Search Results (177)

Warm deep drawing is an effective special deep drawing technique for improving the forming limits of difficult-to-form materials such as aluminum alloys, magnesium alloys, and stainless steels. This paper experimentally investigated the effect of a combined variable process path, which integrates a variable punch speed (VSPD) and a variable blank holder force (VBHF) path, on the warm deep drawing performance of an A5182 aluminum alloy sheet at 300 °C (where the strain rate sensitivity index m equals 0.11). Experiments demonstrated not only a reduction in the forming time and an improved wall thickness uniformity, but also an improvement in the forming limits. The significant improvement in the forming characteristics is discussed in terms of the theoretical three-dimensional process window (SPD-BHF-flange reduction ratio (ΔDR*) space) consisting of the fracture limit and flange wrinkling limit derived from deep drawing theory, and it was shown to be consistent with the experimental results. Finaly, the novel combined VSPD/VBHF process path successfully achieved deep drawing with a challenging drawing ratio (DR) of 3.3. Full article

This paper analyzes the Bagley–Torvik fractional-order equation with generalized fractional Hilfer derivatives of two orders for functions in Banach spaces under conditions expressed in the language of weak topology. We develop a comprehensive theory of fractional-order differential equations of various orders. Our focus is on the equivalence results (or the lack thereof) of this new class of fractional-order Hilfer operators and on maximizing the regularity of the solution. To this end, we examine the equivalence of differential problems involving pseudo-derivatives and integral problems involving Pettis integrals. Our results are novel, even within the context of integer-order differential equations. Another objective is to incorporate fractional-order problems into the growing research field that uses weak topology and function spaces to study vector-valued functions. The auxiliary results obtained in this article are general and applicable beyond its scope. Full article

Biplot methods provide a framework for the simultaneous graphical representation of both rows and columns of a data matrix. Classical biplots were originally developed for continuous data in conjunction with principal component analysis (PCA). In recent years, several extensions have been proposed for binary and nominal data. These variants, referred to as logistic biplots (LBs), are based on logistic rather than linear response models. However, existing formulations remain insufficient for analyzing ordinal data, which are common in many social and behavioral research contexts. In this study, we extend the biplot methodology to ordinal data and introduce the ordinal logistic biplot (OLB). The proposed method estimates row scores that generate ordinal logistic responses along latent dimensions, whereas column parameters define logistic response surfaces. When these surfaces are projected onto the space defined by the row scores, they form a linear biplot representation. The model is based on a framework, leading to a multidimensional structure analogous to the graded response model used in Item Response Theory (IRT). We further examine the geometric properties of this representation and develop computational algorithms—based on an alternating gradient descent procedure—for parameter estimation and computation of prediction directions to facilitate visualization. The OLB method can be viewed as an extension of multidimensional IRT models, incorporating a graphical representation that enhances interpretability and exploratory power. Its primary goal is to reveal meaningful patterns and relationships within ordinal datasets. To illustrate its usefulness, we apply the methodology to the analysis of job satisfaction among PhD holders in Spain. The results reveal two dominant latent dimensions: one associated with intellectual satisfaction and another related to job-related aspects such as salary and benefits. Comparative analyses with alternative techniques indicate that the proposed approach achieves superior discriminatory power across variables. Full article

The performance of iterative schemes used to solve nonlinear operator equations is strongly influenced by the initial guess. Therefore, it is essential to accurately determine convergence radii and develop theoretical strategies to broaden the region where convergence is guaranteed in order to enhance the reliability and efficiency of these methods. A crucial tool for this purpose is local convergence analysis, which investigates behavior near the true solution to establish convergence criteria. This work is dedicated to extending the convergence region of a parameter-based iteration scheme of the fifth-order. We carry out a comprehensive local convergence study within the framework of Banach spaces and derive precise formulas for the convergence radius, error estimates, and convergence zones associated with the method. A notable advantage of our approach is that it relies solely on the first derivative and avoids the need for additional conditions, making it easier to apply and significantly expanding the convergence region relative to earlier approaches. The theoretical contributions are further validated through a series of numerical experiments applied to diverse classes of nonlinear equations. Furthermore, the examination of the basins of attraction and their symmetry provides a deeper understanding of the method’s dynamic characteristics, robustness, and effectiveness in tackling complex-valued polynomial equations. Full article

