We consider the Einstein/Yang-Mills equations in 3+ 1 space time dimensions with SU (2) gauge group and prove rigorously the existence of a globally defined smooth static solution. We show that the associated Einstein metric is asymptotically flat and the total mass is finite. Thus, for non-abelian gauge fields the Yang/Mills repulsive force can balance the gravitational attractive force and prevent the formation of singularities in spacetime.

A nonlinear, nonlocal cochlear model of the transmission line type is studied in order to capture the multitone interactions and resulting tonal suppression effects. The model can serve as a module for voice signal processing, and is a one-dimensional (in space) damped dispersive nonlinear PDE based on the mechanics and phenomenology of hearing. It describes the motion of the basilar membrane (BM0 in the cochlea driven by input pressure waves. Both elastic dampling and selective longitudinal fluid damping are present. The forner is nonlinear and nonlocal in BM displacement, and plays a kep role in capturing tonal interactions. The latter is active only near the exit boundary (helicotrema), and is built in to damp out the remaining long waves. The initial boundary value problem is numerically solved with a semi-implicit second order finite difference method. Solutions reach a multi-frequency quai-steady state

A sensor pixel integrates optical intensity across its extent, and we explore the role that this integration plays in phase space tomography. The literature is inconsistent in its treatment of this integration—some approaches model this integration explicitly, some approaches are ambiguous about whether this integration is taken into account, and still some approaches assume pixel values to be point samples of the optical intensity. We show that making a point-sample assumption results in apodization of and thus systematic error in the recovered ambiguity function, leading to underestimating the overall degree of coherence. We explore the severity of this effect using a Gaussian Schell-model source and discuss when this effect, as opposed to noise, is the dominant source of error in the retrieved state of coherence.

This paper aims to mathematically advance the field of quantitative thermo-acoustic imaging. Given several electromagnetic data sets, we establish for the first time an analytical formula for reconstructing the absorption coefficient from thermal energy measurements. Since the formula involves derivatives of the given data up to the third order, it is unstable in the sense that small measurement noises may cause large errors. However, in the presence of measurement noise, the obtained formula, together with a noise regularization technique, provides a good initial guess for the true absorption coefficient. We finally correct the errors by deriving a reconstruction formula based on the least square solution of an optimal control problem and prove that this optimization step reduces the errors occurring and enhances the resolution.

All continuous GL(n) covariant valuations that map convex bodies to convex bodies are completely classified. This establishes a characterization of moment and projection operators and shows that the Holmes-Thompson area is the unique Minkowski area that is also a bivaluation.