Search Results (65)

This paper presents a proof-of-concept investigation into a novel hermetically sealed tunable-medium Extrinsic Fabry–Pérot Interferometer (EFPI) temperature sensor architecture. A series of tuneable-sensitivity EFPI temperature sensors is demonstrated, comprising a large-diameter fused silica diaphragm with a 800 $\mathsf{\mu }\mathrm{m}$ diameter, significantly exceeding conventional designs (typically ∼125 $\mathsf{\mu }\mathrm{m}$), with polished diaphragm thicknesses ranging from 28 to 49 $\mathsf{\mu }\mathrm{m}$, housed in hermetically sealed rigid melting point capillaries with a 1.8 mm internal diameter. By exploiting thermally induced pressure differentials generated by a tunable Krytox GPL 105 oil/air fill fraction within the sealed rigid cavity, the sensors demonstrate a continuously tuneable sensitivity design space spanning 0.45 to 190 $\mathrm{n}\mathrm{m}/\mathrm{K}$. An exact nonlinear thermal pressure model is derived and validated, replacing the linearised approximation which is shown to be inapplicable at fill fractions approaching unity. The low-sensitivity configuration (0.45 $\mathrm{n}\mathrm{m}/\mathrm{K}$) was characterised at the National Standards Authority of Ireland (NSAI) National Metrology Laboratory against ITS-90 fixed points: the Triple Point of Water (273.16 K) and the Gallium Fixed Point (302.9146 K), with traceability to the International Temperature Scale of 1990 (ITS-90), yielding an instrument-limited resolution of $<1.1$ mK, consistent with the metrological validation environment. The high-sensitivity configurations (21 and 190 $\mathrm{n}\mathrm{m}/\mathrm{K}$) were characterised on a laboratory bench, achieving instrument-limited theoretical resolutions of <24 $\mathsf{\mu }\mathrm{K}$ and $<2.6$ $\mathsf{\mu }\mathrm{K}$ respectively, pending future metrological validation. The 190 $\mathrm{n}\mathrm{m}/\mathrm{K}$ sensitivity represents an improvement of approximately 21.7× over the closest directly comparable prior Citationutilised fusion splicing and manual polishing. Future development priorities include metrological validation of the high-sensitivity configurations, long-term stability characterisation, thermal cycling, and progression towards an all-glass hermetically sealed construction. Full article

We develop a matrix-theoretic framework for the natural embedding of the exceptional Lie algebra ${\mathfrak{g}}_2=\mathrm{Der}\left(\mathbb{O}\right)$ in $\mathfrak{so}\left(8\right)$, use it to make constructive a recent existence result on octonionic triality, and derive geometric applications for moduli spaces of principal bundles. Specifically, the derivation condition for $\widehat{D}\in \mathfrak{so}\left(7\right)$ is reformulated as a homogeneous linear system in the 21 entries of $\widehat{D}$, whose solution space is identified with ${\mathfrak{g}}_2=ker\mathsf{\Psi }$, where $\mathsf{\Psi }:\mathfrak{so}\left(7\right)\to {\Lambda }^3{\left({\mathbb{R}}^7\right)}^{*}$ is the Lie derivative with respect to the associative 3-form $\phi$ on $\mathrm{Im}\left(\mathbb{O}\right)$. It is proved that $\mathrm{rank}\mathsf{\Psi }=7$, and an algorithm is given for computing an orthonormal basis of ${\mathfrak{g}}_2$. The image $\mathsf{\Psi }\left({\widehat{A}}_{\sigma }\right)$ of the triality generator is computed for all triples, yielding six nonzero components and squared norm 12. As geometric applications, the map $\mathsf{\Psi }$ is globalized to a morphism of adjoint bundles, giving an intrinsic characterization of the $G_2$-reductible locus in $\mathcal{M}\left(\mathrm{SO}\right(7\left)\right)$. The orthogonal decomposition of $\mathfrak{so}\left(8\right)$ globalizes to an explicit splitting of the adjoint bundle of any $\mathrm{SO}\left(8\right)$-principal bundle admitting a $G_2$-reduction. Finally, $\mathcal{M}\left(G_2\right)$ is identified as a connected component of the triality fixed-point locus in $\mathcal{M}\left(\mathrm{Spin}\right(8\left)\right)$, with an explicit description of the tangent and normal spaces in terms of the Lie-algebraic decomposition. Full article

