Search Results (36)

Motivated by the fact that the Fibonacci sequence is the simplest nontrivial second-order recurrence with a rational generating function, we develop a Fibonacci-weighted Hardy theory for bicomplex holomorphic functions. Starting from the coefficient norm ${\sum }_{n\ge 0}{\left|a_n\right|}^2/F_{n+1}$, we obtain a bicomplex Hilbert module whose reproducing kernel is governed by ${(1-t-t^2)}^{-1}$ and whose maximal disk of holomorphy is determined sharply by the nearest kernel singularity, giving the radius ${\rho }_F={\phi }^{-1/2}$ (the square-root inverse of the golden ratio $\phi$). The arithmetic recurrence makes several objects fully explicit: we derive closed formulas for the kernels through the idempotent decomposition of $\mathbb{BC}$, compute exact norms of the shift powers and a golden-ratio spectral radius, and package the local theory into a sheaf of Fibonacci-holomorphic germs that are compatible with the bicomplex idempotent splitting. We also treat $(p,q)$-Fibonacci weights, obtaining a one-parameter family of rational kernels ${(1-pt-q{t}^2)}^{-1}$ and corresponding operator bounds. In addition to providing a concrete bicomplex model within weighted Hardy theory, the resulting explicit kernels furnish benchmark examples for kernel-based interpolation and for the operator theory of unilateral weighted shifts. Full article

Accurate fault diagnosis of mining hoisting head sheave systems is critical for ensuring operational safety in harsh underground environments. This study proposes a multi-source fault diagnosis framework that fuses vibration and acoustic information using a Convolutional Neural Network and Random Forest (CNN-RF). To support mechanism understanding and validate the experimental platform, finite element and multi-body dynamics simulations (ANSYS/ADAMS) are employed for physical verification and fault signature analysis, while the CNN-RF model is trained and tested exclusively using experimentally acquired vibration and acoustic data. For feature construction, vibration signals are transformed into time–frequency representations (including STFT, CWT, and generalized S-Transform (GST)), and acoustic signals are characterized using Mel-Frequency Cepstral Coefficients (MFCCs). Experimental results demonstrate that vibration–acoustic fusion improves diagnostic performance compared with single-modality baselines; the best performance is achieved by GST+MFCC with the proposed CNN-RF classifier, reaching an accuracy of 98.96%. Future work will conduct cross-condition validation under varying speeds and loads and investigate missing-modality robustness to further assess generalization and deployment reliability. Full article

Steel wire ropes are key load-bearing components in systems such as mine hoisting, bridge cableways, elevators, and cranes, and frictional wear is among the earliest occurring and most easily accumulated form of damage. Under actual working conditions, micro-relative sliding occurs both along the internal wires of the rope and at the contact surfaces with sheaves and ropes, leading to frictional wear, crack propagation, and fatigue failure. Frictional wear, a complex phenomenon influenced by structural layout, contact load, vibration conditions, lubrication, and environmental corrosion, critically determines the service life and load-bearing capacity of steel wire ropes. Recent experimental and numerical studies have significantly clarified the fundamental mechanisms and patterns of internal and external frictional wear in steel wire ropes, offering theoretical support for the distribution of wear, fatigue evolution, and fracture behavior. Meanwhile, non-destructive testing techniques have emerged as a vital tool for the real-time monitoring of wear conditions in steel wire ropes. This review summarizes the research progress on the generation, characteristics, effects, and protection of frictional wear in steel wire ropes, and proposes future directions for tribology and service safety research of steel wire ropes. Full article

This paper establishes a comprehensive framework for the hereditary transfer of categorical completeness and cocompleteness to categories of internal group objects in D-modules. We prove that while completeness of $\mathbf{Grp}\left(\mathbf{D}\text{-}\mathbf{Mod}\right)$ follows unconditionally from the completeness of the base category $\mathbf{D}\text{-}\mathbf{Mod}$, cocompleteness requires $\mathbf{D}\text{-}\mathbf{Mod}$ to be regular, cocomplete, and admit a free group functor left adjoint to the forgetful functor. Explicit constructions are provided for limits via componentwise operations and for colimits through coequalizers of relations induced by group axioms over free group objects. The theory reveals fundamental geometric obstructions: differentially constrained subcategories such as holonomic D-modules fail to be cocomplete due to characteristic variety constraints that prevent free group constructions. Applications demonstrate cocompleteness in topological D-module groups and D-module sheaves, while counterexamples in differential geometric groups exhibit necessary analytic constraints. Additional results include regularity inheritance under product-preserving free group functors, internal hom-object constructions in locally Cartesian closed settings yielding Tannaka-type dualities, and monadicity criteria for locally presentable base categories. This work unifies categorical algebra with differential geometric obstruction theory, resolving fundamental questions on exactness transfer while enabling new constructions in homotopical algebra and internal representation theory for D-modules. Full article

