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Abstract: Abstract 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 results. Theoretical and numerical results show that large environmental perturbations can inhibit the spread of tuberculosis. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1147-y
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Abstract: Abstract A graph G is a fractional (k, m)-deleted graph if removing any m edges from G, the resulting subgraph still admits a fractional k-factor. Let k ≥ 2 and m ≥ 1 be integers. Denote \(\lfloor{2m \over k}\rfloor^{\ast}=\lfloor{2m \over k}\rfloor\) if \(2m \over k\) is not an integer, and \(\lfloor{2m \over k}\rfloor^{\ast}=\lfloor{2m \over k}\rfloor - 1\) if \(2m \over k\) is an integer. In this paper, we prove that G is a fractional (k, m)-deleted graph if δ(G) ≥ k + m and isolated toughness meets $$I\left( G \right) > \left\{ {\matrix{{3 - {1 \over m},\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} & {{\text{if}}\,k = 2\,{\text{and}}\,m \ge 3,} \cr {k + {{{{\left\lfloor {{{2m} \over k}} \right\rfloor }^*}} \over {m + 1 - {{\left\lfloor {{{2m} \over k}} \right\rfloor }^*}}},} & {{\text{otherwise}}.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \cr } } \right.$$ Furthermore, we show that the isolated toughness bound is tight. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1067-x
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Abstract: Abstract Several eigenvalue properties of the third-order boundary value problems with distributional potentials 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 nd 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. PubDate: 2025-01-01 DOI: 10.1007/s10255-023-1064-5
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Abstract: Abstract The multicolor Ramsey number rk(C4) is the smallest integer N such that any k-edge coloring of KN contains a monochromatic C4. The current best upper bound of rk(C4) was obtained by Chung (1974) and independently by Irving (1974), i.e., rk(C4) ≤ k2 + k + 1 for all k ≥ 2. There is no progress on the upper bound since then. In this paper, we improve the upper bound of rk(C4) by showing that rk(C4) ≤ k2 + k − 1 for even k ≥ 6. The improvement is based on the upper bound of the Turán number ex(n, C4), in which we mainly use the double counting method and many novel ideas from Firke, Kosek, Nash, and Williford [J. Combin. Theory, Ser. B 103 (2013), 327–336]. PubDate: 2025-01-01 DOI: 10.1007/s10255-023-1074-3
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Abstract: Abstract The focusing modified Korteweg-de Vries (mKdV) equation with multiple high-order poles under the nonzero boundary conditions is first investigated via developing a Riemann-Hilbert (RH) approach. We begin with the asymptotic property, symmetry and analyticity of the Jost solutions, and successfully construct the RH problem of the focusing mKdV equation. We solve the RH problem when 1/S11(k) has a single high-order pole and multiple high-order poles. Furthermore, we derive the soliton solutions of the focusing mKdV equation which corresponding with a single high-order pole and multiple high-order poles, respectively. Finally, the dynamics of one- and two-soliton solutions are graphically discussed. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1037-3
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Abstract: Abstract 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. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1143-2
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Abstract: Abstract 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 \(\phi \left( s \right) = {s^{{1 \over {{\alpha _k}}} + \sum\limits_{i = 1}^k {\left( {1 - {{{\alpha _i}} \over {{\alpha _k}}}} \right)} }}\log \,\log\,{1 \over s}\) 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]. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1051-5
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Abstract: Abstract 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. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1070-2
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Abstract: Abstract In this paper, the diffusive nutrient-microorganism model subject to Neumann boundary conditions 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 homogeneous/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. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1079-6