In this article, we construct a framework for analyzing the equilibrium and stability of networked multi-sector economic systems via fixed-point analysis. We represent directional intersectoral dependencies, nonlinear feedback effects, and heterogeneous adjustment dynamics in the model by the coupled and tripled fixed-point theory in the graphically extended suprametric spaces. The graphical structure encodes supply-chain and influence networks, whereas asymmetric and nonuniform interaction strengths are encoded in the suprametric setting. Furthermore, we prove the existence, uniqueness, and convergence of equilibrium solutions under new generalized contraction conditions. We apply the theoretical findings in nonlinear state systems in which prices in interdependent markets are adjusted using integral equations. The results of numerical simulations show consistent convergence, and the sensitivity parameter of the network structure significantly influences the determination of economic stability and speed of adjustment. Full article

Target detection in synthetic aperture radar (SAR) images is constrained by three primary challenges. First, speckle noise overlaps heavily with the high-frequency features of target edges in the frequency domain, so standard convolutions cannot suppress noise without sacrificing edge texture. Second, the scattering signature of a SAR target varies markedly with viewing angle, and a fixed-parameter convolution kernel cannot accommodate this spatial non-stationarity. Third, deep and shallow levels of the feature pyramid differ in semantics and resolution, and a naive element-wise sum either introduces noise interference or loses small-target signals. We propose the Frequency–Spatial Detection Network (FSDNet), whose core FSDBlock cascades three operators to address these failure modes in turn. Wavelet Convolution (WTConv) projects features into Haar sub-bands and applies independent low- and high-frequency kernels prior to inverse-DWT reconstruction, suppressing noise while preserving edges. Receptive-Field Attention Convolution (RFAConv) generates location-conditional kernels and so adapts to non-stationary scattering. Spatial Context Self-Attention (SCSA) aggregates discrete scattering points into coherent target representations via long-range grouped attention. At the fusion stage, CGAFusion replaces FPN element-wise addition with a channel–spatial–pixel triple-attention soft switch that mitigates deep–shallow semantic mismatch. On HRSID, FSDNet attains mAP₅₀ $= 92.3$% and mAP_50:95 $= 68.6$%. On SSDD, it attains mAP₅₀ $= 98.7$% and mAP_50:95 $= 74.2$%. Both sets of results consistently surpass the baseline methods. Against the strongest YOLO baseline (YOLOv11n), FSDNet improves HRSID mAP₅₀ by $+1.7$ percentage points (pp) and mAP_50:95 by $+2.3$ pp, and SSDD mAP₅₀ by $+0.5$ pp and mAP_50:95 by $+2.7$ pp; against the capacity-fair YOLOv11s reference (∼51% more parameters), FSDNet still leads on mAP₅₀, mAP_50:95, recall, and F1. Ablation studies and power-spectral-density analyses corroborate the contribution of each module and confirm WTConv’s role in preserving high-frequency target features. Full article

