In this paper, we analyze the generalized Ulam-Hyers stability of affine type AQ Functional Equation in various Banach Spaces using Direct and Fixed Methods

In an outstanding article published in 2008, Suzuki obtained a nice generalization of the Banach contraction principle from which derived a characterization of metric completeness. Although Suzuki’s theorem has been successfully generalized and extended in several directions and contexts, we here show by means of a simple example that the problem of achieving, in an obvious way, its full extension to the framework of w-distances does not have an emphatic response. Motivated by this fact we introduce the concept of presymmetric w-distance on metric spaces, we give some properties and examples of this new structure and show that it provides a reasonable setting to obtain a real and hardly forced w-distance generalization of Suzuki’s theorem. This is realized in our main result, which is a fixed point theorem that involves presymmetric w-distances and certain contractions of Suzuki-type. We also discuss the relationship between our main result and the well-known w-distance full generalization of the Banach contraction principle, due to Suzuki and Takahashi. Connected to this approach we prove another fixed point result that compare with our main result through some examples. Finally, we state a characterization of metric completeness by using our fixed point results.

Pathological aseptic calcification is the most common form of structural valvular degeneration (SVD), leading to premature failure of heart valve bioprostheses (BHVs). The processing methods used to obtain GA-fixed pericardium-based biomaterials determine the hemodynamic characteristics and durability of BHVs. This article presents a comparative study of the effects of several processing methods on the degree of damage to the ECM of GA-fixed pericardium-based biomaterials as well as on their biostability, biocompatibility, and resistance to calcification. Based on the assumption that preservation of the native ECM structure will enable the creation of calcinosis-resistant materials, this study provides a soft biomimetic approach for the manufacture of GA-fixed biomaterials using gentle decellularization and washing methods. It has been shown that the use of soft methods for preimplantation processing of materials, ensuring maximum preservation of the intactness of the pericardial ECM, radically increases the resistance of biomaterials to calcification. The data obtained are of interest for the development of new calcinosis-resistant biomaterials for the manufacture of BHVs.

About 50% of colorectal cancer patients develop liver metastases. Patients with metastatic colorectal cancer have 5-year survival rates below 20% despite new therapeutic regimens. Tumor heterogeneity has been linked with poor treatment response and clinical outcome, but was so far mainly studied via bulk genomic analyses. In this study we performed spatial proteomics via MALDI mass spectrometry imaging on six patient-matched CRC primary tumor and liver metastases to characterize interpatient, intertumor and intratumor hetereogeneity. We found several peptide features that were enriched in vital tumor areas of primary tumors and liver metastasis and tentatively derived from tumor cell specific proteins such as annexin A4 and prelamin A/C. Liver metastases of colorectal cancer showed higher heterogeneity between patients than primary tumors while within patients both entities show similar intratumor heterogeneity sometimes organized in zonal pattern. Together our findings give new insights into the spatial proteomic heterogeneity of primary CRC and patient-matched liver metastases.

Acute low back pain (LBP) stands as a leading cause of activity limitation and work absenteeism, and its associated healthcare expenditures are expected to become substantial when acute LBP develops into a chronic and even refractory condition. Therefore, early intervention is crucial to prevent progression to chronic pain whose management is particularly challenging and for which the most effective pharmacological therapy is still controversial. Current guideline treatment recommendations vary and are mostly driven by expertise with opinion differing across different interventions. Thus, it is difficult to formulate evidence-based guidance when relatively few randomized clinical trials did explore the diagnosis and management of LBP while employing different selection criteria, statistical analyses, and outcome measurements. This narrative review aims to provide a critical appraisal of current acute LBP management by discussing the unmet needs and areas of improvement from bench-to-bedside and proposes multimodal analgesia as the way forward to attain an effective and prolonged pain relief and functional recovery in patients with acute LBP.