The reliable and safe operation of traction elevators depends on traction capacity, which is degraded by traction sheave groove wear. The resulting slippage reduces transmission efficiency and may cause a catastrophic failure due to the sudden loss of friction. After analyzing slippage mechanisms, we propose a prediction model that combines the Improved Pelican Optimization Algorithm (IPOA) with an Extreme Learning Machine (ELM). A mechanism analysis identifies key inputs—the wear amount, payload, and wire rope tension—providing a basis for model construction. The approach uses Halton sequence initialization, adaptive nonlinear weighting, and Gaussian perturbation, which improve the handling of nonlinearities. IPOA is then employed to optimize the ELM parameters, yielding the IPOA-ELM model. Experiments across multiple wear conditions show that IPOA-ELM predicts slippage more accurately than a traditional ELM. The study clarifies how traction sheave groove wear induces rope slippage and demonstrates the effectiveness of the proposed model under varying wear and load conditions, offering a practical reference for failure mechanism analysis and preventive strategies in elevator traction systems. Full article

This work establishes definitive conditions for the inheritance of categorical completeness and cocompleteness by categories of internal group objects. We prove that while the completeness of $\mathbf{Grp}\left(\mathcal{C}\right)$ follows unconditionally from the completeness of the base category $\mathcal{C}$, cocompleteness requires $\mathcal{C}$ to be regular, cocomplete, and admit a free group functor left adjoint to the forgetful functor. Explicit limit and colimit constructions are provided, with colimits realized via coequalizers of relations induced by group axioms over free group objects. Applications demonstrate cocompleteness in topological groups, ordered groups, and group sheaves, while Lie groups serve as counterexamples revealing necessary analytic constraints—particularly the impossibility of equipping free groups on non-discrete manifolds with smooth structures. Further results include the inheritance of regularity when the free group functor preserves finite products, the existence of internal hom-objects in locally Cartesian closed settings, monadicity for locally presentable $\mathcal{C}$, and homotopical extensions where model structures on $\mathbf{Grp}\left(\mathcal{M}\right)$ reflect those of $\mathcal{M}$. This framework unifies classical category theory with geometric obstruction theory, resolving fundamental questions on exactness transfer and enabling new constructions in homotopical algebra and internal representation theory. Full article

Salbutamol sulfate is a selective β2-receptor agonist used to treat asthma and chronic obstructive pulmonary disease. The crystals of salbutamol sulfate usually appear as needles with a relatively large aspect ratio, showing poor powder properties. In this study, spherical particles of salbutamol sulfate were obtained via antisolvent crystallization. Four different antisolvents, including ethanol, n-propanol, n-butanol, and sec-butanol, were selected, and their effects on crystal form and morphology were compared. Notably, a new solvate of salbutamol sulfate with sec-butanol has been obtained. The novel crystal form was characterized by single-crystal X-ray diffraction, revealing a 1:1 stoichiometric ratio between solvent and salbutamol sulfate in the crystal lattice. In addition, the effects of crystallization temperature, solute concentration, ratio of antisolvent to solvent, feeding rate, and stirring rate on the morphology of spherical particles were investigated in different antisolvents. We have found that crystals grown from the n-butanol–water system at optimal conditions (25 °C, antisolvent/solvent ratio of 9:1, and drug concentration of 0.2 g·mL⁻¹) could be developed into compact and uniform spherulites. The morphological evolution process was also monitored, and the results indicated a spherulitic growth pattern, in which sheaves of plate-like crystals gradually branched into a fully developed spherulite. This work paves a feasible way to develop new crystal forms and prepare spherical particles of pharmaceuticals. Full article

