查看更多>>摘要：This paper is concerned with the Cauchy problem of the multi-dimensional incompressible magnetohydrodynamic equations with inhomogeneous density and fractional dissipation. It is shown that when alpha+beta-1 + n/2 satisfying 1 <=beta <=alpha <= min{ 3 beta/2 , n/2 , 1 + n/4 } and max { n/4 , n +1/6 } < alpha for n >= 3 , the inhomogeneous incompressible MHD equations have a unique global strong solution for the initial data in some Sobolev spaces without requiring small conditions. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：We study the optimal portfolio allocation problem from a Bayesian perspective using value at risk (VaR) and conditional value at risk (CVaR) as risk measures. By applying the posterior predictive distribution for the future portfolio return, we derive relevant quantities needed in the computations of VaR and CVaR, and express the optimal portfolio weights in terms of observed data only. This is in contrast to the conventional method where the optimal solution is based on unobserved quantities which are estimated. We also obtain the expressions for the weights of the global minimum VaR (GMVaR) and global minimum CVaR (GMCVaR) portfolios, and specify conditions for their existence. It is shown that these portfolios may not exist if the level used for the VaR or CVaR computation are too low. By using simulation and real market data, we compare the new Bayesian approach to the conventional plug-in method by studying the accuracy of the GMVaR portfolio and by analysing the estimated efficient frontiers. It is concluded that the Bayesian approach outperforms the conventional one, in particular at predicting the out-of-sample VaR. (C) 2022 The Author(s). Published by Elsevier Inc.
查看更多>>摘要：In this paper, we propose a stochastic SEIRS rabies epidemic models with two patches to investigate the spatial spread of rabies under the influence of environmental noise. Adopting a new technique to construct the stochastic Lyapunov functions, we obtain the sufficient conditions for the existence of an ergodic stationary distribution. In addition, if the movement of dogs is forbidden, we obtain the exact expression of probability density function around a quasi-equilibrium point. Finally, numerical simulations are employed to verify our analytical results and reveal the impact of stochastic perturbations on rabies transmission.(c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Under an arc-coloring c of a digraph D , if for each pair of vertices (u, v ) , there exists a directed walk from u to v satisfying that any two consecutive arcs of it have different colors, we say that D is properly-walk connected, and c is a proper-walk coloring of D . The proper-walk connection number (wc) over right arrow of D is the least integer k such that D has a proper-walk coloring with k colors. Fiedorowicz, Sidorowicz, Sopena (Appl. Math. Comput. 410 (2021) 126253) conjectured that if D is a hamiltonian digraph with delta (D) >= 2, then (wc) over right arrow (D) <= 2 . In this paper, we disprove the conjecture by constructing two families of counterexamples. Also, we present some cases for a hamiltonian digraph D having (wc) over right arrow (D ) = 2 . In addition, we find that Observation 15 is not true in the same paper. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper we investigate the limiting behaviour of Conditional Tail Expectation (CTE) and its decomposition for a sum of real-valued tail-dependent random variables with regularly varying distributions. Asymptotic proportions to the corresponding Value at Risk (VaR) measures are obtained for a flexible dependence structure. For a certain practical case considering an investment portfolio exact formulas are derived and sensitivity to model parameters is analysed. We also carry out a simulation study verifying our results and revealing the speed of convergence for different values of parameters. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：We present monostatic sampling methods for limited-aperture scattering problems in two dimensions. The direct sampling method (DSM) is well known to provide a robust, stable, and fast numerical scheme for imaging inhomogeneities from multistatic measurements even with only one or two incident fields. However, in practical applications, monostatic measurements in limited-aperture configuration are frequently encountered. A monostatic sampling method (MSM) was studied in full-aperture configuration in recent literature. In this paper, we develop MSM in limited-aperture configuration and derive an asymptotic formula of the corresponding indicator function. Based on the asymptotic formula, we then analyze the imaging performance of the proposed method depending on the range of measurement directions and the geometric, material properties of inhomogeneities. Furthermore, we propose a modified numerical scheme with multi-frequency measurements that improve imaging performance, especially for small anomalies. Numerical simulations are presented to validate the analytical results. (C) 2022 The Authors. Published by Elsevier Inc.
