Search Results (162)

A data set on Stark broadening parameters defining the Lorentzian line profile (spectral line widths and shifts) for 31 multiplets of four-times-charged nitrogen ion (N V), with lines broadened by impacts with electrons (e), protons (p), He II ions, $\alpha$ particles (He III), and B III, B IV, B V, and B VI ions, is given. The above-mentioned data have been calculated within the frame of the semiclassical perturbation theory, for temperatures from 50,000 K to 1,000,000 K, and densities of perturbers from 10¹⁵ cm⁻³ up to 10²¹ cm⁻³. These data are, first of all, of interest for diagnostics and modeling of laser-driven plasma in experiments and investigations of proton–boron fusion, especially when the target is boron nitride (BN). Data on Stark broadening by collisions with e, p, He II ions, and $\alpha$ particles are useful for the investigation of stellar plasma, in particular for white dwarf atmospheres and subphotospheric layer modeling. Full article

The principles of least effort and the illusion of control may influence the decision-making process. It is challenging for a decision-maker to maintain complete independence when assessing the membership and non-membership degrees of indicators. However, existing neutrosophic sets and q-rung orthopair fuzzy sets assume full independence of such information. In view of this, this paper proposes a new neutrosophic set, namely the q-type semi-dependent neutrosophic set (QTSDNS), based on the classical neutrosophic set, whose membership and non-membership degrees are interrelated. QTSDNS is a generalized form of classical semi-dependent fuzzy sets, such as the intuitionistic neutrosophic set. It contains a regulatory parameter, which allows for decision-makers to flexibly adjust the model. Furthermore, a multi-attribute group decision-making (MAGDM) algorithm is proposed by integrating QTSDNS with evidence theory to solve the supplier selection problem. The algorithm first utilizes QTSDNS to represent the preference information of experts, then employs the q-TSDNWAA (or q-TSDNWGA) operator to aggregate the evaluation information of individual experts. Following the analysis of the mathematical relationship between QTSDNS and evidence theory, evidence theory is used to aggregate the evidence from each expert to obtain the group trust interval. Then, the best supplier is determined using interval number ranking methods. Finally, a numerical example is provided to demonstrate the feasibility of the proposed method. Full article

The Lorentz-breaking theory not only modifies the geometric structure of curved spacetime but also significantly alters the quantum dynamics of bosonic and fermionic fields in black hole spacetime, leading to observable physical effects on Hawking temperature and Bekenstein–Hawking entropy. This study establishes the first systematic theoretical framework for entropy modifications of charged accelerating Anti-de Sitter black holes, incorporating gauge-invariant corrections derived from Lorentz-violating quantum field equations in curved spacetime. The obtained analytical expression coherently integrates semi-classical approximations with higher-order quantum perturbative contributions. Furthermore, the methodologies employed and the resultant conclusions are subjected to rigorous analysis, establishing their physical significance for advancing fundamental investigations into black hole entropy. Full article

This article investigates fundamental inequalities within a golden-like statistical manifold (GLSM) equipped with a semi-symmetric metric connection (SSMC). We explore key geometric and analytical properties, including curvature relations and inequalities analogous to those in classical information geometry. The interplay between the golden-like structure and the SSMC yields new insights into the underlying differential geometric framework. Our results extend known inequalities in the statistical manifold (SM), providing a foundation for further studies in optimization and divergence theory within this generalized framework. Full article

