Search Results (98)

The integrity of natural gas pipelines will decrease with an increase in operating time, thus causing pipeline leaks and accidents. However, it is challenging to improve the precision and automation of existing sensors to raise leak prediction and classification precision. Therefore, based on deep learning, a 1D convolutional neural network (CNN) incorporating the channel attention mechanism is proposed for recognizing and classifying the type of natural gas pipeline leakage. Firstly, the data reconstruction of the leaked acoustic signals, which have been classified by energy modes, is performed by feature augmentation and Bessel filtering. Subsequently, a lightweight CNN is proposed, and an attention mechanism is introduced to optimize the model performance. The results show that the training performance of the network with the attention mechanism is superior to that of the original network and the network with batch normalization. The attention mechanism network is then used to train the leakage signals with different features of engineering parameters. Finally, the test accuracy achieves 97.81%, validating the effectiveness of the proposed method for identifying and classifying natural gas leaks. It presents new ideas for the implementation of deep learning in the natural gas and chemical industries. Full article

In this article, we investigate the regularization and qualitative properties of parabolic Ginzburg–Landau equations in variable exponent Herz spaces. These spaces capture both local and global behavior, providing a natural framework for our analysis. We establish boundedness results for fractional Bessel–Riesz operators, construct examples highlighting their advantage over classical Riesz potentials, and recover several known theorems as special cases. As an application, we analyze a parabolic Ginzburg–Landau operator with VMO coefficients, showing that our estimates ensure the boundedness and continuity of solutions. Full article

The aim of this manuscript is to introduce the fractional integral inequalities of H-H types via multiplicative (Antagana-Baleanu) A-B fractional operators. We also provide the fractional version of the H-H type of the product and quotient of multiplicative superquadratic and multiplicative subquadratic functions via the same operators. Superquadratic functions, have stronger convexity-like behavior. They provide sharper bounds and more refined inequalities, which are valuable in optimization, information theory, and related fields. The use of multiplicative fractional operators establishes a nonlinear fractional structure, enhancing the analytical tools available for studying dynamic and nonlinear systems. The authenticity of the obtained results are verified by graphical and numerical illustrations by taking into account some examples. Additionally, the study explores applications involving special means, special functions and moments of random variables resulting in new fractional recurrence relations within the multiplicative calculus framework. These contributions not only generalize existing inequalities but also pave the way for future research in both theoretical mathematics and real-world modeling scenarios. Full article

Here in this paper, we establish the basic inclusion relations among the harmonic class $\mathbb{HF}(\sigma ,\eta )$ with the classes $S_{\mathcal{HF}}^{*}$ of starlike harmonic functions and $K_{\mathcal{HF}}$ of convex harmonic functions defined in open symmetric unit disk U. Moreover, we investigate inclusion connections for the harmonic classes $\mathcal{T}{\mathfrak{N}}_{\mathbb{HF}}\left(\varrho \right)$ and $\mathcal{T}{\mathfrak{Q}}_{\mathbb{HF}}\left(\varrho \right)$ of harmonic functions by applying the operator $\mathrm{\Lambda }$ associated with the Bessel function. Furthermore, several special cases of the main results are obtained for the particular case $\sigma =0$. Full article

In this study, we examine the error bounds related to Milne-type inequalities and a widely recognized Newton–Cotes method, originally developed for three-times-differentiable convex functions within the context of Jensen–Mercer inequalities. Expanding on this foundation, we explore Milne–Mercer-type inequalities and their application to a more refined class of three-times-differentiable s-convex functions. This work introduces a new identity involving such functions and Jensen–Mercer inequalities, which is then used to improve the error bounds for Milne-type inequalities in both Jensen–Mercer and classical calculus frameworks. Our research highlights the importance of convexity principles and incorporates the power mean inequality to derive novel inequalities. Furthermore, we provide a new lemma using Caputo–Fabrizio fractional integral operators and apply it to derive several results of Milne–Mercer-type inequalities pertaining to $(\alpha ,m)$-convex functions. Additionally, we extend our findings to various classes of functions, including bounded and Lipschitzian functions, and explore their applications to special means, the q-digamma function, the modified Bessel function, and quadrature formulas. We also provide clear mathematical examples to demonstrate the effectiveness of the newly derived bounds for Milne–Mercer-type inequalities. Full article

