Search Results (733)

The main objective of this research is to obtain interesting estimates for Jensen’s gap in the integral sense, along with their applications. The convexity of a fifth-order absolute function is used to established proposed estimates of Jensen’s gap. We performed numerical computations to compare our estimates with previous findings. With the use of the primary findings, we are able to obtain improvements of the Hölder inequality and Hermite–Hadamard inequality. Furthermore, the primary results lead to some inequalities for power means and quasi-arithmetic means. We conclude by outlining the information theory applications of our primary inequalities. Full article

The accurate identification of seismic faults, which serve as crucial fluid migration pathways in hydrocarbon reservoirs, is of paramount importance for reservoir characterization. Traditional interpretation is inefficient. It also struggles with complex geometries, failing to meet the current exploration demands. Deep learning boosts fault identification significantly but struggles with edge accuracy and noise robustness. To overcome these limitations, this research introduces SwiftSeis-AWNet, a novel lightweight and high-precision network. The network is based on an optimized MedNeXt architecture for better fault edge detection. To address the noise from simple feature fusion, a Semantics and Detail Infusion (SDI) module is integrated. Since the Hadamard product in SDI can cause information loss, we engineer an Attention-Weighted Semantics and Detail Infusion (AWSDI) module that uses dynamic multi-scale feature fusion to preserve details. Validation on field seismic datasets from the Netherlands F3 and New Zealand Kerry blocks shows that SwiftSeis-AWNet mitigates challenges like the loss of small-scale fault features and misidentification of fault intersection zones, enhancing the accuracy and geological reliability of automated fault identification. Full article

A refined version of the q-Hermite–Hadamard inequalities for strongly convex functions is introduced in this paper, utilizing both left and right q-integrals. Tighter bounds and more accurate estimates are derived by incorporating strong convexity. New q-trapezoidal and q-midpoint estimates are also presented to enhance the precision of the results. The improvements in the results compared to previous work are demonstrated through numerical examples in terms of precision and tighter bounds, and the advantages of using strongly convex functions are showcased. Full article

Traditional antenna arrays for direction-of-arrival (DOA) estimation typically require numerous elements to achieve target performance, increasing system complexity and cost. Reconfigurable intelligent surfaces (RISs) offer a promising alternative, yet their performance critically depends on phase coding design. To address this, we propose a phase coding design method for RIS-aided DOA estimation with a single receiving channel. First, we establish a system model where averaged received signals construct a power-based formulation. This transforms DOA estimation into a compressed sensing-based sparse recovery problem, with the RIS far-field power radiation pattern serving as the measurement matrix. Then, we derive the decoupled expression of the measurement matrix, which consists of the phase coding matrix, propagation phase shifts, and array steering matrix. The phase coding design is then formulated as a Frobenius norm minimization problem, approximating the Gram matrix of the equivalent measurement matrix to an identity matrix. Accordingly, the phase coding design problem is reformulated as a Frobenius norm minimization problem, where the Gram matrix of the equivalent measurement matrix is approximated to an identity matrix. The phase coding is deterministically constructed as the product of a unitary matrix and a partial Hadamard matrix. Simulations demonstrate that the proposed phase coding design outperforms random phase coding in terms of angular estimation accuracy, resolution probability, and the requirement of coding sequences. Full article

The implementation of low-cost sensitive and selective gas sensors for monitoring fruit ripening and quality strongly depends on their long-term stability. Gas sensor drift undermines the long-term reliability of low-cost sensing platforms, particularly in precision agriculture. We present a real-time drift compensation framework based on a lightweight Temporal Convolutional Neural Network (TCNN) combined with a Hadamard spectral transform. The model operates causally on incoming sensor data, achieving a mean absolute error below 1 mV on long-term recordings (equivalent to <1 particle per million (ppm) gas concentration). Through quantization, we compress the model by over 70%, without sacrificing accuracy. Demonstrated on a combustion-type gas sensor system (dubbed GMOS) for ethylene monitoring, our approach enables continuous, drift-corrected operation without the need for recalibration or dependence on cloud-based services, offering a generalizable solution for embedded environmental sensing—in food transportation containers, cold storage facilities, de-greening rooms and directly in the field. Full article