This paper investigates the structural properties of solutions of vector equilibrium systems and mixed variational inequalities in topological vector spaces. Based on Himmelberg-type fixed point theorem, combined with the analysis of set-valued mapping and quasi-monotone conditions, the existence criteria of solutions for two classes of generalized equilibrium problems with weak compactness constraints are constructed. This work introduces an innovative application of the measurable selection theorem of semi-continuous function space to eliminate the traditional compactness constraints, and provides a more universal theoretical framework for game theory and the economic equilibrium model. In the analysis of mixed variational problems, the topological stability of the solution set under the action of generalized monotone mappings is revealed by constructing a new KKM class of mappings and introducing the theory of pseudomonotone operators. In particular, by replacing the classical compactness assumption with pseudo-compactness, this study successfully extends the research boundary of scholars on variational inequalities, and its innovations are mainly reflected in the following aspects: (1) constructing a weak convergence analysis framework applicable to locally convex topological vector spaces, (2) optimizing the monotonicity constraint of mappings by introducing a semi-continuous asymmetric condition, and (3) in the proof of the nonemptiness of the solution set, the approximation technique based on the family of relatively nearest neighbor fields is developed. The results not only improve the theoretical system of variational analysis, but also provide a new mathematical tool for the non-compact parameter space analysis of economic equilibrium models and engineering optimization problems. This work presents a novel combination of measurable selection theory and pseudomonotone operator theory to handle non-compact constraints, advancing the theoretical framework for economic equilibrium analysis. Full article

This feature paper explores the comparative pedagogical roles of concrete and virtual manipulatives in preservice mathematics teacher education. Based on a design-based research (DBR) methodology, this study investigates the effects of tangible tools (e.g., base-ten blocks, fraction circles) and digital applications (e.g., GeoGebra Classic 6, Polypad) on preservice teachers’ problem solving, conceptual understanding, engagement, and instructional reasoning. Data were collected through surveys (n = 53), semi-structured interviews (n = 25), and classroom observations (n = 30) in a Spanish university’s teacher education program. Key findings show that both forms of manipulatives significantly enhance engagement and conceptual clarity, but are affected by logistical and digital access barriers. This paper further proposes a theoretically grounded model for simulating manipulatives through ICT-based environments, enabling scalable and adaptive mathematics teacher training. By linking constructivist learning theory, the Technologically Enhanced Learning Environment (TELE) framework, and simulation-based pedagogy, this model aims to replicate the cognitive, affective, and collaborative affordances of manipulatives in virtual contexts. Distinct from prior work, this study contributes an integrated theoretical and practical framework, contextualized through empirical classroom data, and presents a clear plan for real-world ICT-based implementation. The findings provide actionable insights for teacher educators, edtech developers, and policymakers seeking to expand equitable and engaging mathematics education through simulation and blended modalities. Full article

We investigate pseudo-complex General Relativity (pcGR)—a coordinate-extended formulation of General Relativity (GR)—within the framework of Hořava-Lifshitz gravity, a regularized theory featuring anisotropic scaling. The pcGR framework bridges GR with modified gravitational theories through the introduction of a minimal length scale. Focusing on Schwarzschild black holes, we derive the Wheeler-deWitt equation, obtaining a quantized description of pcGR. Using perturbative methods and semi-classical approximations, we analyze the solutions of the equations and their physical implications. A key finding is the avoidance of the central singularity due to nonlinear interaction terms in the Hořava-Lifshitz action. Notably, extrinsic curvature (kinetic energy) contributions prove essential for singularity resolution, even in standard GR. Furthermore, the theory offers new perspectives on dark energy, proposing an alternative mechanism for its accumulation. Full article

The entanglement entropy of a random tensor network (RTN) is studied using tools from free probability theory. Random tensor networks are simple toy models that help in understanding the entanglement behavior of a boundary region in the anti-de Sitter/conformal field theory (AdS/CFT) context. These can be regarded as specific probabilistic models for tensors with particular geometry dictated by a graph (or network) structure. First, we introduce a model of RTN obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). The entanglement spectrum of the resulting random state is analyzed along a given bipartition of the local Hilbert spaces. The limiting eigenvalue distribution of the reduced density operator of the RTN state is provided in the limit of large local dimension. This limiting value is described through a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, an explicit formula for the limiting eigenvalue distribution is provided using classical and free multiplicative convolutions. The physical implications of these results are discussed, allowing the analysis to move beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN. Full article