In the context of growing global concerns about food safety, sustainability, and corporate responsibility, voluntary food safety certifications (VFSC) such as ISO 22000, FSSC 22000, HACCP, and Halal play a critical role in shaping the performance of food processing companies. This study analyzes the impact of VFSC on the triple bottom line (TBL) performance, encompassing environmental, economic, and social aspects, of food processing companies in Pakistan. To accomplish this objective, the study utilizes panel data from 19 listed companies involved in food processing while fixed-effect regressions are employed for empirical estimations. The results indicate that the resource efficiency of ISO 22000-certified food processing companies is, on average, 0.17 points greater than that of non-certified companies. Likewise, the sales of the companies that implement ISO 22000 are, on average, 0.13 percentage points higher than those of companies with no ISO 22000. This suggests that implementing ISO 22000 has a significant impact on enhancing the environmental and economic performance of food processing companies. Furthermore, the sales of companies implementing FSSC 22000 are, on average, 0.17 percentage points higher, whereas the sales of companies implementing HACCP are, on average, 0.23 percentage points higher than those of non-certified companies. Finally, the social performance of companies implementing FSSC 22000 is, on average, 0.06 points higher, whereas the social performance of companies implementing HACCP is, on average, 0.05 points higher than that of non-certified companies. This implies that the implementation of FSSC 22000 and HACCP contributes positively to economic and social performance. These findings offer profound insights for managers, decision-makers, and relevant actors in the food sector, highlighting the importance of strategically implementing VFSC to achieve long-term sustainability and competitiveness. Full article

Background and Objectives: Collared, triple-tapered femoral stems have gained increasing popularity in primary total hip arthroplasty (THA) due to their stable metaphyseal fixation and ability to restore native hip biomechanics. This study evaluated the short-term clinical and functional outcomes of a novel collared triple-tapered femoral stem design in primary THA. Materials and Methods: This was a retrospective review of all patients who underwent primary, elective THA using a collared, triple-tapered femoral system at a single, urban, high-volume, academic hospital between September 2024 and February 2025. All procedures were performed by fellowship-trained arthroplasty surgeons. A total of 101 patients (102 hips) with a median follow-up of 1.1 years (range, 1.0 to 1.4 years) were included. Results: Most procedures were performed for primary osteoarthritis (96%). Mean operative time, from skin incision to skin closure, was 93 min, and most femoral stems implanted had a high offset (89%). Most patients were discharged home (96%), with a mean length of stay of 27 h. Within 90 days, three patients were readmitted for surgery-related reasons: one for superficial wound dehiscence, and two for periprosthetic joint infection (PJI). One PJI was treated with irrigation and debridement, antibiotics, and implant retention (DAIR) two months after primary THA. The other required a DAIR three weeks after primary THA, followed by a single-stage revision one week later. No dislocations, periprosthetic fractures, mechanical failures, or aseptic revisions of the femoral stem occurred. All stems were well-fixed at the latest follow-up, with no aseptic loosening observed. Mean Hip disability and Osteoarthritis Outcome Score, Joint Replacement (HOOS, JR) improvement was 15.0 points at six weeks, 25.2 points at three months, and 45.3 points at one year. Conclusions: Our results support encouraging early outcomes with no femoral aseptic complications observed using this novel collared, triple-tapered femoral system. A longer follow-up period is needed to assess mid- and long-term durability. Full article

This paper introduces a novel framework by merging the concepts of non-Archimedean generalized Menger spaces and ($\varkappa -\mathsf{ϝ}$)-weak proximal contractions. Extending the best proximity point concept to a triple of sets, we establish new existence theorems for these contractions without requiring the probabilistic P-property, representing a meaningful advancement beyond prior findings, which is a significant generalization of existing results. The study leverages two control functions ($\varkappa$ and $\mathsf{ϝ}$) within the contraction condition to derive optimal approximate solutions to fixed-point equations for non-self mappings. Consequently, our core results not only extend but also unify a range of established theorems within classical probabilistic and G-metric spaces. We present a significant application to theoretical computer science by proving that a self-mapping acting on infinite words possesses a unique fixed point. Full article

This article introduces novel methodologies, coordinate systems, and procedures in computational geometry that further develop a Euclidean-based relationalistic framework. The objective is to describe tools using object-oriented relational elements with symmetry, anchored to a fixed point in a relational model, that generate structured point sets serving as blueprints for geometric figures and physical structures representing their source objects. Geometric operations and transformations construct ratio figures and ordered proportional structures. Using discrete $\mathbb{N}$-Euclidean geometry, two relational coordinate systems are introduced—polar-vertex coordinates and radial coordinates—both formed through discrete geometric operations. A relational unit circle of fixed magnitude is defined by a 4::1 proportional equivalence between radius and angular ratios, independent of real-number or arc-length geometry. Euclid’s theory of proportion is extended from static abstract magnitudes to symmetry-driven geometric construction, and a square-pyramid geometric blueprint is produced from an Earth ratio figure with accurate dimensional magnitudes. The findings reveal a novel commensurability between the radius of a circle and the side length of a square using a shared fixed point coupled via a 3:4:5 Pythagorean-triple triangle, introducing the concept of ordered proportions. Full article

