Search Results (32)

This paper proposes a new accelerated fixed-point algorithm based on a double-inertial extrapolation technique for solving structured variational inclusion and convex bilevel optimization problems. The underlying framework leverages fixed-point theory and operator splitting methods to address inclusion problems of the form $0\in (A+B)(x)$, where A is a cocoercive operator and B is a maximally monotone operator defined on a real Hilbert space. The algorithm incorporates two inertial terms and a relaxation step via a contractive mapping, resulting in improved convergence properties and numerical stability. Under mild conditions of step sizes and inertial parameters, we establish strong convergence of the proposed algorithm to a point in the solution set that satisfies a variational inequality with respect to a contractive mapping. Beyond theoretical development, we demonstrate the practical effectiveness of the proposed algorithm by applying it to data classification tasks using Deep Extreme Learning Machines (DELMs). In particular, the training processes of Two-Hidden-Layer ELM (TELM) models is reformulated as convex regularized optimization problems, enabling robust learning without requiring direct matrix inversions. Experimental results on benchmark and real-world medical datasets, including breast cancer and hypertension prediction, confirm the superior performance of our approach in terms of evaluation metrics and convergence. This work unifies and extends existing inertial-type forward–backward schemes, offering a versatile and theoretically grounded optimization tool for both fundamental research and practical applications in machine learning and data science. Full article

The present work aims to study the effect of cyclic loading on the tensile behavior of a chemically stabilized sandy soil, whether or not reinforced with polypropylene or sisal fibers. To this end, a series of splitting tensile strength tests were carried out by varying the frequency of the cyclic loading. During cyclic loading a substantial decrease in accumulated plastic axial displacement was observed with rising frequency when fibers were incorporated. On average, the reduction was 28% for polypropylene fibers and 14% for sisal fibers. For the polypropylene fibers, this effect is more pronounced because of a greater number of randomly distributed fibers, creating a strong and dense interlocking network. Regarding the load-displacement characteristics, fiber inclusion leads to a more ductile tensile response, which is identified by a secondary peak strength and residual strength. The cyclic loading frequency does not show a distinct trend concerning the post-cyclic tensile strength behavior; this behavior is dependent on the mechanical properties of materials (cemented matrix and fibers). Nevertheless, the cyclic stage resulted in an increased post-cyclic tensile strength for sisal fibers (ranging from 23% to 51%), although no clear trend was observed with respect to frequency variation. In contrast, for polypropylene fibers, the cyclic stage resulted in a more ductile tensile mechanical response, with post-cyclic tensile strength increasing from 1% to 16% as the frequency decreased. Full article

Herein, we present two hybrid inertial self-adaptive iterative methods for determining the combined solution of the split variational inclusions and fixed-point problems. Our methods include viscosity approximation, fixed-point iteration, and inertial extrapolation in the initial step of each iteration. We employ two self-adaptive step sizes to compute the iterative sequence, which do not require the pre-calculated norm of a bounded linear operator. We prove strong convergence theorems to approximate the common solution of the split variational inclusions and fixed-point problems. Further, we implement our methods and results to examine split variational inequality and split common fixed-point problems. Finally, we illustrate our methods and compare them with some known methods existing in the literature. Full article

This paper introduces a new algorithm that combines the forward–backward splitting algorithms with a double inertial technique, utilizing the previous three iterations. The weak convergence theorem is established under certain mild conditions in a Hilbert space, including a relaxed inertial method in real numbers. An example of infinite dimension space is given with numerical results to support our proposed algorithm. The algorithm is applied to an asymmetrical educational dataset of students from 109 schools, utilizing asymmetric inputs as nine attributes to predict the output as students’ mathematical integrated skills. The algorithm’s performance is compared with other algorithms in the literature to demonstrate its effectiveness. The proposed algorithm demonstrates comparable precision, recall, accuracy, and F1 score but performs a relatively lower number of iterations. The contributions of each performance aspect to the mathematical integration skill of students are discussed to improve students’ mathematical learning. Full article

This study addresses the issue of construction stagnation affecting the adhesion and tensile properties of hydraulic asphalt concrete with acid aggregate. It investigates the impact of rest periods on the tensile characteristics of such materials under standard construction conditions. The influence of varying rest durations and asphalt temperatures on the tensile behavior of the concrete is assessed through indoor experiments. The bonding between asphalt and aggregate is examined, along with the tensile property variations of the concrete. The study found that the standstill time significantly affects the adhesion of asphalt, with the adhesion decreasing progressively with increased temperature and rest time, irrespective of the addition of anti-stripping agents. However, the inclusion of these agents can mitigate the reduction in adhesion. Furthermore, the study identified that rest duration has a more substantial impact on adhesion than temperature. The splitting tests demonstrate that the tensile properties of asphalt concrete are considerably affected by the resting time. Over a period of 0, 10, 20, and 30 days of rest, an increase in splitting strength and a decrease in splitting displacement were observed. The findings offer valuable insights for predicting the tensile performance of asphalt concrete in practical engineering applications after a period of rest. Full article