In this paper, we investigate a class of fuzzy partially differentiable models for Caputo–Hadamard-type Goursat problems with generalized Hukuhara difference, which have been widely recognized as having a significant role in simulating and analyzing various kinds of processes in engineering and physical sciences. By transforming the fuzzy partially differentiable models into equivalent integral equations and employing classical Banach and Schauder fixed-point theorems, we establish the existence and uniqueness of solutions for the fuzzy partially differentiable models. Furthermore, in order to overcome the complexity of obtaining exact solutions of systems involving Caputo–Hadamard fractional derivatives, we explore numerical approximations based on trapezoidal and Simpson’s rules and propose three numerical examples to visually illustrate the main results presented in this paper. Full article

This study is organized to introduce the concept of center–radius $\left(cr\right)$-ordered fuzzy number-valued convex mappings. Based on this class of mappings, we have initiated the idea of fuzzy number-valued extended $cr$-ℏ convex mappings incorporating control mapping ℏ. Furthermore, several potential new classes of convexity will be provided to discuss its generic nature. Also, some essential properties, criteria, and detailed characterizations through Jensen’s and Hermite–Hadamard-like inequalities are provided, incorporating Riemann–Liouville fractional operators, which are defined by $\rho$-level mappings. To validate the proposed fractional bounds through simulations, we consider both triangular and trapezoidal fuzzy numbers. Our results are based on totally ordered fuzzy-valued mappings, which are new and generic. The under-consideration class also includes a blend of new classes of convexity, which are controlled by non-negative mapping ℏ. In previous studies, the researchers have focused on different partially ordered relations. Full article

This paper addresses the existence of solutions to a Hadamard fractional differential equation of arbitrary order on an infinite interval, subject to integral boundary conditions that incorporate both Riemann–Stieltjes integrals and Hadamard fractional derivatives. Due to the presence of nontrivial solutions in the associated homogeneous boundary value problem, the problem is classified as resonant. The Mawhin continuation theorem is utilized to derive the main findings. Full article

This study presents, for the first time, a new class of interval-valued superquadratic stochastic processes and examines their core properties through the lens of the center-radius total order relation on intervals. These processes serve as a powerful tool for modeling uncertainty in stochastic systems involving interval-valued data. By utilizing their intrinsic structure, we derive sharpened versions of Jensen-type and Hermite–Hadamard-type inequalities, along with their fractional extensions, within the framework of mean-square stochastic Riemann–Liouville fractional integrals. The theoretical findings are validated through extensive graphical representations and numerical simulations. Moreover, the applicability of the proposed processes is demonstrated in the domain of information theory by constructing novel stochastic divergence measures and Shannon’s entropy grounded in interval calculus. The outcomes of this work lay a solid foundation for further exploration in stochastic analysis, particularly in advancing generalized integral inequalities and formulating new stochastic models under uncertainty. Full article

The study of various subclasses of univalent functions involving the solutions to various differential equations is not totally new, but studies of analytic functions with respect to $(\mathsf{\ell },\kappa )$-symmetric points are rarely conducted. Here, using a differential operator which was defined using the Hadamard product of Mittag–Leffler function and general analytic function, we introduce a new class of starlike functions with respect to $(\mathsf{\ell },\kappa )$-symmetric points associated with the vertical domain. To define the function class, we use a Carathéodory function which was recently introduced to study the impact of various conic regions on the vertical domain. We obtain several results concerned with integral representations and coefficient inequalities for functions belonging to this class. The results obtained by us here not only unify the recent studies associated with the vertical domain but also provide essential improvements of the corresponding results. Full article

The ATSC 3.0 standard supports ultra-high-definition broadcasting and introduces transmitter identification (TxID) to enable robust operation in single-frequency networks (SFNs). TxID typically relies on long spreading codes to minimize interference, but this approach limits the achievable data transmission rate. To address this limitation, we propose a novel scheme that combines cross-polarization discrimination (XPD) and frequency symbol spreading (FSS) to reduce interference from additional data on standard broadcast signals without increasing the system complexity. In the proposed system, vertically polarized antennas transmit standard broadcast signals, while horizontally polarized antennas transmit additional data. FSS utilizes orthogonal Hadamard codes in the frequency domain to enhance signal robustness in multipath fading environments. The simulation results demonstrate improved bit error rate (BER) and throughput under varying XPD conditions (5–15 dB), with further gains achieved through the use of longer spreading codes and adaptive modulation. The proposed method requires only minor hardware modifications and is fully compatible with existing ATSC 3.0 infrastructure. Full article