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Abstract: Abstract 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 \({\cal O}(n^{2 \over 3} \log {n \over \epsilon})\) and \({\cal O}(n^{3 \over 4} \log {n \over \epsilon})\) 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 \({\cal O}({\sqrt n} \ \log n \ \log{n \over \epsilon})\) 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. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1146-z
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Abstract: Abstract Let F, G and H be three graphs with G ⊆ H. We call G an F-saturated graph relative to H, if there is no copy of F in G but there is a copy of F in G + e for any e ∈ E(H) E(G). The F-saturation game on host graph H consists of two players, named Max and Min, who alternately add edges of H to G such that each chosen edge avoids creating a copy of F in G, and the players continue to choose edges until G becomes F-saturated relative to H. Max wishes to maximize the length of the game, while Min wishes to minimize the process. Let satg(F, H) (resp. sat′g(F, H)) denote the number of edges chosen when Max (resp. when Min) starts the game and both players play optimally. In this article, we show that satg(P5, Kn) = sat′g(P5, Kn) = n + 2 for n ≥ 15, and satg(P5, Km,n), sat′g(P5, Km,n) lie in \(\left\{ {m + n - \left\lfloor {{{m - 2} \over 4}} \right\rfloor ,\,m + n - \left\lceil {{{m - 3} \over 4}} \right\rceil } \right\}\) if \(n \ge {5 \over 2}m\) and m ≥ 4, respectively. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1125-4
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Abstract: Abstract 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 infinity 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. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1144-1
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Abstract: Abstract This research paper addresses a topic of interest to many researchers and engineers due to its effective applications in various industrial areas. It focuses on the thermoelastic laminated beam model with nonlinear structural damping, nonlinear time-varying delay, and microtemperature effects. Our primary goal is to establish the stability of the solution. To achieve this, and under suitable hypotheses, we demonstrate energy decay and construct a Lyapunov functional that leads to our results. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1151-2
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Abstract: Abstract 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. PubDate: 2025-01-01 DOI: 10.1007/s10255-024-1123-6
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Abstract: Abstract This paper is devoted to solving a reflected backward stochastic differential equation (BSDE in short) with one continuous barrier and a quasi-linear growth generator g, which has a linear growth in (y, z), except the upper direction in case of y < 0, and is more general than the usual linear growth generator. By showing the convergence of a penalization scheme we prove existence and comparison theorem of the minimal Lp (p > 1) solutions for the reflected BSDEs. We also prove that the minimal Lp solution can be approximated by a sequence of Lp solutions of certain reflected BSDEs with Lipschitz generators. PubDate: 2024-10-01 DOI: 10.1007/s10255-024-1133-4
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Abstract: Abstract In this paper, a stochastic Lotka-Volterra system with infinite delay is considered. A new concept of extinction, namely, the almost sure β-extinction is proposed and sufficient conditions for the solution to be almost sure β-extinction are obtained. When the positive equilibrium exists and the intensities of the noises are small enough, any solution of the system is attracted by the positive equilibrium. Finally, numerical simulations are carried out to support the results. PubDate: 2024-10-01 DOI: 10.1007/s10255-024-1078-7