In addressing the dual challenges of sustainable waste management and environmental conservation in the construction industry, particularly the disposal of waste tire crumb rubber (CR) and the demand for eco-friendly building materials, this study explores a novel solution. It examines the sustainable incorporation of waste tire crumb rubber and mineral additions—namely silica fume (SF), marble slurry powder (MSP), and fly ash (FA)—as partial substitutes for natural fine aggregates and cement in concrete. Through comprehensive testing of seventeen concrete samples, the study reveals that the specific mix of R10S5M10F15 that contained 10% crumb rubber as replacement of fine aggregates, and 5% silica fume, 10% marble slurry powder and 15% fly ash as replacements of cement, not only achieves compressive and split tensile strength comparable to the control mix, while the 90 days flexural strength was improved by 4.48%; credited to SF’s pozzolanic action and the filler effects of MSP and FA, but also that the inclusion of CR, while reducing compressive strength due to material variations, enhances ductility and improves resistance to sulfate and acid attacks, despite increasing water absorption. The primary goal of this research is to investigate the feasibility and effectiveness of using waste materials in concrete to foster more sustainable construction practices. The objectives include a detailed assessment of the mechanical properties and durability of concrete incorporating these waste materials, aiming to determine the optimal mix proportions for their effective utilization. This study’s novelty lies in its detailed analysis of the synergistic effects of combining CR, SF, MSP, and FA in concrete, contributing to the field by offering a sustainable alternative approach to traditional concrete formulations and highlighting the delicate balance required for optimized concrete performance. Full article

The aim of this paper is to propose an inertial-type AA-viscosity algorithm for approximating the common solutions of the split variational inclusion problem, the generalized equilibrium problem and the common fixed-point problem of nonexpansive mappings. The strong convergence of an iterative sequence obtained through the proposed method is proved under some mild assumptions. Consequently, approximations of the solution of the split feasibility problem, the relaxed split feasibility problem, the split common null point problem and the split minimization problem are given. The applicability of our proposed algorithm has been illustrated with the help of a numerical example. Our iterative method was then compared graphically with different comparable methods in the existing literature. Full article

In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every iteration, and the stepsize is defined self-adaptively without a prior estimate of the Lipschitz constant. A convergence theorem is demonstrated to be strong even under lenient conditions and to showcase the suggested method’s efficiency and precision. Some numerical tests are given. Moreover, the significance of the proposed method is demonstrated through its application to an image reconstruction issue. Full article

In this article, the problem of solving a strongly monotone variational inequality problem over the solution set of a monotone inclusion problem in the setting of real Hilbert spaces is considered. To solve this problem, two methods, which are improvements and modifications of the Tseng splitting method, and projection and contraction methods, are presented. These methods are equipped with inertial terms to improve their speed of convergence. The strong convergence results of the suggested methods are proved under some standard assumptions on the control parameters. Also, strong convergence results are achieved without prior knowledge of the operator norm. Finally, the main results of this research are applied to solve bilevel variational inequality problems, convex minimization problems, and image recovery problems. Some numerical experiments to show the efficiency of our methods are conducted. Full article

We study three classes of variational inclusion problems in the framework of a real Hilbert space and propose a simple modification of Tseng’s forward-backward-forward splitting method for solving such problems. Our algorithm is obtained via a certain regularization procedure and uses self-adaptive step sizes. We show that the approximating sequences generated by our algorithm converge strongly to a solution of the problems under suitable assumptions on the regularization parameters. Furthermore, we apply our results to an elastic net penalty problem in statistical learning theory and to split feasibility problems. Moreover, we illustrate the usefulness and effectiveness of our algorithm by using numerical examples in comparison with some existing relevant algorithms that can be found in the literature. Full article

Recent advances in embedded antenna and sensor technologies for 5G communications have galvanized a response toward the investigation of their electromagnetic performance for urban contexts and civil engineering applications. This article quantitatively investigates the effects of material loading on an evolved antecedent hexagonal complementary split-ring resonator (CSRR)-loaded antenna design through simulation and experimentation. Optimization of the narrowband antenna system was first performed in a simulation environment to achieve resonance at 3.50 GHz, featuring an impedance bandwidth of 1.57% with maximum return loss and theoretical gain values of 20.0 dB and 1.80 dBi, respectively. As a proof-of-concept, a physical prototype is fabricated on a printed circuit board followed by a simulation-based parametric study involving antenna prototypes embedded into Ordinary Portland Cement pastes with varying weight percentages of iron(III) oxide inclusions. Simulation-derived and experimental results are mutually verified, achieving a systemic downward shift in resonant frequency and corresponding variations in impedance matching induced by changes in loading reactance. Finally, an inversion modeling procedure is employed using perturbation theory to extrapolate the relative permittivity of the dielectric loaded materials. Our proposed analysis contributes to optimizing concrete-embedded 5G antenna sensor designs and establishes a foundational framework for estimating unknown dielectric parameters of cementitious composites. Full article

