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Let p_[1,r;t] be defined by ∑n=0∞p[1,r;t](n)qn=(E1Er)t, where t is a non-zero rational number, r ≥ 1 is an integer and Er=∏n=0∞(1−qr(n+1)) for |q| < 1. The function p_[1,r;t](n) is the generalisation of the two-colour partition function p_[1,r;−1](n). In this paper, the authors prove some new congruences modulo odd prime ℓ by taking r = 5, 7, 11 and 13, and non-integral rational values of t.

Using q-series expansion/identities, the authors established general congruence modulo prime number for two-colour partition function.

In the paper, the authors study congruence properties of two-colour partition function for fractional values. The authors also give some particular cases as examples.

The partition functions for fractional value is studied in 2019 by Chan and Wang for Ramanujan's general partition function and then extended by Xia and Zhu in 2020. In 2021, Baruah and Das also proved some congruences related to fractional partition functions previously investigated by Chan and Wang. In this sequel, some congruences are proved for two-colour partitions in this paper. The results presented in the paper are original.

The purpose of this paper is to show a comparative study of different direction-of-arrival (DOA) estimation techniques, namely, multiple signal classification (MUSIC) algorithm, delay-and-sum (DAS) beamforming, support vector regression (SVR), multivariate linear regression (MLR) and multivariate curvilinear regression (MCR).

The relative delay between the microphone signals is the key attribute for the implementation of any of these techniques. The machine-learning models SVR, MLR and MCR have been trained using correlation coefficient as the feature set. However, MUSIC uses noise subspace of the covariance-matrix of the signals recorded with the microphone, whereas DAS uses the constructive and destructive interference of the microphone signals.

Variations in root mean square angular error (RMSAE) values are plotted using different DOA estimation techniques at different signal-to-noise-ratio (SNR) values as 10, 14, 18, 22 and 26dB. The RMSAE curve for DAS seems to be smooth as compared to PR1, PR2 and RR but it shows a relatively higher RMSAE at higher SNR. As compared to (DAS, PR1, PR2 and RR), SVR has the lowest RMSAE such that the graph is more suppressed towards the bottom.

DAS has a smooth curve but has higher RMSAE at higher SNR values. All the techniques show a higher RMSAE at the end-fire, i.e. angles near 90°, but comparatively, MUSIC has the lowest RMSAE near the end-fire, supporting the claim that MUSIC outperforms all other algorithms considered.

Different from Marx's analysis of the dialectical relationship between the production and realization of surplus value, the Okishio theorem only shows one aspect of the contradictory movement of the total social capital, that is, the reverse effect of the realization of surplus value on the production of surplus value.

The production of surplus value and the realization of surplus value are simplified into one process. This simplification eliminates the contradiction between the production and realization of surplus value, and the antagonistic contradiction between accumulation and consumption and the antagonistic production-distribution relationship in capitalist society are naturally covered up.

Therefore, it cannot explain the actual expansion way of the falling general rate of profit as the historical development law of capitalism. Nevertheless, it should be noted that the Okishio theorem places the analysis of the general rate of profit back into the social reproduction model with department equilibrium, which points out the significance of wage income to the realization of surplus value and outlines the macro mechanism of the realization of surplus value reacting to the production of surplus value. It also strongly promotes the research progress of the law that the profit rate tends to decline.

The mistake of the Okishio theorem is that the exchange process in the labor market forms the real wage rate. It determines the production price of wage goods, which thereby determines that the production price of capital goods and general rate of profit, the production of surplus value and realization of surplus value are simplified into the same process, and only the value that can be realized is the real value.

This paper reports a new technique for achieving optimized design for power system stabilizers. In any large scale interconnected systems, disturbances of small magnitudes are very common and low frequency oscillations pose a major problem. Hence small signal stability analysis is very important for analyzing system stability and performance. Power System Stabilizers (PSS) are used in these large interconnected systems for damping out low-frequency oscillations by providing auxiliary control signals to the generator excitation input. In this paper, collective decision optimization (CDO) algorithm, a meta-heuristic approach based on the decision making approach of human beings, has been applied for the optimal design of PSS. PSS parameters are tuned for the objective function, involving eigenvalues and damping ratios of the lightly damped electromechanical modes over a wide range of operating conditions. Also, optimal locations for PSS placement have been derived. Comparative study of the results obtained using CDO with those of grey wolf optimizer (GWO), differential Evolution (DE), Whale Optimization Algorithm (WOA) and crow search algorithm (CSA) methods, established the robustness of the algorithm in designing PSS under different operating conditions.