The paper investigates the regularization of solutions to nonlinear Volterra integral equations of the first kind, under the assumption that a solution exists and belongs to the space of continuous functions. The kernel of the equation is a differentiable function and vanishes on the diagonal at an interior point of the integration interval. By applying an appropriate differential operator (with respect to x), the Volterra integral equation of the first kind is reduced to a Volterra integral equation of the third kind, equivalent with respect to solvability. The subdomain method is employed by partitioning the integration interval into two subintervals. Within the imposed constraints, a compatibility condition for the solutions is satisfied at the junction point of the partial subintervals. A Lavrentiev-type regularizing operator is constructed that preserves the Volterra structure of the equation. The uniform convergence of the regularized solution to the exact solution is proved, and conditions ensuring the uniqueness of the solution in Hölder space are established. Full article

The primary aim of this study is to establish new Wirtinger-type inequalities involving fractional derivatives, which are essential tools in analysis and applied mathematics. We derive generalized Wirtinger-type inequalities incorporating the $(k,\psi )$-Caputo fractional derivatives using Taylor’s expansion. The inequalities are derived in $L_p$ spaces $(p>1)$ through Hölder’s inequality. A detailed analytical discussion is provided to further examine the derived inequalities. The theoretical findings are validated through numerical examples and graphical representations. Furthermore, the novelty and applicability of the proposed technique are demonstrated through the applications of the resulting inequalities to derive new results related to the arithmetic–geometric mean inequality. Full article

With the rise of embodied agents and indoor service robots, object detection has become a critical component supporting semantic mapping, path planning, and human–robot interaction. However, indoor scenes often face challenges such as severe occlusion, large-scale variations, small and densely packed objects, and complex textures, making existing methods struggle in terms of both robustness and accuracy. This paper proposes MDF-YOLO, a multi-domain fusion detection framework based on Hölder regularity guidance. In the backbone, neck, and feature recovery stages, the framework introduces the CrossGrid Memory Block, Hölder-Based Regularity Guidance–Hierarchical Context Aggregation module, and Frequency-Guided Residual Block, achieving complementary feature modeling across the state space, spatial domain, and frequency domain. In particular, the HG-HCA module uses the Hölder regularity map as a guiding signal to balance the dynamic equilibrium between the macro and micro paths, thus achieving adaptive coordination between global consistency and local discriminability. Experimental results show that MDF-YOLO significantly outperforms mainstream detectors in metrics such as mAP@0.5, mAP@0.75, and mAP@0.5:0.95, achieving values of 0.7158, 0.6117, and 0.5814, respectively, while maintaining near real-time inference efficiency in terms of FPS and latency. Ablation studies further validate the independent and synergistic contributions of CGMB, HG-HCA, and FGRB in improving small-object detection, occlusion handling, and cross-scale robustness. This study demonstrates the potential of Hölder regularity and multi-domain fusion modeling in object detection, offering new insights for efficient visual modeling in complex indoor environments. Full article

In this paper, we study the problem of uniqueness of fixed points for operators acting from a Banach space X into a subspace Y with a stronger norm. Our main objective is to preserve the expected regularity of fixed points, as determined by the norm of Y, while analyzing their uniqueness without imposing the classical or generalized contraction condition on Y. The results presented here provide generalized uniqueness theorems that extend existing fixed-point theorems to a broader class of operators and function spaces. The results are used to study fractional initial value problems in generalized Hölder spaces. Full article

This paper investigates a slow–fast stochastic reaction–diffusion–advection equation with Hölder-continuous coefficients, where the irregularity of the coefficients presents significant analytical challenges. Our approach fundamentally relies on techniques from Poisson equations in Hilbert spaces, through which we establish optimal strong convergence rates for the approximation of the averaged solution by the slow component. The key advantage that this paper presents is that the coefficients are merely Hölder continuous yet the optimal rate can still be obtained, which is crucial for subsequent central limit theorems and numerical approximations. Full article

