Search Results (322)

The quanta-to-energy ratio plays a crucial role in converting energy units to quantum units in the context of photosynthetically active radiation (PAR). Despite its widespread use, the effects of atmospheric particles and solar zenith angle (SZA) on the quanta-to-energy ratio remain unclear. In this study, both simulation and observation data revealed that the principal wavelength, which can be transformed into the quanta-to-energy ratio using a constant, exhibits a slow initial growth, followed by a rapid increase beyond 60° solar zenith angles and a subsequent dramatic decrease after reaching its maximum value. The measured quanta-to-energy ratio demonstrates a variable range of less than 3% for SZA under 70° in a cloudless atmosphere, with significant changes only occurring at zenith angles above 80°. Simulation data indicate that ozone, wind speed, surface-level pressure, surface air temperature, and relative humidity have negligible effects on the quanta-to-energy ratio. The Ångstrom exponent exerts a minor influence on the quanta-to-energy ratio by affecting diffuse radiation. Visibility, however, is found to have a substantial impact on the quanta-to-energy ratio. As a result, two relationships are established, linking the principal wavelength to visibility and the diffuse fraction of PAR. The principal wavelength serves as an effective measure of solar spectrum variability, remaining unaffected by radiation energy. This implies that atmospheric parameters which do not alter the solar spectrum will not influence the principal wavelength. The strong correlations between the principal wavelength, visibility, and the diffuse fraction of PAR suggest a broader range of applications for the principal wavelength in various research domains, opening up new avenues for exploration and potential contributions to numerous fields. Full article

Background/Objectives: In critically ill patients, achieving a mean arterial pressure (MAP) of 65 mmHg is a recommended resuscitation goal to ensure proper tissue oxygenation. Unfortunately, some patients do not benefit from providing such a value, suggesting that other indices are needed for better hemodynamic assessment. Capillary refill time (CRT) has emerged as an established marker for peripheral perfusion and a therapeutic target in critical illness, but its relationship with other exponents of hypoperfusion during vasopressor support after resuscitation period still warrants further research. This study aimed to investigate whether in critically ill patients after initial resuscitation, CRT would provide information independent of other, readily accessible hemodynamic variables. Methods: Critically ill patients who were mechanically ventilated after the resuscitation period and receiving vasopressors were prospectively studied between December 2022 and June 2023. Vasopressor support was measured using norepinephrine equivalent doses (NEDs). CRT, MAP and NED were assessed simultaneously and analyzed using Spearman’s rank correlation. Results: A total of 92 patients were included and 210 combined MAP-CRT-NED-Lactate records were obtained. There was no correlation between CRT and MAP (R = −0.1, p = 0.14) or lactate (R = 0.11, p = 0.13), but there was a positive weak correlation between CRT and NED (R = 0.25, p = 0.0005). In patients with hypotension, in 83% of cases (15/18), CRT was within normal range, despite different doses of catecholamines. When assessing patients with high catecholamine doses, in 58% cases (11/19), CRT was normal and MAP was usually above 65 mmHg. Conclusions: Capillary refill time provides additional hemodynamic information that is not highly related with the values of mean arterial pressure, lactate level and vasopressor doses. It could be incorporated into routine physical examination in critically ill patients who are beyond initial resuscitation. Full article

The field of wireless communication has undergone revolutionary changes driven by technological advancements in recent years. Central to this evolution is wireless ad hoc networks, which are characterized by their decentralized nature and have introduced numerous possibilities and challenges for researchers. Moreover, most of the existing Internet of Things (IoT) networks are based on ad hoc networks. This study focuses on the exploration of interference management and Medium Access Control (MAC) schemes. Through statistical derivations and systematic simulations, we evaluate the efficacy of guard zone-based MAC protocols under Rayleigh fading channel conditions. By establishing a link between network parameters, interference patterns, and MAC effectiveness, this work contributes to optimizing network performance. A key aspect of this study is the investigation of optimal guard zone parameters, which are crucial for interference mitigation. The adaptive guard zone scheme demonstrates superior performance compared to the widely recognized Carrier Sense Multiple Access (CSMA) and the system-wide fixed guard zone protocol under fading channel conditions that mimic real-world scenarios. Additionally, simulations reveal the interactions between network variables such as node density, path loss exponent, outage probability, and spreading gain, providing insights into their impact on aggregated interference and guard zone effectiveness. Full article

We establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. The SDGs have q players and are driven by a general-dimensional vector Lévy process. By establishing a vector-form Ito-Ventzell formula and a 4-tuple vector-field solution to the unified SPDE, we obtain a Pareto optimal Nash equilibrium policy process or a saddle point policy process to the SDG in a non-zero-sum or zero-sum sense. The unified SPDE is in both a general-dimensional vector form and forward–backward coupling manner. The partial differential operators in its drift, diffusion, and jump coefficients are in time-variable and position parameters over a domain. Since the unified SPDE is of general nonlinearity and a general high order, we extend our recent study from the existing Brownian motion (BM)-driven backward case to a general Lévy-driven forward–backward coupled case. In doing so, we construct a new topological space to support the proof of the existence and uniqueness of an adapted solution of the unified SPDE, which is in a 4-tuple strong sense. The construction of the topological space is through constructing a set of topological spaces associated with a set of exponents $\{{\gamma }_1,{\gamma }_2,\dots \}$ under a set of general localized conditions, which is significantly different from the construction of the single exponent case. Furthermore, due to the coupling from the forward SPDE and the involvement of the discontinuous Lévy jumps, our study is also significantly different from the BM-driven backward case. The coupling between forward and backward SPDEs essentially corresponds to the interaction between noise encoding and noise decoding in the current hot diffusion transformer model for generative AI. Full article

This study introduces an empirical model designed to predict the maximum values of time-dependent data across four turbulence-related fields: hydrogen combustion in renewable energy systems, urban microclimate effects on cultural heritage, shipping emissions, and road vehicle emissions. The model, which is based on the mean, standard deviation, and integral time scale, employs two parameters: a fixed exponent ‘ν’ (0.3) reflecting time scale sensitivity, and a variable parameter ‘b’ that accounts for application-specific uncertainties. Integrated into the Computational Fluid Dynamics (CFD) framework, specifically the Reynolds-Averaged Navier–Stokes (RANS) methodology, the model addresses the RANS approach’s limitation in predicting extreme values due to its inherent averaging process. By incorporating the empirical model, this study enhances RANS simulations’ ability to predict critical values, such as peak hydrogen concentrations and maximum urban wind speeds, which is essential for safety and reliability assessments. Validation against experimental and numerical data across the four fields demonstrates strong agreement, highlighting the model’s potential to improve CFD-RANS predictions of extreme events. This advancement offers significant implications for future CFD-RANS applications, particularly in scenarios demanding fast and reliable maximum value predictions. Full article

Olivine-like NaFePO₄ glasses and nanocomposites are promising materials for cathodes in sodium batteries. Our previous studies focused on the preparation of NaFePO₄ glass, transforming it into a nanocomposite using high-pressure–high-temperature treatment, and comparing both materials’ structural, thermal, and DC electric conductivity. This work focuses on specific features of AC electric conductivity, containing messages on the dynamics of translational processes. Conductivity spectra measured at various temperatures are scaled by apparent DC conductivity and plotted against frequency scaled by DC conductivity and temperature in a so-called master curve representation. Both glass and nanocomposite conductivity spectra are used to test the (effective) exponent using Jonscher’s scaling law. In both materials, the values of exponent range from 0.3 to 0.9, with different relation to temperature. It corresponds to the electronic conduction mechanism change from low-temperature Mott’s variable range hopping (between Fe²⁺/Fe³⁺ centers) to phonon-assisted hopping, which was suggested by previous DC measurements. Following the pressure treatment, AC conductivity activation energies were reduced from $E_{AC}\approx 0.40 \mathrm{e}\mathrm{V}$ for glass to $E_{AC}\approx 0.18 \mathrm{e}\mathrm{V}$ for nanocomposite and are lower than their DC counterpart, following a typical empirical relation with the value of the exponent. While pressure treatment leads to a 2–3-orders-of-magnitude rise in the AC and apparent DC conductivity due to the reduced distance between the hopping centers, a nonmonotonic relation of AC power exponent and temperature is observed. It occurs due to the disturbance of polaron interactions with Na⁺ mobile ions. Full article