This study examines the spatial impact of FDI on the poverty of 44 African countries. In achieving this, the study uses the Driscoll-Kraay fixed effect instrumental variable regression, instrumental variable generalised method of moments estimator (IV-GMM), and the spatial durbin model. The empirical investigation of this study yielded four significant findings: (1) neighbouring countries’ FDI has a positive and significant impact on the incidence and intensity of host country’s poverty. (2) Improved institutional quality in neighbouring countries has a significant impact on FDI-poverty reduction nexus of the host country. (3) the empirical results lend support for a significant spatial spillover of poverty in the region. (4) the marginal effect results indicate that countries within the region are no longer in isolation or independent, i.e., the level of poverty in a particular country is influenced by its determinants in the neighbouring country. This result is robust to the alternative proximity matrix, which is the inverse distance. Since there is spatial interdependence among African countries, we recommend that African governments through the African Union (AU) should not only champion the institutional reform in the region, but also establish a binding mechanism to ensure reform implementation.

The purpose of this paper is to prove strong convergent theorems for Browder's type iterations and Halpern's type iterations of a family of nonexpansive mappings in a complete geodesic space with curvature bounded above by a positive number. Moudafi's viscosity type methods are also discussed without the nice projection property.

Causal relationships lie at the very core of our scientific description of biophysical phenomena. Nevertheless, observable facts such as chaotic dynamics, symmetry breaks, long-range collisionless neural interactions, zero-value energy singularities, particle/wave duality, ecological approaches to visual perception elude cause effect inductive explanations. We illustrate how simple topological claims, seemingly useless and far away from scientific inquiry (e.g., “given at least some wind on Earth, there must at all times be a cyclone or anticyclone somewhere”; “if one stirs to dissolve a lump of sugar in a cup of coffee, it appears there is always a point without motion”; “at any moment, there is always a pair of antipodal points on the Earth’s surface with equal temperatures and barometric pressures”) describe a real world, made of projections and mappings unsupplied with causality. Unavoidable, necessary, passive, spontaneous changes in systems’ shapes, dimensions and symmetries incarnate biophysical quantifiable counterparts of abstract mathematical concepts. Real features arising from topological mechanisms do not require causal powers to be produced, because are independent of exerted physical forces, energetic fields’ actions and thermodynamic constraints. Providing examples that shed novel interpretative light on phenomena such as double slit experiments, cellular mechanisms and brain function, we conclude as follows: countless scientific matters can be accessed through methodological weapons which not just break causality, replace temporal correlations and probabilistic a priori knowledge of previous cases, but also permit augments in available information devoid of entropy increases and energy losses.

The Doubly-Fed Induction Generator (DFIG) has significant features in comparison with Fixed Speed Wind Turbine (FSWT), which has popularized its application in power system. Due to partial rated back-to-back converters in the DFIG, Fault Ride-Through (FRT) capability improvement is one of the great subjects regarding new grid code requirements. To enhance the FRT capability of the DFIG, many studies have been carried out. Fault current limiting devices as one of the techniques are utilized to limit the current level and protect switches of the back-to-back converter from over-current damage. In this paper, a review is done based on fault current limiting characteristic of the proposed fault current limiting devices Therefore, Fault Current Limiters (FCLs) and Series Dynamic Braking Resistors (SDBRs) are mainly taken into account. Operation of all configurations including their advantages and disadvantages is explained. Impedance type and the fault current limiting devices’ location are two important factors, which significantly affect the DFIG behaviour in the fault condition. These two factors are basically studied by the simulation and their effects on the key parameters of the DFIG are investigated. Finally, future works in respect to the FCL application in the FRT improvement of the DFIG have also been discussed.

