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26 June 2025, Volume 45 Issue 3 Previous Issue    Next Issue

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Variable Kernel Marcinkiewicz Integral and its Commutator on the Nonhomogeneous Variable Exponent Herz-Morrey-Hardy Space Shao Xukui, Wang Suping, Tao Shuangping Acta mathematica scientia,Series A. 2025, 45 (3):  653-664.  Abstract ( 122 )   RICH HTML PDF (566KB) ( 170 )   Save By the property about the function $\Omega(x,z)$, the boundedness of parameterized Marcinkiewicz integral operators with variable kernels $\mu^{\theta}_{\Omega}$ and their commutator $\mu^{\theta}_{\Omega,b}$ generated by $ \mathrm{BMO}(\mathbb{R}^{n})$ functions $b$ are established on the nonhomogeneous variable exponent Herz-Morrey-Hardy space, which extends results that have been achieved in previous research. References | Related Articles | Metrics

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Plancherel-Pôlya Type Characterization of Product Weighted Besov and Product Weighted Triebel-Lizorkin Spaces Based on Wavelet Basis Li Ziyan, Tao Xiangxing Acta mathematica scientia,Series A. 2025, 45 (3):  665-686.  Abstract ( 59 )   RICH HTML PDF (651KB) ( 159 )   Save On the product spaces of homogeneous type in the sense of Coifman and Weiss, this paper introduces the product weighted Besov space and product weighted Triebel-Lizorkin space based on wavelet basis, and establishes the Plancherel-Pôlya type characterizations of product weighted Besov spaces and product Triebel-Lizorkin spaces via the wavelet reproducing formula and the almost orthogonal estimation, which means that the space are independent of the choice of the orthonormal wavelet basis. References | Related Articles | Metrics

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Weak Musicelak-Orlicz-Triebel-Lizorkin Spaces with Variable Smooth Exponent Dai Yujiao, Xu Jingshi Acta mathematica scientia,Series A. 2025, 45 (3):  687-701.  Abstract ( 50 )   RICH HTML PDF (614KB) ( 130 )   Save Weak Musielak-Orlicz-Triebel-Lizorkin spaces with variable smooth exponent are first introduced. Then we establish a vector estimate for weak Musielak-Orlicz spaces. As an application we give equivalent quasi-norms in these new spaces by means of Peetre 's maximal functions. Finally, we obtain the boundedness of the $ \varphi $ transform on these new spaces and their atomic and molecular decompositions. References | Related Articles | Metrics

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Some Properties about Band Operators Huang Jieyi, Cheng Na Acta mathematica scientia,Series A. 2025, 45 (3):  702-706.  Abstract ( 58 )   RICH HTML PDF (416KB) ( 102 )   Save The paper first gives the relationship between band operators and band preserving operators, band operators and orthomorphism, and second gives the condition that the inverse of an invertible band operator is a band operator by using the rich center property in Riesz spaces. References | Related Articles | Metrics

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$J$-Self-Adjointness and Green's Function of Discontinuous Second-Order Differential Operator with Eigenparameters in the Boundary Conditions Fu Huijie, Xu Meizhen Acta mathematica scientia,Series A. 2025, 45 (3):  707-725.  Abstract ( 55 )   RICH HTML PDF (603KB) ( 81 )   Save In this paper, the $J$-self-adjointness and Green's function of a class of discontinuous second-order complex coefficient differential operator with eigenparameters in the boundary conditions of both endpoints are considered. By introducing a linear operator $A$ related to the problem in a suitable Hilbert space, the considered problem can be interpreted as the study of the operator in this space, and it is proved that the operator $A$ is $J$-self-adjoint. In addition, the basic solutions of the operator and the asymptotic formula of the basic solutions are given. Furthermore, the Green's function and the resolvent operator of this operator are derived, and the asymptotic formula of Green's function is given. References | Related Articles | Metrics