The atmosphere is a complex nonlinear system, with the information of its temperature, water vapor, pressure, and cloud being crucial aspects of remote-sensing data analysis. There exist intricate interactions among these internal components, such as convection, radiation, and humidity exchange. Atmospheric phenomena span multiple spatial and temporal scales, from small-scale thunderstorms to large-scale events like El Niño. The dynamic interactions across different scales, along with external disturbances to the atmospheric system, such as variations in solar radiation and Earth surface conditions, contribute to the chaotic nature of the atmosphere, making long-term predictions challenging. Grasping the intrinsic chaotic dynamics is essential for advancing atmospheric analysis, which holds profound implications for enhancing meteorological forecasts, mitigating disaster risks, and safeguarding ecological systems. To validate the chaotic nature of the atmosphere, this paper reviewed the definitions and main features of chaotic systems, elucidated the method of phase space reconstruction centered on Takens’ theorem, and categorized the qualitative and quantitative methods for determining the chaotic nature of time series data. Among quantitative methods, the Wolf method is used to calculate the Largest Lyapunov Exponents, while the G–P method is used to calculate the correlation dimensions. A new method named Improved Saturated Correlation Dimension method was proposed to address the subjectivity and noise sensitivity inherent in the traditional G–P method. Subsequently, the Largest Lyapunov Exponents and saturated correlation dimensions were utilized to conduct a quantitative analysis of FY-4A and Himawari-8 remote-sensing infrared observation data, and ERA5 reanalysis data. For both short-term remote-sensing data and long-term reanalysis data, the results showed that more than 99.91% of the regional points have corresponding sequences with positive Largest Lyapunov exponents and all the regional points have correlation dimensions that tended to saturate at values greater than 1 with increasing embedding dimensions, thereby proving that the atmospheric system exhibits chaotic properties on both short and long temporal scales, with extreme sensitivity to initial conditions. This conclusion provided a theoretical foundation for the short-term prediction of atmospheric infrared radiation field variables and the detection of weak, time-sensitive signals in complex atmospheric environments. Full article

This study developed more realistic stochastic models of pipe failures that incorporate leak types and dimensions based on different pipe materials. The distributions of pipe failure types and properties were identified by analysing photographic records of failed pipes in Auckland, New Zealand. A stochastic model generated leaks in a typical DMA consisting of different pipe materials to different Infrastructure Leakage Index (ILI) levels. After analysing 100 networks for each scenario, the study observed that different pipe materials had distinct leakage exponent distributions. This study provides a tool for better understanding leakage behaviour in different pipe materials and evaluating methods for better water loss management. Full article

Function spaces play a crucial role in the study and application of mathematical inequalities. They provide a structured framework within which inequalities can be formulated, analyzed, and applied. They allow for the extension of inequalities from finite-dimensional spaces to infinite-dimensional contexts, which is crucial in mathematical analysis. In this note, we develop various new bounds and refinements of different well-known inequalities involving Hilbert spaces in a tensor framework as well as mixed Moore norm spaces with variable exponents. The article begins with Newton–Milne-type inequalities for differentiable convex mappings. Our next step is to take advantage of convexity involving arithmetic–geometric means and build various new bounds by utilizing self-adjoint operators of Hilbert spaces in tensorial frameworks for different types of generalized convex mappings. To obtain all these results, we use Riemann–Liouville fractional integrals and develop several new identities for these operator inequalities. Furthermore, we present some examples and consequences for transcendental functions. Moreover, we developed the Hermite–Hadamard inequality in a new and significant way by using mixed-norm Moore spaces with variable exponent functions that have not been developed previously with any other type of function space apart from classical Lebesgue space. Mathematical inequalities supporting tensor Hilbert spaces are rarely examined in the literature, so we believe that this work opens up a whole new avenue in mathematical inequality theory. Full article

This paper is concerned with the following $L^2$-subcritical Kirchhoff-type equation $-\left(a+b{\left({\int }_{{\mathbb{R}}^2}{|\nabla u|}^{2}dx\right)}^s\right)\Delta u+V\left(x\right)u=\mu u+\beta {\left|u\right|}^{2}u,x\in {\mathbb{R}}^2$, with ${\int }_{{\mathbb{R}}^2}{\left|u\right|}^{2}dx=1$. We give a detailed analysis of the limit property of the $L^2$-normalized solution when exponent s tends toward 0 from the right (i.e., $s\searrow 0$). Our research extends previous works, in which the authors have displayed the limit behavior of $L^2$-normalized solutions when $s=1$ as $a\searrow 0$ or $b\searrow 0$. Full article