We establish a modular-space framework for the study of tripled fixed points and tripled best proximity points. Under suitable assumptions on the underlying modular (convexity, the ${\Delta }_2$ property, uniform continuity, and uniform convexity-type properties), we prove that Banach theorems guarantee the existence, uniqueness, and convergence of modular iterative schemes. In particular, we develop results for cyclic $\rho$–Kannan contraction maps and pairs, showing that both tripled fixed points and tripled best proximity points arise uniquely and attract all iterative trajectories. An illustrative example in the space $L^2[0,1]$ with integral operators demonstrates the applicability of the theory and the predicted rate of convergence. These results extend classical fixed point methods to a broader modular setting and open the way for applications in nonlinear functional equations. Full article

Gulf Cooperation Council (GCC) economies are investing heavily in digital infrastructure to diversify beyond hydrocarbons, yet the productivity returns from these investments remain uncertain. This study examines whether digital adoption enhances labor productivity in GCC economies (2000–2023). We construct a Composite Digital Index (CDI) from broadband subscriptions, internet use, and mobile penetration. Interpreting the Gulf economies as socio-technical systems, we frame digital adoption, productivity, and investment (measured by GCF) as a reinforcing loop, with government effectiveness amplifying the cycle and oil rents dampening it. Using panel data methods, including fixed-effects and long-run estimators, we find that digital adoption yields persistent productivity gains. In the long run, a one-point increase in CDI is associated with a 12.6 percentage point rise in labor productivity growth (p < 0.05). This effect triples—to approximately 38.5 percentage points—when moderated by strong government effectiveness (CDI × Governance interaction: +26.3; p < 0.01). Conversely, the productivity payoff declines significantly with oil-rent dependence: for every 10 percentage-point rise in oil rents, the marginal effect of digital adoption drops by 3.4 points. These gains are significantly larger where government effectiveness is stronger, while oil dependence weakens them. The findings imply that infrastructure adoption alone is insufficient: institutions and fiscal structures condition whether digital adoption translate into sustained productivity growth. Policy priorities should focus on institutional reform, fiscal diversification, and enabling firm-level digital absorption—particularly in high-rent economies—so that adoption translates into broad-based productivity dividends. Full article

Background: The distal biceps brachii tendon inserts proximally and posteriorly on the bicipital tuberosity of the radius and it is a forearm supinator but also contributes to flexion of the elbow. Chronic distal biceps tendon ruptures are relatively rare, often complicated by tendon and muscle retraction, and, therefore, their primary repair is difficult or impossible. The gold standard treatment of these chronic lesions is its anatomic reinsertion at the radial tuberosity after tendon reconstruction, using autograft or allograft tissue, but there is no agreement about the most appropriate surgical technique. Untreated injuries usually result in elbow joint deficits and decreased muscular strength. We report the preliminary results in a group of patients treated with a tripled autologous semitendinosus graft. Methods: In the present retrospective study, we report the results in a series of 13 patients surgically treated using tripled autologous semitendinosus graft, fixed to the residual distal biceps tendon, starting from the myotendinous junction, and using tension-slide technique (Biceps Button—Arthrex, Inc, Naples, FL 34108, USA) in association with an interference screw. Eleven males and two females, with a mean age of 46, participated in the study. Results: At mean follow-up check-in of 35 months, clinical results were assessed using the DASH score and MEPS, with a mean value of 11 points and 87 points, respectively. Tensiomyography was also performed to evaluate muscular strength. Six patients had excellent results and seven had good results. No patient had either a tendon re-rupture, or a peripheral neurological deficit, or symptomatic heterotopic ossifications. Seven patients had a mild deficit in elbow motion and six patients had a mild deficit in forearm prono-supination. Upon tensiomyography evaluation, five patients showed a mild deficit in flexion and supination strength. All patients returned to their previous daily and sporting activities. Conclusions: According to our results, in patients affected by chronic distal biceps tendon rupture, surgical treatment performed using tripled autologous semitendinosus autograft secured to the radial tuberosity using the tension-slide technique and interference screw is associated with satisfactory outcomes. Full article

