Search Results (39)

In this paper we study photon entanglement in the framework of Maxwell–Schwartz field theory. The ambient state space is the complex Maxwellian distribution space $W={\mathcal{S}}^{\prime }({\mathbb{M}}_4,{\mathbb{C}}^3)$, whose elements are fields of the form $F=\overrightarrow{E}+ic\overrightarrow{B}$. Polarization is realized as a two-dimensional complex subspace of W, generated by suitable linearly polarized Maxwellian solutions associated with opposite propagation directions. This yields canonical polarization sectors $P_A$ and $P_B$, each naturally isomorphic to ${\mathbb{C}}^2$. Within this setting, the Bell singlet state is represented by a non-factorizable tensorial Maxwellian field in $P_A\otimes P_B\subset W\otimes W$. By means of the induced rotated polarization bases, the standard joint probabilities of the photon polarization experiment are recovered exactly, and the correlation law $E(a,b)=-cos\left(2\right(a-b\left)\right)$ is obtained. Consequently, the usual CHSH value $2\sqrt{2}$ is reproduced in the Maxwell–Schwartz framework. To clarify the meaning of this violation, we first formulate the CHSH inequality in a purely measure-theoretic form, as a theorem about four correlators represented on a single probability space by bounded measurable functions. We then show that the correlators produced by the intrinsic Maxwellian Bell state do not admit such a common representation. The obstruction is structural: the ontic state is a global non-product field configuration, and the four correlations arise from different polarization resolutions of the same tensorial Maxwellian state. A second main result concerns the Born rule. For $L^2$ scalar quantum states in the domain of the Maxwellian correspondence, we prove that the squared Hilbert norm, times the constant ${\epsilon }_0$, coincides with the electromagnetic energy of the associated field. This leads to an energy interpretation of the Born rule: the Born probability density is identified with the normalized electromagnetic energy density up to an interference term depending on the chosen Maxwell–Schwartz isomorphism, which assumes the role of a quantum context. In the context of the Aspect and collaborators’ experiment, we prove that, on the other hand, the polarization probabilities become energy contributions of the corresponding field components. These results show that photon entanglement, Bell inequality violation, and the Born rule admit a coherent interpretation within Maxwell–Schwartz field theory, where the basic ontological objects are electromagnetic-like fields rather than abstract state vectors. Full article

In this paper, we formulate and prove necessary conditions of efficiency for a new class of multiobjective variational models governed by higher order partial derivatives. More precisely, we consider a multiobjective optimization model of minimizing a vector of multiple integral functionals subject to certain higher order differential equations and/or inequations. The main results are derived by applying suitable techniques coming from variational calculus. The current contribution lies in vector-valued functionals given by multiple integrals, constraint coupling, and the characterization of efficiency criteria. Full article

Educational equality is essential for achieving social justice and sustainable development. Accurately predicting the trend of educational inequality is important for improving education systems and ensuring equitable resource allocation. In this paper, the Educational Gini (E-Gini) index is calculated based on the population aged 6 and above in China from 2002 to 2024, quantifying educational inequality. To forecast the future trend in the E-Gini index, a hybrid prediction framework based on the grey prediction model (GM(1,1)) and Cuckoo search-support vector regression (CS-SVR) model is proposed. This framework incorporates three influencing factors, including government budget spending on education, per capita consumption expenditure on education, and the Consumer Price Index (CPI) for education. The results show that the E-Gini of China generally declines from 2002 to 2024 with fluctuations. The proposed approach predicts the E-Gini value of 2024 as 0.220130, while the actual value is 0.2206, corresponding to an absolute error of 0.000470 and a relative error of 0.213%. In the benchmark comparison, the proposed model outperforms the linear trend model, the univariate GM(1,1), the naive persistence model, ARIMA, and the standard SVR model. The comparative analysis demonstrates that the proposed framework effectively captures the inherent patterns of educational inequality and reveals its trends. The proposed framework serves as a valuable tool for forecasting trends in educational inequality and informing policy decisions. Full article

In this article, we introduce the notion of approximate convexity for set-valued mappings, specifically in the forms of approximate pseudoconvexity and approximate quasiconvexity. These generalizations are motivated by the need to handle optimization problems involving multi-valued operators and vector-valued objective functions, where classical convexity assumptions are too restrictive. We demonstrate that the proposed framework preserves the essential structural features of convex analysis while broadening its applicability. After that, we investigate the introduced definitions through illustrative examples. Furthermore, we consider a set-valued optimization problem and rigorously investigate the relationships among its efficient solutions and the solutions of generalized Minty and Stampacchia variational inequality problems. The results provide a coherent theoretical bridge between optimality conditions and variational inequality formulations for set-valued mappings. Full article

