Fixed angle inverse scattering in the presence of a Riemannian metric

We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption on the metric, we obtain uniqueness and stability results in the inverse scattering problem for a potential with data generated by two incident waves from opposite directions. Further, similar results are given using one measurement provided the potential also satisfies a symmetry assumption. This work extends the results of [Rakesh and M. Salo, Fixed angle inverse scattering for almost symmetric or controlled perturbations, SIAM J. Math. Anal. 52 2020, 6, 5467–5499] and [Rakesh and M. Salo, The fixed angle scattering problem and wave equation inverse problems with two measurements, Inverse Problems 36 2020, 3, Article ID 035005] from the Euclidean case to certain Riemannian metrics.

Abel transform of exponential functions for planetary and cometary atmospheres with application to observation of 46P/Wirtanen and to the OI 557.7 nm emission at Mars.

<p>Line-of-sight integration of emissions from planetary and cometary atmospheres is the Abel transform of the emission rate, under the spherical symmetry assumption. Indefinite integrals constructed from the Abel transform integral are useful for implementing remote sensing data analysis methods, such as the numerical inverse Abel transform giving the volume emission rate compatible with the observation. We obtain analytical expressions based on a suitable, non-alternating, series development to compute those indefinite integrals. We establish expressions allowing absolute accuracy control of the convergence of these series depending on the number of terms involved. We compare the analytical method with numerical computation techniques, which are found to be sufficiently accurate as well. Inverse Abel transform fitting is then tested in order to establish that the expected emission rate profiles can be retrieved from the observation of both planetary and cometary atmospheres. We show that the method is robust, especially when Tikhonov regularization is included, although it must be carefully tuned when the observation varies across many orders of magnitude. A first application is conducted over observation of comet 46P/Wirtanen, showing some variability possibly attributable to an evolution of the contamination by dust and icy grains. A second application is considered to deduce the 557.7 nm volume emission rate profile of the metastable oxygen atom in the upper atmosphere of planet Mars.</p>

A Quantified Coalgebraic van Benthem Theorem

The classical van Benthem theorem characterizes modal logic as the bisimulation-invariant fragment of first-order logic; put differently, modal logic is as expressive as full first-order logic on bisimulation-invariant properties. This result has recently been extended to two flavours of quantitative modal logic, viz. fuzzy modal logic and probabilistic modal logic. In both cases, the quantitative van Benthem theorem states that every formula in the respective quantitative variant of first-order logic that is bisimulation-invariant, in the sense of being nonexpansive w.r.t. behavioural distance, can be approximated by quantitative modal formulae of bounded rank. In the present paper, we unify and generalize these results in three directions: We lift them to full coalgebraic generality, thus covering a wide range of system types including, besides fuzzy and probabilistic transition systems as in the existing examples, e.g. also metric transition systems; and we generalize from real-valued to quantale-valued behavioural distances, e.g. nondeterministic behavioural distances on metric transition systems; and we remove the symmetry assumption on behavioural distances, thus covering also quantitative notions of simulation.

Equitable Voting Rules

May's theorem (1952), a celebrated result in social choice, provides the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that grant voters identical roles. We show that a weakening of May's symmetry assumption allows for a far richer set of rules that still treat voters equally. We show that such rules can have minimal winning coalitions comprising a vanishing fraction of the population, but not less than the square root of the population size. Methodologically, we introduce techniques from group theory and illustrate their usefulness for the analysis of social choice questions.

Mechanical analytical modelling of non-axisymmetric overbraiding

Overbraiding allows the production of complex hollow composite preforms. Various mechanical modelling methods have been proposed in the literature to help optimizing this process. However, these are either analytical, and computationally fast, but limited to axisymmetric braiding, or based on finite element methods (FEM) but computationally very expensive. The present work proposes a novel approach to model mechanically and in a computationally efficient manner the braid along its formation and deposition. Thereby, the geometrical and mechanical equilibrium of the whole braid in the convergence zone is described without symmetry assumption using a system of equations which is solved using the Newton-Raphson method. The new model, treating yarn-yarn friction, is evaluated using results from the literature, and demonstrates that friction is not the only physical mechanism that must be considered to simulate accurately the process. Finally, significant calculation time reduction is obtained compared to the most recent FEM simulations.

Noether symmetry approach to the non-minimally coupled $$Y(R)F^2$$ gravity

We use Noether symmetry approach to find spherically symmetric static solutions of the non-minimally coupled electromagnetic fields to gravity. We construct the point-like Lagrangian under the spherical symmetry assumption. Then we determine Noether symmetry and the corresponding conserved charge. We derive Euler-Lagrange equations from this point-like Lagrangian and show that these equations are same with the differential equations derived from the field equations of the model. Also we give two new exact asymptotically flat solutions to these equations and investigate some thermodynamic properties of these black holes.

Local modal participation analysis of nonlinear systems using Poincaré linearization

The paper studies an extension to nonlinear systems of a recently proposed approach to the definition of modal participation factors. A definition is given for local mode-in-state participation factors for smooth nonlinear autonomous systems. While the definition is general, the resulting measures depend on the assumed uncertainty law governing the system initial condition, as in the linear case. The work follows Hashlamoun et al. (IEEE Trans Autom Control 54(7):1439–1449 2009) in taking a mathematical expectation (or set-theoretic average) of a modal contribution measure over an uncertain set of system initial state. Poincaré linearization is used to replace the nonlinear system with a locally equivalent linear system. It is found that under a symmetry assumption on the distribution of the initial state, the tractable calculation and analytical formula for mode-in-state participation factors found for the linear case persists to the nonlinear setting. This paper is dedicated to the memory of Professor Ali H. Nayfeh.

Fixed point theorems on a γ-generalized quasi-metric spaces

The concept of \gamma-generalized quasi-metric spaces is newly introduced in this paper with the symmetry assumption removed. The existence of fixed points of our newly introduced (\gamma-\phi)-contraction mappings, defined on \gamma-generalized quasi-metric spaces, is proved. Our results generalize many known related results in literature.