Search Results (264)

This paper explores fixed points for both contractive and non-contractive mappings in traditional b-metric spaces, preordered b-metric spaces, and random b-metric spaces. Our findings provide insights into the behavior of mappings under various constraints and extend our approach to include coincidence and common fixed-point theorems in these spaces. We present new examples and graphical representations for the first time, offering novel results and enhancing several related findings in the literature, while broadening the scope of earlier works of Ran and Reurings, Nieto and Rodríguez-López, Górnicki, and others. Full article

Natural Ventilation Effectiveness (NVE) is a performance metric that quantifies when outdoor airflows can be used as a cooling strategy to achieve indoor thermal comfort. Based on standard ventilation threshold and building energy simulation (BES) models, the NVE relates available and required airflows to quantify the usefulness of natural ventilation (NV) through design and building evaluation. Since wind is a significant driving force for ventilation, wind pressure coefficients ($C_p$) represent a critical boundary condition when assessing building airflows. Therefore, this paper investigates the impact of different $C_p$ sources on wind-driven NVE results to see how sensitive the metric is to this variable. For that, an experimental house and a measurement period were used to develop and calibrate the initial BES model. Four $C_p$ sources are considered: an analytical model from the BES software (i), surface-averaged $C_p$ values for building windows that were calculated with Computational Fluid Dynamics (CFD) simulations using OpenFOAM through a cloud-based platform (ii_a,b,c), and two databases—AIVC (iii) and Tokyo Polytechnic University (TPU) (iv). The results show a variance among the $C_p$ sources, which directly impacts airflow predictions; however, its effect on the performance metric was relatively small. The variation in the NVE outcomes with different $C_p$’s was 3% at most, and the assessed building could be naturally ventilated around 75% of the investigated time on the first floor and 60% in the ground floor spaces. Full article

This article presents a spatiotemporal super-resolution (SR) reconstruction model for two common flame types, a swirling and then a jet flame, using double generative adversarial network (GAN) architectures. The approach develops two sets of generator and discriminator networks to learn topographic and temporal features and infer high spatiotemporal resolution turbulent flame structure from supplied low-resolution counterparts at two time points. In this work, numerically simulated 3D turbulent swirling and jet flame structures were used as training data to update the model parameters of the GAN networks. The effectiveness of our model was then thoroughly evaluated in comparison to other traditional interpolation methods. An upscaling factor of 2 in space, which corresponded to an 8-fold increase in the total voxel number and a double time frame acceleration, was used to verify the model’s ability on a swirling flame. The results demonstrate that the assessment metrics, peak signal-to-noise ratio (PSNR), overall error (E_R), and structural similarity index (SSIM), with average values of 35.27 dB, 1.7%, and 0.985, respectively, in the spatiotemporal SR results, can reach acceptable accuracy. As a second verification to highlight the present model’s potential universal applicability to flame data of diverse types and shapes, we applied the model to a turbulent jet flame and had equal success. This work provides a different method for acquiring high-resolution 3D structure and further boosting repeat rate, demonstrating the potential of deep learning technology for combustion diagnosis. Full article

Background: Diffusion-weighted imaging (DWI), a pivotal component of multiparametric magnetic resonance imaging (mpMRI), plays a pivotal role in the detection, diagnosis, and evaluation of gastric cancer. Despite its potential, DWI is often marred by substantial anatomical distortions and sensitivity artifacts, which can hinder its practical utility. Presently, enhancing DWI’s image quality necessitates reliance on cutting-edge hardware and extended scanning durations. The development of a rapid technique that optimally balances shortened acquisition time with improved image quality would have substantial clinical relevance. Objectives: This study aims to construct and evaluate the unsupervised learning framework called attention dual contrast vision transformer cyclegan (ADCVCGAN) for enhancing image quality and reducing scanning time in gastric DWI. Methods: The ADCVCGAN framework, proposed in this study, employs high b-value DWI (b = 1200 ${\mathrm{s}/\mathrm{mm}}^2$) as a reference for generating synthetic b-value DWI (s-DWI) from acquired lower b-value DWI (a-DWI, b = 800 ${\mathrm{s}/\mathrm{mm}}^2$). Specifically, ADCVCGAN incorporates an attention mechanism CBAM module into the CycleGAN generator to enhance feature extraction from the input a-DWI in both the channel and spatial dimensions. Subsequently, a vision transformer module, based on the U-net framework, is introduced to refine detailed features, aiming to produce s-DWI with image quality comparable to that of b-DWI. Finally, images from the source domain are added as negative samples to the discriminator, encouraging the discriminator to steer the generator towards synthesizing images distant from the source domain in the latent space, with the goal of generating more realistic s-DWI. The image quality of the s-DWI is quantitatively assessed using metrics such as the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), feature similarity index (FSIM), mean squared error (MSE), weighted peak signal-to-noise ratio (WPSNR), and weighted mean squared error (WMSE). Subjective evaluations of different DWI images were conducted using the Wilcoxon signed-rank test. The reproducibility and consistency of b-ADC and s-ADC, calculated from b-DWI and s-DWI, respectively, were assessed using the intraclass correlation coefficient (ICC). A statistical significance level of p < 0.05 was considered. Results: The s-DWI generated by the unsupervised learning framework ADCVCGAN scored significantly higher than a-DWI in quantitative metrics such as PSNR, SSIM, FSIM, MSE, WPSNR, and WMSE, with statistical significance (p < 0.001). This performance is comparable to the optimal level achieved by the latest synthetic algorithms. Subjective scores for lesion visibility, image anatomical details, image distortion, and overall image quality were significantly higher for s-DWI and b-DWI compared to a-DWI (p < 0.001). At the same time, there was no significant difference between the scores of s-DWI and b-DWI (p > 0.05). The consistency of b-ADC and s-ADC readings was comparable among different readers (ICC: b-ADC 0.87–0.90; s-ADC 0.88–0.89, respectively). The repeatability of b-ADC and s-ADC readings by the same reader was also comparable (Reader1 ICC: b-ADC 0.85–0.86, s-ADC 0.85–0.93; Reader2 ICC: b-ADC 0.86–0.87, s-ADC 0.89–0.92, respectively). Conclusions: ADCVCGAN shows excellent promise in generating gastric cancer DWI images. It effectively reduces scanning time, improves image quality, and ensures the authenticity of s-DWI images and their s-ADC values, thus providing a basis for assisting clinical decision making. Full article

