Search Results (1,577)

This work explores the geometric properties of the Turanian of the modified Bessel function of the first kind (TMBF). Using the properties of the digamma function, we establish conditions under which the normalized TMBF satisfies starlikeness, convexity, k-starlikeness, k-uniform convexity, pre-starlikeness, lemniscate starlikeness, and convexity, and under which exponential starlikeness and convexity are obtained. By combining methods from complex analysis, inequalities, and functional analysis, the article advances the theory of Bessel functions and hypergeometric functions. The established results could be useful in approximation theory and bounding the behavior of functions. Full article

This study presents a novel category of nonconvex functions in Banach spaces, referred to as quasi-lower $C^2$ functions on nonempty closed sets. We establish the existence of solutions for nonconvex variational problems involving quasi-lower $C^2$ functions defined in Banach spaces. To illustrate the applicability of our findings, an example is provided in $L^p$ spaces. Full article

We prove the inequalities of the weighted Hermite–Hadamard type the and Hermite–Hadamard–Mercer type for an extremely rich class of geometrically arithmetically-h-convex functions (GA-h-CFs) via generalized Hadamard–Fractional integral operators (HFIOs). The two generalized fractional integral operators (FIOs) are Hadamard proportional fractional integral operators (HPFIOs) and Hadamard k-fractional integral operators (HKFIOs). Moreover, we also present the results for subclasses of GA-h-CFs and show that the inequalities proved in this paper unify the results from the recent related literature. Furthermore, we compare the two generalizations in view of the fractional operator parameters that contribute to the generalizations of the results and assess the better approximation via graphical tools. Finally, we present applications of the new inequalities via HPFIOs and HKFIOs by establishing interpolation relations between arithmetic mean and geometric mean and by proving the new upper bounds for the Tsallis relative operator entropy. Full article

Copper electrolysis is a crucial process in copper smelting. The surface of cathodic copper plates is often affected by various electrolytic process factors, resulting in the formation of nodule defects that significantly impact surface quality and disrupt the downstream production process, making the prompt detection of these defects essential. At present, the detection of cathode copper plate nodules is performed by manual identification. In order to address the issues with manual convex nodule identification on the surface of industrial cathode copper plates in terms of low accuracy, high effort, and low efficiency in the manufacturing process, a lightweight YOLOv5 model combined with the BiFormer attention mechanism is proposed in this paper. The model employs MobileNetV3, a lightweight feature extraction network, as its backbone, reducing the parameter count and computational complexity. Additionally, an attention mechanism is introduced to capture multi-scale information, thereby enhancing the accuracy of nodule recognition. Meanwhile, the F-EIOU loss function is employed to strengthen the model’s robustness and generalization ability, effectively addressing noise and imbalance issues in the data. Experimental results demonstrate that the improved YOLOv5 model achieves a precision of 92.71%, a recall of 91.24%, and a mean average precision (mAP) of 92.69%. Moreover, a single-frame detection time of 4.61 ms is achieved by the model, which has a size of 2.91 MB. These metrics meet the requirements of practical production and provide valuable insights for the detection of cathodic copper plate surface quality issues in the copper electrolysis production process. Full article

In this paper, we consider a control architecture for a mobile robot equipped with visual sensors to pursue a target object in an environment with convex-shaped obstacles. The pursuit involves crucial occlusion avoidance and field of view maintenance, referred to as visual safety. Our goal is to achieve this safety through a multi-layered control architecture consisting of a planning layer and a safety layer. We propose functions that represent occlusion avoidance and field of view maintenance and derive conditions for these to act as control barrier functions. Utilizing these functions, we implement an optimal control at the planning layer and an optimization-based control at the safety layer. The effectiveness of this method is verified through two tasks: guiding the target object into a target location and preventing the target object from entering a target location. Full article

In this paper, we introduce a novel fractal–fractional identity, from which we derive new Simpson-type inequalities for functions whose first-order local fractional derivative exhibits generalized s-convexity in the second sense. This work introduces an approach that uses the first-order local fractional derivative, enabling the treatment of functions with lower regularity requirements compared to earlier studies. Additionally, we present two distinct methodological frameworks, one of which achieves greater precision by refining classical outcomes in the existing literature. The paper concludes with several practical applications that demonstrate the utility of our results. Full article

As a key task in machine learning, data classification is essential to find a suitable coordinate system to represent the data features of different classes of samples. This paper proposes the mutual-energy inner product optimization method for constructing a feature coordinate system. First, by analyzing the solution space and eigenfunctions of the partial differential equations describing a non-uniform membrane, the mutual-energy inner product is defined. Second, by expressing the mutual-energy inner product as a series of eigenfunctions, it shows the significant advantage of enhancing low-frequency features and suppressing high-frequency noise, compared to the Euclidean inner product. And then, a mutual-energy inner product optimization model is built to extract the data features, and the convexity and concavity properties of its objective function are discussed. Next, by combining the finite element method, a stable and efficient sequential linearization algorithm is constructed to solve the optimization model. This algorithm only solves positive definite symmetric matrix equations and linear programming with a few constraints, and its vectorized implementation is discussed. Finally, the mutual-energy inner product optimization method is used to construct feature coordinates, and multi-class Gaussian classifiers are trained on the MINST training set. Good prediction results of the Gaussian classifiers are achieved on the MINST test set. Full article