This paper proposes a co-aperture reflective metasurface that successfully generates four-channel Bessel vortex beams with equal divergence angle in both Ka and Ku bands. Initially, a frequency-selective surface (FSS) is employed to suppress inter-unit crosstalk. Subsequently, modified cross-dipole metasurface units are implemented using spin-decoupling theory to achieve independent multi-polarization control. Through theoretical calculation-based divergence angle engineering, the dual-concentric-disk structure integrated with multi-polarization control demonstrates enhanced aperture utilization efficiency compared to conventional partitioning strategies, yielding high-purity equal-divergence-angle Bessel vortex beams across multiple modes. Finally, experiments on the metasurface fabricated via printed circuit board (PCB) technology verify that the design simultaneously generates x-polarization +1 mode and y-polarization +2 mode equal divergence angle Bessel vortex beams in the Ku band and ±3 mode beams in the Ka band. Vortex beam divergence angles remain stable at 9° ± 0.5° under diverse polarization states and modes, with modal purity reaching 65–80% at the main radiation direction. This work provides a straightforward implementation method for generating equal-divergence-angle vortex beams applicable to Orbital Angular Momentum (OAM) multimode multiplexing and vortex wave detection. Full article

This paper focuses on the numerical modeling of drug diffusion in biological tissues using fractional time-dependent parabolic equations with non-local boundary conditions. The model includes a Caputo fractional derivative to capture the non-local effects and memory inherent in biological processes, such as drug absorption and transport. The theoretical framework of the problem is based on the work of Alhazzani, et al.,which demonstrates the solution’s goodness, existence, and uniqueness. Building on this foundation, we present a robust numerical method designed to deal with the complexity of fractional derivatives and non-local interactions at the boundaries of biological tissues. Numerical simulations reveal how fractal order and non-local boundary conditions affect the drug concentration distribution over time, providing valuable insights into drug delivery dynamics in biological systems. The results underscore the potential of fractal models to accurately represent diffusion processes in heterogeneous and complex biological environments. Full article

In this study, we apply the Laplace Transform Homotopy Analysis Method (LTHAM) to numerically solve a fractional-order telegraph equation with a Bessel operator. The iterative scheme developed is tested on multiple examples to evaluate its efficiency. Our observations indicate that the method generates an approximate solution in series form, which converges rapidly to the analytic solution in each instance. The convergence of these series solutions is assessed both geometrically and numerically. Our results demonstrate that LTHAM is a reliable, powerful, and straightforward approach to solving fractional telegraph equations, and it can be effectively extended to solve similar types of equations. Full article

This paper investigates a new class of fractional integral operators, namely, the exponentially damped Riesz-type operators within the framework of variable exponent Lebesgue spaces $L^{\mathtt{p}(·)}$. To the best of our knowledge, the boundedness of such operators has not been addressed in any existing functional setting. We establish their boundedness under appropriate log-Hölder continuity and growth conditions on the exponent function $\mathtt{p}(·)$. To highlight the novelty and practical relevance of the proposed operator, we conduct a comparative analysis demonstrating its effectiveness in addressing convergence, regularity, and stability of solutions to partial differential equations. We also provide non-trivial examples that illustrate not only these properties but also show that, under this operator, a broader class of functions becomes locally integrable. The exponential decay factor notably broadens the domain of boundedness compared to classical Riesz and Bessel–Riesz potentials, making the operator more versatile and robust. Additionally, we generalize earlier results on Sobolev-type inequalities previously studied in constant exponent spaces by extending them to the variable exponent setting through our fractional operator, which reduces to the classical Riesz potential when the decay parameter $\lambda =0$. Applications to elliptic PDEs are provided to illustrate the functional impact of our results. Furthermore, we develop several new structural properties tailored to variable exponent frameworks, reinforcing the strength and applicability of the proposed theory. Full article