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Breakdown of Solutions to a Weakly Coupled System of Semilinear Wave Equations Feng Zhendong, Guo Fei, Li Yuequn Acta mathematica scientia,Series A. 2025, 45 (3):  726-747.  Abstract ( 97 )   RICH HTML PDF (741KB) ( 67 )   Save This paper addresses the Cauchy problem for a weakly coupled system of semilinear wave equations with scale-invariant dampings, mass, and general nonlinear memory terms. Firstly, a local (in time) existence result for this problem is established using Banach's fixed point theorem, subject to suitable assumptions on the exponents $p, q$ and coefficients $\mu_1, \mu_2$.Here, $p$ and $q$ represent the powers of the nonlinear memory terms, while $\mu_1$ and $\mu_2$ denote the coefficients of the dampings and mass terms, respectively. It is noteworthy that Palmieri's decay estimates for the solution to the corresponding linear homogeneous equation play a crucial role in proving the local well-posedness result. Subsequently, employing an iteration technique in conjunction with the test function method, we obtain a blowup result for energy solutions. References | Related Articles | Metrics

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Finite Time Blow up of Solutions for Nonlinear Wave Equation with the Damping Term at Arbitrarily Positive Initial Energy Li Qian, Xing Yanyuan Acta mathematica scientia,Series A. 2025, 45 (3):  748-755.  Abstract ( 53 )   RICH HTML PDF (479KB) ( 110 )   Save This paper studies the finite time blow up of solutions for a initial boundary value problem of a viscoelastic wave equation with the strong damping term and linear weak damping term at high initial energy level. By using the concavity method, we obtain some new sufficient conditions on initial data such that the solution with arbitrarily positive initial energy blows up in finite time. References | Related Articles | Metrics

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Existence and Multiplicity of Solutions to a Class of Klein-Gordon-Maxwell Systems Duan Yu, Sun Xin Acta mathematica scientia,Series A. 2025, 45 (3):  756-766.  Abstract ( 44 )   RICH HTML PDF (576KB) ( 77 )   Save This article concerns the following Klein-Gordon-Maxwell system $\begin{equation*} \begin{cases} -\Delta u+ V(x)u-(2\omega+\phi)\phi u=f(x,u)+K(x)|u|^{s-2}u, & x\in \mathbb{R}^{3},\\ \Delta \phi=(\omega+\phi)u^2, & x\in \mathbb{R}^{3}, \end{cases} \end{equation*}$ where $\omega> 0$ is a constant. When $f$ satisfies local condition just in a neighborhood of the origin, existence and multiplicity of nontrivial solutions can be proved via variational methods and Moser iteration. Our result completes some recent works concerning research on solutions of this system. References | Related Articles | Metrics

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Darboux Transformation and Exact Solutions of the Nonlocal Reverse Space-Time Higher-Order Nonlinear Schrödinger Equation Lu Gaojie, Han Zhong, Liu Lu Acta mathematica scientia,Series A. 2025, 45 (3):  767-775.  Abstract ( 53 )   RICH HTML PDF (919KB) ( 59 )   Save Under investigation in this paper is the nonlocal reverse space-time higher-order nonlinear Schrödinger (HNLS) equation which can be derived from the Ablowitz-Kaup-Newell-Segur linear scattering problem. The Darboux transformation is provided in the form of determinants. By applying the Darboux transformation, we arrive at exact solutions of the nonlocal reverse space-time HNLS equation, including soliton, complextion and rogue wave solutions. Finally, the dynamical behaviors of solutions are elucidated graphically. These results could be used to understand related physical phenomena in nonlinear optics and relevant fields. Figures and Tables | References | Related Articles | Metrics