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Abstract: Abstract In this paper, we study mulit-dimensional oblique reflected backward stochastic differential equations (RBSDEs) in a more general framework over finite or infinite time horizon, corresponding to the pricing problem for a type of real option. We prove that the equation can be solved uniquely in Lp(1 < p ≤ 2)-space, when the generators are uniformly continuous but each component taking values independently. Furthermore, if the generator of this equation fulfills the infinite time version of Lipschitzian continuity, we can also conclude that the solution to the oblique RBSDE exists and is unique, despite the fact that the values of some generator components may affect one another. PubDate: 2024-10-01 DOI: 10.1007/s10255-024-1136-1
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Abstract: Abstract In this paper, we design the differentially private variants of the classical Frank-Wolfe algorithm with shuffle model in the optimization of machine learning. Under weak assumptions and the generalized linear loss (GLL) structure, we propose a noisy Frank-Wolfe with shuffle model algorithm (NoisyFWS) and a noisy variance-reduced Frank-Wolfe with the shuffle model algorithm (NoisyVRFWS) by adding calibrated laplace noise under shuffling scheme in the ℓp(p ∈ [1, 2])-case, and study their privacy as well as utility guarantees for the Hölder smoothness GLL. In particular, the privacy guarantees are mainly achieved by using advanced composition and privacy amplification by shuffling. The utility bounds of the NoisyFWS and NoisyVRFWS are analyzed and obtained the optimal excess population risks \({\cal O}({n^{ - {{1 + \alpha } \over {4\alpha }}}} + {{\log (d)\sqrt {\log ({1 \mathord{\left/ {\vphantom {1 \delta }} \right.} \delta })} } \over {n\epsilon\,}})\) and \({\cal O}({n^{ - {{1 + \alpha } \over {4\alpha }}}} + {{\log (d)\sqrt {\log ({1 \mathord{\left/ {\vphantom {1 \delta }} \right.} \delta })} } \over {{n^2\epsilon}\,}})\) with gradient complexity \({\cal O}({n^{ - {{{{(1 + \alpha )}^2}} \over {4{\alpha ^2}}}}})\) for \(\alpha \in \left[ {{1 \mathord{\left/ {\vphantom {1 {\sqrt 3 ,\,1}}} \right.} {\sqrt 3 ,\,1}}} \right]\) . It turns out that the risk rates under shuffling scheme are a nearly-dimension independent rate, which is consistent with the previous work in some cases. In addition, there is a vital tradeoff between (α, L)-Hölder smoothness GLL and the gradient complexity. The linear gradient complexity \({\cal O}(n)\) is showed by the parameter α = 1. PubDate: 2024-10-01 DOI: 10.1007/s10255-024-1095-6
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Abstract: Abstract The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid $$\left\{ {\matrix{ {u_t^\varepsilon + {u^\varepsilon } \cdot \nabla {u^\varepsilon } - \Delta {u^\varepsilon } + \nabla {{\rm{P}}^\varepsilon } = {n^\varepsilon }\nabla {c^\varepsilon },} \hfill & {{\rm{in}}} \hfill & {{\mathbb{R}^d} \times \left( {0,\infty } \right),} \hfill \cr {\nabla \cdot {u^\varepsilon } = 0,} \hfill & {{\rm{in}}} \hfill & {{\mathbb{R}^d} \times \left( {0,\infty } \right),} \hfill \cr {n_t^\varepsilon + {u^\varepsilon } \cdot \nabla {n^\varepsilon } - \Delta {n^\varepsilon } = - \nabla \cdot \left( {{n^\varepsilon }\nabla {c^\varepsilon }} \right),} \hfill & {{\rm{in}}} \hfill & {{\mathbb{R}^d} \times \left( {0,\infty } \right),} \hfill \cr {{1 \over \varepsilon }c_t^\varepsilon - \Delta {c^\varepsilon } = {n^\varepsilon },} \hfill & {{\rm{in}}} \hfill & {{\mathbb{R}^d} \times \left( {0,\infty } \right),} \hfill \cr {\left( {{u^\varepsilon },{n^\varepsilon },{c^\varepsilon }} \right){ _{t = 0}} = \left( {{u_0},{n_0},{c_0}} \right),} \hfill & {{\rm{in}}} \hfill & {{\mathbb{R}^d},} \hfill \cr } } \right.$$ where d ≥ 2. It is known that for each ϵ > 0 and all sufficiently small initial data (u0, n0, c0) belongs to certain Fourier space, the problem possesses a unique global solution (uϵ, nϵ, cϵ) in Fourier space. The present work asserts that these solutions stabilize to (u∞, n∞, c∞) as ϵ−1 → 0. Moreover, we show that cϵ(t) has the initial layer as ϵ−1 → 0. As one expects its limit behavior maybe give a new viewlook to understand the system. PubDate: 2024-10-01 DOI: 10.1007/s10255-024-1134-3
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Abstract: Abstract 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 model 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 suffcient conditions for the global asymptotic stability 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 R0, but also with the growth rate of normal vascular endothelial cells promoted by the vascular endothelial growth factor. PubDate: 2024-07-03 DOI: 10.1007/s10255-024-1096-5
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