The zero-error capacity of discrete memoryless channels (DMCs), introduced by Shannon, is a fundamental concept in information theory with significant operational relevance, particularly in settings where even a single transmission error is unacceptable. Despite its importance, no general closed-form expression or algorithm is known for computing this capacity. In this work, we investigate the computability-theoretic boundaries of the zero-error capacity and establish several fundamental limitations. Our main result shows that the zero-error capacity of noisy channels is not Banach–Mazur-computable and therefore is also not Borel–Turing-computable. This provides a strong form of non-computability that goes beyond classical undecidability, capturing the inherent discontinuity of the capacity function. As a further contribution, we analyze the deep connections between (i) the zero-error capacity of DMCs, (ii) the Shannon capacity of graphs, and (iii) Ahlswede’s operational characterization via the maximum-error capacity of 0–1 arbitrarily varying channels (AVCs). We prove that key semi-decidability questions are equivalent for all three capacities, thus unifying these problems into a common algorithmic framework. While the computability status of the Shannon capacity of graphs remains unresolved, our equivalence result clarifies what makes this problem so challenging and identifies the logical barriers that must be overcome to resolve it. Together, these results chart the computational landscape of zero-error information theory and provide a foundation for further investigations into the algorithmic intractability of exact capacity computations. Full article

To address the limitations of existing wind turbine airfoil databases, the high computational cost, and low efficiency of noise prediction, this paper proposes a wind turbine airfoil noise prediction method based on generalized airfoil sets and residual neural networks. Firstly, taking a database of 31 commonly used wind turbine airfoils as a reference, a generalized airfoil set with diverse geometric contours was generated. This was achieved by employing airfoil functional integration theory, B-spline curves, and the Class function/Shape function Transformation (CST) method while varying coefficients and control vector parameters. Secondly, the BPM semi-empirical model was used to compute the noise for the generalized airfoil set, which served as the data labels for deep learning. Finally, classical machine learning models were utilized to construct the airfoil noise prediction model. The results demonstrate that the airfoil noise prediction model constructed with the residual neural network (ResNet-18) achieved the highest prediction accuracy, with a mean squared error (MSE) of 0.0282 and a coefficient of determination (R²) of 0.99972. Additionally, the trained model exhibited computational efficiency that was 17.5 times higher than the BPM model. Full article

It has been shown that at the present stage of the evolution of the universe, cosmological acceleration is an inevitable kinematical consequence of quantum theory in semiclassical approximation. Quantum theory does not involve such classical concepts as Minkowski or de Sitter spaces. In classical theory, when choosing Minkowski space, a vacuum catastrophe occurs, while when choosing de Sitter space, the value of the cosmological constant can be arbitrary. On the contrary, in quantum theory, there is no uncertainties in view of the following: (1) the de Sitter algebra is the most general ten-dimensional Lie algebra; (2) the Poincare algebra is a special degenerate case of the de Sitter algebra in the limit $R\to \infty$ where R is the contraction parameter for the transition from the de Sitter to the Poincare algebra and R has nothing to do with the radius of de Sitter space; (3) R is fundamental to the same extent as c and ℏ: c is the contraction parameter for the transition from the Poincare to the Galilean algebra and ℏ is the contraction parameter for the transition from quantum to classical theory; (4) as a consequence, the question (why the quantities (c, ℏ, R) have the values which they actually have) does not arise. The solution to the problem of cosmological acceleration follows on from the results of irreducible representations of the de Sitter algebra. This solution is free of uncertainties and does not involve dark energy, quintessence, and other exotic mechanisms, the physical meaning of which is a mystery. Full article

Data on spectral line widths and shifts broadened by interactions with charged particles, for 44 lines in the spectrum of ionized tin, for collisions with electrons and H II and HeII ions, are presented as online available tables. We obtained them by employing the semiclassical perturbation theory for temperatures, T, within the 5000–100,000 K range, and for a grid of perturber densities from 10¹⁴ cm⁻³ to 10²⁰ cm⁻³. The presented Stark broadening data are of interest for the analysis and synthesis of ionized tin lines in the spectra of hot and dense stars, such as, for example, for white dwarfs and hot subwarfs, and for the modelling of their atmospheres. They are also useful for the diagnostics of laser-induced plasmas for high-order harmonics generation in ablated materials. Full article

