Search Results (243)

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

Caregiver self-regulation may be a critical component of caregivers’ effective delivery of caregiver-mediated interventions (CMIs). CMIs are a highly evidence-based group of interventions that target a broad range of challenges, including social communication, emotion regulation, and externalizing behaviors, for autistic and neurotypical children. CMIs teach caregivers to be “coaches” to help their children learn and practice skills in daily life. However, being a good “coach” likely requires caregivers to optimally self-regulate their emotions, thoughts, and behaviors when working with their children in moments that are often emotionally heightened. Caregiver self-regulation is a set of skills that promote parenting autonomy and confidence: self-sufficiency, self-efficacy, self-management, personal agency, and problem solving. This conceptual paper will briefly discuss the literature on the role of caregiver self-regulation in CMIs and argue that future implementation research on CMIs should measure caregiver self-regulation because, in line with recent expansion of the theory of planned behavior, caregiver self-regulation may predict more effective implementation of CMIs. We also argue, in line with CFIR 2.0, that supporting caregiver self-regulation could ultimately improve the implementation of CMIs with regard to each implementation outcome in the Implementation Outcomes Framework. For example, enhancing caregiver self-regulation may improve CMI appropriateness (by increasing alignment with each caregiver’s values and culture), adoption (by increasing engagement to finish the full CMI protocol), and even CMI sustainability (by increasing caregivers’ ability to problem-solve and generalize to new child challenges independently, freeing up provider time to work with new caregivers and allowing the agency to provide the CMI for a reduced relative cost). Should future research demonstrate that caregiver self-regulation is an implementation determinant, future implementation strategies may need to include support for caregiver self-regulation, because it may explain or enhance the implementation of CMIs across early intervention and community mental health systems. Full article

This paper explores some frame bundles and physical implications of Killing vector fields on the two-sphere ${\mathbb{S}}^2$, culminating in a novel application to Maxwell’s equations in free space. Initially, we investigate the Killing vector fields on ${\mathbb{S}}^2$ (represented by the unit sphere of ${\mathbb{R}}^3$), which generate the isometries of the sphere under the rotation group $SO\left(3\right)$. These fields, realized as functions $K_v:{\mathbb{S}}^2\to {\mathbb{R}}^3$, defined by $K_v\left(q\right)=v\times q$ for a fixed $v\in {\mathbb{R}}^3$ and any $q\in {\mathbb{S}}^2$, generate a three-dimensional Lie algebra isomorphic to $\mathfrak{so}\left(3\right)$. We establish an isomorphism $K:{\mathbb{R}}^3\to \mathcal{K}\left({\mathbb{S}}^2\right)$, mapping vectors $v=au$ (with $u\in {\mathbb{S}}^2$) to scaled Killing vector fields $a{K}_u$, and analyze its relationship with $SO\left(3\right)$ through the exponential map. Subsequently, at a fixed point $e\in {\mathbb{S}}^2$, we construct a smooth orthonormal right-handed tangent frame $f_e:{\mathbb{S}}^2\backslash \{e,-e\}\to T{\left({\mathbb{S}}^2\right)}^2$, defined as $f_e\left(u\right)=({\widehat{K}}_e\left(u\right),u\times {\widehat{K}}_e\left(u\right))$, where ${\widehat{K}}_e$ is the unit vector field of the Killing field $K_e$. We verify its smoothness, orthonormality, and right-handedness. We further prove that any smooth orthonormal right-handed frame on ${\mathbb{S}}^2\backslash \{e,-e\}$ is either $f_e$ or a rotation thereof by a smooth map $\rho :{\mathbb{S}}^2\backslash \{e,-e\}\to SO\left(3\right)$, reflecting the triviality of the frame bundle over the parallelizable domain. The paper then pivots to an innovative application, constructing solutions to Maxwell’s equations in free space by combining spherical symmetries with quantum mechanical de Broglie waves in tempered distribution wave space. The deeper scientific significance lies in bringing together differential geometry (via $SO\left(3\right)$ symmetries), quantum mechanics (de Broglie waves in Schwartz distribution theory), and electromagnetism (Maxwell’s solutions in Schwartz tempered complex fields on Minkowski space-time), in order to offer a unifying perspective on Maxwell’s electromagnetism and Schrödinger’s picture in relativistic quantum mechanics. Full article