Let X be a compact Riemann surface of genus $g\ge 2$, G be a complex semisimple Lie group, and ${\mathcal{M}}_G\left(X\right)$ be the moduli space of stable principal G-bundles. This paper studies the fixed point set of involutions on ${\mathcal{M}}_G\left(X\right)$ induced by an anti-holomorphic involution $\tau$ on X and a Cartan involution $\theta$ of G, producing an involution $\sigma ={\theta }_{\ast }\circ {\tau }_{\ast }$. These fixed points are shown to correspond to stable $G_{\mathbb{R}}$-bundles over the real curve $(X_{\tau },\tau )$, where $G_{\mathbb{R}}$ is the real form associated with $\theta$. The fixed point set ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ consists of exactly $2^r$ connected components, each a smooth complex manifold of dimension ${\displaystyle \frac{(g-1)\dim G}{2}}$, where r is the rank of the fundamental group of the compact form of G. A cohomological obstruction in $H^2(X_{\tau },{\pi }_1\left(G_{\mathbb{R}}\right))$ characterizes which bundles are fixed. A key result establishes a derived equivalence between coherent sheaves on ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ and on the fixed point set of the dual involution on the moduli space of $G^{\vee }$-local systems, where $G^{\vee }$ denotes the Langlands dual of G. This provides an extension of the Geometric Langlands Correspondence to settings with involutions. An application to the Chern–Simons theory on real curves interprets ${\mathcal{M}}_G{\left(X\right)}^{\sigma }$ as a $(B,B,B)$-brane, mirror to an $(A,A,A)$-brane in the Hitchin system, revealing new links between real structures, quantization, and mirror symmetry. Full article

This study introduces an innovative GNSS-based monitoring system designed to evaluate deformation in mining headframes, effectively addressing the limitations of traditional methods, such as inadequate real-time capabilities and complex data processing requirements. The research was conducted at the Liuzhuang Mine in Anhui Province, China, where a monitoring network was established, consisting of one reference station and eight GNSS stations strategically positioned on sheave platforms and structural supports. Over a period of 66 days, high-frequency 3D deformation data were collected and processed using advanced methodologies, including cubic spline interpolation, generalized extreme studentized deviate (GESD) outlier removal, and Gaussian filtering. Spatiotemporal analysis, employing the “base state with amendments” model, indicated that 90% of the deformations (ΔX, ΔY, ΔH) were confined within ±8 mm, with more significant fluctuations observed near the sheave wheels due to mechanical stress. Correlation analysis identified the distance to the sheave wheel as the primary factor influencing horizontal deformation, with Pearson correlation coefficients exceeding 0.67, while vertical settlement remained stable. Risk thresholds, derived from statistical fluctuations, demonstrated that 99.2% of the data fell within safe limits during validation. In comparison to traditional approaches, the GNSS system delivers enhanced precision, real-time functionality, and a decreased field workload. This study presents a scalable framework for assessing headframe safety and guides the optimization of sensor placement in analogous mining settings. It is proposed that future integration with multi-source sensors, such as inertial navigation systems, will further augment monitoring robustness. Full article

Steel wire rope serves as a critical load-bearing and transmission component in the transportation equipment utilized in coal mines. It exhibits various forms of damage during prolonged service, which significantly jeopardizes the safety reliability of the transportation equipment. To investigate the formation process of the surface wear of steel wire rope and its influence on mechanical properties, the tribological evolution and performance degradation of the transmission wire rope under rope–sheave contact and rope–rope contact were studied in this paper. The wire rope’s friction coefficient (COF) is stable between 0.7 and 0.8 under two contact conditions. It is more likely to lead to the accumulation of frictional heat under the condition of rope–sheave contact. The primary wear mechanisms of transmission wire ropes are adhesive wear and fatigue wear. Additionally, the wear evolution leads to the nonlinear degradation of the tensile strength and bending fatigue life of the wire rope, and the wear damage caused by rope–sheave contact is more harmful. As the sliding distance between the wire rope and the sheave increases, the breaking force decreases from approximately 48 kN to 23 kN, and the number of bending fatigues of the wire rope before scrapping is reduced from approximately 6200 times to 200 times. Full article

Persistent topological Laplacians constitute a new class of tools in topological data analysis (TDA). They are motivated by the necessity to address challenges encountered in persistent homology when handling complex data. These Laplacians combine multiscale analysis with topological techniques to characterize the topological and geometrical features of functions and data. Their kernels fully retrieve the topological invariants of corresponding persistent homology, while their non-harmonic spectra provide supplementary information. Persistent topological Laplacians have demonstrated superior performance over persistent homology in the analysis of large-scale protein engineering datasets. In this survey, we offer a pedagogical review of persistent topological Laplacians formulated in various mathematical settings, including simplicial complexes, path complexes, flag complexes, digraphs, hypergraphs, hyperdigraphs, cellular sheaves, and N-chain complexes. Full article