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Traveling Fronts in a Social Tension-Outbursts Multi-Scale Reaction-Diffusion Equation with Allee Effect Zheng Yanping, Shen Jianhe Acta mathematica scientia,Series A. 2025, 45 (3):  776-789.  Abstract ( 36 )   RICH HTML PDF (957KB) ( 104 )   Save Based on the geometric singular perturbation theory, and combining with the tools of generalized rotating vector field and phase plane analysis, this paper studies the existence of traveling fronts for a class of multi-scale reaction-diffusion system describing social tension-outbursts with Allee effect. Under three different limiting assumptions on scales, we obtain three different dimension-reduction settings to get the low-dimensional systems processing heteroclinic connections. Thus, we obtain the existence of traveling fronts connecting different steady-state solutions of the multi-scale reaction-diffusion system mentioned-above. Figures and Tables | References | Related Articles | Metrics

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Nonlinear Stability of Traveling Waves for Stochastic Kuramoto-Sivashinsky Equation Liu Yu, Chen Guanggan, Li Shuyong Acta mathematica scientia,Series A. 2025, 45 (3):  790-806.  Abstract ( 38 )   RICH HTML PDF (594KB) ( 63 )   Save This work is concerned with the nonlinear stability of traveling wave for the stochastic Kuramoto-Sivashinsky equation. By stochastic phase shift method and splitting time argument, we prove that the traveling wave solution of the deterministic system retain the nonlinear stability when the noise intensity of the stochastic system is small enough and its initial value is sufficiently close to the traveling wave of the corresponding deterministic system. References | Related Articles | Metrics

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Multiple Solutions for a Class of $\psi$-Caputo-Type Fractional Differential Equations with Instantaneous and Non-Instantaneous Impulses Yao Wangjin, Zhang Huiping Acta mathematica scientia,Series A. 2025, 45 (3):  807-823.  Abstract ( 37 )   RICH HTML PDF (641KB) ( 59 )   Save In recent years, as an extension of integer-order differential equations, fractional differential equations have became a popular research object. They play an important role in modeling many practical problems of science and engineering, such as anomalous diffusion, fluid flow, epidemiology, viscoelastic mechanics, etc. In this paper, a class of fractional differential equation involving $\psi$-Caputo fractional derivative with instantaneous and non-instantaneous impulses is considered. By using variational methods and two types of three critical point theorems, the existence of at least three classical solutions is obtained when $\mu\in \mathbb{R}$. Moreover, some recent results are improved and extended. In the end, two examples are given to verify the feasibility and effectiveness of the obtained results. References | Related Articles | Metrics

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Two-Point and Four-Point Limit Cycles in Discontinuous Planar Piecewise Linear Systems Li Zhengkang Acta mathematica scientia,Series A. 2025, 45 (3):  824-842.  Abstract ( 40 )   RICH HTML PDF (1134KB) ( 96 )   Save In this paper, we study the existence, coexistence and maximum number of coexisting elements for two-point and four-point limit cycles in discontinuous planar piecewise linear systems separated by nonregular separation line. Refs. [29, 30] (Llibre & Teixeira, 2017 & 2018) posed two open problems: Can piecewise linear differential systems without equilibria or with only centers produce limit cycles? Assume that two subsystems are composed of a Hamiltonian system without equilibrium points or a linear system with center type equilibrium. Via the method of first integral, it is proved that the maximum number of two-point limit cycles that intersect with nonregular separation line boundary at two points is 2, and the maximum number of four point limit cycles that intersect with nonregular separation line boundary at four points is 1. Under the premise of the existence of one four-point limit cycle, only a unique two-point limit cycle could coexist with it. In addition, we also provides accurate numerical results by numerical simulations. Figures and Tables | References | Related Articles | Metrics

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The Poincaré Bifurcation of a Class of Pendulum Equations Xu Junwen, Wu Hongxing, Sun Yangjian Acta mathematica scientia,Series A. 2025, 45 (3):  843-849.  Abstract ( 37 )   RICH HTML PDF (532KB) ( 119 )   Save In this paper, we mainly study the number of limit cycles bifurcate form the periodic orbits of pendulum equations under the perturbations for trigonometric polynomials of degree two. By improving the criterion function of determining the lowest upper bound of the number of zeros of Abelian Integrals, we show that the period annulus (around the origin) can be bifurcate at most two limit cycle (counting multiplicities). Figures and Tables | References | Related Articles | Metrics