Cyclen-based ligands are among the most preferred ones in radiopharmacy, where they are mainly applied for transferring radioisotopes through the human body. A crucial criterion is the stability of their metal–ligand complexes, which depends on the stabilization of the free ligand in solution. However, these flexible ligands can have numerous conformations, and for a reliable evaluation of the dissociation energy, the most stable one(s) in solution must be known. In the present study, the low-energy conformational space of four anionic (2-) cyclen-based ligands has been elucidated in aqueous solution by a joint molecular mechanics (MM)/Density Functional Theory (DFT) procedure. The results revealed a significant preference for C₂ symmetric structures, more or less resembling the arrangements in their metal complexes. The computed dissociation energies agree with the experimentally found stability trend for the Pb²⁺ complexes with ligands containing picolinate pendant arms. For complexes with mixed donor groups (carboxyl, amide, pyridine), significant thermodynamic stabilities were predicted. Full article

The experimental IR and Raman vibrational spectra of a hydrated La(III) complex with a 1,2,3-triazole ligand were characterized by using four different Density Functional Theory (DFT) levels and two accurate scaling procedures. In the theoretical calculations, the hydration water in the experimental sample was considered under the Discrete Model (DM) with different numbers of explicit water molecules and different positions around the La(III) ion and the carboxylate groups. The predicted IR spectra at the M06-2X/Lanl2dz level appear to be the closest to the experimental ones. Based on the optimized structures, molecular properties and global chemical descriptors were also calculated, and the findings obtained are discussed in detail herein. Additionally, several photophysical properties were determined in both the free ligand and in several lanthanide complexes, and with the sample in the solid state and in DMSO solution. A blue shift in the fluorescence of the complexes was observed compared to the free ligand, as well as in the solid-state sample compared to the solution. Full article

This study investigates the impact of oxygen-containing functional groups (COO-Li, CO-Li, and O-Li) on the electronic and optical properties of graphene, with a focus on hydrogen sensing applications. Using density functional theory (DFT) calculations, we evaluated the thermodynamic feasibility of the functionalization and hydrogen adsorption processes. The Gibbs free energy changes (ΔG) for the functionalization of pristine graphene were calculated as −1233, −1157, and −1119 atomic units (a.u.) for COO-Li, CO-Li, and O-Li, respectively. These negative values indicate that the functionalization processes are spontaneous (ΔG < 0), with COO-Li being the most thermodynamically favorable. Furthermore, hydrogen adsorption on the functionalized graphene surfaces also exhibited spontaneous behavior, with ΔG values of −1269, −1204, and −1175 a.u., respectively. These results confirm that both functionalization and subsequent hydrogen adsorption are energetically favorable, enhancing the potential of these materials for hydrogen sensing applications. Among the functional groups we simulated, COO-Li exhibited the largest surface area and volume, which were attributed to the high electronegativity and steric influence of the carboxylate moiety. Based on the previously described results, we analyzed the interaction of these functionalized graphene systems with molecular hydrogen. The adsorption of two H₂ molecules per system demonstrated favorable thermodynamics, with lithium atoms serving as active sites for external adsorption. The presence of lithium atoms significantly enhanced hydrogen affinity, suggesting strong potential for sensing applications. Further, electronic structure analysis revealed that all functionalized systems exhibit semiconducting behavior, with band gap values modulated by the nature of the functional group. FTIR (Fourier-Transform Infrared Spectroscopy) and Raman spectroscopy confirmed the presence of characteristic vibrational modes associated with Li-H interactions, particularly in the 659–500 cm⁻¹ range. These findings underscore the promise of lithium-functionalized graphene, especially with COO-Li, as a tunable platform for hydrogen detection, combining favorable thermodynamics, tailored electronic properties, and spectroscopic detectability. Full article