Prediction is a critical task in targeted online advertising, where predictions better than random guessing can translate to real economic return. This study aims to use machine learning (ML) methods to identify individuals who respond well to certain linguistic styles/persuasion techniques based on Aristotle’s means of persuasion, rhetorical devices, cognitive theories and Cialdini’s principles, given their psychometric profile.

A total of 1,022 individuals took part in the survey; participants were asked to fill out the ten item personality measure questionnaire to capture personality traits and the dysfunctional attitude scale (DAS) to measure dysfunctional beliefs and cognitive vulnerabilities. ML classification models using participant profiling information as input were developed to predict the extent to which an individual was influenced by statements that contained different linguistic styles/persuasion techniques. Several ML algorithms were used including support vector machine, LightGBM and Auto-Sklearn to predict the effect of each technique given each individual’s profile (personality, belief system and demographic data).

The findings highlight the importance of incorporating emotion-based variables as model input in predicting the influence of textual statements with embedded persuasion techniques. Across all investigated models, the influence effect could be predicted with an accuracy ranging 53%–70%, indicating the importance of testing multiple ML algorithms in the development of a persuasive communication (PC) system. The classification ability of models was highest when predicting the response to statements using rhetorical devices and flattery persuasion techniques. Contrastingly, techniques such as authority or social proof were less predictable. Adding DAS scale features improved model performance, suggesting they may be important in modelling persuasion.

In this study, the survey was limited to English-speaking countries and largely Western society values. More work is needed to ascertain the efficacy of models for other populations, cultures and languages. Most PC efforts are targeted at groups such as users, clients, shoppers and voters with this study in the communication context of education – further research is required to explore the capability of predictive ML models in other contexts. Finally, long self-reported psychological questionnaires may not be suitable for real-world deployment and could be subject to bias, thus a simpler method needs to be devised to gather user profile data such as using a subset of the most predictive features.

The findings of this study indicate that leveraging richer profiling data in conjunction with ML approaches may assist in the development of enhanced persuasive systems. There are many applications such as online apps, digital advertising, recommendation systems, chatbots and e-commerce platforms which can benefit from integrating persuasion communication systems that tailor messaging to the individual – potentially translating into higher economic returns.

This study integrates sets of features that have heretofore not been used together in developing ML-based predictive models of PC. DAS scale data, which relate to dysfunctional beliefs and cognitive vulnerabilities, were assessed for their importance in identifying effective persuasion techniques. Additionally, the work compares a range of persuasion techniques that thus far have only been studied separately. This study also demonstrates the application of various ML methods in predicting the influence of linguistic styles/persuasion techniques within textual statements and show that a robust methodology comparing a range of ML algorithms is important in the discovery of a performant model.

The purpose of this study is to find the optimum design of Reinforced Concrete (RC) pile foundation to enable efficient use of structural concrete with greater consequences for global environment and economy.

A non-linear optimisation technique based on the Generalised Reduced Gradient (GRG) algorithm was implemented to find the minimum cost of RC pile foundation in frictional soil. This was achieved by obtaining the optimum pile satisfying the serviceability and ultimate limit state requirements of BS 8004 and EC 7. The formulated structural optimisation procedure was applied to a case study project to assess the efficiency of the proposed design formulation.

The results prove that the GRG method in Excel solver is an active, fast, accurate and efficient computer programme to obtain optimum pile design. The application of the optimisation for the case study project shows up to 26% cost reduction compared to the conventional design.

The design and formulation of design constraints will be limited to provisions of BS 8004 and EC 7.

Since the minimum quantity of concrete was attained through optimisation, then minimum cement will be used and thus result in minimum CO₂ emission. Therefore, the optimum design of concrete structures is a vital solution to limit the damage to the Earth's climate and the physical environment resulting from high carbon emissions.

The current study considers the incorporation of different soil ground parameters in the optimisation process rather than assuming any pile capacity value for the optimisation process.

In the current literature, there is little systematic research on the relationship among adjustment of the income distribution, change in economic structure and improvement of macroeconomic efficiency.

This paper expands Marx's reproduction schema into the “Marx–Sraffa” three-department structure table comprising fixed capital, general means of production and means of consumption and employs China's input–output table from 1987 to 2015 to portray the relationship between income distribution and macroeconomic efficiency under investment-driven growth.

This paper calculates the wage–profit curve of China's economy and evaluates the space of macroeconomic efficiency improvement in China based on the deviation between actual and potential income distribution structure.

