Forecasting Real GDP Growth for Africa

We propose a simple and reproducible methodology to create a single equation forecasting model (SEFM) for low-frequency macroeconomic variables. Our methodology is illustrated by forecasting annual real GDP growth rates for 52 African countries, where the data are obtained from the World Bank and start in 1960. The models include lagged growth rates of other countries, as well as a cointegration relationship to capture potential common stochastic trends. With a few selection steps, our methodology quickly arrives at a reasonably small forecasting model per country. Compared with benchmark models, the single equation forecasting models seem to perform quite well.

Equalities and inequalities for several variables mappings

In this paper, some special mappings of several variables such as the multicubic and the multimixed quadratic–cubic mappings are introduced. Then, the systems of equations defining a multicubic and a multimixed quadratic–cubic mapping are unified to a single equation. Under some mild conditions, it is shown that a multimixed quadratic–cubic mapping can be multiquadratic, multicubic and multiquadratic–cubic. Furthermore, by applying a known fixed-point theorem, the Hyers–Ulam stability of multimixed quadratic–cubic, multiquadratic, multicubic and multiquadratic–cubic are studied in non-Archimedean normed spaces.

Subsurface stresses in an elliptical Hertzian contact

The traditional solution for the stresses below an elliptical Hertzian contact expresses the results in terms of incomplete Legendre elliptic integrals, so are necessarily based on the length of the semi-major axis a and the axis ratio k. The result is to produce completely different equations for the stresses in the x and y directions; and although these equations are now well-known, their derivation from the fundamental, symmetric, integrals is far from simple. When instead Carlson elliptic integrals are used, they immediately match the fundamental integrals, allowing the equations for the stresses to treat the two semi-axes equally, and so providing a single equation where two were needed before. The numerical evaluation of the Carlson integrals is simple and rapid, so the result is that more convenient answers are obtained more conveniently. A bonus is that the temptation to record the depth of the critical stresses as a fraction of the length of the semi-major axis is removed. Thomas and Hoersch’s method of finding all the stresses along the axis of symmetry has been extended to determine the full set of stresses in a principal plane. The stress patterns are displayed, and a comparison between the answers for the planes of the major and minor semiaxes is made. The results are unchanged from those found from equations given by Sackfield and Hills, but not previously evaluated. The present equations are simpler, not only in the simpler elliptic integrals, but also for the “tail” of elementary functions.

Matrix model partition function by a single constraint

In the recent study of Virasoro action on characters, we discovered that it gets especially simple for peculiar linear combinations of the Virasoro operators: particular harmonics of $${\hat{w}}$$ w ^ -operators. In this letter, we demonstrate that even more is true: a singlew-constraint is sufficient to uniquely specify the partition functions provided one assumes that it is a power series in time-variables. This substitutes the previous specifications in terms of two requirements: either a string equation imposed on the KP/Toda $$\tau $$ τ -function or a pair of Virasoro generators. This mysterious single-entry definition holds for a variety of theories, including Hermitian and complex matrix models, and also matrix models with external matrix: the unitary and cubic Kontsevich models. In these cases, it is equivalent to W-representation and is closely related to super integrability. However, a similar single equation that completely determines the partition function exists also in the case of the generalized Kontsevich model (GKM) with potential of higher degree, when the constraint algebra is a larger W-algebra, and neither W-representation, nor superintegrability are understood well enough.

Financial inclusion, corporate social responsibility and firm performance – analysis of interactive relationship

Purpose Prior studies on corporate social responsibility (CSR) and performance have frequently used unidirectional, single-equation regression although the literature recommends the reciprocal association of CSR with firm performance. This paper aims to elucidate the interactive relationship of CSR spending with financial inclusion (FI) and firm performance. The study also explores the moderating impact of the level of FI on the CSR-firm performance relationship. Design/methodology/approach This study uses a simultaneous equations model to capture the FI, CSR and firm performance relationships and apply a three-stage regression approach and generalised method of moments approach to address possible endogeneity. Findings The results confirm a positive association of CSR spending with performance but a negative relationship of FI with performance. This paper also finds that FI negatively moderates the CSR spending-performance relationship. Practical implications The positive impact of CSR spending and the negative impact of FI on performance in mandatory CSR regimes provides valuable input in policy formulation. The results of the study will also be useful to national and international organisations, such as the International Monetary Fund and the World Bank. Originality/value This study uses a simultaneous equations model to capture the reciprocal association of CSR spending with firm performance, whereas prior studies on CSR and performance have frequently used unidirectional, single-equation regression. This paper also finds that FI negatively moderates the CSR spending- performance relationship. Including FI and exploring the moderating impact of the level of FI on the CSR-firm performance relationship is novel.

