Seismic hazard analysis for engineering sites based on the stochastic finite-fault method

Seismic hazard analyses are mainly performed using either deterministic or probabilistic methods.However,there are still some defects in these statistical model-based approaches for regional seismic risk assessment affected by the near-field of large earthquakes.Therefore,we established a deterministic seismic hazard analysis method that can characterize the entire process of ground motion propagation based on stochastic finite-fault simulation,and we chose the site of the Xiluodu dam to demonstrate the method.This method can characterize earthquake source properties more realistically than other methods and consider factors such as the path and site attenuation of seismic waves.It also has high computational efficiency and is convenient for engineering applications.We first analyzed the complexity of seismogenic structures in the Xiluodu dam site area,and then an evaluation system for ground motion parameters that considers various uncertainties is constructed based on a stochastic finitefault simulation.Finally,we assessed the seismic hazard of the dam site area comprehensively.The proposed method was able to take into account the complexity of the seismogenic structures affecting the dam site and provide multi-level parameter evaluation results corresponding to different risk levels.These results can be used to construct a dam safety assessment system of an earthquake in advance that provides technical support for rapidly and accurately assessing the post-earthquake damage state of a dam,thus determining the influence of an earthquake on dam safety and mitigating the risk of potential secondary disasters.

Column sufficient tensors and tensor complementarity problems

Stimulated by the study of sufficient matrices in linear complementarity problems, we study column sufficient tensors and tensor complementarity problems. Column sufficient tensors constitute a wide range of tensors that include positive semi-definite tensors as special cases. The inheritance property and invariant property of column sufficient tensors are presented. Then, various spectral properties of symmetric column sufficient tensors are given. It is proved that all H-eigenvalues of an even-order symmetric column sufficient tensor are nonnegative, and all its Z-eigenvalues are nonnegative even in the odd order case. After that, a new subclass of column sufficient tensors and the handicap of tensors are defined. We prove that a tensor belongs to the subclass if and only if its handicap is a finite number. Moreover, several optimization models that are equivalent with the handicap of tensors are presented. Finally, as an application of column sufficient tensors, several results on tensor complementarity problems are established.

PROPERTIES OF TENSOR COMPLEMENTARITY PROBLEM AND SOME CLASSES OF STRUCTURED TENSORS

This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor ,4 such that the tensor complementarity problem （q, A）： finding an x ∈R^n such that x ≥ 0, q＋Axm-1 ≥ 0, and xT（q＋Ax^m-1） = 0, has a solution for each vector q ∈R^n. Several subclasses of Q-tensors are given： F-tensors, R-tensors, strictly semi-positive tensors and semi-positive R0-tensors. We prove that a nonnegative tensor is a Q-tensor if and only if all of its principal diagonal entries are positive, and so the equivalence of Q-tensor, R-tensors, strictly semi-positive tensors was showed if they are nonnegative tensors. We also show that a tensor is an R0-tensor if and only if the tensor complementarity problem （0, A） has no non-zero vector solution, and a tensor is a R-tensor if and only if it is an R0-tensor and the tensor complementarity problem （e,A） has no non-zero vector solution, where e = （1, 1…. , 1）T

？ositive eigenvalue-eigenvector of lonlinear positive mappings

We show that an （eventually） strongly increasing and positively homogeneous mapping T defined on a Banach space can be turned into an Edelstein contraction with respect to Hilbert＇s projective metric. By applying the Edelstein contraction theorem, a nonlinear version of the famous Krein- Rutman theorem is presented, and a simple iteration process {T^kx/｜｜T^kx｜｜} （ x ∈ P^＋） is given for finding a positive eigenvector with positive eigenvalue of T. In particular, the eigenvalue problem of a nonnegative tensor A can be viewed as the fixed point problem of the Edelstein contraction with respect to Hilbert＇s projective metric. As a result, the nonlinear Perron-Frobenius property of a nonnegative tensor A is reached easily.