Search Results (1,828)

Simultaneous values of glucose rate of change (RoC) and glucose can be presented in a dynamic glucose region plot, and risk spaces can be specified for (RoC, glucose) values expected to remain in the target range (glucose 3.9–10.0 mmol/L) or leave or return to the target range within the next 30 min. We downloaded continuous glucose monitoring (CGM) data for 60 days from persons with type 1 diabetes using two different systems for automated insulin delivery (AID), A (n = 65) or B (n = 85). The relative distribution of (RoC, glucose) values in risk spaces was compared. The fraction of all (RoC, glucose) values anticipated to remain in the target range in the next 30 min was higher with system A (62.5%) than with system B (56.8%) (difference 5.7, 95% CI (2.2–9.2%), p = 0.002). The fraction of (RoC, glucose) values in the target range with a risk of progressing to the above range (glucose > 10.0 mmol/L) was slightly lower in system A than in B (difference −1.1 (95% CI: −1.8–−0.5%, p < 0.001). Dynamic glucose region plots and the concept of risk spaces are novel strategies to obtain insight into glucose homeostasis and to demonstrate clinically relevant differences comparing two AID systems. Full article

In this paper, we study direct and inverse problems for a spatial-fractional Black–Scholes equation with space-dependent volatility. For the direct problem, we provide CN-WSGD (Crank–Nicholson and the weighted and shifted Grünwald difference) scheme to solve the initial boundary value problem. The latter aims to recover the implied volatility via observable option prices. Using a linearization technique, we rigorously derive a mathematical formulation of the inverse problem in terms of a Fredholm integral equation of the first kind. Based on an integral equation, an efficient numerical reconstruction algorithm is proposed to recover the coefficient. Numerical results for both problems are provided to illustrate the validity and effectiveness of proposed methods. Full article

Porous materials are characterized by the pore surface area (S) and volume (V) accessible to a confined fluid. For mesoporous materials NMR measurements of diffusion are used to assess the S/V ratio, because at short times, only the diffusivity of molecules in the adsorbed layer is affected by confinement and the fractional population of these molecules is proportional to the S/V ratio. For materials with sub-nanometer pores, this might not be true, as the adsorbed layer can encompass the entire pore volume. Here, using molecular simulations, we explore the role played by S and S/V in determining the dynamical behavior of two carbon-bearing fluids—CO₂ and ethane—confined in sub-nanometer pores of silica. S and V in a silicalite model representing a sub-nanometer porous material are varied by selectively blocking a part of the pore network by immobile methane molecules. Three classes of adsorbents were thus obtained with either all of the straight (labeled ‘S-major’) or zigzag channels (‘Z-major’) remaining open or a mix of a fraction of both types of channel blocked, resulting in half of the total pore volume being blocked (‘Half’). While the adsorption layers from opposite surfaces overlap, encompassing the entire pore volume for all pores except the intersections, the diffusion coefficient is still found to be reduced at high S/V, especially for CO₂, albeit not so strongly as would be expected in the case of wider pores. This is because of the presence of channel intersections that provide a wider pore space with non-overlapping adsorption layers. Full article

With the rapid proliferation of real-time digital communication, particularly in multimedia applications, securing transmitted image data has become a vital concern. While chaotic systems have shown strong potential for cryptographic use, most existing approaches rely on low-dimensional, integer-order architectures, limiting their complexity and resistance to attacks. Advances in fractional calculus and memristive technologies offer new avenues for enhancing security through more complex and tunable dynamics. However, the practical deployment of high-dimensional fractional-order memristive chaotic systems in hardware remains underexplored. This study addresses this gap by presenting a secure image transmission system implemented on a field-programmable gate array (FPGA) using a universal high-dimensional memristive chaotic topology with arbitrary-order dynamics. The design leverages four- and five-dimensional hyperchaotic oscillators, analyzed through bifurcation diagrams and Lyapunov exponents. To enable efficient hardware realization, the chaotic dynamics are approximated using the explicit fractional-order Runge–Kutta (EFORK) method with the Caputo fractional derivative, implemented in VHDL. Deployed on the Xilinx Artix-7 AC701 platform, synchronized master–slave chaotic generators drive a multi-stage stream cipher. This encryption process supports both RGB and grayscale images. Evaluation shows strong cryptographic properties: correlation of $-6.1081\times {10}^{-5}$, entropy of 7.9991, NPCR of 99.9776%, UACI of 33.4154%, and a key space of $2^{1344}$, confirming high security and robustness. Full article

