Investigation of the Effect of Artificial Internal Defects on the Tensile Behavior of Laser Powder Bed Fusion 17–4 Stainless Steel Samples: Simultaneous Tensile Testing and X-Ray Computed Tomography

Experimental Mechanics - Insufficient data are available to fully understand the effects of metal additive manufacturing (AM) defects for widespread adoption of the emerging technology....     

Twice Q-polynomial distance-regular graphs of diameter 4

It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

On the output function in a Ginsburg’s machine

We give the form of the output function in Ginsburg’s machine in which the input and output dictionaries are abelian groups and the transition function is of a special form.