This paper presents some of the most significant findings in the design of a hydraulic servomechanism for flight controls, which were primarily achieved by the first author during his activity in an aviation institute. These results are grouped into four main topics. The first one outlines a classical theory, from the 1950s–1970s, of the analysis of nonlinear automatic systems and namely the issue of absolute stability. The uninformed public may be misled by the adjective “absolute”. This is not a “maximalist” solution of stability but rather highlights in the system of equations a nonlinear function that describes, for the case of hydraulic servomechanisms, the flow-control dependence in the distributor spool. This function is odd, and it is therefore located in quadrants 1 and 3. The decision regarding stability is made within the so-called Lurie problem and is materialized by a matrix inequality, called the Lefschetz condition, which must be satisfied by the parameters of the electrohydraulic servomechanism and also by the components of the control feedback vector. Another approach starts from a classical theorem of V. M. Popov, extended in a stochastic framework by T. Morozan and I. Ursu, which ends with the description of the local and global spool valve flow-control characteristics that ensure stability in the large with respect to bounded perturbations for the mechano-hydraulic servomechanism. We add that a conjecture regarding the more pronounced flexibility of mathematical models in relation to mathematical instruments (theories) was used. Furthermore, the second topic concerns, the importance of the impedance characteristic of the mechano-hydraulic servomechanism in preventing flutter of the flight controls is emphasized. Impedance, also called dynamic stiffness, is defined as the ratio, in a dynamic regime, between the output exerted force (at the actuator rod of the servomechanism) and the displacement induced by this force under the assumption of a blocked input. It is demonstrated in the paper that there are two forms of the impedance function: one that favors the appearance of flutter and another that allows for flutter damping. It is interesting to note that these theoretical considerations were established in the institute’s reports some time before their introduction in the Aviation Regulation AvP.970. However, it was precisely the absence of the impedance criterion in the regulation at the appropriate time that ultimately led, by chance or not, to a disaster: the crash of a prototype due to tailplane flutter. A third topic shows how an important problem in the theory of automatic systems of the 1970s–1980s, namely the robust synthesis of the servomechanism, is formulated, applied and solved in the case of an electrohydraulic servomechanism. In general, the solution of a robust servomechanism problem consists of two distinct components: a servo-compensator, in fact an internal model of the exogenous dynamics, and a stabilizing compensator. These components are adapted in the case of an electrohydraulic servomechanism. In addition to the classical case mentioned above, a synthesis problem of an anti-windup (anti-saturation) compensator is formulated and solved. The fourth topic, and the last one presented in detail, is the synthesis of a fuzzy supervised neurocontrol (FSNC) for the position tracking of an electrohydraulic servomechanism, with experimental validation, in the laboratory, of this control law. The neurocontrol module is designed using a single-layered perceptron architecture. Neurocontrol is in principle optimal, but it is not free from saturation. To this end, in order to counteract saturation, a Mamdani-type fuzzy logic was developed, which takes control when neurocontrol has saturated. It returns to neurocontrol when it returns to normal, respectively, when saturation is eliminated. What distinguishes this FSNC law is its simplicity and efficiency and especially the fact that against quite a few opponents in the field, it still works very well on quite complicated physical systems. Finally, a brief section reviews some recent works by the authors, in which current approaches to hydraulic servomechanisms are presented: the backstepping control synthesis technique, input delay treated with Lyapunov–Krasovskii functionals, and critical stability treated with Lyapunov–Malkin theory. Full article

Gas sensors can provide early warning of fires by detecting pyrolysis gas components in the sheaths of high-voltage cables. However, air humidity significantly affects the thermal decomposition gas production characteristics of the outer sheath of high-voltage cables, which in turn affects the accuracy of this warning method. In this paper, the thermal decomposition and gas production characteristics of the polyethylene (PE) outer jacket of high-voltage cables under different air humidities (20–100%) are studied, and the corresponding density functional theory (DFT) simulation calculations are performed using Gaussian 09W software. The results show that with the increase in humidity, the thermal decomposition gas yield of the PE outer jacket of high-voltage cables exhibits a decreasing trend. Under high-humidity conditions (≥68.28%RH), the generation of certain thermal decomposition gases is significantly reduced or even ceases. Meanwhile, the influence of moisture on the thermal decomposition characteristics of PE was analyzed at the micro level through simulation, indicating that the H-free radicals generated by moisture promote the initial decomposition of PE, but the subsequent combination of hydroxyl groups with terminal chain C forms a relatively stable alkoxy structure, increasing the activation energy of the reaction (by up to 44.7 kJ/mol) and thus inhibiting the generation of small-molecule gases. An experimental foundation is laid for the final construction of a fire warning method for high-voltage cables based on the information of thermal decomposition gas of the outer sheath. Full article

Levelers are indispensable additives for achieving void-free, bottom-up superconformal copper filling of microvias. Establishing the molecular-level correlation between leveler structure and performance is therefore essential to the continued advancement of microelectronic copper-plating technology. Herein, nitro blue tetrazolium chloride (NBT) is identified as an efficient leveler for copper microvia superfilling. A multiscale strategy—combining electrochemical measurements, X-ray photoelectron spectroscopy (XPS), density functional theory (DFT) calculations, and molecular dynamics (MD) simulations—is employed to elucidate the action mechanism of NBT and pinpoint its electroactive sites. Electrochemical tests show that NBT markedly suppresses copper deposition and, together with polyethylene glycol (PEG), effectively resists competitive adsorption by bis-(3-sulfopropyl) disulfide (SPS), thereby enhancing the microvia superfilling performance of the PEG–SPS–NBT additive system. DFT results reveal that the nitro groups and tetrazolium rings constitute the primary adsorption centers on the copper surface; the nitro groups additionally strengthen intermolecular interactions between NBT and PEG. MD simulations further confirm that NBT anchors onto the Cu(111) surface predominantly through these NO₂ groups and the tetrazolium ring, while co-adsorbed PEG enhances the overall adsorption strength of NBT. The electroplating experiment demonstrates that NBT can act as an effective leveler for microvia superfilling. Moreover, XPS analyses further confirm the synergistic co-adsorption of NBT and PEG and verify that the NO₂ groups and tetrazolium rings are the dominant adsorption sites of NBT. Collectively, the electroplating, XPS, electrochemical, DFT, and MD findings clarify the structure–activity relationship of NBT and provide rational guidelines for designing next-generation copper-plating levelers. Full article

