Summary Real‐time hybrid simulation (RTHS) is an effective and versatile tool for the examination of complex structural systems with rate dependent behaviors. To meet the objectives of such a test, appropriate consideration must be given to the partitioning of the system into physical and computational portions (i.e., the configuration of the RTHS). Predictive stability and performance indicators (PSI and PPI) were initially established for use with only single degree‐of‐freedom systems. These indicators allow researchers to plan a RTHS, to quantitatively examine the impact of partitioning choices on stability and performance, and to assess the sensitivity of an RTHS configuration to de‐synchronization at the interface. In this study, PSI is extended to any linear multi‐degree‐of‐freedom (MDOF) system. The PSI is obtained analytically and it is independent of the transfer system and controller dynamics, providing a relatively easy and extremely useful method to examine many partitioning choices. A novel matrix method is adopted to convert a delay differential equation to a generalized eigenvalue problem using a set of vectorization mappings, and then to analytically solve the delay differential equations in a computationally efficient way. Through two illustrative examples, the PSI is demonstrated and validated. Validation of the MDOF PSI also includes comparisons to a MDOF dynamic model that includes realistic models of the hydraulic actuators and the control‐structure interaction effects. Results demonstrate that the proposed PSI can be used as an effective design tool for conducting successful RTHS. Copyright © 2016 John Wiley & Sons, Ltd

We study the Light-Ray transform of integrating vector fields on the Minkowski time-space R 1+n , n ≥ 2, with the Minkowski metric. We prove a support theorem for vector fields vanishing on an open set of light-like lines.We provide examples to illustrate the application of our results to the inverse problem for the hyperbolic Dirichlet-to-Neumann map.2010 Mathematics Subject Classification. 44A12, 46F12, 53C65.

Let X be an open subset of R 2 . We study the dynamic operator, A, integrating over a family of level curves in X when the object changes between the measurement. We use analytic microlocal analysis to determine which singularities can be recovered by the data-set. Our results show that not all singularities can be recovered, as the object moves with a speed lower than the X-ray source. We establish stability estimates and prove that the injectivity and stability are of a generic set if the dynamic operator satisfies the visibility, no conjugate points, and local Bolker conditions. We also show this results can be implemented to Fan beam geometry.with a smooth motion where the limited data case has been analyzed, and characterization of visible and added singularities have been investigated. Our work in this paper is motivated by these dynamic measurements. We first show this dynamic problem can be reduced to an integral geometry problem integrating over level curves. By an appropriate change of variable (see section 2), A can be written asTherefore, we study the following general operator:Af (s, t) = φ(t,x)=s µ(t, x)f (x)dS s,t ,

We study an inverse scattering problem of a perturbed biharmonic operator. we show that the high-frequency asymptotic of scattering amplitude of the biharmonic operator uniquely determines curl A and V − 1 2 ∇ • A. We also study the near-field scattering problem and show that the high-frequency asymptotic expansion up to certain error in terms of frequency λ recovers the same two above quantities with no additional information about A and V . We also prove stability estimates for curl A and V − 1 2 ∇ • A.

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