Archimedes Screw Design: An Analytical Model for Rapid Estimation of Archimedes Screw Geometry

In designing Archimedes screws, determination of the geometry is among the fundamental questions that may affect many aspects of the Archimedes screw powerplant. Most plants are run-of-river and highly depend on local flow duration curves that vary from river to river. An ability to rapidly produce realistic estimations for the initial design of a site-specific Archimedes screw plant helps to facilitate and accelerate the optimization of the powerplant design. An analytical method in the form of a single equation was developed to rapidly and easily estimate the Archimedes screw geometry for a specific site. This analytical equation was developed based on the accepted, proved or reported common designs characteristics of Archimedes screws. It was then evaluated by comparison of equation predictions to existing Archimedes screw hydropower plant installations. The evaluation results indicate a high correlation and reasonable relative difference. Use of the equation eliminates or simplifies several design steps and loops and accelerates the development of initial design estimations of Archimedes screw generators dramatically. Moreover, it helps to dramatically reduce one of the most significant burdens of small projects: the nonscalable initial investigation costs and enables rapid estimation of the feasibility of Archimedes screw powerplants at many potential sites.

Characterization and Stability of Multimixed Additive-Quartic Mappings: A Fixed Point Application

In this article, we introduce the multi-additive-quartic and the multimixed additive-quartic mappings. We also describe and characterize the structure of such mappings. In other words, we unify the system of functional equations defining a multi-additive-quartic or a multimixed additive-quartic mapping to a single equation. We also show that under what conditions, a multimixed additive-quartic mapping can be multiadditive, multiquartic, and multi-additive-quartic. Moreover, by using a fixed point technique, we prove the Hyers-Ulam stability of multimixed additive-quartic functional equations thus generalizing some known results.

Understanding Thermal Lagging Behaviors in Thermoelectric Elements with the Dual-Phase-Lag Model

This study investigates the heat transport mechanism in semiconductor elements within a homogeneous thermoelectric cooling system using the dual-phase-lag model. The thermal lagging behavior is analyzed and explored during the energy transport process. The coupled energy and constitutive partial differential equations are solved simultaneously to reduce the complexity of the high-order spatial and time derivatives. This approach simplifies the mathematical solution process and reduces numerical instabilities when compared to the conventional methodology in which either the temperature or heat flux are solved individually with a single equation. The effect of the thermal lagging behavior on energy transport is examined and compared to results by using the Cattaneo-Vernotte model. Furthermore, the phase-lag behavior on the temperature and heat flux profiles are investigated in detail. This study provides perceptive information for engineering applications in which microscale heat transport phenomenon plays a significant role during the design process. Adding the dual-phase-lag model to the traditional heat diffusion model will be a complementary option for engineers in the thermoelectric industry.

Estimation of Discharge and Total Water Level at Yedgaon Dam using Data Driven Techniques

A reservoir operation planning using Data driven Techniques is gaining its momentum in hydrological area with good prediction and Estimation capabilities. The present work aims at using the 5 years data of Water Level to estimate the discharge and water level at the Yedgaon dam which is like pick up weir having its own yield and storage. It receives water from Dimbhe (though DLBC), Wadaj (through MLBC), Manikdoh (through river) and through Pimpalgaojoge (through river), in the Kukadi project of Maharashtra State, India. 4 different models were developed to estimate the water level using the Data Driven Techniques: M5 Model Tree, Support Vector Regression, Multi Gene Genetic Programming and Random Forest. The Accuracy of the developed models is assessed by the values of coefficient of correlation, coefficient of efficiency, mean absolute error and root mean squared error and comparison is done between actual values and Predicted values. The results indicated that the MGGP model was superior as compared to other techniques with correlation coefficient as 0.86 with an advantage of a single equation to estimate the water level.