This paper investigates the global polynomial synchronization (GPS) problem for quaternion-valued neural networks (QVNNs) featuring proportional delay, parameter uncertainty, and external disturbance. A combined approach of sliding mode control (SMC) and a non-separation strategy is adopted to achieve this goal. First, an integral-type sliding surface is designed for the system. Then, by constructing a delay-free Lyapunov functional and leveraging the properties of the quaternion vector norm and inequality techniques, sufficient conditions are derived to achieve GPS for the sliding mode dynamics. Furthermore, both a SMC law and an adaptive SMC law are designed, with a reachability analysis confirming that the system trajectories reach the predefined sliding surface in finite time. Finally, numerical examples with graphical analysis are provided to verify the obtained results, along with their application in color image pattern storage and retrieval. Full article

This paper investigates the structural properties of solutions of vector equilibrium systems and mixed variational inequalities in topological vector spaces. Based on Himmelberg-type fixed point theorem, combined with the analysis of set-valued mapping and quasi-monotone conditions, the existence criteria of solutions for two classes of generalized equilibrium problems with weak compactness constraints are constructed. This work introduces an innovative application of the measurable selection theorem of semi-continuous function space to eliminate the traditional compactness constraints, and provides a more universal theoretical framework for game theory and the economic equilibrium model. In the analysis of mixed variational problems, the topological stability of the solution set under the action of generalized monotone mappings is revealed by constructing a new KKM class of mappings and introducing the theory of pseudomonotone operators. In particular, by replacing the classical compactness assumption with pseudo-compactness, this study successfully extends the research boundary of scholars on variational inequalities, and its innovations are mainly reflected in the following aspects: (1) constructing a weak convergence analysis framework applicable to locally convex topological vector spaces, (2) optimizing the monotonicity constraint of mappings by introducing a semi-continuous asymmetric condition, and (3) in the proof of the nonemptiness of the solution set, the approximation technique based on the family of relatively nearest neighbor fields is developed. The results not only improve the theoretical system of variational analysis, but also provide a new mathematical tool for the non-compact parameter space analysis of economic equilibrium models and engineering optimization problems. This work presents a novel combination of measurable selection theory and pseudomonotone operator theory to handle non-compact constraints, advancing the theoretical framework for economic equilibrium analysis. Full article

This paper introduces a novel field-oriented control (FOC) strategy for an open-end stator three-phase winding induction motor (OEW-TP-IM) using dual space vector modulation-pulse width modulation (SVM-PWM) inverters. This configuration reduces common mode voltage at the motor’s terminals, enhancing efficiency and reliability. The study presents a backstepping control approach combined with a mean value theorem (MVT)-based observer to improve control accuracy and stability. Stability analysis of the backstepping controller for key control loops, including flux, speed, and currents, is conducted, achieving asymptotic stability as confirmed through Lyapunov’s methods. An advanced observer using sector nonlinearity (SNL) and time-varying parameters from convex theory is developed to manage state observer error dynamics effectively. Stability conditions, defined as linear matrix inequalities (LMIs), are solved using MATLAB R2016b to optimize the observer’s estimator gains. This approach simplifies system complexity by measuring only two line currents, enhancing responsiveness. Comprehensive simulations validate the system’s performance under various conditions, confirming its robustness and effectiveness. This strategy improves the operational dynamics of OEW-TP-IM machine and offers potential for broad industrial applications requiring precise and reliable motor control. Full article

Starting from some systems of vector equilibrium problems, we obtain the existence of the solution for a class of weighted equilibrium problems, under different types of generalized pseudo-monotonicity assumptions. We present both new and previous results, making a connection between them and giving a few examples. Using the main theorem, we derive the solution existence for the initial systems and discuss a corresponding set-valued problem. Finally, we consider the case of a real normed space. We extend some previously obtained results from the literature about weighted variational inequalities, and we also give proofs for some results we previously announced. We give some relevant examples for our notions. Full article

In this paper, we extend the concept of b-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the b-metric setting: fixed-point theorems, stability results, and a variant of Ekeland’s variational principle. As a consequence, we also derive a variant of Caristi’s fixed-point theorem. 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

