查看更多>>摘要：This article proves the existence and uniqueness conditions of the solution of two-dimensional time-space tempered fractional diffusion-wave equation.We find analytical solution of the equation via the two-step Adomian decomposition method(TSADM).The existence result is obtained with the help of some fixed point theorems,while the uniqueness of the solution is a consequence of the Banach contraction principle.Additionally,we study the stability via the Ulam-Hyers stability for the considered problem.The existing techniques use numerical algorithms for solving the two-dimensional time-space tempered fractional diffusion-wave equation,and thus,the results obtained from them are the approximate solution of the problem with high computational and time complexity.In comparison,our proposed method eliminates all the difficulties arising from numerical methods and gives an analytical solution with a straightforward process in just one iteration.
查看更多>>摘要：We couple together existing ideas,existing results,special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of the Cauchy problem for an n-dimensional incompressible Navier-Stokes equations.We also use the global smooth solution of the corresponding heat equation to approximate the global weak solutions of the incompressible Navier-Stokes equations.
查看更多>>摘要：As an extension of linear regression in functional data analysis,functional linear regression has been studied by many researchers and applied in various fields.However,in many cases,data is collected sequentially over time,for example the financial series,so it is necessary to consider the autocorrelated structure of errors in functional regression background.To this end,this paper considers a multiple functional linear model with autoregressive errors.Based on the functional principal component analysis,we apply the least square procedure to estimate the functional coefficients and autoregression coefficients.Under some regular conditions,we establish the asymptotic properties of the proposed estimators.A simulation study is conducted to investigate the finite sample performance of our estimators.A real example on China's weather data is applied to illustrate the validity of our model.
查看更多>>摘要：In this paper,a stochastic SEITR model is formulated to describe the transmission dynamics of tuberculosis with incompletely treatment.Sufficient conditions for the existence of a stationary distribution and extinction are obtained.In addition,numerical simulations are given to illustrate these analytical result-s.Theoretical and numerical results show that large environmental perturbations can inhibit the spread of tuberculosis.
Jun WANGZhen-long CHENWei-jie YUANGuang-jun SHEN...
114-132页
查看更多>>摘要：Let X={X(t),t ∈ R+} be a centered space anisotropic Gaussian process values in Rd with non-stationary increments,whose components are independent but may not be identically distributed.Under certain conditions,then almost surely c1 ≤ φ-m(X([0,1]))≤ c2,where φ denotes the exact Hausdorff measure associated with function φ(s)=s1/αk+k∑i=1(1-αi/αk)log log 1/s for some 1 ≤ k ≤ d,(α1,…,αd)∈(0,1]d.We also obtain the exact Hausdorff measure of the graph of X on[0,1].
查看更多>>摘要：Interior-point methods(IPMs)for linear programming(LP)are generally based on the logarithmic barrier function.Peng et al.(J.Comput.Technol.6:61-80,2001)were the first to propose non-logarithmic kernel functions(KFs)for solving IPMs.These KFs are strongly convex and smoothly coercive on their domains.Later,Bai et al.(SIAM J.Optim.15(1):101-128,2004)introduced the first KF with a trigonometric barrier term.Since then,no new type of KFs were proposed until 2020,when Touil and Chikouche(Filomat.34(12):3957-3969,2020;Acta Math.Sin.(Engl.Ser.),38(1):44-67,2022)introduced the first hyperbolic KFs for semidefinite programming(SDP).They established that the iteration complexities of algorithms based on their proposed KFs are O(n2/3 log n/ɛ) and O(n3/4 log n/ɛ) for large-update methods,respectively.The aim of this work is to improve the complexity result for large-update method.In fact,we present a new parametric KF with a hyperbolic barrier term.By simple tools,we show that the worst-case iteration complexity of our algorithm for the large-update method is O(√n log n log n/ε)iterations.This coincides with the currently best-known iteration bounds for IPMs based on all existing kind of KFs.The algorithm based on the proposed KF has been tested.Extensive numerical simulations on test problems with different sizes have shown that this KF has promising results.
查看更多>>摘要：The asymptotic analysis theory is a powerful mathematical tool employed in the study of complex systems.By exploring the behavior of mathematical models in the limit as certain parameters tend toward infin-ity or zero,the asymptotic analysis facilitates the extraction of simplified limit-equations,revealing fundamental principles governing the original complex dynamics.We will highlight the versatility of asymptotic methods in handling different scenarios,ranging from fluid mechanics to biological systems and economic mechanisms,with a greater focus on the financial markets models.This short overview aims to convey the broad applicability of the asymptotic analysis theory in advancing our comprehension of complex systems,making it an indispensable tool for researchers and practitioners across different disciplines.In particular,such a theory could be applied to reshape intricate financial models(e.g.,stock market volatility models)into more manageable forms,which could be tackled with time-saving numerical implementations.
查看更多>>摘要：In this paper,the diffusive nutrient-microorganism model subject to Neumann boundary condi-tions is considered.The Hopf bifurcations and steady state bifurcations which bifurcate from the positive constant equilibrium of the system are investigated in details.In addition,the formulae to determine the direction of Hopf and steady state bifurcations are derived.Our results show the existence of spatially homoge-neous/nonhomogeneous periodic orbits and steady state solutions,which indicates the spatiotemporal dynamics of the system.Some numerical simulations are also presented to support the analytical results.
查看更多>>摘要：Several eigenvalue properties of the third-order boundary value problems with distributional po-tentials are investigated.Firstly,we prove that the operators associated with the problems are self-adjoint and the corresponding eigenvalues are real.Next,the continuity and differential properties of the eigenvalues of the problems are given,especially we find the differential expressions for the boundary conditions,the coefficient functions and the endpoints.Finally,we show a brief application to a kind of transmission boundary value problems of the problems studied here.
查看更多>>摘要：Kawasaki disease(KD)is an acute,febrile,systemic vasculitis that mainly affects children under five years of age.In this paper,we propose and study a class of 5-dimensional ordinary differential equation mod-el describing the vascular endothelial cell injury in the lesion area of KD.This model exhibits forward/backward bifurcation.It is shown that the vascular injury-free equilibrium is locally asymptotically stable if the basic reproduction number R0＜1.Further,we obtain two types of sufficient conditions for the global asymptotic sta-bility of the vascular injury-free equilibrium,which can be applied to both the forward and backward bifurcation cases.In addition,the local and global asymptotic stability of the vascular injury equilibria and the presence of Hopf bifurcation are studied.It is also shown that the model is permanent if the basic reproduction number R0＞1,and some explicit analytic expressions of ultimate lower bounds of the solutions of the model are given.Our results suggest that the control of vascular injury in the lesion area of KD is not only correlated with the basic reproduction number Ro,but also with the growth rate of normal vascular endothelial cells promoted by the vascular endothelial growth factor.
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