Search Results (2,110)

Quantum network correlations are crucial for long-distance quantum communication, quantum cryptography, and distributed quantum computing. Detecting network steering is particularly challenging in complex network structures. We have studied the steering inequality criteria for a 2-forked 3-layer tree-shaped network. Assuming the first and third layers are trusted and the second layer is untrusted, we derived a steering inequality criterion using the correlation matrix between trusted and untrusted observables. In particular, we apply the steering criterion to three classes of measurements which are of special significance: local orthogonal observables, mutually unbiased measurements, and general symmetric informationally complete measurements. We further illustrate the effectiveness of our method through an example. Full article

This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized $(r^{\star },q^{\star })$ distributions. First, boundary conditions are applied to reduce the model to a second-order nonlinear ordinary differential equation. The Galilean transformation is subsequently applied to reformulate the second-order ordinary differential equation into an unperturbed dynamical system. Next, phase portraits of the system are examined under all possible conditions of the discriminant of the associated cubic polynomial, identifying regions of stability and instability. The Runge–Kutta method is employed to construct the phase portraits of the system. The Hamiltonian function of the unperturbed system is subsequently derived and used to analyze energy levels and verify the phase portraits. Under the influence of an external periodic perturbation, the quasi-periodic and chaotic dynamics of dust ion acoustic waves are explored. Chaos detection tools confirm the presence of quasi-periodic and chaotic patterns using Basin of attraction, Lyapunov exponents, Fractal Dimension, Bifurcation diagram, Poincaré map, Time analysis, Multi-stability analysis, Chaotic attractor, Return map, Power spectrum, and 3D and 2D phase portraits. In addition, the model’s response to different initial conditions was examined through sensitivity analysis. Full article

Let ${\mathcal{A}}_n$ be the class of specific analytic functions $f\left(z\right)=z+{\displaystyle \sum _{k=1}^{\infty }}{a}_{1+{\displaystyle \frac{k}{n}}}{z}^{1+{\displaystyle \frac{k}{n}}}(n\in \mathbb{N}=\{1,2,3,\dots \})$ in the open unit disk $\mathbb{U}.$ For $f\left(z\right)\in {\mathcal{A}}_n,$ fractional derivatives $D_z^{\lambda }f\left(z\right)$ and $D_z^{j+\lambda }f\left(z\right)$$(0\le \lambda <1,j\in \mathbb{N})$ are defined by using Gamma functions. Applying such fractional derivatives, we introduce a new subclass ${\mathcal{A}}_n(j,\lambda ,\alpha ,\beta )$ of ${\mathcal{A}}_n.$ In this paper, we establish sufficient conditions for $f\left(z\right)$ for ${\mathcal{A}}_n(j,\lambda ,\alpha ,\beta ),$ coefficient inequalities for $|a_{1+{\displaystyle \frac{1}{n}}}|$ and $|a_{1+{\displaystyle \frac{k}{n}}}|$$(k=2,3,4,\dots )$ of $f\left(z\right)\in {\mathcal{A}}_n(j,\lambda ,\alpha ,\beta ),$ and some interesting argument properties of fractional derivatives for $f\left(z\right)\in {\mathcal{A}}_n$ through an example. Full article

In compressed sensing, it is believed that the L₀ norm minimization is the best way to enforce a sparse solution. However, the L₀ norm is difficult to implement in a gradient-based iterative image reconstruction algorithm. The total variation (TV) norm minimization is considered a proper substitute for the L₀ norm minimization. This paper points out that the TV norm is not powerful enough to enforce a piecewise-constant image. This paper uses the limited-angle tomography to illustrate the possibility of using the L₀ norm to encourage a piecewise-constant image. However, one of the drawbacks of the L₀ norm is that its derivative is zero almost everywhere, making a gradient-based algorithm useless. Our novel idea is to replace the zero value of the L₀ norm derivative with a zero-mean random variable. Computer simulations show that the proposed L₀ norm minimization outperforms the TV minimization. The novelty of this paper is the introduction of some randomness in the gradient of the objective function when the gradient is zero. The quantitative evaluations indicate the improvements of the proposed method in terms of the structural similarity (SSIM) and the peak signal-to-noise ratio (PSNR). Full article