In this paper, we first introduce a parametric identity for generalized differentiable functions using a generalized fractal–fractional integral operators. Based on this identity, we establish several variants of parameterized inequalities for functions whose local fractional derivatives in absolute value satisfy generalized convexity conditions. Furthermore, we demonstrate that our main results reduce to well-known Ostrowski- and Simpson-type inequalities by selecting suitable parameters. These inequalities contribute to finding tight bounds for various integrals over fractal spaces. By comparing the classical Hölder and Power mean inequalities with their new generalized versions, we show that the improved forms yield sharper and more refined upper bounds. In particular, we illustrate that the generalizations of Hölder and Power mean inequalities provide better results when applied to fractal integrals, with their tighter bounds supported by graphical representations. Finally, a series of applications are discussed, including generalized special means, generalized probability density functions and generalized quadrature formulas, which highlight the practical significance of the proposed results in fractal analysis. 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 examines a family of operators that combine the features of fractional-order and classical operators. Our goal is to obtain results on their invertibility in function spaces, based on their inherent improving properties. The class of proportional operators we study is extensive and includes both fractional-order and classical operators. This leads to interesting function spaces in which we obtain the right- and left-handed properties of invertibility. Thus, we extend and unify results concerning fractional-order and proportional operators. To confirm the relevance of our results, we have supplemented the paper with a series of results on the equivalence of differential and integral forms for various problems, including terminal value problems. Full article

Resonators are passive components that respond to an excitation signal by oscillating at their natural frequency with an exponentially decreasing amplitude. When combined with antennas, resonators enable purely passive chipless sensors that can be read wirelessly. In this contribution, we investigate the properties of dielectric resonators, which combine the following functionalities: They store the readout signal for a sufficiently long time and couple to free space electromagnetic waves to act as antennas. Their mode spectrum, along with their resonant frequencies, quality factor, and coupling to electromagnetic waves, is investigated using a commercial finite element program. The fundamental mode exhibits a too-low overall Q factor. However, some higher modes feature overall Q factors of several thousand, which allows them to act as transponders operating without integrated circuits, batteries, or antennas. To experimentally verify the simulations, isolated dielectric resonators exhibiting modes with similarly high radiation-induced and dissipative quality factors were placed on a low-loss, low permittivity ceramic holder, allowing their far-field radiation properties to be measured. The radiation patterns investigated in the laboratory and outdoors agree well with the simulations. The resulting radiation patterns show a directivity of approximately 7.5 dBi at 2.5 GHz. The sensor was then heated in a ceramic furnace with the readout antenna located outside at room temperature. Wireless temperature measurements up to 700 °C with a resolution of 0.5 °C from a distance of 1 m demonstrated the performance of dielectric resonators for practical applications. Full article

Springback represents the deflection of a workpiece after releasing the forming tools or dies, which influences the quality and precision of the final products. It is basically governed by the elastic strain recovery of the material after unloading. Most approaches only implement reverse bending to determine the final shape of the formed product. However, stretch plays significant role whe the blank is held by a blank holder. In this paper, an algorithm is presented to calculate the contributions of both stretch loads and bending moments to elastic deformation during springback for each element, and to combine them mathematically and geometrically to achieve the final shape of the product. Comparing the results of this algorithm for different sheet metal forming processes with experimental measurements demonstrates that this technique successfully predicts a wide range of springback with reasonable accuracy. The advantage of this approach is its accuracy, which is not sensitive to hardening and softening mechanisms, the magnitude of plastic deformation during the forming process, or the size of the object. The application of the proposed formulation is limited to long profiles (plane-strain cases). However, it can be extended to more general applications by adding the effect of torsion and developing equations in 3D space. Due to the explicit nature of the calculations, data-processing time would be reduced significantly compared to the sophisticated algorithms used in commercial software. Full article

In this paper, our first objective is to define the idea of grand variable Herz spaces. Then, our main goal is to prove boundedness results for operators, including the rough Riesz potential operator of variable order and the fractional Hardy operators, on grand variable Herz spaces under some proper assumptions. To prove the boundedness results, we use Holder-type and Minkowski inequalities. In the proof of the main result, we use different techniques. We divide the summation into different terms and estimate each term under different conditions. Then, by combining the estimates, we prove that the rough Riesz potential operator of variable order and the fractional Hardy operators are bounded on grand variable Herz spaces. It is easy to show that the rough Riesz potential operator of variable order generalizes the Riesz potential operator and that the fractional Hardy operators are generalized versions of simple Hardy operators. So, our results extend some previous results to the more generalized setting of grand variable Herz spaces. Full article