results for au:Bai_X in:math

- A continuous-time random walk in the quarter plane with homogeneous transition rates is considered. Given a non-negative reward function on the state space, we are interested in the expected stationary performance. Since a direct derivation of the stationary probability distribution is not available in general, the performance is approximated by a perturbed random walk, whose transition rates on the boundaries are changed such that its stationary probability distribution is known in closed form. A perturbed random walk for which the stationary distribution is a sum of geometric terms is considered and the perturbed transition rates are allowed to be inhomogeneous. It is demonstrated that such rates can be constructed for any sum of geometric terms that satisfies the balance equations in the interior of the state space. The inhomogeneous transitions relax the pairwise-coupled structure on these geometric terms that would be imposed if only homogeneous transitions are used. An explicit expression for the approximation error bound is obtained using the Markov reward approach, which does not depend on the values of the inhomogeneous rates but only on the parameters of the geometric terms. Numerical experiments indicate that inhomogeneous perturbation can give smaller error bounds than homogeneous perturbation.
- Aug 24 2017 math.CO arXiv:1708.07003v1In this paper, we enumerate lattice paths with certain constraints and apply the corresponding results to develop formulas for calculating the dimensions of submodules of a class of modules for planar upper triangular rook monoids. In particular, we show that the famous Catalan numbers appear as the dimensions of some special modules; we also obtain some combinatorial identities
- Apr 11 2017 math.AP arXiv:1704.02728v1In this paper, we gives a complete classification of the global dynamics of two- species Lotka-Volterra competition models with nonlocal dispersals: where K, P represent nonlocal operators, under the assumptions that the nonlo- cal operators are symmetric, the models admit two semi-trivial steady states and 0<bc<1. In particular, when both semi-trivial steady states are locally stable, it is proved that there exist infinitely many steady states and the solution with non- negative and nontrivial initial data converges to some steady state. Furthermore, we generalize these results to the case that competition coefficients are location-dependent and dispersal strategies are mixture of local and nonlocal dispersals.
- This paper investigates the task assignment problem for multiple dispersed robots constrained by limited communication range. The robots are initially randomly distributed and need to visit several target locations while minimizing the total travel time. A centralized rendezvous-based algorithm is proposed, under which all the robots first move towards a rendezvous position until communication paths are established between every pair of robots either directly or through intermediate peers, and then one robot is chosen as the leader to make a centralized task assignment for the other robots. Furthermore, we propose a decentralized algorithm based on a single-traveling-salesman tour, which does not require all the robots to be connected through communication. We investigate the variation of the quality of the assignment solutions as the level of information sharing increases and as the communication range grows, respectively. The proposed algorithms are compared with a centralized algorithm with shared global information and a decentralized greedy algorithm respectively. Monte Carlo simulation results show the satisfying performance of the proposed algorithms.
- Oct 14 2016 math.RT arXiv:1610.04122v1In this paper, we discuss modules and structures of the planar upper triangular rook monoid B_n. We first show that the order of B_n is a Catalan number, then we investigate the properties of a module V over B_n generated by a set of elements v_S indexed by the power set of 1, ..., n. We find that every nonzero submodule of V is cyclic and completely decomposable; we give a necessary and sufficient condition for a submodule of V to be indecomposable. We show that every irreducible submodule of V is 1-dimensional. Furthermore, we give a formula for calculating the dimension of every submodule of V. In particular, we provide a recursive formula for calculating the dimension of the cyclic module generated by v_S, and show that some dimensions are Catalan numbers, giving rise to new combinatorial identities.
- Aug 15 2016 math.OC arXiv:1608.03843v1Small-Signal Stability Constrained Optimal Power Flow (SSSC-OPF) can provide additional stability measures and control strategies to guarantee the system to be small-signal stable. However, due to the nonsmooth property of the spectral abscissa function, existing algorithms solving SSSC-OPF cannot guarantee convergence. To tackle this computational challenge of SSSC-OPF, we propose a Sequential Quadratic Programming (SQP) method combined with Gradient Sampling (GS) for SSSCOPF.At each iteration of the proposed SQP, the gradient of the spectral abscissa unction is randomly sampled at the current iterate and additional nearby points to make the search direction computation effective in nonsmooth regions. The method can guarantee SSSC-OPF is globally and efficiently convergent to stationary points with probability one. The effectiveness of the proposed method is tested and validated on WSCC 3-machine 9-bus system, New England 10-machine 39-bus system, and IEEE 54-machine 118-bus system.
- Dec 09 2015 math.AP arXiv:1512.02380v1In this paper, the global dynamics of two-species Lotka-Volterra competition models with nonlocal dispersals is studied. Under the assumption that dispersal kernels are symmetric, we prove that except for very special situations, local stability of semi-trivial steady states implies global stability, while when both semi-trivial steady states are locally unstable, the positive steady state exists and is globally stable. Moreover, our results cover the case that competition coefficients are location-dependent and dispersal strategies are mixture of local and nonlocal dispersals.
- Aug 27 2015 math.OC arXiv:1508.06422v1Recently, many structured tensors are defined and their properties are discussed in the literature. In this paper, we introduce a new class of structured tensors, called exceptionally regular tensor, which is relevant to the tensor complementarity problem. We show that this class of tensors is a wide class of tensors which includes many important structured tensors as its special cases. By constructing two examples, we demonstrate that an exceptionally regular tensor can be, but not always, an $R$-tensor. We also show that within the class of the semi-positive tensors, the class of exceptionally regular tensors coincides with the class of $R$-tensors. In addition, we consider the tensor complementarity problem with an exceptionally regular tensor or an $R$-tensor or a $P_0+R_0$-tensor, and show that the solution sets of these classes of tensor complementarity problems are nonempty and compact.
- Aug 26 2015 math.OC arXiv:1508.06012v1Recently, the tensor complementarity problem (TCP for short) has been investigated in the literature. An important question involving the property of global uniqueness and solvability (GUS-property) for a class of TCPs was proposed by Song and Qi in their paper "Properties of Some Classes of Structured Tensors". In the present paper, we give an answer to this question by constructing two counter-examples. We also show that the solution set of this class of TCPs is nonempty and compact. In particular, we introduce a class of related structured tensors, and show that the corresponding TCP has the GUS-property.
- Let $ R \subset \R $ be a GCD-domain. In this paper, Weinberg's conjecture on the $ n \times n $ matrix algebra $ M_{n}(R) \ (n \geq 2) $ is proved. Moreover, all the lattice orders (up to isomorphisms) on a full $ 2 \times 2 $ matrix algebra over $ R $ are obtained.
- Feb 05 2010 math.PR arXiv:1002.1046v5In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz conditions on their coefficients.
- In this paper we will discuss the optimal risk transfer problems when risk measures are generated by G-expectations, and we present the relationship between inf-convolution of G-expectations and the inf-convolution of drivers G.
- In this paper, we construct an irreducible vertex module for twisted affine Lie algebra of type A_2l^(2).
- The presentation of two-parameter quantum groups of type E-series in the sense of Benkart-Witherspoon [BW1] is given, which has a Drinfel'd quantum double structure. The universal $R$-matrix and a convex PBW-type basis are described for type E_6 (as a sample), and the conditions of those isomorphisms from these quantum groups into the one-parameter quantum doubles are discussed.