discrete-time approximation approach, the authors solve the continuous-time contract design problem, which evolves into a nonlinear ordinary differential equation (ODE).

The optimal equity share that the VC provides to the EN decreases over time. In accordance with the empirical evidence, the EN's optimistic beliefs regarding the project's profitability positively affect its equity share. However, the interactions between the optimal equity share, project risk and both partners' degrees of risk aversion are not monotonic. Moreover, the authors find that the optimal equity share increases with the degree of complementarity, which indicates that the EN is willing to cooperate with the VC. This study’s results also show that the optimal equity shares at each time are interdependent if the VC is risk-averse and independent if the VC is risk-neutral.

In conclusion, the authors highlight two potential directions for future research. First, the authors only considered a single VC, whereas in practice, a risk project may be carried out by multiple VCs, and it is interesting to discuss how the degree of complementarity affects the number of VCs that ENs contract. Second, the authors may introduce jumps and consider more general multivariate stochastic volatility models for output dynamics and analyze the characteristics of the optimal contracts. Third, further research can deal with other forms of discretionary output functions concerning complementarity, such as Cobb–Douglas and constant elasticity of substitution (See Varian, 1992).

The results of this study have several implications. First, it offers a novel approach to designing dynamic contracts that are specific and easy to operate. To improve the complicated venture investment situation and abate conflict between contractual parties, this study plays a good reference role. Second, the synergy effect proposed in this study provides a theoretical explanation for the executive compensation puzzle in economics, in which managers are often “rewarded for luck” (Bertrand and Mullainathan, 2001; Wu et al., 2018). This result indicates a realistic perspective on financing and establishing cooperative relationships, which enhances the efficiency of venture investment. Third, from an empirical standpoint, one can apply this framework to study research and development (R&D) problems.

First, the authors introduce asymmetric beliefs and Bayesian learning to study the dynamic contract design problem and discuss their effects on equity share. Second, the authors incorporate the VC's effort into the contracting problem, and analyze the synergistic effect of effort complementarity on the optimal dynamic contract.

The purpose of this paper is to investigate self-competence—the ability to act responsibly on one's own—and likely nonlinear wage returns across different levels of self-competence as part of training curricula.

The authors identify the teaching of self-competence at the occupational level by applying machine-learning methods to the texts of occupational training curricula. Defining three levels of self-competence (high, medium, and low) and using individual labor market data, the authors examine nonlinearities in wage returns to different levels of self-competence.

The authors find nonlinear returns to teaching self-competence: a medium level of self-competence taught in an occupation has the largest wage returns compared to low or high levels. However, in occupations with a high cognitive requirement profile, a high level of self-competence generates positive wage returns.

This paper first adds to research on the importance of teaching noncognitive skills for economic outcomes, which recently—in addition to personality traits research—has primarily focused on social skills by introducing self-competence as another largely unexplored but important noncognitive skill. Second, the paper studies not only average but also nonlinear wage returns, showing that the right level of self-competence is crucial, i.e. neither teaching too little nor too much self-competence provides favorable returns because of trade-offs with other skills (e.g. technical or professional skills). Third, the paper also examines complementarities between cognitive skills and noncognitive skills, again pointing toward nonlinear returns, i.e. only in occupations with a high cognitive requirement profile, high levels of self-competence generate positive wage returns.

The aim of this study is to (1) construct a standard framework for assessing the capability of bioenergy enterprises' digital green innovation partners; (2) quantify the choice of partners for digital green innovation by bioenergy enterprises; (3) propose based on a dual combination empowerment niche digital green innovation field model.

Fuzzy set theory is combined into field theory to investigate resource complementarity. The successful application of the model to a real case illustrates how the model can be used to address the problem of digital green innovation partner selection. Finally, the standard framework and digital green innovation field model can be applied to the practical partner selection of bioenergy enterprises.

Digital green innovation technology of superposition of complementarity, mutual trust and resources makes the digital green innovation knowledge from partners to biofuels in the enterprise. The index rating system included eight target layers: digital technology innovation level, bioenergy technology innovation level, bioenergy green level, aggregated digital green innovation resource level, bioenergy technology market development ability, co-operation mutual trust and cooperation aggregation degree.

This study helps to (1) construct the evaluation standard framework of digital green innovation capability based on the dual combination empowerment theory; (2) develop a new digital green innovation domain model for bioenergy enterprises to select digital green innovation partners; (3) assist bioenergy enterprises in implementing digital green innovation practices.