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Volume Growth for Gradient Steady Solitons of the Extended Ricci Flow Chen Chizhou, Guo Hongxin Acta mathematica scientia,Series A. 2025, 45 (3):  850-857.  Abstract ( 30 )   RICH HTML PDF (494KB) ( 56 )   Save In this paper, we derive an estimate on the level surface of the potential function of the complete noncompact gradient steady soliton of extended Ricci flow. We show that the average curvature of the level surface of the potential function grows at most linearly with respect to the distance function under certain conditions. Based on that, we prove that the area of the level surface grows at most linearly and the volume of the sublevel sets grows at most quadratically. References | Related Articles | Metrics

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Traveling Waves for a Discrete Diffusive Vaccination Model with Delay Wu Wenbin, Ren Xue, Zhang Ran Acta mathematica scientia,Series A. 2025, 45 (3):  858-874.  Abstract ( 40 )   RICH HTML PDF (707KB) ( 65 )   Save This paper considers the traveling wave solutions of a discrete diffusion vaccination model with time delay. The model comprehensively considers factors such as natural population growth, infection, recovery, and vaccination, as well as the time delay effect of direct contact infection between susceptible individuals, vaccinated individuals, and infected individuals. By establishing appropriate lattice dynamical system, the existence and asymptotic behavior of the traveling wave solutions are obtained. Further results indicate that vaccination rates, the mobility of infected individuals, and transmission rates have a significant impact on the formation and speed of traveling wave solutions. These findings have important theoretical and practical significance for formulating effective vaccination strategies and controlling the spread of infectious diseases. Figures and Tables | References | Related Articles | Metrics

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Steady-State Bifurcation for a Vegetation Model with Shading Effect Liang Juan, Guo Zunguang, Zhang Hongtao Acta mathematica scientia,Series A. 2025, 45 (3):  875-887.  Abstract ( 32 )   RICH HTML PDF (1032KB) ( 41 )   Save A vegetation-water reaction-diffusion model with shading effect under no-flux boundary conditions is studied. The existence of steady-state bifurcation of the model is firstly proved, and the conditions for the generation of steady-state bifurcation are obtained. Then the structure of the non-constant steady-state solution in the case of single eigenvalues is obtained by using the Crandall-Rabinowitz bifurcation theorem. By adopting the implicit function theorem and the techniques of space decomposition, the structure of the non-constant steady-state solution in the case of double eigenvalues is obtained. Finally, numerical simulations are shown to verify the theoretical analysis results. Figures and Tables | References | Related Articles | Metrics

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Mean Square Exponential Synchronization of a Class of Proportional Delay Stochastic Neural Networks and Its Application Ren Hongyue, Zhou Liqun Acta mathematica scientia,Series A. 2025, 45 (3):  888-901.  Abstract ( 52 )   RICH HTML PDF (2218KB) ( 86 )   Save A class of proportional delay inertial stochastic neural networks is used as the driving-response systems. The mean square exponential synchronization of the studied system is analyzed by reducing the order method, adopting a state feedback controller, utilizing Itô integral, constructing a novel Lyapunov functional, and utilizing the properties of calculus. The criteria for determining the mean square exponential synchronization of the studied system are obtained. Finally, the accuracy of the judgment criteria obtained is verified through a numerical example and simulations, and the application of the studied exponential synchronization in image encryption and decryption is presented. Figures and Tables | References | Related Articles | Metrics