The objective of this manuscript is to investigate the existence, uniqueness criteria and Ulam–Hyers stability of solutions to tripled systems of the Hilfer–Hadamard type supplemented with symmetric nonlocal multi-point Riemann–Liouville integral boundary conditions. By converting the considered problem into an equivalent fixed-point problem, the existence and uniqueness are proven by application of the Leray–Schauder nonlinear alternative and Banach’s contraction principle, respectively. In addition, we discuss the Ulam–Hyers stability and generalized Ulam–Hyers stability of the results, and illustrative examples are also presented to demonstrate their correctness and effectiveness. Full article

Cancer-associated fibroblasts (CAFs) constitute a heterogeneous population of cells within the tumor microenvironment and are associated with cancer development and drug resistance. The absence of a universal classification for CAFs hinders their research and therapeutic targeting. To define CAF phenotypes, we developed patient-derived cell cultures of breast cancer (BC) and validated and characterized four distinct CAF subtypes (S1–S4) by Costa’s classification. Three out of five primary cell cultures of BC demonstrated different functional features rather than fixed cellular states due to the plasticity of the CAF phenotype. CAF crosstalk with cancer cells supported their survival in the presence of anticancer drugs. Based on the analysis of the cytotoxic effect of doxorubicin, cisplatin and tamoxifen, it was demonstrated that CAF-S4 and CAF-S1 cells were sensitive to the action of all drugs investigated, despite the fact that they possessed different mechanisms of action. CAF-S2 cells exhibited the highest level of resistance to the antitumour agents. Homotypic and heterotypic spheroids with CAFs could be used to model the fibrotic area of BC in vitro. The patient-derived cell cultures of CAFs formed spheroids. Hypoxia-activated CAF-S4 have been shown to stimulate the metastatic potential of triple-negative BC cells in a heterotypic spheroid model. Consequently, this study could be a starting point for the development of novel therapeutic strategies that target CAFs and their interactions with cancer cells. Full article

We unify a known technique used for fixed points and coupled, tripled and N-tupled fixed points for weak monotone maps, i.e., maps that exhibit monotone properties for each of their variables. We weaken the classical contractive condition in partially ordered metric spaces by requiring it to hold only for a sequence of successive iterations, generated by the considered map, provided that it is a monotone one. We show that some known results are a direct consequence of the main result. The introduced technique shows that the partial order in the constructed Cartesian space is induced by both the partial order in the considered metric space and by the monotone properties of the investigated maps. We illustrate the main result, which is applied to solve a nonlinear matrix equation, following key ideas from Berzig, Duan & Samet. We present an illustrative example. We comment that a similar approach can be used to solve systems of nonlinear matrix equations. Full article

This paper introduces a novel class of generalized contractions, termed $(\alpha ,\eta ,(Q,h),\mathcal{L})$-contraction mapping, within the context of triple controlled metric-type spaces, extending the framework of fixed point theory in controlled structures. The proposed mapping is defined using $\alpha$-admissible and $\eta$-subadmissible functions, in conjunction with a control pair $(Q,h)$ of upper class of type I, and incorporates Wardowski’s function $\mathcal{L}$-contraction condition. Under suitable hypotheses, we establish both the existence and uniqueness of fixed points for this class of mappings. Several corollaries are derived as special cases of the main result. Moreover, we provide a nontrivial application by analyzing the solvability of a nonlinear equation involving powers of the sine function, thereby illustrating the utility of the developed theory. Full article