The main objective of this research is to obtain interesting estimates for Jensen’s gap in the integral sense, along with their applications. The convexity of a fifth-order absolute function is used to established proposed estimates of Jensen’s gap. We performed numerical computations to compare our estimates with previous findings. With the use of the primary findings, we are able to obtain improvements of the Hölder inequality and Hermite–Hadamard inequality. Furthermore, the primary results lead to some inequalities for power means and quasi-arithmetic means. We conclude by outlining the information theory applications of our primary inequalities. Full article

Since the monotonicity of the best approximant is crucial to establish partial ordering methods, in this paper, we, respectively, characterize the best approximants in Banach function spaces and Lorentz spaces ${\mathrm{\Gamma }}_{p,w}$, in which we especially focus on the monotonicity characterizations. We first study monotonicity characterizations of the metric projection operator onto sublattices in general Banach function spaces by the property $H_g$. The sufficient and necessary conditions for monotonicity of the metric projection onto cones and sublattices are then, respectively, established in ${\mathrm{\Gamma }}_{p,w}$. The Lorentz spaces ${\mathrm{\Gamma }}_{p,w}$ are also shown to be reflexive under the condition $R{B}_p$, which is the basis for the existence of the best approximant. As applications, by establishing the partial ordering methods based on the obtained monotonicity characterizations, the solvability and approximation theorems for best proximity points are deduced without imposing any contractive and compact conditions in ${\mathrm{\Gamma }}_{p,w}$. Our results extend and improve many previous results in the field of the approximation and partial ordering theory. Full article

In this paper, we develop a geometric formulation of datasets. The key novel idea is to formulate a dataset to be a fuzzy topological measure space as a global object and equip the space with an atlas of local charts using graphs of fuzzy linear logical functions. We call such a space a logifold. In applications, the charts are constructed by machine learning with neural network models. We implement the logifold formulation to find fuzzy domains of a dataset and to improve accuracy in data classification problems. Full article

Financial market forecasting remains challenging due to complex nonlinear dynamics and regime-dependent behaviors that traditional models struggle to capture effectively. This research introduces the Adaptive Financial Reservoir Network with Hypernetwork Flow (AFRN–HyperFlow) framework, a novel ensemble architecture integrating Echo State Networks, temporal convolutional networks, mixture density networks, adaptive Hypernetworks, and deep state-space models for enhanced financial time-series prediction. Through comprehensive feature engineering incorporating technical indicators, spectral decomposition, reservoir-based representations, and flow dynamics characteristics, the framework achieves superior forecasting performance across diverse market conditions. Experimental validation on 26,817 balanced samples demonstrates exceptional results with an F1-score of 0.8947, representing a 12.3% improvement over State-of-the-Art baseline methods, while maintaining robust performance across asset classes from equities to cryptocurrencies. The adaptive Hypernetwork mechanism enables real-time regime-change detection with 2.3 days average lag and 95% accuracy, while systematic SHAP analysis provides comprehensive interpretability essential for regulatory compliance. Ablation studies reveal Echo State Networks contribute 9.47% performance improvement, validating the architectural design. The AFRN–HyperFlow framework addresses critical limitations in uncertainty quantification, regime adaptability, and interpretability, offering promising directions for next-generation financial forecasting systems incorporating quantum computing and federated learning approaches. Full article

This study introduces two novel methodologies for solving systems of Fredholm integral equations, with particular emphasis on second-kind equations. The first method integrates the Sinc-collocation technique with a newly developed singular exponential transformation, enhancing convergence behavior and numerical stability. A comprehensive convergence analysis is conducted to support this approach. The second method employs a double exponential transformation, leading to a pair of linear equations whose solvability is established using the double projection method. Rigorous theoretical analysis is presented, including convergence theorems and newly derived error bounds. A system of two Fredholm integral equations is treated as a practical case study. Numerical examples are provided to illustrate the effectiveness and accuracy of the proposed methods, substantiating the theoretical results. Full article

