Search Results (48)

This paper investigates the existence of square-mean S-asymptotically $(\omega ,c)$-periodic solutions for a class of neutral impulsive stochastic differential equations driven by fractional Brownian motion, addressing the challenge of modeling long-range dependencies, delayed feedback, and abrupt changes in systems like biological networks or mechanical oscillators. By employing semigroup theory to derive mild solution representations and the Banach contraction principle, we establish sufficient conditions–such as Lipschitz continuity of nonlinear terms and growth bounds on the resolvent operator—that guarantee the uniqueness and existence of such solutions in the space ${\mathcal{S}AP}_{\omega ,c}([0,\infty ),L^2(\Omega ,\mathbb{H}))$. The important results demonstrate that under these assumptions, the mild solution exhibits square-mean S-asymptotic $(\omega ,c)$-periodicity, enabling robust asymptotic analysis beyond classical periodicity. We illustrate these findings with examples, such as a neutral stochastic heat equation with impulses, revealing stability thresholds and decay rates and highlighting the framework’s utility in predicting long-term dynamics. These outcomes advance stochastic analysis by unifying neutral, impulsive, and fractional noise effects, with potential applications in control theory and engineering. Full article

This article introduces a new type of contractions via $\phi$-admissibility and ${\omega }_b$-distance called generalized ${\omega }_b^{\phi }$-contractions. We prove the existence of fixed points for this type of contractions under some conditions. Moreover, we give an example to demonstrate the applications of our results. Full article

Hemolysis, or the breakdown of red blood cells, observed in medical devices has been a significant concern for many years, particularly when mechanical stress on the cells is considered. This study focuses on evaluating extensional stresses in two configurations of the U.S. Food and Drug Administration (FDA) nozzle: the Gradual Cone (GC) and Sudden Contraction (SC) models. The nozzle geometries were created as 3D models using Ansys Fluent 18.2 and its pre-processing software ICEM CFD. The mesh was constructed with hexahedral elements with O-grid topologies. Effects of varying flow conditions were observed by modeling five experimental cases of the FDA nozzles, including throat Reynolds numbers of 500, 2000, 3500, 5000, and 6500. Hemolysis potentials of FDA nozzle configurations were examined by analyzing the whole domains. Turbulent modeling was used by applying the shear stress transport k-ω (SST k-ω) model. A threshold of 2.8 Pa for extensional stress was observed. Moreover, the most commonly used power law models were applied to the FDA nozzle to see the effect of extensional stress on power law models. Zhang’s power law models gave the lowest standard error, while Giersiepen’s model gave the highest error on hemolysis predictions. Full article

Accurate flow measurement is crucial for energy efficiency in industrial applications. This study investigates entropy generation in measuring orifice plates under high-pressure conditions (80 bar, 400 °C) using computational fluid dynamics (CFD) in OpenFOAM. Two turbulence models, k-ω SST and Spalart–Allmaras, are employed to analyze compressible steam flow and identify local entropy sources. Building on recent findings, this research explores the hypothesis that the discharge coefficient reflects entropy generation. The orifice plate’s abrupt flow contraction and expansion contribute to significant energy dissipation, affecting exergy efficiency. By quantifying entropy sources through numerical simulations, this study provides insights into optimizing flow metering techniques and reducing irreversibilities. The results show a strong correlation between entropy generation and the discharge coefficient, offering a new approach to improving measurement accuracy. This research supports the advancement of energy-efficient flow measurement methods, aligning with sustainable engineering practices. Full article

In this paper, we present the concept of $(\mathrm{{\rm Y}},\mathrm{\Omega })$-iterativemappings in the setting of fuzzy bipolar metric space. The symmetric property in fuzzy bipolar metric spaces guarantees that the distance between any two elements remains invariant under permutation, ensuring consistency and uniformity in measurement regardless of the order in which the elements are considered. Furthermore, we prove several best proximity point results by utilizing $(\mathrm{{\rm Y}},\mathrm{\Omega })$-fuzzy bipolar proximal contraction, $(\mathrm{{\rm Y}},\mathrm{\Omega })$-Reich–Rus–Ciric type proximal contraction, $(\mathrm{{\rm Y}},\mathrm{\Omega })$-Kannan type proximal contraction and $(\mathrm{{\rm Y}},\mathrm{\Omega })$-Hardy–Rogers type contraction. Furthermore, we provide some non-trivial examples to show the comparison with the existing results in the literature. At the end, we present an application to find the existence and uniqueness of a solution of an integral equation by applying the main result. Full article