Mud pulse telemetry (MPT) systems are a promising approach to transmitting downhole data to the ground. During transmission, the amplitudes of pressure waves decay exponentially with distance, and the channel is often frequency-selective due to reflection and multipath effect. To address these issues, this work proposes a fractional Fourier transform (FrFT)-based channel estimation and equalization method. Leveraging the energy aggregation of linear frequency-modulated signals in the fractional Fourier domain, the time delay and attenuation parameters of the multipath channel can be estimated accurately. Furthermore, a fractional Fourier domain equalizer is proposed to pre-filter the frequency-selective fading channel using fractionally spaced decision feedback equalization. The effectiveness of the proposed method is evaluated through a simulation analysis and field experiments. The simulation results demonstrate that this method can significantly reduce multipath effects, effectively control the impact of noise, and facilitate subsequent demodulation. The field experiment results indicate that the demodulation of real data achieves advanced data rate communication (over 12 bit/s) and a low bit error rate (below 0.5%), which meets engineering requirements in a 3000 m drilling system. Full article

The primary objective of this work is to develop a comprehensive theory of weighted fractional Sobolev spaces within the framework of timescales. To this end, we first introduce a novel class of weighted fractional operators and rigorously define associated weighted integrable spaces on timescales, generalising classical notions to this non-uniform temporal domain. Building upon these foundations, we systematically investigate the fundamental functional-analytic properties of the resulting Sobolev spaces. Specifically, we establish their completeness under appropriate norms, prove reflexivity under appropriate duality pairings, and demonstrate separability under mild conditions on the weight functions. As a pivotal application of our theoretical framework, we derive two robust existence theorems for solutions to the proposed model. These results not only extend classical partial differential equation theory to timescales but also provide a versatile tool for analysing dynamic systems with heterogeneous temporal domains. Full article

It is a well-known fact that the Dzhrbashyan–Nersesyan fractional derivative includes as particular cases the fractional derivatives of Riemann–Liouville, Gerasimov–Caputo, and Hilfer. The notion of resolving a family of operators for a linear equation with the Dzhrbashyan–Nersesyan fractional derivative is introduced here. Hille–Yosida-type theorem on necessary and sufficient conditions of the existence of a strongly continuous resolving family of operators is proved using Phillips-type approximations. The conditions concern the location of the resolvent set and estimates for the resolvent of a linear closed operator A at the unknown function in the equation. The existence of a resolving family means the existence of a solution for the equation under consideration. For such equation with an operator A satisfying Hille–Yosida-type conditions the uniqueness of a solution is shown also. The obtained results are illustrated by an example for an equation of the considered form in a Banach space of sequences. It is shown that such a problem in a space of sequences is equivalent to some initial boundary value problems for partial differential equations. Thus, this paper obtains key results that make it possible to determine the properties of the initial value problem involving the Dzhrbashyan–Nersesyan derivative by examining the properties of the operator in the equation; the results prove the existence and uniqueness of the solution and the correctness of the problem. Full article

In this work, we consider a generalized form of the classical $(2+1)$-dimensional sine-Gordon system. The mathematical model considers a generalized reaction term, and the two-dimensional Laplacian includes the presence of space-fractional derivatives of the Riesz type with two different differentiation orders in general. The system is equipped with a conserved quantity that resembles the energy functional in the integer-order scenario. We propose a numerical model to approximate the solutions of the fractional sine-Gordon equation. A discretized form of the energy-like quantity is proposed, and we prove that it is conserved throughout the discrete time. Moreover, the analysis of consistency, stability, and convergence is rigorously carried out. The numerical model is implemented computationally, and some computer simulations are presented in this work. As a consequence of our simulations, we show that the discrete energy is approximately conserved throughout time, which coincides with the theoretical results. Full article

In this paper, we first introduce a parametric identity for generalized differentiable functions using a generalized fractal–fractional integral operators. Based on this identity, we establish several variants of parameterized inequalities for functions whose local fractional derivatives in absolute value satisfy generalized convexity conditions. Furthermore, we demonstrate that our main results reduce to well-known Ostrowski- and Simpson-type inequalities by selecting suitable parameters. These inequalities contribute to finding tight bounds for various integrals over fractal spaces. By comparing the classical Hölder and Power mean inequalities with their new generalized versions, we show that the improved forms yield sharper and more refined upper bounds. In particular, we illustrate that the generalizations of Hölder and Power mean inequalities provide better results when applied to fractal integrals, with their tighter bounds supported by graphical representations. Finally, a series of applications are discussed, including generalized special means, generalized probability density functions and generalized quadrature formulas, which highlight the practical significance of the proposed results in fractal analysis. Full article