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A Composite Tobit Quantile Subgroup Analysis Regression Approach Based on Doubly Censored Longitudinal Data Wang Zhanfeng, Wang Jingyao, Wu Yaohua, Ming Ruixing Acta mathematica scientia,Series A. 2025, 45 (3):  902-918.  Abstract ( 28 )   RICH HTML PDF (950KB) ( 106 )   Save In clinical trials, there may be differences between individuals, and treatment effects are often heterogeneous, so how to identify the population sensitive to specific treatments has become one of the issues of great concern in the field of precision medicine. In addition, due to the limitation of upper and lower thresholds of measurement methods or instruments, the actual observed data values are usually limited to an interval, resulting in doubly censored data. In this paper, we construct a threshold longitudinal Tobit composite quantile regression model to study the problem of identifying treatment-sensitive subgroups, in order to enhance the identification effect of treatment-sensitive subgroups. For the parameters of the model, we borrow the idea of the Alternating Direction Method of Multipliers algorithm to establish a method for calculating the parameter estimators, and use the random weighting method to calculate the variance of the parameter estimators. Under some regular conditions, we prove the consistency of the parameter estimators. Numerical simulations show that the proposed method is more effective than the single quantile regression method, and verify the feasibility of the random weighting method in estimating the variance of the parameter estimators. Finally, the method proposed in this paper is applied to analyse the data of the CO.17 Trial, identifying the treatment-sensitive subgroups according to age. Figures and Tables | References | Related Articles | Metrics

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Least Squares Estimators of General Linear Model with Censoring Indicators Missing at Random Rao Zhenmin, Wang Jiangfeng, Hu Kang, He Shan Acta mathematica scientia,Series A. 2025, 45 (3):  919-933.  Abstract ( 32 )   RICH HTML PDF (670KB) ( 97 )   Save This article investigates the weighted least squares regression estimators of general linear models with censoring indicators missing at random. Based on three weighting methods of calibration, interpolation, and inverse probability, parameter estimators are constructed respectively. Under appropriate assumptions, asymptotic normality of these estimators has been established, and a new bootstrap testing program based on least squares weighted residual (LSWR) is proposed. Finally, the effectiveness of these estimators and testing procedures are analyzed through numerical simulations and actual data. Figures and Tables | References | Related Articles | Metrics

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Optimal Control Strategy for the SVEITR Pulmonary Tuberculosis Transmission Model Considering Diffusion LI Yazhi, Liu Lili, Tian Yanni Acta mathematica scientia,Series A. 2025, 45 (3):  934-945.  Abstract ( 37 )   RICH HTML PDF (1159KB) ( 66 )   Save A tuberculosis transmission model with diffusion factors was established, introducing four control variables: increasing personal protective awareness, timely detection and treatment, improving treatment level, and reducing recurrence rate. The optimal control problem was discussed theoretically and numerically. Firstly, the existence of optimal control was obtained using the optimal control theory of partial differential equations. Secondly, the characteristics of optimal control were calculated by constructing sensitivity systems and adjoint systems. Finally, the variation of optimal control variables over time was demonstrated through numerical simulations, and the optimal control effect was shown. The results showed that compared with the uncontrolled situation, optimal control can significantly reduce the number of latent, infected, and treated individuals at the termination of control; Compared to a single control scenario, optimal control can reduce the peak of infected individuals, delay peak time, and decrease the final number of infected individuals. The conclusion drawn can provide a theoretical reference for frontline disease prevention and control. Figures and Tables | References | Related Articles | Metrics

