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Abstract: Abstract In this paper, Let Mn denote the maximum of logarithmic general error distribution with parameter v ≥ 1. Higher-order expansions for distributions of powered extremes \(M_n^p\) are derived under an optimal choice of normalizing constants. It is shown that \(M_n^p\) , when v = 1, converges to the Fréchet extreme value distribution at the rate of 1/n, and if v > 1 then \(M_n^p\) converges to the Gumbel extreme value distribution at the rate of \({(\log \log n)^2}/{(\log n)^{1 - {1 \over v}}}\) . PubDate: 2024-03-01 DOI: 10.1007/s11766-024-3859-4

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Abstract: Abstract Consider a pseudo-differential operator $${T_a}f(x) = \int_{{\mathbb{R}^n}} {{e^{ix \cdot \xi}}} a(x,\xi)\hat f(\xi)\,\,{\rm{d}}\xi $$ where the symbol a is in the rough Hörmander class \({L^\infty}S_\rho ^m\) with m ∈ ℝ and ρ ∈ [0, 1]. In this note, when 1 ≤ p ≤ 2, if \(m < \,{{n(\rho - 1)} \over p}\) and \(a \in {L^\infty}S_\rho ^m\) , then for any f ∈ S(ℝn) and x ∈ ℝn, we prove that $$M({T_a}f)(x) \le C{(M( f{ ^p})(x))^{{1 \over p}}}$$ where M is the Hardy-Littlewood maximal operator. Our theorem improves the known results and the bound on m is sharp, in the sense that \({{n(\rho - 1)} \over p}\) can not be replaced by a larger constant. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-4699-y

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Abstract: Abstract In the realm of large-scale machine learning, it is crucial to explore methods for reducing computational complexity and memory demands while maintaining generalization performance. Additionally, since the collected data may contain some sensitive information, it is also of great significance to study privacy-preserving machine learning algorithms. This paper focuses on the performance of the differentially private stochastic gradient descent (SGD) algorithm based on random features. To begin, the algorithm maps the original data into a low-dimensional space, thereby avoiding the traditional kernel method for large-scale data storage requirement. Subsequently, the algorithm iteratively optimizes parameters using the stochastic gradient descent approach. Lastly, the output perturbation mechanism is employed to introduce random noise, ensuring algorithmic privacy. We prove that the proposed algorithm satisfies the differential privacy while achieving fast convergence rates under some mild conditions. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-5037-0

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Abstract: Abstract In this paper, we study spatial cross-sectional data models in the form of matrix exponential spatial specification (MESS), where MESS appears in both dependent and error terms. The empirical likelihood (EL) ratio statistics are established for the parameters of the MESS model. It is shown that the limiting distributions of EL ratio statistics follow chi-square distributions, which are used to construct the confidence regions of model parameters. Simulation experiments are conducted to compare the performances of confidence regions based on EL method and normal approximation method. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-4446-4

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Abstract: Abstract The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system. Firstly, some key ingredients of the method are discussed, for example, Narrow region principle and Decay at infinity. Then, the radial symmetry of the solution of the Logarithmic Laplacian system is obtained. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-4378-z

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Abstract: Abstract The investigation endorsed the convective flow of Carreau nanofluid over a stretched surface in presence of entropy generation optimization. The novel dynamic of viscous dissipation is utilized to analyze the thermal mechanism of magnetized flow. The convective boundary assumptions are directed in order to examine the heat and mass transportation of nanofluid. The thermal concept of thermophoresis and Brownian movements has been re-called with the help of Buongiorno model. The problem formulated in dimensionless form is solved by NDSolve MATHEMATICA. The graphical analysis for parameters governed by the problem is performed with physical applications. The affiliation of entropy generation and Bejan number for different parameters is inspected in detail. The numerical data for illustrating skin friction, heat and mass transfer rate is also reported. The motion of the fluid is highest for the viscosity ratio parameter. The temperature of the fluid rises via thermal Biot number. Entropy generation rises for greater Brinkman number and diffusion parameter. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-3682-y

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Abstract: Abstract The tangential k-Cauchy–Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables, respectively. In this paper, we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg. We investigate quaternionic analysis on the generalized complex Heisenberg. We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-4942-6

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Abstract: Abstract In this paper, we investigate the reverse order law for Drazin inverse of three bounded linear operators under some commutation relations. Moreover, the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-4042-7

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Abstract: Abstract Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove. However, it is known that the version of polynomials with one variable of Fermat’s Last Theorem over ℂ can be proved very concisely. The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate (skew)-polynomials with any characteristic. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-4630-6

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Abstract: Abstract On one hand, we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations. On the other hand, we also investigate the existence and growth of solutions of nonlinear differential-difference equations. These results extend and improve some previous in [5, 14]. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-4132-6