查看更多>>摘要：The vertex (resp. edge) metric dimension of a connected graph G, denoted by dim(G) (resp. edim(G)), is defined as the size of a smallest set S subset of V(G) which distinguishes all pairs of vertices (resp. edges) in G. Bounds dim(G) <= L(G)+ 2c(G) and edim(G) <= L(G) + 2c(G), where c(G) is the cyclomatic number in G and L(G) depends on the number of leaves in G , are known to hold for cacti and it is conjectured that they hold for general graphs. In leafless graphs it holds that L(G) = 0 , so for such graphs the conjectured upper bound becomes 2c(G). In this paper, we show that the bound 2c(G) cannot be attained by leafless cacti, so the upper bound for such cacti decreases to 2c(G) - 1 , and we characterize all extremal leafless cacti for the decreased bound. We conjecture that the decreased bound holds for all leafless graphs, i.e. graphs with minimum degree at least two. We support this conjecture by showing that it holds for all graphs with minimum degree at least three and that it is sufficient to show that it holds for all 2-connected graphs, and we also verify the conjecture for graphs of small order. (c) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Recent studies show that different update rules are invariant regarding the evolutionary outcomes for a well-mixed population or homogeneous network. In this paper, we investi-gate how the Q-learning algorithm, one of the reinforcement learning methods, affects the evolutionary outcomes in square lattice. Especially, we consider the mixed strategy update rule, among which some agents adopt Q-learning method to update their strategies, the proportion of these agents (these agents are denoted as Artificial Intelligence (AI)) is con-trolled by a simple parameter rho. The rest of other agents, the proportion is denoted by 1 - rho, adopt the Fermi function to update their strategies. Through extensive numerical simulations, we found that the mixed strategy-update rule can facilitate cooperation com-pared with the pure Fermi-function-based update rule. Besides, if the proportion of AI is moderate, cooperators among the whole population exhibit conditional behavior and moody conditional behavior. However, if the whole population adopts the pure Fermi-function-based strategy update rule or the pure Q-learning-based strategy update rule, then cooperators among the whole population exhibit the hump-shaped conditional be-havior. Our results provide a new insight to understand the evolution of cooperation from AI's view. (C)& nbsp;2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：What is the maximum Lagrangian of an r-uniform hypergraph that is t-intersecting? For t = 1, the answer is complete; the case r = 3 was determined by Hefetz and Keevash in 2012, and the remaining cases r >= 4 were determined by Bene Watts, Norin and Yepremyan in 2018. For integers n, r, t, i with 1 <= t <= r <= n and 0 <= i <= r t, let F (n, r, t, i) := {e is an element of([n]/r) : |e boolean AND [t + 2i]| >= t + i} be a t-intersecting r-uniform hypergraph. Bene Watts, Norin and Yepremyan further conjectured that if an r-graph G is t-intersecting, then lambda(G) < max lim lambda(F (n, r, t, i))(0 <= i <= r-tn ->infinity). In this paper, we confirm the conjecture for t. {r - 1, r - 2}, and r is an element of {3, 4, 5, 6}. (C) 2022 Elsevier Inc. All rights reserved.
查看更多>>摘要：Without the need of constructing piecewise Barrier Lyapunov functions (BLFs), an innovative low-computation adaptive control strategy is developed to unfasten the asymmetric full state constraints for nonlinear stochastic switched systems by incorporating a series of new-style coordinate transformations into the adaptive backstepping design procedure. Via the incorporation of new-style coordinate transformations, the constrained tracking control can be carried out directly without the transformation from constrained systems to new systems. Then, to tackle the "differential explosion" problem caused by repeated derivative of virtual controllers, an innovative tracking differentiator (TD) technology is introduced into each step of design process to improve the tracking accuracy. Furthermore, the resulting closed-loop system proves to be stable, meanwhile, all signals are bounded in probability. Simulations with comparisons through Norrbin nonlinear systems is made to confirm the validity. (C) 2022 Elsevier Inc. All rights reserved.
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