The purpose of technology mergers and acquisitions (M&A) is to achieve innovation. The authors use the data from the China Patent Research System of China National Intellectual Property Administration to classify technical correlations into three types: similar, complementary and nonrelatedness (cross-sectoral category). And the authors explore three issues: the market reaction to technology-oriented M&A, the impact of technology-oriented M&A on goodwill and how technology-oriented M&A affects innovation.

The authors use data from China Patent Research System of China National Intellectual Property Administration to classify technical correlations into three types: similar, complementary and nonrelatedness (cross-sectoral category). And the authors explore three issues: the market reaction of technology-oriented M&A, the impact of technology-oriented M&A on goodwill and how technology-oriented M&A affects innovation. The empirical research shows that the cross-sectoral M&A is popular in the market and is positively correlated with cumulative abnormal return (CAR) and premium rate of M&A. However, the technology-similarity M&A, which is committed to in-depth exploration of original technology, is negatively correlated with CAR and goodwill.

The empirical research shows that cross-sectoral M&A is popular in the market and is positively correlated with CAR and premium rate of M&A. However, the technology-similarity M&A, which is committed to in-depth exploration of original technology, is negatively correlated with CAR and goodwill. In addition, empirical results show that there is an inverted U-shaped relationship between technology-oriented M&A and innovation output, and the inflection points are 41.8%, 48.9% and 38.8%, respectively.

The research contributions of this paper are as follows: first, most domestic studies simply and roughly measure the degree of technical relevance based on whether the firms belong to the same industry and whether there is common knowledge between them, but the authors provide a more accurate measure of technology-oriented M&A. Second, in the research on the economic consequences of technology-oriented M&As, a large number of literatures have mainly focused on the innovation performance of the acquirer after deals, including the number of patent applications, the number of patent citations, innovation output, etc., and they pay less attention to its impact on the market reaction and goodwill.

A semiparametric stochastic frontier model is proposed for panel data, incorporating several flexible features. First, a constant elasticity of substitution (CES) production frontier is considered without log-transformation to prevent induced non-negligible estimation bias. Second, the model flexibility is improved via semiparameterization, where the technology is an unknown function of a set of environment variables. The technology function accounts for latent heterogeneity across individual units, which can be freely correlated with inputs, environment variables, and/or inefficiency determinants. Furthermore, the technology function incorporates a single-index structure to circumvent the curse of dimensionality. Third, distributional assumptions are eschewed on both stochastic noise and inefficiency for model identification. Instead, only the conditional mean of the inefficiency is assumed, which depends on related determinants with a wide range of choice, via a positive parametric function. As a result, technical efficiency is constructed without relying on an assumed distribution on composite error. The model provides flexible structures on both the production frontier and inefficiency, thereby alleviating the risk of model misspecification in production and efficiency analysis. The estimator involves a series based nonlinear least squares estimation for the unknown parameters and a kernel based local estimation for the technology function. Promising finite-sample performance is demonstrated through simulations, and the model is applied to investigate productive efficiency among OECD countries from 1970–2019.

This paper explores the nonlinear interactions of research and development (R&D) and advertising and their synergistic effect on firm performance using Tobin's Q. This study also aims to investigate differential synergy patterns under varying levels of exports with a precision impact on performance.

Unlike a conventional statistical approach, this study uniquely presents a neural network approach to explore the dynamic interplay of strategic factors. A multilayer perceptron neural network (MPNN) is designed to capture complex interaction patterns through a predictive analytic process.

This study finds that the impact of R&D and advertising is positive, with a greater effect on high-export firms. Moreover, the experiment results show that the synergy of R&D and advertising goes beyond the formatted positive/negative frame and actually has a reinforcing effect.

This study not only conveys the significant nexus of R&D and advertising for firm performance but also provides industry managers' practical means to assess the joint effect of R&D and advertising on firm performance. The proposed analytic mechanism in particular provides pragmatic decision support to managers in harmonizing their R&D and advertising efforts for a foreseeable impact.

This paper presents an innovative analytic process using the MPNN to explore the synergy between R&D and advertising. In addition to offering new perspectives on R&D and advertising, this study presents pragmatic implications for managing those strategic resources to meet performance targets.