To determine the fracture rate of ceramic crowns and causes of ceramic crown failure, this study used keywords—namely “endocrown,” “veneered fixed dental prosthesis,” “monolithic lithium disilicate (LS2),” and “all-ceramic single crown”—to search for articles published in English from 2005 to 2023 in the PubMed electronic database. Rather than using the Boolean logic algorithm between MESH terms and keywords, we accurately calculated the numbers of final clinically tracked cases with crown fractures from the contents of articles. The titles and abstracts of many related articles focused on implant or abutment fracture, while crown fracture was investigated and mentioned only in the main texts of the articles. Our studies included those crowns as well as having more complete data collection. Our search yielded 228, 93, 404, and 358 articles for the keywords “endocrown,” “veneered fixed dental prosthesis,” “monolithic lithium disilicate (LS2),” and “all-ceramic single crown,” respectively. We used the Newcastle–Ottawa Scale (NOS) to assess article quality, and our inclusion criteria were randomized controlled trials (RCT) and cohort study articles involving more than 3 years of follow-up and more than 20 cases. After reviewing, 16 high-quality articles were selected for analysis. The 4.4% crown fracture rate recommended on the basis of most clinical results was achieved in only 6 of the 16 articles. In these 6 articles, the researchers concluded the following reasons that may cause the crown fractures: the thickness of the veneer ceramic material; the connector dimensions; pontic span of the fixed prosthesis; the type of cement; the treatment of the ceramic surface before luting. Other articles inferred that the computer-aided design libraries that were insufficient for the creation of appropriate anatomically supported frameworks for prostheses with ceramic veneers; the thermal expansion coefficient and fracture toughness of the framework material did not match those of the veneer ceramic, resulting in an insufficient area supporting the ceramic veneer then leads to premature crown failure after a long period chewing. The future prospective for material developing could focus on solving those problems and have better clinical results.

In view of the problem of charging and hydrogen filling facilities construction in the transition from fuel vehicles to electric vehicles and hydrogen fuel cell vehicles, in order to meet the electric energy demand of electric vehicles and hydrogen energy demand of hydrogen fuel cell vehicles at the same time, this paper puts forward a method of siting and capacity determination of electric-hydrogen refueling integrated station (EHRIS) based on Voronoi diagram and particle swarm algorithm based on calculating the demand of charging and filling of hydrogen in vehicles. Firstly, OD pair(Origin-Destination) is used to represent the starting point and end point of the car to portray the travel demand of the car, and on the basis of the traffic network model, the shortest driving path of the new energy car is determined by Dijkstra algorithm, and Monte Carlo simulation is used to get the electric-hydrogen energy demand of the car; secondly, the Voronoi diagram is introduced to classify the service scope of the electric-hydrogen charging station to determine the equipment capacity of the electric-hydrogen charging station, while taking into account the electric-hydrogen charging and refueling capacity. Secondly, a Voronoi diagram is introduced to divide the service scope of the EHRIS, determine the capacity of the equipment in the EHRIS, and consider the distance constraints between the sites of EHRIS, so as to make the division of the site and service scope more reasonable. Finally, a dynamic optimal current model framework for distribution networks based on second-order cone relaxation is established, and each element of the active distribution network is planned, so that the distribution network can operate safely and stably after being connected to the EHRIS. With the objective of minimizing the total social cost of EHRIS and considering the constraints of the charging equipment and hydrogen production and injection equipment of the EHRIS, a siting and capacity model to meet the electric-hydrogen energy demand of electric and hydrogen fuel cell vehicles is developed, and solved by a particle swarm algorithm. Finally, the simulation planning is carried out with Sioux Falls city and IEEE33 network, which ensures the stable operation of the power grid while meeting the energy demand of automobiles, and the results verify the effectiveness and feasibility of the proposed method.

Considering rotation-induced centrifugal stiffening, spin softening, and Coriolis effects, the three-dimensional finite element model of a rotating blade with a dovetail structure is built through the contact dynamics theory. The fixed-interface component mode synthesis method is then adopted to reduce the model for high computational efficiency and adequate model accuracy. The effects of the number of normal modes on the first-six-order modal characteristics of the model varying with the rotating speed are studied between the reduced and full models. Next, the influence of rotating speed and friction factor on the nonlinear dynamic characteristics of the model under the action of aerodynamic force are elaborately discussed. The results show that: (1) tenon-mortise joint contact-induced nonlinearity under low rotating speeds results in the intermittent interference of contact surfaces and frequency multiplications of aerodynamic excitation frequency in the spectrum cascades, while that under high rotating speeds causes the continuous interface contact and asynchronous excitation at the tenon-mortise joint; (2) the increase of friction factor results in a lower contact pressure distribution and the right shift of the resonance peak (i.e., hard nonlinearity).