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Dynamics of an Age-Space Structure Pine Wilt Disease Model with Nonlocal Diffusion and Spatial Heterogeneity Wu Peng, Zhang Shuai, Fang Cheng Acta mathematica scientia,Series A. 2025, 45 (3):  946-959.  Abstract ( 38 )   RICH HTML PDF (667KB) ( 53 )   Save Pine wilt disease, as a destructive forest disease, is mainly transmitted through the pine ink beetle.In order to investigale the impact of non-local dispersal and infection age of longhorn beetles on the transmission of the disease in a space heterogeneous environment. In this paper, we propose an age-space structured pine wilt model with nonlocal dispersal. Firstly, we investigate the well-posedness of the model. Secondly, by constructing the general renewal equation of the model, the next-generation operator$\mathcal{R}$is derived, and the basic reproduction number$\mathcal{R}_0$is obtain as the spectral radius of$\mathcal{R}$. As the dynamics threshold of the infectious disease model, $\mathcal{R}_0$ determines the extinction and outbreak of the disease. Finally, the existence of nontrivial solution for the system was proved by using Krasnoselskii fixed point theorem. Furthermore, the asymptotic profiles of the nontrivial solution was proved in spacial case. References | Related Articles | Metrics

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New Results On Gauss Product Inequalities (I) Ma Li, Chen Pengying, Han Xinfang Acta mathematica scientia,Series A. 2025, 45 (3):  960-971.  Abstract ( 34 )   RICH HTML PDF (522KB) ( 55 )   Save Let ($X_1$,$X_2$,$X_3$) be a centered Gaussian random vector with $D(X_i)=1$, $i=1,2,3$. By means of the properties of hypergeometric function and factorization, we prove that $E\big[|X_1^4X_2^3X_3^3|\big]\geq$E$|X_1^4|$E$|X_2^3|$E$|X_3^3|$, and the equal sign holds if and only if $X_1$,$X_2$,$X_3$ are independent. This complements the results of the three dimensional Gauss product inequality in the existing literature. References | Related Articles | Metrics

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Performance Analysis of an Queueing System with A Patient Server and Uninterrupted Multiple Vacations Under the Control of ${(p,N)}$-Policy Yin Lingyu, Tang Yinghui, Yu Miaomiao, Wei Yingyuan Acta mathematica scientia,Series A. 2025, 45 (3):  972-991.  Abstract ( 24 )   RICH HTML PDF (694KB) ( 81 )   Save This paper proposes an $M/G/1$ queueing model with a patient server and uninterrupted multiple vacations under the control of $(p,N)$-policy, in which the $(p,N)$-policy means that when the server returns from vacation and finds the number of customers waiting to be served in the system is greater than or equal a given threshold $N$, the server immediately serves the customers until the system becomes empty again. If there are less than $N$ customers but at least one customer in the system, the server begins its service with probability $p\left( {0 \le p \le 1} \right)$ or stays idle with probability $(1-p)$ until there are $N$ customers in the system and starts its service at once. We employ the total probability decomposition technology, renewal theory and Laplace transform tool to conduct a detailed analysis of the system's performance indicators. The expressions of the Laplace transform of the transient queue length distribution and the recursive expressions of the steady-state queue length distribution are obtained. Furthermore, the probability generating function of the steady-state queue length distribution and the display expression of the average queue length are presented. Finally, numerical examples are presented to discuss the system capacity optimization design and the sensitivity of system parameters on the system's idle rate and the additional average queue-length. Figures and Tables | References | Related Articles | Metrics

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$k$-Nearest Neighbor Kernel Estimation of Conditional Average Treatment Effect with Missing Response Variables Zeng Huajun, Ming Ruixing, Su Peijuan, Huang Shaohang, Xiao Min Acta mathematica scientia,Series A. 2025, 45 (3):  992-1012.  Abstract ( 32 )   RICH HTML PDF (1399KB) ( 103 )   Save Under the Neyman-Rubin potential outcome framework, we construct a $k$-nearest neighbor kernel estimator to measure the conditional average treatment effect in the case of random missing response variables, aiming to evaluate the impact of different treatments on individuals. The paper proves the almost complete convergence and the asymptotic normality of the estimator. The numerical simulation shows that the $k$-nearest neighbor kernel estimator performs well. The real-world data is used for empirical analysis, and the empirical results show that mean absolute error and root mean square error of the $k$-nearest neighbor kernel estimator are smaller. Figures and Tables | References | Related Articles | Metrics