In dynamical systems, Hilbert spaces provide a useful framework for analyzing and solving problems because they are able to handle infinitely dimensional spaces. Many dynamical systems are described by linear operators acting on a Hilbert space. Understanding the spectrum, eigenvalues, and eigenvectors of these operators is crucial. Functional analysis typically involves the use of tensors to represent multilinear mappings between Hilbert spaces, which can result in inequality in tensor Hilbert spaces. In this paper, we study two types of function spaces and use convex and harmonic convex mappings to establish various operator inequalities and their bounds. In the first part of the article, we develop the operator Hermite–Hadamard and upper and lower bounds for weighted discrete Jensen-type inequalities in Hilbert spaces using some relational properties and arithmetic operations from the tensor analysis. Furthermore, we use the Riemann–Liouville fractional integral and develop several new identities which are used in operator Milne-type inequalities to develop several new bounds using different types of generalized mappings, including differentiable, quasi-convex, and convex mappings. Furthermore, some examples and consequences for logarithm and exponential functions are also provided. Furthermore, we provide an interesting example of a physics dynamical model for harmonic mean. Lastly, we develop Hermite–Hadamard inequality in variable exponent function spaces, specifically in mixed norm function space (${\mathcal{l}}^{\mathtt{q}(·)}\left({\mathtt{L}}^{\mathtt{p}(·)}\right)$). Moreover, it was developed using classical Lebesgue space (${\mathtt{L}}_{\mathtt{p}}$) space, in which the exponent is constant. This inequality not only refines Jensen and triangular inequality in the norm sense, but we also impose specific conditions on exponent functions to show whether this inequality holds true or not. Full article

The existence of multiple pairs of smooth positive solutions for a Carrier problem, driven by a $p\left(x\right)$-Laplacian operator, is studied. The approach adopted combines sub-super solutions, truncation, and variational techniques. In particular, after an explicit computation of a sub-solution, obtained combining a monotonicity type hypothesis on the reaction term and the Giacomoni–Takáč’s version of the celebrated Díaz–Saá’s inequality, we derive a multiplicity of solution by investigating an associated one-dimensional fixed point problem. The nonlocal term involved may be a sign-changing function and permit us to obtain the existence of multiple pairs of positive solutions, one for each “positive bump” of the nonlocal term. A new result, also for a constant exponent, is established and an illustrative example is proposed. Full article

This study looks closely into the analysis of the variation of constants formula given by $\Phi \left(t\right)=S\left(t\right)\Phi \left(0\right)+{\int }_0^{t}S(t-\sigma )\mathcal{F}(\sigma ,\Phi \left(\sigma \right))d\sigma ,$ for $t\in [0,T],T>0$, within the context of modular function spaces $L_{\rho }$. Additionally, this research explores practical applications of the variation of constants formula in variable exponent Lebesgue spaces $L^{p(·)}$. Specifically, the study examines these spaces under certain conditions applied to the exponent function $p(·)$ and the functions $\mathcal{F}$ as well as the semigroup $S\left(t\right)$, utilizing the symmetry properties of the algebraic semigroup. This investigation sheds light on the intricate interplay between parameters and functions within these mathematical frameworks, offering valuable insights into their behavior and properties in $L^{p(·)}$. Full article

This paper introduces hybrid models designed to analyze daily and weekly bitcoin return spanning the periods from 18 July 2010 to 28 December 2023 for daily data, and from 18 July 2010 to 24 December 2023 for weekly data. Firstly, the fractal and chaotic structure of the selected variables was explored. Asymmetric Cantor set, Boundary of the Dragon curve, Julia set z² −1, Boundary of the Lévy C curve, von Koch curve, and Brownian function (Wiener process) tests were applied. The R/S and Mandelbrot–Wallis tests confirmed long-term dependence and fractionality. The largest Lyapunov test, the Rosenstein, Collins and DeLuca, and Kantz methods of Lyapunov exponents, and the HCT and Shannon entropy tests tracked by the Kolmogorov–Sinai (KS) complexity test determined the evidence of chaos, entropy, and complexity. The BDS test of independence test approved nonlinearity, and the TeraesvirtaNW and WhiteNW tests, the Tsay test for nonlinearity, the LR test for threshold nonlinearity, and White’s test and Engle test confirmed nonlinearity and heteroskedasticity, in addition to fractionality and chaos. In the second stage, the standard ARFIMA method was applied, and its results were compared to the LieNLS and LieOLS methods. The results showed that, under conditions of chaos, entropy, and complexity, the ARFIMA method did not yield successful results. Both baseline models, LieNLS and LieOLS, are enhanced by integrating them with deep learning methods. The models, LieLSTMOLS and LieLSTMNLS, leverage manifold-based approaches, opting for matrix representations over traditional differential operator representations of Lie algebras were employed. The parameters and coefficients obtained from LieNLS and LieOLS, and the LieLSTMOLS and LieLSTMNLS methods were compared. And the forecasting capabilities of these hybrid models, particularly LieLSTMOLS and LieLSTMNLS, were compared with those of the main models. The in-sample and out-of-sample analyses demonstrated that the LieLSTMOLS and LieLSTMNLS methods outperform the others in terms of MAE and RMSE, thereby offering a more reliable means of assessing the selected data. Our study underscores the importance of employing the LieLSTM method for analyzing the dynamics of bitcoin. Our findings have significant implications for investors, traders, and policymakers. Full article