The results show that there is a downward trend of the profit rate, which meets Marx's theoretical prediction, and the decline in the profit rate is mainly attributed to an increase in the organic composition of capital arising from the rapid growth of fixed capital investment under extended growth. The analysis of macroeconomic efficiency shows that the space for improving macroeconomic efficiency is extremely limited under traditional growth pattern and that China must transform its economic development pattern and foster new economic growth drivers.

The main objective of this study is to investigate an impact of organizational culture on supply chain risk and strategic sourcing. It also examines the relationship between organizational culture and strategic sourcing. By collecting 159 survey responses from supply, executives and managers of U.S. manufacturing firms, it provides empirical evidence that organizational culture and strategic sourcing mitigate supply chain risks. Organizational culture also makes a positive impact on the implementation of strategic sourcing. This study emphasizes the importance of cultural impacts to supply executives and managers in supply chain risk management.

The relationship between risk and return has been widely analysed in the scope of listed companies. However the present literature leaves uncovered an important study area with regards to privately held firms. In order to cover this gap, this study analyses the risk-return trade-off in the context of private enterprises. Furthermore, the authors incorporate the contingent effect of being a family firm on the abovementioned relationship.

Using information from the SABI (Sistema de Análisis de Balances Ibéricos) database, a sample of 2,297 private manufacturing firms were analysed for the period of 2009–2016. So as to ascertain the proposed hypotheses, dynamic panel data methodology was applied. Specifically, the authors estimated the two-step general method of moments (GMM).

The obtained findings reveal that, according to prospect theory arguments, privately held firms adopt a conservative attitude toward risk when results are higher than a target level, while becoming risk seeking when results are lower than a target level. Moreover, the fact of being a family firm softens the risk-return relationship both when performance is above the target level and also when firms find themselves in the lowest performing case.

This article is, to the best of the authors' knowledge, one of the first studies dealing with the risk-return relationship in a privately held firm context. Moreover, the inclusion of being a family firm as a contingent factor in the abovementioned link is a complete novelty.

La relación riesgo-rentabilidad ha sido ampliamente analizada en el ámbito de las empresas cotizadas. Sin embargo, la literatura existente deja al descubierto una importante área de estudio en relación con las empresas no cotizadas. Para cubrir esta brecha, el presente estudio analiza el binomio riesgo-rentabilidad en el contexto de empresas privadas. Adicionalmente, incorporamos el efecto contingente de ser una empresa familiar sobre esta relación.

Utilizando información de la base de datos SABI (Sistema de Análisis de Balances Ibéricos) se analizó una muestra de 2.297 empresas manufactureras privadas para el período 2009–2016. Para comprobar las hipótesis propuestas se aplicó la metodología de datos de panel, específicamente, utilizamos el Método de los Momentos Generalizado (GMM).

Los resultados muestran que, de acuerdo con la Teoría Prospectiva, las empresas no cotizadas presentan una mayor aversión al riesgo cuando su nivel de rentabilidad es superior al valor de referencia establecido, mientras que presentan una mayor propensión al riesgo cuando su rentabilidad es inferior al valor de referencia. Además, el hecho de ser una empresa familiar suaviza la relación riesgo-rentabilidad en ambos escenarios.

Este es uno de los primeros estudios en abordar la relación riesgo-rentabilidad en el contexto de empresas no cotizadas. Además, la inclusión de ser una empresa familiar como factor contingente es completamente novedosa.

Lockdowns and the forced closure of certain industries during the COVID-19 pandemic severely impacted workers, particularly entrepreneurs, who were financially and emotionally involved in their businesses. Two studies have shown that entrepreneurs have a lower willingness to get vaccinated against COVID-19 than employees. In this study, the authors try to replicate the vaccination gap between the two groups. Second, the authors study whether the difference persists when controlling for demographics, vaccination attitudes and the COVID-19 context, including the financial impact of the pandemic, its effect on the wellbeing of workers, and government attitudes. Third, the authors study whether there are differences in how the context of the pandemic relates to vaccination willingness for entrepreneurs and employees.

The authors conduct regression analyses using three large datasets. The authors study vaccination status (February 2022) in a 27-country Eurobarometer sample, vaccination intention (December 2020) in a Dutch sample from the LISS panel and vaccination status (July 2021) in a sample from the Understanding America Study (UAS).

All datasets confirm that entrepreneurs have lower vaccination intention and coverage than employees. Even when controlling for the variables described in the LISS and UAS datasets, this negative difference remains. The study results also indicate that demographics, especially vaccination attitudes, are much more important than contextual influences in the decision to get vaccinated against COVID-19.

The authors are the first to dive further into the vaccination differences between entrepreneurs and employees. They advise further research into the drivers of this gap, specifically relating to the role of personality and social normative influences.