The effects of austenitizing and austempering temperatures on the bainite transformation kinetics and the microstructural and mechanical properties of a medium-carbon high-silicon ultra-fine bainitic steel were investigated via dilatometric measurements, microstructural characterization and mechanical tests. It is demonstrated that the optimum austenitizing temperature exists for 0.3 wt.%C ultra-fine bainitic steel. Although the finer austenite grain at 950 °C provides more bainite nuclei site and form finer bainitic ferrite plates, the lower dislocation density in plates and the higher volume fraction of the retained austenite reduces the strength and impact toughness of ultra-fine steel. When the austenitizing temperature exceeds 1000 °C, the true thickness of bainitic ferrite plates and the volume fraction of blocky retained austenite in the bainite microstructure increase significantly with the increases in austenitizing temperature, which do harm to the plasticity and impact toughness. The effect of austempering temperature on the transformation behavior and microstructural morphology of ultra-fine bainite is greater than that of austenitizing temperature. The prior martensite, formed when the austempering temperature below Ms, can refine the bainitic ferrite plates and improve the strength and impact toughness. However, the presence of prior martensite divides the untransformed austenite and inhibits the growth of bainite sheaves, thus prolonging the finishing time of bainite transformation. In addition, prior martensite also strengthens the stability of untransformed austenite though carbon partition and enhances the volume fraction of blocky retained austenite, which reduces the plasticity of ultra-fine bainitic steel. According to the experimental results, the optimum austempering process for 0.3 wt. %C ultra-fine bainitic steel is through austenitization at 1000 °C and austempering at 340 °C. Full article

Most commercial elevators for buildings exceeding four stories use a cable-driven traction system. Typically, a single traction machine operates by hoisting the main cable on a traction sheave, thus vertically transporting the elevator car through rotational motion of the sheave. This research introduces a groundbreaking advancement aimed at elevating loading capacity to an unprecedented 50 tons—the highest known in the world. The innovation involves the development of a twin traction system, wherein two traction machines collaborate to lift the elevator. This novel elevator system has demonstrated remarkable capabilities, showcasing the ability to transport up to 300 passengers in a single trip. The installation of this high-capacity elevator system has yielded substantial improvements in construction work efficiency and safety protocols, particularly in scenarios where cranes are traditionally used. The newly developed elevator could lift 50 tons of equipment 60 times a day, whereas the crane was limited to 8 times. The positive impact on labor is also noteworthy, with increased safety and health considerations, especially in adverse weather conditions. By eliminating the need for manual stair climbing, the well-being of the workforce is prioritized. Furthermore, the heightened productivity resulting from a significant reduction in wait times for conventional elevators is a key outcome of this transformative technology. This research not only unveils a groundbreaking twin traction system but also highlights its multifaceted features in enhancing efficiency, safety, and overall productivity in various industries. Full article

Topological states of matter can be classified only in terms of global topological invariants. These global topological invariants are encoded in terms of global observable topological phase factors in the state vectors of electrons. In condensed matter, the energy spectrum of the Hamiltonian operator has a band structure, meaning that it is piecewise continuous. The energy in each continuous piece depends on the quasi-momentum which varies in the Brillouin zone. Thus, the Brillouin zone of quasi-momentum variables constitutes the base localization space of the energy eigenstates of electrons. This is a continuous topological parameter space bearing the homotopy of a torus. Since the base localization space has the homotopy of a torus, if we vary the quasi-momentum in a direction, when the edge of the zone is reached, we obtain a closed path. Then, if we lift this loop from the base space to the sections of the sheaf-theoretic fibration induced by the localization of the energy eigenfunctions, we obtain a global topological phase factor which encodes the topological structure of the Brillouin zone. Because it is homotopically equivalent to a torus, the global phase factor turns out to be quantized, taking integer values. The experimental significance of this model stems from the recent discovery that there are observable global topological phase factors in fairly ordinary materials. In this communication, we show that it is the unitary representation theory of the discrete Heisenberg group in terms of commutative modular symplectic variables, giving rise to a joint commutative representation space endowed with an integral and ${\mathbb{Z}}_2$-invariant symplectic form that articulates the specific form of the topological conditions characterizing both the quantum Hall effect and the spin quantum Hall effect under a unified sheaf-theoretic cohomological framework. Full article

A certain Grothendieck topology assigned to a metric space gives rise to a sheaf cohomology theory which sees the coarse structure of the space. Already constant coefficients produce interesting cohomology groups. In degree 0, they see the number of ends of the space. In this paper, a resolution of the constant sheaf via cochains is developed. It serves to be a valuable tool for computing cohomology. In addition, coarse homotopy invariance of coarse cohomology with constant coefficients is established. This property can be used to compute cohomology of Riemannian manifolds. The Higson corona of a proper metric space is shown to reflect sheaves and sheaf cohomology. Thus, we can use topological tools on compact Hausdorff spaces in our computations. In particular, if the asymptotic dimension of a proper metric space is finite, then higher cohomology groups vanish. We compute a few examples. As it turns out, finite abelian groups are best suited as coefficients on finitely generated groups. Full article