This paper aims to present two inertial iterative algorithms for estimating the solution of split variational inclusion $\left({\mathrm{S}}_{\mathrm{p}}{\mathrm{VI}}_{\mathrm{s}}\mathrm{P}\right)$ and its extended version for estimating the common solution of $\left({\mathrm{S}}_{\mathrm{p}}{\mathrm{VI}}_{\mathrm{s}}\mathrm{P}\right)$ and fixed point problem $\left(\mathrm{FPP}\right)$ of a nonexpansive mapping in the setting of real Hilbert spaces. We establish the weak convergence of the proposed algorithms and strong convergence of the extended version without using the pre-estimated norm of a bounded linear operator. We also exhibit the reliability and behavior of the proposed algorithms using appropriate assumptions in a numerical example. Full article

Maxillofacial skeletal surgery often involves the use of patient-specific implants. However, errors in obtaining patient data and designing and manufacturing patient-specific plates and guides can occur even with accurate virtual surgery. To address these errors, bespoke Snowman plates were designed to allow movement of the mandible. This study aimed to compare the stability of bespoke four-hole miniplates with that of a bespoke Snowman plate for bilateral sagittal split ramus osteotomy (SSRO), and to present a method to investigate joint cavity changes, as well as superimpose virtual and actual surgical images of the mandible. This retrospective study included 22 patients who met the inclusion criteria and underwent orthognathic surgery at a university hospital between 2015 and 2018. Two groups were formed on the basis of the plates used: a control group with four-hole bespoke plates and a study group with bespoke Snowman plates. Stability was assessed by measuring the condyle–fossa space and superimposing three-dimensional virtual surgery images on postoperative cone-beam computed tomography (CBCT) scans. No significant differences were observed in the condyle–fossa space preoperatively and 1 year postoperatively between the control and study groups. Superimposing virtual surgery and CBCT scans revealed minimal differences in the landmark points, with no variation between groups or timepoints. The use of bespoke Snowman plates for stabilizing the mandible following SSRO exhibited clinical stability and reliability similar to those with bespoke four-hole plates. Additionally, a novel method was introduced to evaluate skeletal stability by separately analyzing the condyle–fossa gap changes and assessing the mandibular position. Full article

The purpose of this paper is to find a common element of the fixed point set of a nonexpansive mapping and the set of solutions of the general split variational inclusion problem in symmetric Hilbert spaces by using the inertial viscosity iterative method. Some strong convergence theorems of the proposed algorithm are demonstrated. As applications, we use our results to study the split feasibility problem and the split minimization problem. Finally, the numerical experiments are presented to illustrate the feasibility and effectiveness of our theoretical findings, and our results extend and improve many recent ones. Full article

First experimental modeling of decarbonation reactions resulting in the formation of CO₂-fluid and Mg, Fe, Ca, and Mn garnets, with composition corresponding to the garnets of carbonated eclogites of types I and II (ECI and ECII), was carried out at a wide range of lithospheric mantle pressures and temperatures. Experimental studies were performed on a multi-anvil high-pressure apparatus of a “split sphere” type (BARS), in (Mg, Fe, Ca, Mn)CO₃-Al₂O₃-SiO₂ systems (with compositional variations according to those in ECI and ECII), in the pressure interval of 3.0–7.5 GPa and temperatures of 1050–1450 °C (t = 10–60 h). A specially designed high-pressure cell with a hematite buffering container—preventing the diffusion of hydrogen into the platinum capsule—was used, in order to control the fluid composition. Using the mass spectrometry method, it was proven that in all experiments, the fluid composition was pure CO₂. The resulting ECI garnet compositions were Prp₄₈Alm₃₅Grs₁₅Sps₀₂–Prp₄₄Alm₄₀Grs₁₄Sps₀₂, and compositions of the ECII garnet were Prp₅₇Alm₃₄Grs₀₈Sps₀₁–Prp₆₈Alm₂₃Grs₀₈Sps₀₁. We established that the composition of the synthesized garnets corresponds strongly to natural garnets of carbonated eclogites of types I and II, as well as to garnets from xenoliths of diamondiferous eclogites from the Robert Victor kimberlite pipe; according to the Raman characteristics, the best match was found with garnets from inclusions in diamonds of eclogitic paragenesis. In this study, we demonstrated that the lower temperature boundary of the stability of natural garnets from carbonated eclogites in the presence of a CO₂ fluid is 1000 (±20) °C at depths of ~90 km, 1150–1250 (±20) °C at 190 km, and 1400 (±20) °C at depths of about 225 km. The results make a significant contribution to the reconstruction of the fluid regime and processes of CO₂/carbonate-related mantle metasomatism in the lithospheric mantle. Full article