The remaining lifetime of the cable insulation is an important but hard topic for the industry and research groups as there are more and more cables nearing their designed life in China. However, it is hard to accurately and efficiently obtain the ageing characteristic parameters of cross-linked polyethylene (XLPE) cable insulation. This study systematically analyzes the evolution of the remaining insulation lifetime of XLPE cables under different ageing states using the step-stress method combined with the inverse power model (IPM) and a physical-driven model (Crine model). By comparing un-aged and accelerated-aged specimens, the step-stress breakdown tests were conducted to obtain the Weibull distribution characteristics of breakdown voltage and breakdown time. Experimental results demonstrate that the characteristic breakdown field strength and remaining lifetime of the specimens decrease significantly with prolonged ageing. The ageing parameter of the IPM was calculated. It is found that the ageing parameter of IPM increases with the ageing time. However, it can hardly link to the other properties or physic parameters of the material. The activation energy and electron acceleration distance of the Crine model were also calculated. It is found that ageing activation energy stays almost the same in samples with different ageing time, showing that it is a material intrinsic parameter that will not change with the ageing; the electron acceleration distance increases with the ageing time, it makes sense that the ageing process may break the molecule chain of XLPE and increase the size of the free volume. It shows that the Crine model can better fit the physic process of ageing in theory and mathematic, and the acceleration distance of the Crine model is a physical driven parameter that can greatly reflect the ageing degree of the cable insulation and be used as an indicator of the ageing states. Full article

Volatile Organic Compounds (VOCs) are pervasive environmental pollutants with significant implications for air quality and human health. The development of effective technologies for VOC degradation is essential to mitigate their adverse effects. Microwave plasma technology has emerged as a promising solution for VOC abatement due to its ability to generate highly reactive species at ambient conditions, enabling efficient decomposition of VOCs into harmless byproducts. Concurrently, Density Functional Theory (DFT) has become a critical tool for understanding the molecular-level mechanisms of VOC degradation, providing insights into reaction pathways and energy dynamics. This study explores the integration of microwave plasma experiments with DFT simulations to investigate the degradation mechanisms of VOCs under plasma conditions. DFT calculations of microwave plasma degradation for toluene are performed. The results show that on the one hand, toluene can undergo ring-opening. Then, these active molecules or groups react with active free radicals and are ultimately oxidized into CO₂ and H₂O. On the other hand, VOC gas molecules react with active free radicals (O, OH) generated by background gas (O₂ and H₂O) through oxidation reactions, generating organic intermediates such as benzene, benzyl alcohol, and benzoic acid, respectively, which are finally oxidized into CO₂ and H₂O. Our theoretical research results are expected to provide profound insights into the degradation mechanisms of these aromatic hydrocarbon VOCs through microwave plasma and also contribute to a better understanding of the further degradation mechanisms of air pollutants at the molecular level. Full article

Utilizing isomeric monomers to construct covalent organic frameworks (COFs) could easily and precisely regulate their structure in order to raise the photocatalytic performance towards two-step single-electron oxygen reduction reaction (ORR) to hydrogen peroxide (H₂O₂). Herein, isomeric anthraquinone (AQ)-based COFs (designated as 1,4-DQTP and 2,6-DQTP) were successfully fabricated through a simple yet effective one-step solvothermal synthesis approach, only utilizing isomeric monomers with alterations in the catalysts. Specifically, the black 1,4-DQTP displayed a high photocatalytic H₂O₂ production rate of 865.4 µmol g⁻¹ h⁻¹, with 2.44-fold enhancement compared to 2,6-DQTP (354.7 µmol g⁻¹ h⁻¹). Through a series of experiments such as electron paramagnetic resonance (EPR) spectroscopy and the free radical quenching experiments, as well as density functional theory (DFT) calculations, the photocatalytic mechanism revealed that compared with 2,6-DQTP, 1,4-DQTP possessed a stronger and broader visible light absorption capacity, and thus generated more photogenerated e⁻-h⁺ pairs. Ultimately, more photogenerated electrons were enriched on the AQ motif via a more apparent electron push–pull effect, which provided a stable transfer channel for e⁻ and thus facilitated the generation of superoxide anion radical intermediates (•O₂⁻). On the other hand, the negative charge region of AQ’s carbonyl group evidently overlapped with that of TP, indicating that 1,4-DQTP had a higher chemical affinity for the uptake of protons, and thus afforded a more favorable hydrogen donation for H⁺. As a consequence, the rational design of COFs utilizing isomeric monomers could synergistically raise the proton-coupled electron transfer (PCET) kinetics for two-step single-electron ORR to H₂O₂ under visible light illumination. This work provides some insights for the design and fabrication of COFs through rational isomer engineering to modulate their photocatalytic activities. Full article

