Search Results (59)

European integration aims to achieve spatially sustainable development across the member states. However, the success of socio-economic integration is conditioned by structural features of the economies, which, hitherto, appear highly diversified across the EU countries. The paper focuses on the structural conditions of the process of income inequality convergence. It aims to identify differences in the convergence regarding the structural conditions of the economies. To fulfil the research tasks the paper classifies the 27 European member states according to their sectional employment structures using the Ward method. It then tests the appearance of beta convergence using FE panel models for the specified clusters of economies. It also considers structural change, measured by the NAV (norm of absolute value), as a determinant of income inequality convergence. The main research period covers 2009–2021. The findings of the paper confirm that income inequality convergence occurs within the groups of economies specified by different structural conditions. Importantly, the clustering according to the similarity of the employment structure overlaps with the division along the lines of the ‘new’ and ‘old’ member states, which proves the importance of historically shaped institutions for development. However, the observed convergence does not lead to improved social cohesion. Social policy, especially in the ‘new’ member states, is not able to offset the growth in market income inequality additionally stimulated by the structural changes. It can be concluded that an urgent need to design new solutions for social policy concerning structural transformation in employment in the EU emerges. Full article

In this paper, we propose a penalty approach for solving generalized absolute value equations (GAVEs) of the type $Ax-B\left|x\right|=b$, $(A,B\in {\mathbb{R}}^{n\times n},b\in {\mathbb{R}}^n)$. Firstly, we reformulate the GAVEs as variational inequality problems passing through an equivalent horizontal linear complementarity problem. To approximate the resulting variational inequality, a sequence of nonlinear equations containing a penalty term is then defined. Under a mild assumption, we show that the solution of the considered sequence converges to that of GAVE if the penalty parameter tends to infinity. An algorithm is developed where its corresponding theoretical arguments are well established. Finally, some numerical experiments are presented to show that our approach is quite appreciable. Full article

Starting from ${\psi }_k$-Raina’s fractional integrals (${\psi }_k$-RFIs), the study obtains a new generalization of the Hermite–Hadamard–Mercer (H-H-M) inequality. Several trapezoid-type inequalities are constructed for functions whose derivatives of orders 1 and 2, in absolute value, are convex and involve ${\psi }_k$-RFIs. The results of the research are refinements of the Hermite–Hadamard (H-H) and H-H-M-type inequalities. For several types of fractional integrals—Riemann–Liouville (R-L), k-Riemann–Liouville (k-R-L), $\psi$-Riemann–Liouville ($\psi$-R-L), ${\psi }_k$-Riemann–Liouville (${\psi }_k$-R-L), Raina’s, k-Raina’s, and $\psi$-Raina’s fractional integrals ($\psi$-RFIs)—new inequalities of H-H and H-H-M-type are established, respectively. This article presents special cases of the main results and provides numerous examples with graphical illustrations to confirm the validity of the results. This study shows the efficiency of the findings with a couple of applications, taking into account the modified Bessel function and the q-digamma function. Full article

The computational investigation of nonlinear mathematical models presents significant challenges due to their complex dynamics. This paper presents a computational study of a nonlinear hepatitis C virus model that accounts for the influence of alcohol consumption on disease progression. We employ periodic neural networks, optimized using a hybrid genetic algorithm and the interior-point algorithm, to solve a system of six coupled nonlinear differential equations representing hepatitis C virus dynamics. This model has not previously been solved using the proposed technique, marking a novel approach. The proposed method’s performance is evaluated by comparing the numerical solutions with those obtained from traditional numerical methods. Statistical measures such as mean absolute error, root mean square error, and Theil’s inequality coefficient are used to assess the accuracy and reliability of the proposed approach. The weight vector distributions illustrate how the network adapts to capture the complex nonlinear behavior of the disease. A comparative analysis with established numerical methods is provided, where performance metrics are illustrated using a range of graphical tools, including box plots, histograms, and loss curves. The absolute error values, ranging approximately from ${10}^{-6}$ to ${10}^{-10}$, demonstrate the precision, convergence, and robustness of the proposed approach, highlighting its potential applicability to other nonlinear epidemiological models. Full article

The main goal of this study is to provide new q-Fejer and q-Hermite-Hadamard type integral inequalities for uniformly convex functions and functions whose second quantum derivatives in absolute values are uniformly convex. Two basic inequalities as power mean inequality and Holder’s inequality are used in demonstrations. Some particular functions are chosen to illustrate the investigated results by two examples analyzed and the result obtained have been graphically visualized. Full article