In this paper, we discuss potentials for which we obtain multipolar weighted Hardy-type inequalities for a class of weights that are wide enough. Examples of such potentials are shown. The weighted estimates are more general than those stated in previous papers. To obtain the inequalities, we prove an integral identity by introducing a suitable vector-valued function. Full article

This study used the panel data from 15 emerging markets to examine the impact of restrictive macroprudential policies on income inequality from 2000–2019 using Bayesian panel vector autoregression and Bayesian panel dynamics generalised method of moments models. The chosen models are suitable for addressing multiple entity dynamics, accommodating a wide range of variables, handling dense parameterisation, and optimising formativeness and heterogeneous individual-specific factors. The empirical analysis utilised various macroprudential policy proxies and income inequality measures. The results show that when the central banks tighten systems using macroprudential policy instruments to sticker debt-to-income and financial instruments for lower-income borrowers (the bottom 40% of the income distribution), they promote income inequality in these countries while reducing income inequality for high-income borrowers (the high 1 percent of the income distribution). The impact of loan-to-value ratios was found to be insignificant in these countries. Fiscal policy through government expenditure and economic development reduces income inequality, while money supply and oil-price shocks exacerbate it. The study suggests implementing a progressive debt-to-income (DTI) ratio system in emerging markets to address income inequality among lower-income borrowers. This would adjust DTI thresholds based on income brackets, allowing lenient credit access for lower-income borrowers while maintaining stricter limits for higher-income borrowers. This would improve financial stability and reduce income disparities. Additionally, targeted financial literacy programs and a petroleum-linked basic income program could be implemented to distribute oil revenue to lower-income households. A monetary supply stabilisation fund could also be established to maintain financial stability and prevent excessive inflation. Full article

Traditional switching operations require on-site work, and the high voltage generated by arc discharges can pose a risk of injury to the operator. Therefore, a combination of visual servo and robot control is used to localize the switching operation and construct hand–eye calibration equations. The solution to the hand–eye calibration equations is coupled with the rotation matrix and translation vectors, and it depends on the initial value determination. This article presents a convex relaxation global optimization hand–eye calibration algorithm based on dual quaternions. Firstly, the problem model is simplified using the mathematical tools of dual quaternions, and then the linear matrix inequality convex optimization method is used to obtain a rotation matrix with higher accuracy. Afterwards, the calibration equations of the translation vectors are rewritten, and a new objective function is established to solve the coupling influence between them, maintaining positioning precision at approximately 2.9 mm. Considering the impact of noise on the calibration process, Gaussian noise is added to the solutions of the rotation matrix and translation vector to make the data more closely resemble the real scene in order to evaluate the performance of different hand–eye calibration algorithms. Eventually, an experiment comparing different hand–eye calibration methods proves that the proposed algorithm is better than other hand–eye calibration algorithms in terms of calibration accuracy, robustness to noise, and stability, satisfying the accuracy requirements of switching operations. 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

Frequent monitoring of crop moisture levels can significantly improve crop production efficiency and optimise water resource utilisation. The aim of the present study was to generate moisture status maps using thermal infrared imagery, centring on the development of a predictive model for the cotton leaf water potential. The model was constructed using particle swarm optimisation (PSO) in conjunction with the least squares support vector machine (LS-SVM). Traditional SVM models suffer from high computational complexity, long training times, and inequality constraints in predicting leaf water potential. To address such issues, the PSO algorithm was introduced to improve the performance of the LS-SVM model. The PSO-optimised LS-SVM model exhibited notable improvements in performance when evaluated on two distinct test datasets (Alaer and Tumushuke). The research results indicate that the predictive accuracy of the PSO-LS-SVM model significantly improved, as evidenced by an increase of 0.05 and 0.04 in the $R^2$ values, both of which reached 0.95. This improvement is reflected in the corresponding RMSE values, which were reduced to 0.100 and 0.103. Furthermore, a model was established based on data from three cotton growth stages, achieving high predictive accuracy even with fewer training samples. By using the PSO-LS-SVM model to predict leaf water potential information, the predicted data were mapped onto drone images, enabling the transformation of the leaf water potential from a point to an area. The present findings contribute to a more comprehensive understanding of the cotton leaf water potential by visually representing the spatial distribution of crop water status on a large scale. The results hold substantial significance for the improvement of crop irrigation management. Full article