This paper investigates the existence, uniqueness, and finite-time stability of solutions to a class of nonlinear systems governed by the Hadamard fractional derivative. The analysis is carried out using two fundamental tools from fixed point theory: the Krasnoselskii fixed point theorem and the Banach contraction principle. These methods provide rigorous conditions under which solutions exist and are unique. Furthermore, criteria ensuring the finite-time stability of the system are derived. To demonstrate the practicality of the theoretical results, a detailed example is presented. This paper also discusses certain assumptions and presents corollaries that naturally emerge from the main theorems. Full article

This paper introduces a novel version of the Gronwall inequality specifically related to the Hilfer–Hadamard proportional fractional derivative. By utilizing Picard’s method of successive approximations along with the definition of Mittag–Leffler functions, we derive a representation formula for the solution of the Hilfer–Hadamard proportional fractional differential equation featuring constant coefficients, expressed in the form of the Mittag–Leffler kernel. We establish the uniqueness of the solution through the application of Banach’s fixed-point theorem, leveraging several properties of the Mittag–Leffler kernel. The current study outlines optimal stability, a new Ulam-type concept based on classical special functions. It aims to improve approximation accuracy by optimizing perturbation stability, offering flexible solutions to various fractional systems. While existing Ulam stability concepts have gained interest, extending and optimizing them for control and stability analysis in science and engineering remains a new challenge. The proposed approach not only encompasses previous ideas but also emphasizes the enhancement and optimization of model stability. The numerical results, presented in tables and charts, are provided in the application section to facilitate a better understanding. Full article

Crack detection in cement infrastructure is imperative to ensure its structural integrity and public safety. However, most existing methods use multi-scale and attention mechanisms to improve on a single backbone, and this single backbone network is often ineffective in detecting slender or variable cracks in complex scenarios. We propose a novel network, FD²-YOLO, based on frequency-domain dual-stream YOLO, for accurate and efficient detection of cement cracks. Firstly, the model employs a dual backbone architecture, integrating edge and texture features in the frequency domain with semantic features in the spatial domain, to enhance the extraction of crack-related features. Furthermore, the Dynamic Inter-Domain Feature Fusion module (DIFF) is introduced, which uses large-kernel deep convolution and Hadamard to enable the adaptive fusion of features from different domains, thus addressing the problem of difficult feature fusion due to domain differences. Finally, the DIA-Head module has been proposed, which dynamically focuses on the texture and geometric deformation features of cracks by introducing the Deformable Interactive Attention Module (DIA Module) in Decoupled Head and utilizing its Deformable Interactive Attention. Extensive experiments on the RDD2022 dataset demonstrate that FD²-YOLO achieves state-of-the-art performance. Compared with existing YOLO-based models, it improves mAP50 by 1.3%, mAP50-95 by 1.1%, recall by 1.8%, and precision by 0.5%, validating its effectiveness in real-world object detection scenarios. In addition, evaluation on the UAV-PDD2023 dataset further confirms the robustness and generalization of our approach, where FD²-YOLO achieves a mAP50 of 67.9%, mAP50-95 of 35.9%, recall of 61.2%, and precision of 75.9%, consistently outperforming existing lightweight and Transformer-based detectors under more complex aerial imaging conditions. Full article

In this survey, we have included the recent results on Lyapunov-type inequalities for differential equations of fractional order associated with Dirichlet, nonlocal, multi-point, anti-periodic, and discrete boundary conditions. Our results involve a variety of fractional derivatives such as Riemann–Liouville, Caputo, Hilfer–Hadamard, $\psi$-Riemann–Liouville, Atangana–Baleanu, tempered, half-linear, and discrete fractional derivatives. Full article