In the present work we study the existence of solutions for hybrid nonlinear fractional integrodifferential equations. We developed an algorithm by using the operator theoretical techniques in order to obtain the approximate solutions. The main results depend on the Dhage iteration method that were incorporated with the modern hybrid fixed point theorems. The approximate solutions were obtained by using Lipschitz conditions and weaker form of mixed partial continuity. Further, we provide some examples to explain the hypotheses and the related results.

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki's generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that iterative scheme (1.8) converges faster than some other known iterations for Suzuki's generalized non-expansive mappings. To support our claim, we give an illustrative example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

Transition zones are in the places on the track, with a change in the basic composition of the railway body. There are many sections with a sudden change in the stiffness of the structures built. When the trains are running, a longitudinal shock wave is created from the wheels, which hits these building objects with a higher stiffness and deforms the surroundings of these zones. The greatest attention should be paid mainly to the transition points from the fixed track to the classic track with a track bed, including objects of the railway substructure such as bridges, portals of tunnels, etc. As part of the research sections on the main corridor lines, a long-term inspection and monitoring was carried out with a continuous measurement system using the KRAB trolley. Height changes in the deflections of rails are evidence of their behavior. The measurements took place on a fixed track and a track with a ballast. Changes in the height jumps between the fixed railway track and the track with a gravel bed are significant and have been recorded since the tracks were put into operation. These certain height deflections allow designers to develop new, more durable construction designs.

This paper examines the quantitative and qualitative situation of the current fixed and mobile Internet and its expected future. First, the number of users and penetration rate of the Internet, various types of services in different countries, the ranking of countries in terms of the mean and median download and upload Internet data speeds, Internet data volume, and number and location of data centers in the world are presented. The second task introduces and details twelve performance evaluation metrics for broadband Internet access. Third, different wired and wireless Internet technologies are introduced and compared based on data rate, coverage, type of infrastructure, and their advantages and disadvantages. Based on the technical and functional criteria, in the fourth work, two popular wired and wireless Internet platforms, one based on optical fiber and the other based on the 5G cellular network, are compared in the world in general and Australia in particular. Moreover, this paper has a look at Starlink as the latest satellite Internet candidate, especially for rural and remote areas. The fifth task outlines the latest technologies and emerging broadband Internet-based services and applications in the spotlight. Sixthly, it focuses on three problems in the future Internet in the world, namely the digital divide due to the different quality of the Internet and new Internet-based services and applications of emerging technologies, the impact of the Internet on social interactions, and hacking and insecurity on the Internet. Finally, some solutions to these problems are proposed.

Laser scanning 3D imaging technology, because it can get accurate three-dimensional surface data, has been widely used in the search for wrecks and rescue operations, underwater resource development, and other fields. At present, the conventional underwater rotating laser scanning imaging system maintains a relatively fixed light window. However, in low-light situations underwater, the rotation of the scanning device causes some degree of water fluctuation, which warps the light strip data that the system sensor receives about the object's surface. To solve the problem, this research studies an underwater 3D scanning and imaging system that makes use of a fixed-light window and a spinning laser (FWLS). A refraction error compensation algorithm is investigated that is based on the fundamentals of linear laser scanning imaging and the dynamic refraction mathematical model is established by the motion of the imaging device. During the imaging process, the incident angle between the laser and the light window varies due to the scanning mode of the system. The experimental results show that the reconstruction radius error is reduced by 60% (from 2.5 mm to about 1 mm) when the measurement data for a standard sphere with a radius of 20 mm are compensated. Moreover, the compensated point cloud data exhibits a higher degree of correspondence with the model of the standard spherical point cloud. This study has a specific reference value for the refractive error analysis of an underwater laser scanning imaging system, and it provides certain research ideas for the subsequent refractive error analysis of various scanning imaging modalities.