This study explores the potential of using a Siamese Network as a biomarker for assessing the effectiveness of Dolphin-Assisted Therapy (DAT) in children with Spastic Cerebral Palsy (SCP). The problem statement revolves around the need for objective measures to evaluate the impact of DAT on patients with SCP, considering the subjective nature of traditional assessment methods. The methodology involves training a Siamese network, a type of neural network designed to compare similarities between inputs, using data collected from SCP patients undergoing DAT sessions. The study employed Event-Related Potential (ERP) and Fast Fourier Transform (FFT) analyses to examine cerebral activity and brain rhythms, proposing the use of SNN to compare electroencephalographic (EEG) signals of children with cerebral palsy before and after Dolphin-Assisted Therapy. Testing on samples from four children yielded a high average similarity index of 0.9150, indicating consistent similarity metrics before and after therapy. The network is trained to learn patterns and similarities between pre- and post-therapy evaluations, in order to identify biomarkers indicative of therapy effectiveness. Notably, the Siamese Network’s architecture ensures that comparisons are made within the same feature space, allowing for more accurate assessments. The results of the study demonstrate promising findings, indicating different patterns in the output of the Siamese Network that correlate with improvements in symptoms of SCP post-DAT. Confirming these observations will require large, longitudinal studies but such findings would suggest that the Siamese Network could have utility as a biomarker in monitoring treatment responses for children with SCP who undergo DAT and offer them more objective as well as quantifiable manners of assessing therapeutic interventions. Great discrepancies in neuronal voltage perturbations, 7.9825 dB on average at the specific samples compared to the whole dataset (6.2838 dB), imply a noted deviation from resting activity. These findings indicate that Dolphin-Assisted Therapy activates particular brain regions specifically during the intervention. Full article

In this work, we introduce a new type of multivalued fuzzy proximal quasi-contraction. These are generalized contractions which are a hybrid of $\mathcal{H}$-contractive mappings and quasi-contractions. Furthermore, we establish the best proximity point results for newly introduced fuzzy contractions in the context of fuzzy b-metric spaces. Fuzzy b-metric spaces are more general than fuzzy metric spaces and are linked with the cosine distance, which is used in various contexts of artificial intelligence to measure the similarity between elements of a vector space. Full article

Microgravity has been shown to be an excellent tool for protein crystal formation. A retrospective analysis of all publicly available crystallization data, including many that have not yet been published, clearly demonstrates the value of the microgravity environment for producing superior protein crystals. The parameters in the database (the Butler Microgravity Protein Crystal Database, BμCDB) that were evaluated pertain to both crystal morphology and diffraction quality. Success metrics were determined as improvements in size, definition, uniformity, mosaicity, diffraction quality, resolution limits, and B factor. The proteins in the databases were evaluated by molecular weight, protein type, the number of subunits, space group, and Mattew’s Coefficient. Compared to ground experiments, crystals grown in a microgravity environment continue to show improvement across all metrics evaluated. General trends as well as numerical differences are included in the assessment of the BμCDB. The microgravity environment improves crystal formation across a spectrum of metrics and the datasets utilized for this investigation are excellent tools for this evaluation. Full article