In this paper, we present Proinov-type fixed point theorems in the setting of bi-polar metric spaces and fuzzy bi-polar metric spaces. Fuzzy bi-polar metric spaces with symmetric property extend classical metric spaces to address dual structures and uncertainty, ensuring consistency and balance. We provide different concrete conditions on the real-valued functions $\Omega ,\Pi :\left(0,\infty \right)\to \mathbb{R}$ for the existence of fixed points via the $(\Omega ,\Pi )$-contraction in bi-polar metric spaces. Further, we define real-valued functions $\Omega ,\Pi :(0,1]\to \mathbb{R}$ to obtain fixed point theorems in fuzzy bi-polar metric spaces. We apply $\left(\Omega ,\Pi \right)$ fuzzy bi-polar version of a Banach fixed point theorem to show the existence of solutions. Furthermore, we provide some non-trivial examples to show the validity of our results. In the end, we find the existence and uniqueness of a solution of integral equations and boundary value problem used in chemical sciences by applying main results. Full article

In this paper, we propose a new notion, which we name S-contractive mapping, in a framework of vector-valued white noise functionals ${\mathcal{W}}_{\omega }\otimes \mathcal{N}\subset \Gamma \left(H\right)\otimes K\subset {({\mathcal{W}}_{\omega }\otimes \mathcal{N})}^{*}$. And we give concrete definitions of S-contractive mappings for vector-valued white noise functionals. We establish the fixed-point theorems of S-contractive mappings. As applications, by applying the fixed-point theorems of generalized S-contractive mappings, we prove the existence and uniqueness of a generalized form of differential equations of vector-valued white noise functionals with weak conditions and investigate Wick-type differential equations of vector-valued white noise functionals with generalized conditions. Full article

Teaching evaluation performance is an important policy adopted by the governing body of education in Peru to promote the growth of educational quality, professional development, and continuous training of teachers, as well as to ensure educational quality standards, especially in Peruvian elementary education. Therefore, this research aims to develop and evaluate the psychometric properties of a scale that measures the coping strategies adopted by elementary education teachers when evaluating their performance. A study was conducted with 317 teachers between 20 and 70 years old (M = 43.6, SD = 11.8) in public education, from preschool (10.4%) to secondary (24.9%) educational levels, including special and alternative education, and with employment status of contracted (46.1%) and appointed (53.9%). An exploratory factor analysis was performed, from which four factors emerged. These factors were then corroborated by confirmatory factor analysis (χ² = 162, df = 13, CFI = 0.968, TLI = 0.961, RMSEA = 0.061, and SRMR = 0.056) and were named as follows: maladaptive coping, adaptive individual coping, religious coping, and instrumental support coping. Internal reliability was high for the full scale and dimensions (α and ω > 0.8), indicating that it was free of random error, yielding the same results across multiple applications for the same sample. It is concluded that the scale of teachers’ coping strategies towards the evaluation of performance (STCEP) is a valid and reliable instrument to measure coping strategies adopted by elementary education teachers in response to performance evaluation. Full article

In this paper, we delve into the ideas of Geraghty-type proximal contractions and their relation to multivalued, single-valued, and self mappings. We begin by introducing the notions of ${\left(\psi \omega \right)}_{MCP}$-proximal Geraghty contraction and rational ${\left(\psi \omega \right)}_{RMCP}$-proximal Geraghty contraction for multivalued mappings, aimed at establishing coincidence point results. To enhance our understanding and illustrate the concepts, practical examples are provided with each definition. This study extends these contractions to single-valued mappings with the introduction of ${\left(\psi \omega \right)}_{SCP}$-proximal Geraghty contraction and rational ${\left(\psi \omega \right)}_{RSCP}$-proximal Geraghty contraction, supported by relevant examples to reinforce the main results. Then, we explore ${\left(\psi \omega \right)}_{SFP}$ Geraghty contraction and rational ${\left(\psi \omega \right)}_{RSFP}$ contraction for self-mappings, obtaining fixed point theorems and clearly illustrating them through examples. Finally, we apply the theoretical framework developed to investigate the existence and uniqueness of solutions to certain two-dimensional Volterra integral equations. Specifically, we consider the transformation of first-kind Volterra integral equations, which play crucial roles in modeling memory in diverse scientific fields like biology, physics, and engineering. This approach provides a powerful tool for solving difficult integral equations and furthering applied mathematics research. Full article

In the realm of marine science and engineering, hydrofoils play a pivotal role in the efficiency and performance of marine turbines and water-jet pumps. In this investigation, the boundary layer characteristics of an NACA0009 hydrofoil with a blunt trailing edge are focused on. The effectiveness of both the two-equation gamma theta (γ-Re_θt) transition model and the one-equation intermittency (γ) transition model in forecasting boundary layer behavior is evaluated. When considering natural transition, these two models outperform the shear stress transport two-equation (SST k-ω) turbulence model, notably enhancing the accuracy of predicting boundary layer flow distribution for chord-length Reynolds numbers (Re_L) below 1.6 × 10⁶. However, as Re_L increases, both transition models deviate from experimental values, particularly when Re_L is greater than 2 × 10⁶. The results indicate that the laminar separation bubble (LSB) is sensitive to changes in angles of attack (AOA) and Re_L, with its formation observed at AOA greater than 2°. The dimensions of the LSB, including the initiation and reattachment points, are found to contract as Re_L increases while maintaining a constant AOA. Conversely, an increase in AOA at similar Re_L values leads to a reduced size of the LSB. The findings are essential for the design and performance optimization of water-jet pumps, particularly in predicting and flow separation and transition phenomena. Full article