The electrocatalytic CO₂ reduction reaction (CO₂RR) into value-added multi-carbon C₂₊ products holds significant promise for sustainable chemical synthesis and carbon-neutral energy cycles. Among the various strategies developed to enhance CO₂RR, the use of ionic liquids (ILs) has emerged as a powerful approach for modulating the local microenvironment and electronic structure of Cu-based metal catalysts. In this study, to unravel the molecular-level mechanisms underlying these enhancements, density functional theory calculations (DFTs) were employed to systematically explore how ILs with different terminal groups modulate the electronic reconstruction of the Cu surface, further affecting the *CO–*CO coupling and product selectivity. Electronic structure analyses reveal that ILs bearing polar moieties (–SH, –COOH) can synergistically enhance the interfacial electron accumulation and induce an upshift of the Cu d-band center, thereby strengthening *CO adsorption. In contrast, nonpolar IL (CH₃) exhibits negligible effects, underscoring the pivotal role of ILs’ polarity in catalyst surface-state engineering. The free energy diagrams and transition state analyses reveal that ILs with polar groups significantly lower both the reaction-free energy and activation barrier associated with the *CO–*CO coupling step. This energetic favorability selectively inhibits the C₁ product pathways and hydrogen evolution reaction (HER), further improving the selectivity of C₂ products. These theoretical insights not only unveil the mechanistic origins of IL-induced performance enhancement but also offer predictive guidance for the rational design of advanced IL–catalyst systems for efficient CO₂ electroreduction. Full article

An analytical hydroelastic model formulation in three-dimensional and oblique wave cases is developed to analyze the dynamic response of a horizontal, floating elastic plate subject to wave-current interaction under linearized small-amplitude wave theory. The floating elastic plate is moored to the bottom bed and free to the channel walls. Green’s function’s technique is utilised to determine the dispersion relation in 3D, and the series form of Green’s function in different water depths is derived in the oblique wave case. Further, the comparative analysis of phase and group velocities for different wave angles, between the present the existing models, is discussed. The derived dispersion relation is used in the solution by applying the geometrical symmetry velocity decomposition method. The present theoretical results of wave quantities are validated with the recently published and existing numerical hydroelastic model. A comparative analysis revealed a 1.7% difference between the present model and the existing hydroelastic models, and a 7.7% difference when compared to the model’s limiting cases. Several numerical results of the wave quantities, wave force, and vertical displacements are conducted to investigate the influence of current velocity on the hydroelastic response in three dimensions. It has been noted that the value of reflection coefficient diminishes for larger values of current velocity and the vertical displacement correspondingly becomes greater. This analysis will inform the design of elastic plate-based wave energy converters and breakwaters by clarifying how current loads affect the hydroelastic of a floating elastic plate with an oblique angle and three dimensions. Full article

The rational development of single-atom catalysts (SACs) for selective formic acid dehydrogenation (FAD) requires an atomic-scale understanding of metal–support interactions and electronic modulation. In this study, spin-polarized density functional theory (DFT) calculations were performed to systematically examine platinum-group SACs anchored on graphitic carbon nitride (g-C₃N₄). The findings reveal that Pd and Au SACs exhibit superior selectivity toward the dehydrogenation pathway, lowering the free energy barrier by 1.42 eV and 1.39 eV, respectively, compared to the competing dehydration route. Conversely, Rh SACs demonstrate limited selectivity due to nearly equivalent energy barriers for both reaction pathways. Stability assessments indicate robust metal–support interactions driven by d–p orbital hybridization, while a linear correlation is established between the d-band center position relative to the Fermi level and catalytic selectivity. Additionally, charge transfer (ranging from 0.029 to 0.467 e) substantially modulates the electronic structure of the active sites. These insights define a key electronic descriptor for SAC design and offer a mechanistic framework for optimizing selective hydrogen production. Full article