Humankind has entered a new era wherein a main characteristic is the convergence of various technologies providing services exerting major impact upon all aspects of human activity, be it social interactions as well as interactions with the natural environment. Fixed networks are about to play a major role in this convergence, since they form, along with mobile networks, the backbone that provides access to a broad gamut of services, accessible from any point of the globe. It is for this reason that we introduce a forward-looking approach for fixed networks, particularly focused on Fixed 6th Generation (F6G) networks. First, we adopt a novel classification scheme for the main F6G services, comprising six categories. This classification is based on the key service requirements, namely latency, capacity and connectivity. F6G networks differ from those of previous generations (F1G-F5G) in that they concurrently support multiple key requirements. We then propose concrete steps towards transforming the main elements of fixed networks, such as optical transceivers, optical switches etc. such that they satisfy the new F6G service requirements. Our study categorizes the main networking paradigm of optical switching into two categories namely ultra-fast and ultra-high capacity switching, tailored to different service categories. With regard to the transceiver physical layer, we propose: a) use of all-optical processing to mitigate performance barriers of analog to digital and digital to analog converters (ADC/DAC); b) exploitation of optical multi-band transmission, space division-multiplexing and adoption of more efficient modulation formats.

We prove a version of Ekeland Variational Principle (EkVP) in a weighted graph $G$ and its equivalence to Caristi fixed point theorem and to Takahashi minimization principle. The usual completeness and topological notions are replaced with some weaker versions expressed in terms of the graph $G$. The main tool used in the proof is the OSC property for sequences in a graph. Converse results, meaning the completeness of graphs for which one of these principles holds is also considered.

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci-Mann iteration process defined by $$x_{n+1} = t_n T^{\phi(n)}(x_n) + (1-t_n)x_n,$$ for $n \in \mathbb{N}$, when $T$ is a monotone asymptotically nonexpansive self-mapping.

How to disentangle the possible genuine quenching of gA caused by scale anomaly of QCD parameterized by the scale-symmetry-breaking quenching factor qssb from nuclear correlation effects is described. This is done by matching the Fermi-liquid xed (FLFP) point theory to the "Extreme Single Particle (shell) Model" (acronym ESPM) in superallowed Gamow-Teller transitions in heavy doubly-magic shell nuclei. The recently experimentally observed indication for (1-qssb) ≠0 - that one might identify as "fundamental quenching (FQ)" - in certain experiments seems to be alarmingly signicant. I present arguments how symmetries hidden in the matter-free vacuum can emerge and suppress such FQ in strong nuclear correlations. How to conrm or refute this observation is discussed in terms of the superallowed Gamow-Teller transition in the doubly-magic nucleus 100Sn and in the spectral shape in the multifold forbidden β decay of 115In.

This study seeks to determine how economic policy uncertainty (EPU) influences investment decisions and the market value of the Pakistan Stock Exchange. The study examines investment and operational data from 249 energy and petroleum companies between 2015 and 2020, in addition to macroeconomic variables such as EPU. This study investigates the moderating effects of EPU on investments in fixed and intangible assets, as well as its effect on Tobin's Q and the market price per share. The outcomes demonstrate that EPU reduces the costs of both tangible and intangible assets for businesses. In addition, companies with a greater Tobin's Q and market price per share are more impacted by uncertain corporate investment policies. However, financial leverage is found to be negatively correlated with share price and positively correlated with earnings per share and earnings per unit. Tobin's Q is positively correlated with financial leverage, indicating that firms that raise capital through debt are more likely to create value for investors. The research indicates that market-dependent enterprises are more susceptible to the unpredictability of monetary policy. Eventually, the findings suggest that consistent and transparent economic policies may increase the efficiency of corporate investment.