In the study, the authors introduce Qi’s normalized remainder of the Maclaurin power series expansion of the function $\ln \sec x=-\ln \cos x$; in view of a monotonicity rule for the ratio of two Maclaurin power series and by virtue of the logarithmic convexity of the function $(2^x-1)\zeta \left(x\right)$ on $(1,\infty )$, they prove the logarithmic convexity of Qi’s normalized remainder; with the aid of a monotonicity rule for the ratio of two Maclaurin power series, the authors present the monotonic property of the ratio between two Qi’s normalized remainders. Full article

This paper proposes a novel sine step size for warm-restart stochastic gradient descent (SGD). For the SGD based on the new proposed step size, we establish convergence rates for smooth non-convex functions with and without the Polyak–Łojasiewicz (PL) condition. To assess the effectiveness of the new step size, we implemented it across several datasets, including FashionMNIST, CIFAR10, and CIFAR100. This implementation was compared against eight distinct existing methods. The experimental results demonstrate that the proposed sine step size improves the test accuracy of the CIFAR100 dataset by $1.14\%$. This improvement highlights the efficiency of the new step size when compared to eight other popular step size methods. Full article

This paper addresses the decentralized composite optimization problem, where a network of agents cooperatively minimize the sum of their local objective functions with non-differentiable terms. We propose a novel communication-efficient decentralized ADMM framework, termed as CE-DADMM, by combining the ADMM framework with the three-point compressed (3PC) communication mechanism. This framework not only covers existing mainstream communication-efficient algorithms but also introduces a series of new algorithms. One of the key features of the CE-DADMM framework is its flexibility, allowing it to adapt to different communication and computation needs, balancing communication efficiency and computational overhead. Notably, when employing quasi-Newton updates, CE-DADMM becomes the first communication-efficient second-order algorithm based on compression that can efficiently handle composite optimization problems. Theoretical analysis shows that, even in the presence of compression errors, the proposed algorithm maintains exact linear convergence when the local objective functions are strongly convex. Finally, numerical experiments demonstrate the algorithm’s impressive communication efficiency. Full article

In this paper, we deal with the properties and applications of a nonlinear scalarization function for sets by using the Minkowski difference. Under some suitable assumptions, the continuity and convexity concerned with the nonlinear scalarization function for sets are presented. As applications, the path connectedness of the solution sets to set optimization problems and the continuity of the solution mappings of parametric set optimization problems are established. The results achieved do not impose the monotonicity of the set-valued objective mapping, which are obviously different from the related ones in the literature. Full article

Efficient and economical hydrocarbon extraction relies on a clear understanding of fluid flow dynamics in subsurface reservoirs, where multiphase flow in porous media poses complex modeling challenges. Traditional numerical methods for solving the governing partial differential equations (PDEs) provide effective solutions but struggle with the high computational demands required for accurately capturing fine-scale flow dynamics. In response, this study introduces a physics-informed generative adversarial network (GAN) framework for addressing the Buckley–Leverett (B-L) equation with non-convex flux functions. The proposed framework consists of two novel configurations: a Physics-Informed Generator GAN (PIG-GAN) and Dual-Informed GAN (DI-GAN), both of which are rigorously tested in forward and inverse problem settings for the B-L equation. We assess model performance under noisy data conditions to evaluate robustness. Our results demonstrate that these GAN-based models effectively capture the B-L shock front, enhancing predictive accuracy while embedding fluid flow equations to ensure model interpretability. This approach offers a significant advancement in modeling complex subsurface environments, providing an efficient alternative to traditional methods in fluid dynamics applications. Full article

Human-driven changes in land cover and use can significantly impact species ants community structures, often leading to a decline in taxonomic diversity or species homogenization. Ant morphology, used as a proxy for ecological function, offers a valuable framework for understanding the effects of anthropogenic disturbances on ant diversity. This study explored the morphological diversity of ant assemblages in agricultural ecosystems and secondary forests in Italy and the Brazilian Amazon, analyzing how these communities are structured and adapted to different environments. The research aims to understand the ecological interactions and the role of ants in maintaining biodiversity in these contexts. The study was conducted in the Ticino River Natural Park, Italy, and the Paragominas mosaic in Pará, Brazil. The ants were sampled using epigean pitfall traps at 15 agricultural and 13 forest sites. In the secondary forests, the species richness was significantly higher in both countries compared to agricultural areas. In general, the Community Weighted Mean (CWM) of the selected traits (head length, head width, interocular distance, mandible length, eye width, Weber’s length, and tibia length) of Brazilian ants was higher than those of Italian. However, the CWM of agricultural areas of the two countries was more similar. We noticed the convex hull (i.e., the volume of an assemblage in the morphological space) of Brazilian secondary forests was still larger than Italian secondary forests when both assemblages have the same number of species. Morphological homogenization was more pronounced in agricultural settings, whereas secondary forests showed more variability, highlighting the role of environmental filtering in shaping ant communities across land use types. Full article

We define new classes of meromorphic p-valent convex functions, respectively, meromorphic close-to-convex functions, by using an extension of Wanas operator in order to study the preservation properties of these classes, when a well-known integral operator is used. We find the conditions which allow this operator to preserve the classes mentioned above, and we will remark the symmetry between these classes. Full article

The study of the Hankel determinant generated by the Maclaurin series of holomorphic functions belonging to particular classes of normalized univalent functions is one of the most significant problems in geometric function theory. Our goal in this study is first to define a family of alpha-convex functions associated with modified sigmoid functions and then to investigate sharp bounds of initial coefficients, Fekete-Szegö inequality, and second-order Hankel determinants. Moreover, we also examine the logarithmic and inverse coefficients of functions within a defined family regarding recent issues. All of the estimations that were found are sharp. Full article