We characterize the non-uniqueness in the inverse problem for the stationary transport model, in which the absorption a and the scattering coefficient k of the media are to be recovered from the albedo operator. We show that “gauge equivalent” pairs (a, k) yield the same albedo operator, and that we can recover uniquely the class of the gauge equivalent pairs. We apply this result to show uniqu...

‎In this paper‎, ‎we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation‎. ‎Moreover‎, ‎the finite-time blow-up of the solution for the equation is investigated by the concavity method‎.

In this paper, we prove the existence and uniqueness of solution to the impulsive fuzzy functional differential equations under generalized Hukuhara differentiability via the principle of contraction mappings. Some examples are provided to illustrate the result.

In Biometrics, facial uniqueness is commonly inferred from impostor similarity scores. In this paper, we show that such uniqueness measures are highly unstable in the presence of image quality variations like pose, noise and blur. We also experimentally demonstrate the instability of a recently introduced impostor-based uniqueness measure of [Klare and Jain 2013] when subject to poor quality fa...

In this paper we prove that the lack of uniqueness for solutions of the tree dyadic model of turbulence is overcome with the introduction of a suitable noise. The uniqueness is a weak probabilistic uniqueness for all l-initial conditions and is proven using a technique relying on the properties of the q-matrix associated to a continuous time Markov chain.

In [4], the authors proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved in [4].

In [4], the authors proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved in [4].

We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong uniqueness results are improved. Classical uniqueness results for this equation follow naturally.

I provide a new proof of uniqueness of equilibrium in a wide class of global games. I show that the joint best-response in these games is a contraction. The uniqueness result then follows as a corollary of the contraction property. Furthermore, the contraction mapping approach provides a revealing intuition for why uniqueness arises: Complementarities in games generate multiplicity of equilibri...

We consider congestion games on networks with nonatomic users and userspecific costs. We are interested in the uniqueness property defined by Milchtaich [Milchtaich, I. 2005. Topological conditions for uniqueness of equilibrium in networks. Math. Oper. Res. 30, 225–244] as the uniqueness of equilibrium flows for all assignments of strictly increasing cost functions. He settled the case with two...