Long-range electron transfer (ET) is an essential component of all biological systems. Reactions of metalloproteins are important in this context. Recent work on protein “charge ladders” has revealed how the redox state of embedded metal ions can influence the ionization of amino acid residues at protein surface sites. Inspired by these observations, we carried out a variable pH investigation of intramolecular ET reactions in a ruthenium-modified protein system built on azurin from Pseudomonas aeruginosa. We also generate a Pourbaix diagram that describes the variable pH redox behavior of a Ru model complex, Ru(2,2′-bipyridyl)₂(imidazole)₂(PF₆)₂. The intramolecular ET rate constants for the oxidation of azurin-Cu⁺ by flash-quench-generated Ru³⁺ oxidants do not follow the predictions of the semi-classical ET rate expression with fixed values of reorganization energy (λ) and electronic coupling (H_DA). Based on the pH dependence of the Ru^3+/2+ redox couple, we propose a model where pure ET is operative at acidic pH values (≤ 7) and the mechanism changes to proton-coupled electron transfer at pH ≥ 7.5. The implications of this mechanistic proposal are discussed in the context of biological redox reactions and with respect to other examples of intramolecular ET reactions in the literature. Full article

Optimising existing knowledge sets and encouraging the integration of interdisciplinary study findings can facilitate the advanced functions of biodiversity required for sustainable urban landscapes. Urban Green Spaces (UGS) can reach across an urban landscape, including indoor environments. The existing and traditional knowledge sets and practices for urban development and greening provide extensive and pertinent guidance; they are however variably implemented. More recent and advanced knowledge sets where properly utilised can optimise and provide advanced function. When adequately brought together, advanced sustainability for urban landscapes can significantly improve global sustainability performance. This article uses the final step of classic grounded theory to contextualise, verify and define refined wilding as a substantiating concept for functional biodiversity as theory for urban landscapes and for sustainable urban development. Refined wilding works toward wild refined UGS that functionally connect across an urban space and landscape, including positive influential flows with grey and transparent spaces. Where used to guide urban design, strategies, vision and goals this concept can provide (i) a conceptual framing that optimises and encourages an organisation of interdisciplinary and advanced knowledge, improving and advancing sustainable urban development, and (ii) a specificity, and overarching and comprehensive guidance for various UGS types toward the positive outcome of functional biodiversity. Functionally biodiverse UGS and landscapes require lower maintenance and perform at an advanced level for human health, economic development, the natural environment, and built or paved environments and landscapes. In turn, addressing how human activity and modification of urban landscapes can significantly degrade human health and the natural environment, or underachieve. Refined wilding (i) substantiates functional biodiversity as a positive outcome for urban landscapes, with a balance between ecological functions and functions for human populations; (ii) considers quality, function, and connectivity of and between UGS and spaces where UGS could be introduced or improved; (iii) enables an improvement, and addresses common barriers to UGS accomplishing advanced functions for urban sustainability; (iv) encourages urban wilding by functional native and non-native selections, and natural and semi-natural UGS; (v) positively influences and is influenced by grey (built environment) and transparent spaces (blue/aquatic and air). Full article

In the present paper, we revisit the determination of Feshbach resonances in the elastic and fine-structure cross-sections of the spectral lines of ionized atoms colliding with electrons. The Gailitis approximation will be recalled and used to calculate the Feshbach resonances. A historical point of view will be used, emphasizing the interest of interdisciplinary research, with a back and forth between physics and astrophysics. First, the theory of Feshbach (arising at end of the 1950s and beginning of the 1960s) resonances will be briefly recalled and applied to the calculation of the cross-sections. In the beginning of the 1970s, the insertion of Feshbach resonances in spectroscopic diagnostics calculations permitted researchers to interpret the intensities of solar coronal lines. Then, in the middle of the 1970s, this gave rise to the idea of including the Feshbach resonances in the calculation of electron impact broadening (the so-called “Stark” broadening) of isolated spectral lines of ionized atoms. Finally, in the recent example of the Stark broadening of the Mo VI $5\mathrm{d} {}^2\mathrm{D}_{5/2}-5\mathrm{p} {}^{2}P°_{3/2}$ line, the S-matrices will be calculated using the semi-classical perturbation formalism and will be compared to those of the more recent quantum distorted wave formalism. Full article