This study presents novel formulations of fractional integral inequalities, formulated using generalized fractional integral operators and the exploration of convexity properties. A key identity is established for twice-differentiable functions with the absolute value of their second derivative being convex. Using this identity, several generalized fractional Hermite–Hadamard-type inequalities are developed. These inequalities extend the classical midpoint and trapezoidal-type inequalities, while offering new perspectives through convexity properties. Also, some special cases align with known results, and an illustrative example, accompanied by a graphical representation, is provided to demonstrate the practical relevance of the results. Moreover, the findings may offer potential applications in numerical integration, optimization, and fractional differential equations, illustrating their relevance to various areas of mathematical analysis. Full article

Effectively controlling the carbon emissions intensity of the transportation sector (TSCEI) is essential to promote the sustainable development of the transportation industry in China. This study, which builds upon trend analysis, the Dagum Gini coefficient, and spatial autocorrelation analysis to reveal the spatiotemporal differentiation of TSCEI, employs both traditional and spatial Markov chain to analyze the dynamic evolution of TSCEI and forecast its future development trend. Furthermore, econometric models are constructed to examine the convergence characteristics of TSCEI. The empirical results reveal the following key findings: (1) TSCEI in China has significantly declined, exhibiting a spatial distribution pattern of “higher in the north, lower in the south; higher in the west, lower in the east”. (2) Inter-regional differences are the main contributors to overall TSCEI disparities, with provincial TSCEI exhibiting positive spatial autocorrelation, primarily characterized by high–high and low–low agglomeration. (3) TSCEI tends to gradually shift from high- to low-intensity states over time, with an equilibrium probability of 90.98% for transferring to lower intensity state. Provincial TSCEI shows significant spatial spillover effects, influenced by neighboring provinces’ states. (4) TSCEI demonstrates convergence characteristics at national and regional levels, including $\sigma$ convergence, absolute and conditional $\beta$ convergence, with the transportation energy structure and technological progress playing a particularly prominent role in facilitating the convergence of TSCEI towards lower values. The policy implications of promoting TSCEI convergence and reducing spatial inequality are discussed. Full article

The Theil index is one of the most popular indices of economic inequality, one reason for which is no doubt due to its convenient additive decomposition property. One of its weaknesses, however, is its lack of any intuitively meaningful interpretations. Another, and more serious, limitation of Theil’s index, as argued in this paper, is its lack of the value-validity property. That is, this index does not meet a particular condition based on metric distances between income-share distributions required in order for the range of potential index values to provide true, realistic, and valid representations of the economic inequality characteristic. After outlining the value-validity condition, this paper derives a simple transformation of Theil’s index that meets this condition to a high degree of approximation. Randomly generated income-share distributions are used to demonstrate and verify the validity of the corrected index. The new index formulation, which is simply a power function of Theil’s index, can then be used to make appropriate and reliable representations of absolute and relative difference comparisons of economic inequalities. Full article

Background: Monitoring immunization inequalities is crucial for achieving equity in vaccine coverage. Summary measures of health inequality provide a single numerical expression of immunization inequality. However, the impact of different summary measures on conclusions about immunization inequalities has not been thoroughly studied. Methods: We used disaggregated data from household surveys conducted in 92 low- and middle-income countries between 2013 and 2022. Inequality was assessed for two indicators of childhood immunization coverage [three doses of combined diphtheria, tetanus, and pertussis (DTP) vaccine and non-receipt of DTP vaccine or “zero-dose”] across three dimensions of inequality (place of residence, economic status, and subnational region). We calculated 16 summary measures of health inequality and compared the results. Results: These measures of inequality showed more similarities than differences, but the choice of measure can affect inequality assessment. Absolute and relative measures sometimes produced differing results, showing the importance of using both types of measures when assessing immunization inequality. Outliers influenced differences and ratios, but the effect of outlier estimates was moderated through the use of complex measures, which consider all subgroups and their population sizes. The choice of appropriate complex measure depends on the audience, interpretation, and outlier sensitivity. Conclusions: Summary measures are useful for assessing changes in inequality over time and making comparisons across different geographical areas and vaccines, but assumptions and value judgements made when selecting summary measures of inequality should be made explicit in research. Full article