This study focuses on investigating the asymptotic and oscillatory behavior of a new class of fourth-order nonlinear neutral differential equations. This research aims to achieve a qualitative advancement in the analysis and understanding of the relationships between the corresponding function and its derivatives. By utilizing various techniques, innovative criteria have been developed to ensure the oscillation of all solutions of the studied equations without resorting to additional constraints. Effective analytical tools are provided, contributing to a deeper theoretical understanding and expanding their application scope. The paper concludes by presenting examples that illustrate the practical impact of the results, highlighting the theoretical value of the research in the field of functional differential equations. Full article

In this study, we establish new oscillation criteria for solutions of the fourth-order differential equation $(a$$\varphi \left(u\right)$$u^{‴})$+q$(u\circ h)=0$, which is of a functional type with a delay. The oscillation behavior of solutions of fourth-order delay equations has been studied using many techniques, but previous results did not take into account the existence of the function $\varphi$ except in second-order studies. The existence of $\varphi$ increases the difficulty of obtaining monotonic and asymptotic properties of the solutions and also increases the possibility of applying the results to a larger area of special cases. We present two criteria to ensure the oscillation of the solutions of the studied equation for two different cases of $\varphi$. Our approach is based on using the comparison principle with equations of the first or second order to benefit from recent developments in studying the oscillation of these orders. We also provide several examples and compare our results with previous ones to illustrate the novelty and effectiveness. Full article

Let $\Lambda \subseteq {\mathbb{R}}^d$ be a discrete uniformly separated subset. In the unweighted case and $p=2$, Landau obtained the necessary conditions for sampling and interpolation of functions in Paley–Wiener space in terms of the upper and lower uniform densities of $\Lambda$. In this paper, we generalize the above results to the weighted case, and give some necessary density conditions for $L_p$ weighted sampling and interpolating sets for all $0<p<\infty$. Full article

This study addresses the standardization of Singular Distributed Parameter Systems (SDPSs). It focuses on classifying and simplifying first- and second-order linear SDPSs using characteristic matrix theory. First, the study classifies first-order linear SDPSs into three canonical forms based on characteristic curve theory, with an example illustrating the standardization process for parabolic SDPSs. Second, under regular conditions, first-order SDPSs can be decomposed into fast and slow subsystems, where the fast subsystem reduces to an Ordinary Differential Equation (ODE) system, while the slow subsystem retains the spatiotemporal characteristics of the original system. Third, the standardization and classification of second-order SDPSs is proposed using three reversible transformations that achieve structural equivalence. Finally, an illustrative example of a building temperature control is built with SDPSs. The simulation results show the importance of system standardization in real-world applications. This research provides a theoretical foundation for SDPS standardization and offers insights into the practical implementation of distributed temperature systems. Full article

Crossover trials are specifically designed to evaluate treatment effects within individual participants through within-subject comparisons. In a standard AB/BA crossover trial, participants are randomly allocated to one of two treatment sequences: either the AB sequence (where patients receive treatment A first and then cross over to treatment B after a washout period) or the BA sequence (where patients receive B first and then cross over to A after a washout period). Asymptotic and approximate unconditional test procedures, based on two Wald-type statistics, the likelihood ratio statistic, and the score test statistic for the odds ratio (OR), are developed to evaluate the equality of treatment effects in this trial design. Additionally, confidence intervals for OR are constructed, accompanied by an approximate sample size calculation methodology to control the interval width at a pre-specified precision. Empirical analyses demonstrate that asymptotic test procedures exhibit robust performance in moderate to large sample sizes, though they occasionally yield unsatisfactory type I error rates when the sample size is small. In such cases, approximate unconditional test procedures emerge as a rigorous alternative. All proposed confidence intervals achieve satisfactory coverage probabilities, and the approximate sample size estimation method demonstrates high accuracy, as evidenced by empirical coverage probabilities aligning closely with pre-specified confidence levels under estimated sample sizes. To validate practical utility, two real examples are used to illustrate the proposed methodologies. Full article

In this paper, we introduce a new sequence, which approximates the Euler–Mascheroni constant $\gamma$ and converges faster to its limit, with the convergence rate $n^{-5}$. Also, for this constant, new inequalities are established. Our result, compared to other sequences with convergence rates $n^{-2}$, $n^{-3}$, or $n^{-4}$, improves some known results. Full article