The effects of trace Ce on the microstructure and texture of non-oriented silicon steel during recrystallization and grain growth were examined using X-ray diffraction and electron backscatter diffraction. Additionally, this study focused on investigating the mechanisms by which trace Ce influences the evolution of the {114} <481> and γ-fiber textures. During the recrystallization process, as the recrystallization fraction of annealed sheets increased, the intensity of α-fiber texture decreased, while the intensities of α*-fiber and γ-fiber textures increased. The {111} <112> grains preferentially nucleated in the deformed γ-grains and their grain-boundary regions and tended to form a colony structure with a large amount of nucleation. In addition, the {100} <012> and {114} <481> grains mainly nucleated near the deformed α-grains, which were evenly distributed but found in relatively small quantities. The hindering effect of trace Ce on dislocation motion in cold-rolled sheets results in a 2–7% lower recrystallization ratio for the annealed sheets, compared to conventional annealed sheets. Trace Ce suppresses the nucleation and growth of γ-grains while creating opportunities for α*-grain nucleation. During grain growth, trace Ce reduces γ-grain-boundary migration rate in annealed sheets, providing growth space for {114} <418> grains. Consequently, the content of the corresponding {114} <481> texture increased by 6.4%, while the γ-fiber texture content decreased by 3.6%. Full article

An iterative fractional Doppler shift and channel joint estimation algorithm is proposed for orthogonal time frequency space (OTFS) satellite communication systems. In the algorithm, we search the strongest path and estimate its fractional Doppler offset, and compensate the Doppler shift to the nearest integer to estimate the coefficient of the path. Then signal of the path and its inter-Doppler interference are reconstructed and canceled from the received data with these two estimated parameters. The estimation and cancel process are iteratively conducted until the strongest path in the remained paths is less than the predetermined threshold. The channel information can be reconstructed by the estimated parameters of the paths. The normalized mean squared error (NMSE) of the proposed channel estimation algorithm is less than 1/5 of the available algorithms at a high signal-to-noise ratio (SNR) region, and its BER has about 4dB SNR gain compared with those of the available algorithms when the bit error rate (BER) is ${10}^{-3}$. Full article

This paper is focused on developing a Galerkin finite element framework for the fractional Allen–Cahn equation with regularized logarithmic potential over the ${\mathbb{R}}^d$ ($d=1,2,3$) domain, where the regularization of the singular potential extends beyond the classical double-well formulation. A fully discrete finite element scheme is developed using a k-th-order finite element space for spatial approximation and a backward Euler scheme for the temporal discretization of a regularized system. The existence and uniqueness of numerical solutions are rigorously established by applying Brouwer’s fixed-point theorem. Moreover, the proposed numerical framework is shown to preserve the discrete energy dissipation law analytically, while a priori error estimates are derived. Finally, numerical experiments are conducted to verify the theoretical results and the inherent physical property, such as phase separation phenomenon and coarsening processes. The results show that the fractional Allen–Cahn model provides enhanced capability in capturing phase transition characteristics compared to its classical equation. Full article

We develop novel extensions in the theory of weighted Lorentz spaces. In particular, we generalize classical results by introducing variable-exponent Lorentz spaces, establish sharp constants and quantitative bounds for maximal operators, and extend the framework to encompass fractional maximal operators. Moreover, we analyze endpoint cases through the study of oscillation operators and reveal new connections with weighted Hardy spaces. These results provide a unifying approach that not only refines existing inequalities but also opens new avenues in harmonic analysis and partial differential equations. Full article

This work investigates fractional stochastic Schrödinger evolution equations in a Hilbert space, incorporating complex potential symmetry and Poisson jumps. We establish the existence of mild solutions via stochastic analysis, semigroup theory, and the Mönch fixed-point theorem. Sufficient conditions for exponential stability are derived, ensuring asymptotic decay. We further explore trajectory controllability, identifying conditions for guiding the system along prescribed paths. A numerical example is provided to validate the theoretical results. Full article

The assessment of systemic congestion in acute heart failure (AHF) remains clinically challenging, particularly across different left ventricular ejection fraction (LVEF) phenotypes. This study aimed to evaluate whether differences exist in the degree of congestion, assessed through a multimodal approach including physical examination, biomarkers (NT-proBNP, CA125), and point-of-care ultrasound using the Venous Excess Ultrasound (VExUS) protocol, between patients with preserved (HFpEF) and reduced ejection fraction (HFrEF). We conducted a prospective observational study involving 90 hospitalized AHF patients, 80 of whom underwent a complete VExUS assessment. Although patients with HFrEF exhibited higher levels of NT-proBNP and CA125, and more frequent signs of third-space fluid accumulation such as pleural effusion and ascites, no statistically significant differences were found in VExUS grades between the two groups. These findings suggest that the VExUS protocol provides consistent and reproducible information on systemic venous congestion, regardless of LVEF phenotype. Its integration into clinical practice may help refine congestion assessment and optimize diuretic therapy. Further multicenter studies with larger populations are warranted to validate its diagnostic and prognostic utility and to determine its potential role in guiding individualized treatment strategies in AHF. Full article