Systems thinking calls for a shift of our mindset from seeing just parts to seeing the whole reality in its structured dynamic unity and interconnectedness. Systems thinking fosters a sensibility to see subtle connections between components and parts of reality, especially the free enterprise capitalist system (FECS). It enables us to see ourselves as active participants or partners of FECS and not mere induced factors of its production–distribution–consumption processes. Systems thinking seeks to identify the economic “structures” that underlie complex situations in FECS that bring about high versus low leveraged changes. A system is strengthened and reinforced by feedback of reciprocal exchanges that makes the system alive, transparent, human, and humanizing.

In Part I, we explore basic laws or patterns of behaviors as understood by systems thinking; in Part II we examine the basic archetypes or structured behaviors of systems thinking; in both parts we strive to see reality through the lens of critical thinking to help us understand patterns and structures of behavior among systems and their component parts. In conclusion, we argue for compatibility and complementarity of critical thinking and systems thinking to identify and resolve management problems created by our flawed thinking, and sedimented by our wanton assumptions, presumptions, suppositions and presuppositions, biases, and prejudices. Such thinking will also identify unnecessary economic and political structures of the self-serving policies we create, which imprison us.

In recent years, the topic of women's entrepreneurship has gained increasing attention from researchers and policymakers. Its role in economic growth and development has been widely recognized in several studies. However, the relationship between gender in entrepreneurship and innovation is an underexplored aspect in particular at a country-level perspective. This paper aims to answer the following question: Does female entrepreneurship impact innovation at a national level?

Using a panel dataset of 35 Organization for Economic Co-operation and Development (OECD) member countries over the period 2002–2019, the authors carried out a comprehensive econometric analysis, based on the fixed-effect model, the random-effect model and the feasible generalized least squares estimator, as well as a battery of tests to prevent problems of multicollinearity, heteroscedasticity and autocorrelation of the error terms. In doing so, the authors found consistent and robust results on the linear and nonlinear relationship between women's entrepreneurship and innovation, using selected country indicators from the Global Entrepreneurship Monitor (GEM) consortium, the Worldwide Governance Indicators (WGI) and the World Development Indicators (WDI), including female self-employment, female nascent entrepreneurship and R&D investment and controlling for the same relationships in the case of men's entrepreneurship.

This study shows that the level of R&D investment, which according to the literature can be considered as a proxy of innovation, is higher when the level of women's entrepreneurship is low. However, exploring more in depth this relationship and the relationship between male entrepreneurship and innovation, the authors found two important and new results. The first one involves the different impact on R&D investment of female self-employment and female nascent entrepreneurship. In particular, female self-employment appears to have a linear negative impact on the R&D, while the impact of female nascent entrepreneurship is statistically nonsignificant. The second one affects the nonlinearity of the negative effect, suggesting that very different challenges are possible at different levels of women's entrepreneurship. In addition, analyzing the role of human capital in the relationship between R&D investment and women entrepreneurship, it emerges that higher education (as the main component of human capital) makes early-stage women's entrepreneurship more technologically consuming, which promotes R&D investment. A higher level of education lessens the significance of the negative relationship between the simplest type of women entrepreneurship (female self-employment) and R&D investment.

The originality of the study is that it provides new evidence regarding the link between women's entrepreneurship and innovation at the macro level, with a specific focus on self-employed women entrepreneurs and early-stage women entrepreneurship. In this sense, to the best of the authors' knowledge, this study is among the few showing a nonlinear relationship between women's entrepreneurship and country-level innovation and a negative impact only in the case of female self-employment. Moreover, this study has relevant implications from a policymaking perspective, in terms of promoting more productive women's entrepreneurship.

In this paper, the authors study the nonlinear matrix equation Xp=Q±A(X-1+B)-1AT, that occurs in many applications such as in filtering, network systems, optimal control and control theory.

The authors present some theoretical results for the existence of the solution of this nonlinear matrix equation. Then the authors propose two iterative schemes without inversion to find the solution to the nonlinear matrix equation based on Newton's method and fixed-point iteration. Also the authors show that the proposed iterative schemes converge to the solution of the nonlinear matrix equation, under situations.

The efficiency indices of the proposed schemes are presented, and since the initial guesses of the proposed iterative schemes have a high cost, the authors reduce their cost by changing them. Therefore, compared to the previous scheme, the proposed schemes have superior efficiency indices.

Finally, the accuracy and effectiveness of the proposed schemes in comparison to an existing scheme are demonstrated by various numerical examples. Moreover, as an application, by using the proposed schemes, the authors can get the optimal controller state feedback of $x(t+1) = A x(t) + C v(t)$.