We study the class of random entire functions given by power series, in which the coefficients are formed as the product of an arbitrary sequence of complex numbers and two sequences of random variables. One of them is the Rademacher sequence, and the other is an arbitrary complex-valued sequence from the class of sequences of random variables, determined by a certain restriction on the growth of absolute moments of a fixed degree from the maximum of the module of each finite subset of random variables. In the paper we prove sharp Wiman–Valiron’s type inequality for such random entire functions, which for given $p\in (0;1)$ holds with a probability p outside some set of finite logarithmic measure. We also considered another class of random entire functions given by power series with coefficients, which, as above, are pairwise products of the elements of an arbitrary sequence of complex numbers and a sequence of complex-valued random variables described above. In this case, similar new statements about not improvable inequalities are also obtained. Full article

In this work, novel Ostrowski-type inequalities for dissimilar function classes and generalized fractional integrals (FITs) are presented. We provide a useful identity for differentiable functions under FITs, which results in special expressions for functions whose derivatives have convex absolute values. A new condition for bounded variation functions is examined, as well as expansions to bounded and Lipschitzian derivatives. Our comprehension is improved by comparison with current findings, and recommendations for future study areas are given. Full article

The Cohen–Grossberg neural network is studied in the case when the dynamics of the neurons is modeled by a Riemann–Liouville fractional derivative with respect to another function and an appropriate initial condition is set up. Some inequalities about both the quadratic function and the absolute values functions and their fractional derivatives with respect to another function are proved and they are based on an appropriate modification of the Razumikhin method. These inequalities are applied to obtain the bounds of the norms of any solution of the model. In particular, we apply the squared norm and the absolute values norms. These bounds depend significantly on the function applied in the fractional derivative. We study the asymptotic behavior of the solutions of the model. In the case when the function applied in the fractional derivative is increasing without any bound, the norms of the solution of the model approach zero. In the case when the applied function in the fractional derivative is equal to the current time, the studied problem reduces to the model with the classical Riemann–Liouville fractional derivative and the obtained results gives us sufficient conditions for asymptotic behavior of the solutions for the corresponding model. In the case when the function applied in the fractional derivative is bounded, we obtain a finite bound for the solutions of the model. This bound depends on the initial function and the solution does not approach zero. An example is given illustrating the theoretical results. Full article

In this paper, a signal model and a mathematical analysis of an efficient approach are derived to acquire the approximate magnitude of a complex signal by inducing a pre-biased or a pre-scaled factor in the design criteria. According to the deductive results, the pre-biased or pre-scaled factor can be 2∼3 dB, which is determined through its application. The numerical evaluations show that the mean square error (MSE) of the proposed efficient approach for the random signal is around −33 dB. Based on the design templates for the considered approaches, the occupied areas of the proposed type-1 and -2 approaches are merely 0.13 and 0.09 times the area of the direct-method, respectively. As a result, the proposed efficient approach is certainly a cost-efficient method for obtaining the approximate magnitude of a complex signal. Full article

In this study, an integral identity is given in order to present some Hermite–Hadamard–Mercer-type inequalities for functions whose powers of the absolute values of the third derivatives are convex. Several consequences and three applications to special means are given, as well as four examples with graphics which illustrate the validity of the results. Moreover, several Hermite–Hadamard–Mercer-type inequalities for fractional integrals for functions whose powers of the absolute values of the third derivatives are convex are presented. Full article

Positive and unlabeled learning (PU learning) is a significant binary classification task in machine learning; it focuses on training accurate classifiers using positive data and unlabeled data. Most of the works in this area are based on a two-step strategy: the first step is to identify reliable negative examples from unlabeled examples, and the second step is to construct the classifiers based on the positive examples and the identified reliable negative examples using supervised learning methods. However, these methods always underutilize the remaining unlabeled data, which limits the performance of PU learning. Furthermore, many methods require the iterative solution of the formulated quadratic programming problems to obtain the final classifier, resulting in a large computational cost. In this paper, we propose a new method called the absolute value inequality support vector machine, which applies the concept of eccentricity to select reliable negative examples from unlabeled data and then constructs a classifier based on the positive examples, the selected negative examples, and the remaining unlabeled data. In addition, we apply a hyperparameter optimization technique to automatically search and select the optimal parameter values in the proposed algorithm. Numerical experimental results on ten real-world datasets demonstrate that our method is better than the other three benchmark algorithms. Full article