In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations are analyzed, giving error estimates for the fixed-point approximation. Afterwards, the iteration proposed by Kirk in 1971 is considered, studying its convergence, stability, and error estimates in the context of a quasi-normed space. The properties proved can be applied to other types of contractions, since the self-maps defined contain many others as particular cases. For instance, if the underlying set is a metric space, the contractions of type Kannan, Chatterjea, Zamfirescu, Ćirić, and Reich are included in the class of contractivities studied in this paper. These findings are applied to the construction of fractal surfaces on Banach algebras, and the definition of two-variable frames composed of fractal mappings with values in abstract Hilbert spaces. Full article

By revisiting an open question raised by Kirk and Shahzad, we are able to prove a generalized version of Nadler’s fixed-point theorem in the context of strong b-metric space. Such a result leads us to prove a new version of Dontchev and Hager’s inverse mapping theorem. Some examples are provided to illustrate the results. Full article

In this study, we significantly extend the concept of modular metric-like spaces to introduce the notion of b-metric-like spaces. Furthermore, by incorporating a binary relation $\mathfrak{R}$, we develop the framework of $\mathfrak{R}$-modular b-metric-like spaces. We establish a groundbreaking fixed point theorem for certain extensions of Geraghty-type contraction mappings, incorporating both $𝒵$ simulation function and $E$-type contraction within this innovative structure. Moreover, we present several novel outcomes that stem from our newly defined notations. Afterwards, we introduce an unprecedented concept, the graphical modular b-metric-like space, which is derived from the binary relation $\mathfrak{R}$. Finally, we examine the existence of solutions for a class of functional equations that are pivotal in dynamic programming and in solving initial value problems related to the electric current in an RLC parallel circuit. Full article

This paper introduces a broadband triple-pole triple-throw (3P3T) RF MEMS switch with a frequency range from DC to 380 GHz. The switch achieves precise signal control and efficient modulation through its six-port design. It achieves an insertion loss of −0.66 dB across its frequency range, with isolation and return loss metrics of −32 dB and −15 dB, respectively. With its low actuation voltage of 6.8 V and rapid response time of 2.28 μs, the switch exemplifies power-efficient and prompt switching performance. The compact design is ideal for integration into space-conscious systems. This switch is pivotal for 6G research and has potential applications in satellite communications, military radar systems, and next-generation radio applications that require multi-antenna access. Full article

In this study, we introduce novel concepts within the framework of fuzzy bipolar b-metric spaces, focusing on various mappings such as ${\psi }_{\alpha }$-contractive and ${\mathcal{ϝ}}_{\eta }$-contractive mappings, which are essential for quantifying distances between dissimilar elements. We establish fixed-point theorems for these mappings, demonstrating the existence of invariant points under certain conditions. To enhance the credibility and applicability of our findings, we provide illustrative examples that support these theorems and expand the existing knowledge in this field. Furthermore, we explore practical applications of our research, particularly in solving integral equations and fractional differential equations, showcasing the robustness and utility of our theoretical advancements. Symmetry, both in its traditional sense and within the fuzzy context, is fundamental to our study of fuzzy bipolar b-metric spaces. The introduced contractive mappings and fixed-point theorems expand the theoretical framework and offer robust tools for addressing practical problems where symmetry is significant. Full article

This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness of fixed points and fulfill the Suzuki-type nonlinear hybrid contractions on various generalized metrics. Full article

This article introduces the concept of generalized $(ff\mathcal{F},\mathtt{b},\breve{\varphi })$ contraction in the context of $\mathtt{b}$-metric spaces by utilizing the idea of $\mathcal{F}$ contraction introduced by Dariusz Wardowski. The main findings of the research focus on the existence of best proximity points for multi-valued $(ff\mathcal{F},\mathtt{b},\breve{\varphi })$ contractions in partially ordered $\mathtt{b}$-metric spaces. The article provides examples to illustrate the main results and demonstrates the existence of solutions to a second-order differential equation and a fractional differential equation using the established theorems. Additionally, several corollaries are presented to show that the results generalize many existing fixed-point and best proximity point theorems. Full article

Picard iteration is on the basis of a great number of numerical methods and applications of mathematics. However, it has been known since the 1950s that this method of fixed-point approximation may not converge in the case of nonexpansive mappings. In this paper, an extension of the concept of nonexpansiveness is presented in the first place. Unlike the classical case, the new maps may be discontinuous, adding an element of generality to the model. Some properties of the set of fixed points of the new maps are studied. Afterwards, two iterative methods of fixed-point approximation are analyzed, in the frameworks of b-metric and Hilbert spaces. In the latter case, it is proved that the symmetrically averaged iterative procedures perform well in the sense of convergence with the least number of operations at each step. As an application, the second part of the article is devoted to the study of fractal mappings on Hilbert spaces defined by means of nonexpansive operators. The paper considers fractal mappings coming from $\phi$-contractions as well. In particular, the new operators are useful for the definition of an extension of the concept of $\alpha$-fractal function, enlarging its scope to more abstract spaces and procedures. The fractal maps studied here have quasi-symmetry, in the sense that their graphs are composed of transformed copies of itself. Full article