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Abstract: Abstract In this paper, we consider the limit distribution of the error density function estimator in the first-order autoregressive models with negatively associated and positively associated random errors. Under mild regularity assumptions, some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process. In order to illustrate these results, some simulations such as confidence intervals and mean integrated square errors are provided in this paper. It shows that the residual density estimator can replace the density “estimator” which contains errors. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-4558-x

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Abstract: Abstract Currently, there is no solid criterion for judging the quality of the estimators in factor analysis. This paper presents a new evaluation method for exploratory factor analysis that pinpoints an appropriate number of factors along with the best method for factor extraction. The proposed technique consists of two steps: testing the normality of the residuals from the fitted model via the Shapiro-Wilk test and using an empirical quantified index to judge the quality of the factor model. Examples are presented to demonstrate how the method is implemented and to verify its effectiveness. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-3544-7

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Abstract: Abstract Consider a nonstandard continuous-time bidimensional risk model with constant force of interest, in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent. Under some mild conditions, we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval. If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed, it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-4213-6

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Abstract: Abstract This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program. Influenced by the work of Kaltenbacher, Lasiecka and Marchand (Control Cybernet. 2011, 40: 971–988), we establish an observability inequality of the conservative problem, and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system. PubDate: 2024-03-01 DOI: 10.1007/s11766-024-4133-5

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Abstract: Abstract Dependent competing risks model is a practical model in the analysis of lifetime and failure modes. The dependence can be captured using a statistical tool to explore the relationship among failure causes. In this paper, an Archimedean copula is chosen to describe the dependence in a constant-stress accelerated life test. We study the Archimedean copula based dependent competing risks model using parametric and nonparametric methods. The parametric likelihood inference is presented by deriving the general expression of likelihood function based on assumed survival Archimedean copula associated with the model parameter estimation. Combining the nonparametric estimation with progressive censoring and the nonparametric copula estimation, we introduce a nonparametric reliability estimation method given competing risks data. A simulation study and a real data analysis are conducted to show the performance of the estimation methods. PubDate: 2023-12-01 DOI: 10.1007/s11766-023-3457-x

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Abstract: Abstract The main object of this paper is to deduce the bibasic Humbert functions Ξ1 and Ξ2 Some interesting results and elementary summations technique that was successfully employed, q–recursion, q–derivatives relations, the q–differential recursion relations, the q–integral representations for Ξ1 and Ξ2 are given. The summation formula derives a list of p–analogues of transformation formulas for bibasic Humbert functions that have been studied, also some hypergeometric functions properties of some new interesting special cases have been given. PubDate: 2023-12-01 DOI: 10.1007/s11766-023-4848-8

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Abstract: Abstract This paper proposes a method combining blue the Haar wavelet and the least square to solve the multi-dimensional stochastic Itô-Volterra integral equation. This approach is to transform stochastic integral equations into a system of algebraic equations. Meanwhile, the error analysis is proven. Finally, the effectiveness of the approach is verified by two numerical examples. PubDate: 2023-12-01 DOI: 10.1007/s11766-023-4748-y

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Abstract: Abstract In this paper, using inhomogeneous Calderón’s reproducing formulas and the space of test functions associated with a para-accretive function, the inhomogeneous Besov and Triebel-Lizorkin spaces are established. As applications, pointwise multiplier theorems are also obtained. PubDate: 2023-12-01 DOI: 10.1007/s11766-023-3499-0

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Abstract: Abstract In this paper, we ameliorate the model proposed in [13], by incorporating the influence of hepatitis B e antigen (HBeAg) status of mothers on vertical transmission. We use the improved model to fit reported HBV new infections in the Zhejiang Province of China. Also to predict the course of the Hepatitis B (HBV) infection in this Chinese area, and in Tokombere, located in sub-Saharan Africa(SSA). Furthermore, we apply optimal control techniques in view to re-examine the effects of the newborn vaccination, the universal vaccination and the treatment of chronic carriers in preventing the HBV infection. Simulation results show that treatment slightly steps in the optimal strategy, while immunisation is an effective measure. On the other hand, they indicate that the control measures and immunization programs implemented in Zhejiang Province are effective. Besides, they suggest that in SSA, a package of several policies centred on birth dose vaccination should be implemented. PubDate: 2023-12-01 DOI: 10.1007/s11766-023-4332-5

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Abstract: Abstract In this paper, we first discuss the boundedness of certain integral operator Tt on the normal weight general function space F(p, μ, s) in the unit ball Bn of ℂn. As an application of this operator, we prove that the Gleason’s problem is solvable on F(p, μ, s). PubDate: 2023-12-01 DOI: 10.1007/s11766-023-4840-3