Constructing an innovation system centered on new-quality productivity is key to achieving China's technological independence and high-quality development, especially against the backdrop of rapid advancements in artificial intelligence. This article utilizes provincial panel data from China spanning 2010 to 2022 and applies kernel density estimation and the Moran's I index to study the spatiotemporal evolution of artificial intelligence and new-quality productivity. The findings indicate a clustering trend in the development of both factors across regions. Causal empirical analysis using a two-way fixed-effects model reveals that artificial intelligence positively influences new-quality productivity, with conclusions validated by robustness and endogeneity tests.

It is known that the class of p-normed spaces (0 < p ≤ 1) is an important generalization of usual normed spaces with rich topological and geometrical structure, but the most of tools and general principles in nature with nonlinearity have not been developed yet, thus the main goal of this paper is to develop tools for nonlinear analysis under the framework of p-vector spaces. In particular, we first develop the general fixed point theorems which provide solutions to answer Schauder conjecture since 1930’s in the affirmative for p-vector spaces when p = 1 (which is just general topological vector spaces); then the one best approximation result for upper semi-continuous mappings is given, which is used as a powerful tool to establish fixed points for non-self set-valued mappings with either inward or outward set conditions; and finally we establish comprehensive existence results of solutions for Birkhoff-Kellogg Problems, and the general principle of nonlinear alternative by including Leray-Schauder alternative and related results. The results given in this paper not only include the corresponding results in the existing literature as special cases, but also expected to be useful tools for the study of nonlinear problems arising from theory to practice.

Progesterone receptor (PGR) expression level determines biological characteristics of the serous ovarian carcinoma, and low PGR expression appears to be associated with chemoresistance and worse outcome. In this study, we aimed to find relationships between tumor progesterone receptor level and RNA-profile (miRNAs, piwiRNAs, and mRNAs), determining its biological characteristics and behavior. For this purpose, we applied next generation sequencing of small noncoding RNAs, quantitative RT-PCR, and immunohistochemistry to analyze FFPE and frozen tumor samples as well as blood plasma from patients with benign cystadenoma (BSC), serous borderline tumour (SBT), low-grade and high-grade serous ovarian carcinoma (LGSOC and HGSOC, respectively). We found significant upregulation of MMP7 and MUC16 and downregulation of PGR in LGSOC and HGSOC in comparison with BSC. The tissue content of miR-199a-5p, miR-214-3p, miR-424-3p, miR-424-5p, miR-125b-5p significantly inversely correlated with the expression level of MUC16 and blood serum CA125 concentration, and significantly directly correlated with the PGR expression level in tumor tissue. On the contrary, the tissue content of miR-16-5p, miR-17-5p, miR-20a-5p, miR-93-5p, responsible for epithelial-mesenchymal transition (EMT) of the cell, significantly directly correlated with the blood serum CA125 concentration and significantly inversely correlated with the PGR expression level in the tumor tissue. Levels of the EMT-associated miRNAs significantly directly correlated with the content of hsa_piR_022437, hsa_piR_009295, hsa_piR_020813, hsa_piR_004307, hsa_piR_019914 in tumor tissues. Among them, expression level of hsa_piR_004307 significantly inversly correlated with the PGR expression level in the tumor. Two optimal logistic regression models were developed based on the quantitation of hsa_piR_020813, miR-16-5p, hsa_piR_022437 or hsa_piR_004307, hsa_piR_019914, miR-93-5p in the tumor tissue, both of which significantly diagnose PGR-negative tumor phenotype with 93% sensitivity. According to FunRich3.1.3 functional enrichment analysis tool, 72 gene-targets of miRNA and piRNA identified here as markers of PGR-negative ovarian tumor phenotype were proven to be mutated in different cancers such as ovarian, breast, colorectal, liver, stomach, lung, endometrial, thyroid cancer. Among them, the blood plasma levels of miR-16-5p and hsa_piR_022437 can be used to diagnose PGR-negative tumor phenotype with 86% sensitivity before surgery and chemotherapy to choose the treatment strategy for this most aggressive type of ovarian cancer (for instance, neoadjuvant chemotherapy followed by cytoreduction in combination with hyperthermic intraperitoneal chemotherapy) to increase the effectiveness of treatment and longevity of the patient.