This paper investigates the large time behavior for the reaction–diffusion equation with memory and the forcing term $g\in H^{-1}\left(\Omega \right).$ We prove the existence of a global attractor in $L^2\left(\Omega \right)\times L_{\mu }^2(\mathbb{R};H_0^1\left(\Omega \right))$. Due to the lower regularity of g, one can hardly use the traditional energy estimates to derive the existence of a bounded absorbing set in the higher regularity space and then the compactness of the semigroup. Here, we utilize the contractive function method to establish the asymptotic smoothness of the semigroup. Full article

The nozzle, as a critical jet component in dry powder fire extinguishing systems, significantly affects jet characteristics through its geometric configuration. To explore the influence of structural parameters on ultrafine dry powder gas-solid two-phase jet characteristics, a bidirectional coupled numerical model based on the SST k-ω turbulence model and the Discrete Phase Model is employed. This study examines how variations in the semi-expansion angle (α) and semi-contraction angle (β) of the nozzle affect compressible gas flow behavior and particle distribution trajectories through a combination of simulations and experiments. The results indicate that when α = 2°, the gas jet is in an under-expanded state, leading to increased particle dispersion due to the stripping effect of the surrounding high-speed airflow. Within the range of x = 0–180 mm, the dry powder exhibits a diffusion trend. When α = 4.5°, the gas jet core region is the longest, providing optimal particle acceleration. Under constant inlet pressure, reducing α enhances particle collimation. The reduction of α alters the gas jet state, with α = 2° showing better powder diffusion compared to α = 6°. However, an excessively small α is detrimental to increasing the range of dry powder. With consistent structural parameters, the diffusion and range of dry powder remain the same across different β values, and variations in β have a relatively minor impact on supersonic jet characteristics. These findings offer theoretical guidance for optimizing and improving nozzles in ultrafine dry powder fire extinguishing systems. Full article

In this article, we construct sufficient conditions that secure the non-emptiness and compactness of the set of antiperiodic solutions of an impulsive fractional differential inclusion involving an ω-weighted ϱ–Hilfer fractional derivative, $D_{0,t}^{\sigma ,v,\varrho ,\omega }$, of order $\sigma \in (1,2),$ in infinite-dimensional Banach spaces. First, we deduce the formula of antiperiodic solutions for the observed problem. Then, we give two theorems regarding the existence of these solutions. In the first, by using a fixed-point theorem for condensing multivalued functions, we show the non-emptiness and compactness of the set of antiperiodic solutions; and in the second, by applying a fixed-point theorem for contraction multivalued functions, we prove the non-emptiness of this set. Because many types of famous fractional differential operators are particular cases from the operator $D_{0,t}^{\sigma ,v,\varrho ,\omega }$, our results generalize several recent results. Moreover, there are no previous studies on antiperiodic solutions for this type of fractional differential inclusion, so this work is novel and interesting. We provide two examples to illustrate and support our conclusions. Full article

This study aimed to evaluate the spasmolytic activity of an underground parts extract of Gentiana asclepiadea L. (Gentianaceae), assess its antioxidant and antimicrobial activities, and explore the impact of extract encapsulation on the aforementioned bioactivities. An extract encapsulated by spray drying with whey protein, pure extract, and pure whey protein were comparatively tested. The main compounds identified via HPLC-DAD analysis underwent in silico ADME assessment. The spasmolytic effect was tested on a model of spontaneous rat ileum contractions, and the mechanism of action was further evaluated on acetylcholine-, KCl-, CaCl₂-, BaCl₂-, histamine-, N(ω)-nitro-L-arginine methyl ester-, and glibenclamide-modified contractions. The most abundant compounds were secoiridoids (dominantly gentiopicroside), followed by C-glycosylated flavonoids and xanthones. Both pure and encapsulated extracts achieved significant spasmolytic effects, despite the spasmogenic activity of pure whey protein. The extract may exert its spasmolytic effect through multiple pathways, predominantly by antagonizing the Ca²⁺ channel and opening the K⁺ channel, while the nitric oxide pathway appears not to be involved. The antimicrobial and antioxidant activities of the pure extract were moderate. The extract stabilized by encapsulation retained all of the tested bioactivities of the unencapsulated extract. The obtained results suggest that G. asclepiadea has potential for use in the treatment of some gastrointestinal complaints and that the encapsulated extract could be a valuable functional ingredient in pharmaceutical and food products. Full article

This study aims to prove the existence and uniqueness of the $(\omega ,c)$-periodic solution as a specific solution to Hadamard impulsive boundary value integro-differential equations with fixed lower limits. The results are proven using the Banach contraction, Schaefer’s fixed point theorem, and the Arzelà–Ascoli theorem. Furthermore, we establish the necessary conditions for a set of solutions to the explored boundary values with impulsive fractional differentials. Finally, we present two examples as applications for our results. Full article