Studying Cassini’s photoelectrons during a series of solar eclipses in Saturn, using data from Cassini's Langmuir Probe

<p>The Langmuir Probe (LP) onboard Cassini was one of the three experiments that could measure the cold inner magnetospheric plasma, along with the Radio and Plasma Waves Science (RPWS) and the Cassini Plasma Spectrometer (CAPS). While the century-old LP theory looks quite straight-forward, in reality things are much more complicated.</p> <p>The operation of the LP is quite simple: by applying positive bias voltages, the probe attracts the electrons and repels the ions of the surrounding plasma. From the resulting current-voltage curve characteristics of the ambient electrons can be estimated, i.e. density and temperature. When negative bias voltages are applied to the probe the characteristics of the ambient ions can be estimated, i.e. density, temperature, and mass.</p> <p>Though the LP operation and interpretation are quite simple and straightforward, there are assumptions made and therefore the theoretical models may not always reflect the actual plasma conditions in Saturn’s magnetosphere. For this study we are focused on the effect of the photoelectrons, i.e. electrons that are generated by the incident sunlight on Cassini’s surfaces, which are difficult to be observed and corrected for in a laboratory plasma.</p> <p>We developed a robust algorithm that identifies the transitions of the LP in and out of shadow caused by the Saturn and its rings. The LP data inside and outside the eclipses are compared using the algorithm developed. In this presentation we will discuss the impact of the photoelectron generation from the spacecraft surfaces to the LP current-voltage curves, and understand the variations of the measured plasma density connected with the photoelectrons.</p>

Lp-Theory for the fractional time stochastic heat equation with an infinite-dimensional fractional Brownian motion

In this paper, we study the [Formula: see text]-theory of the fractional time stochastic heat equation [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] denotes the Caputo derivative of order [Formula: see text], and [Formula: see text] is a sequence of i.i.d. fractional Brownian motions with a same Hurst index [Formula: see text]. The integral with respect to fractional Brownian motion is the Skorohod integral. By using the Malliavin calculus techniques and fractional calculus, we obtain a generalized Littlewood–Paley inequality, and prove the existence and uniqueness of [Formula: see text]-solution to such equation.

Lexicographic Methods for Fuzzy Linear Programming

Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world decision-making problems that arise in uncertain and ever-changing environments since its introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming (LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development. Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can appear in the model components in different ways. Hence, despite fifty years of research, new formulations of FLP problems and solution methods are still being proposed. Among the existing formulations, those using fuzzy numbers (FNs) as parameters and/or decision variables for handling inexactness and vagueness in data have experienced a remarkable development in recent years. Here, a long-standing issue has been how to deal with FN-valued objective functions and with constraints whose left- and right-hand sides are FNs. The main objective of this paper is to present an updated review of advances in this particular area. Consequently, the paper briefly examines well-known models and methods for FLP, and expands on methods for fuzzy single- and multi-objective LP that use lexicographic criteria for ranking FNs. A lexicographic approach to the fuzzy linear assignment (FLA) problem is discussed in detail due to the theoretical and practical relevance. For this case, computer codes are provided that can be used to reproduce results presented in the paper and for practical applications. The paper demonstrates that FLP that is focused on lexicographic methods is an active area with promising research lines and practical implications.

Lp-theory of boundary integral operators for domains with unbounded smooth boundary

The paper is devoted to the ${L^{p}}$-theory of boundary integral operators for boundary value problems described by anisotropic Helmholtz operators with variable coefficients in unbounded domains with unbounded smooth boundary. We prove the invertibility of boundary integral operators for Dirichlet and Neumann problems in the Bessel-potential spaces ${H^{s,p}(\partial D)}$, ${p\in(1,\infty)}$, and the Besov spaces ${B_{p,q}^{s}(\partial D)}$, ${p,q\in[1,\infty]}$. We prove also the Fredholmness of the Robin problem in these spaces and give the index formula.