This paper investigates the Bessel–Riesz operator within the framework of variable Lebesgue spaces. We extend existing results by establishing boundedness under more general conditions. The analysis is based on the Hardy–Littlewood maximal function, Hölder’s inequality, and dyadic decomposition techniques. For a given domain space, we construct a suitable range space such that the operator remains bounded. Conversely, for a prescribed range space, we identify a corresponding domain space that guarantees boundedness. Illustrative examples are included to demonstrate the construction of such spaces. The main results hold when the essential infimum of the exponent function exceeds one, and we also establish weak-type estimates in the limiting case. Full article

In modern industries, bearings are often subjected to challenges from environmental noise and variations in operating conditions during their operation, which affects existing fault diagnosis methods that rely on signals from single types of sensors. These methods often fail to provide comprehensive and stable fault information, thereby affecting the diagnostic performance. To address this issue, this paper introduces a multi-source and multi-domain information fusion method for the fault diagnosis (M2IFD) of bearings, integrating an attention mechanism to enhance the diagnosis process. The proposed method is structured into three main stages: initially, the original signal undergoes transformation into frequency and time–frequency domains using envelope spectral transform (EST) and Bessel transform (BT) to extract richer fault features. In the second stage, features are extracted independently from each transformed domain and combined with a channel attention mechanism for feature fusion, preserving the unique information from each signal source. Finally, multi-domain features are further fused through an attention mechanism to improve fault classification accuracy. Extensive comparison experiments conducted on the Paderborn dataset illustrate that the proposed M2IFD method significantly enhances fault recognition accuracy across various operating conditions, showcasing its adaptability and robustness. This approach presents new avenues for bearing fault diagnosis, with significant implications for both theoretical and practical applications. Full article

In this paper, we define a new generalization of three-variable q-Laguerre polynomials and derive some properties. By using these polynomials, we introduce a new generalization of three-variable q-Laguerre-based Appell polynomials (3VqLbAP) through a generating function approach involving zeroth-order q-Bessel–Tricomi functions. These polynomials are studied by means of generating function, series expansion, and determinant representation. Also, these polynomials are further examined within the framework of q-quasi-monomiality, leading to the establishment of essential operational identities. We then derive operational representations, as well as q-differential equations for the three-variable q-Laguerre-based Appell polynomials. Some examples are constructed in terms of q-Laguerre–Hermite-based Bernoulli, Euler, and Genocchi polynomials in order to illustrate the main results. Full article

In this article, we established the necessary and sufficient conditions as well as the inclusion relations for a few subclasses of univalent functions associated with Bessel functions. Furthermore, we investigated an integral operator linked to Bessel functions and elaborated on several mapping properties. The study includes various theorems, corollaries and the consequences derived from the main results. Full article

This paper develops novel results in the harmonic analysis of Bessel operators, extending their theory to higher-dimensional and non-Euclidean spaces. We present a refined framework for Hardy spaces associated with Bessel operators, emphasizing atomic decompositions, dual spaces, and connections to Sobolev and Besov spaces. The spectral theory of families of boundary-interpolating operators is also expanded, offering precise eigenvalue estimates and functional calculus applications. Furthermore, we explore Bessel operators under non-standard measures, such as fractal and weighted geometries, uncovering new analytical phenomena. Key implications include advanced insights into singular integrals, heat kernel behavior, and the boundedness of Riesz transforms, with potential applications in fractal geometry, constrained wave propagation, and mathematical physics. Full article

In this manuscript, we establish the boundedness of the Bessel–Riesz operator $I_{\alpha ,\gamma }f$ in variable Lebesgue spaces $L^{p(·)}$. We prove that $I_{\alpha ,\gamma }f$ is bounded from $L^{p(·)}$ to $L^{p(·)}$ and from $L^{p(·)}$ to $L^{q(·)}$. We explore various scenarios for the boundedness of $I_{\alpha ,\gamma }f$ under general conditions, including constraints on the Hardy–Littlewood maximal operator $\mathcal{M}$. To prove these results, we employ the boundedness of $\mathcal{M}$, along with Hölder’s inequality and classical dyadic decomposition techniques. Our findings unify and generalize previous results in classical Lebesgue spaces. In some cases, the results are new even for constant exponents in Lebesgue spaces. Full article