Almost conservation laws for stochastic nonlinear Schrödinger equations

In this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the I-method (= the method of almost conservation laws) to the stochastic setting. As a model example, we consider the defocusing stochastic cubic nonlinear Schrödinger equation (SNLS) on $${\mathbb {R}}^3$$ R 3 with additive stochastic forcing, white in time and correlated in space, such that the noise lies below the energy space. By combining the I-method with Ito’s lemma and a stopping time argument, we construct global-in-time dynamics for SNLS below the energy space.

The Buying Time Argument within the Solar Radiation Management Discourse

In this article, we will establish a version of the buying time argument (BTA) in favor of Sulphur Aerosol Injection (SAI) Climate Engineering (CE). The idea is not to promote the deployment of such scheme, but rather to present the strongest possible argument pro SAI in order to look at its presuppositions, implications, critical points and uncertainties. In discussing BTA being the only morally sound argument in favor of SAI, the stakes and the overall framework will become visible. If, however, the strongest pro-SAI argument enables us to recognize some major flaws of this technology, this option should be disregarded.

Solving the mixed problem for the Klein–Gordon–Fock type equation with integral conditions in the case of the inhomogeneous matching conditions

The classical solution of the mixed problem with integral conditions for the Klein–Gordon–Fock type equation in the half strip is considered when inhomogeneous matching conditions are fulfilled. An equivalent conjugation problem is formulated where conjugation conditions are set on characteristics. Constructed inhomogeneous conditions uniquely define gaps of the solution or its derivatives on characteristics and given gaps can be either remained or smoothed while the time argument increases depending on the kernel of the integral operator in unlocal conditions. The solution of this problem is reduced to solving the second-type Volterra integral equations and their systems. The unique solution of these equations in the class of the twice continuously differentiable functions exists when the initial functions are smooth enough. While considering the given problem the method of characteristics is used to construct both an analytical solution, when the solution of the integral equation can be found explicitly, and an approximate solution. Moreover, approximate solutions can be constructed in numerical and analytical form. When the numerical solution is constructed, matching conditions are significant and need to be considered while developing numerical methods.

Epicurean Challenges to the Disvalue of Death

In global health, several practices rely on the assumption that death has a disvalue for those who die. This includes the fact that we prioritize extending human lives rather than creating new ones, the combination Years Lived with Disability (YLD) and Years of Life Lost (YLL) into Disability-Adjusted Life Years (DALYs), as well as managing the trade-off between morbidity and mortality reduction in a health priority setting. According to Epicureanism, however, death cannot have any disvalue for those who die. Three main arguments are offered on behalf of Epicureanism: the view that we cannot experience death (the experience argument), the view that there is no time where death harms us (the time argument), and the view that there is a symmetry between the nonexistence before and after our lives (the symmetry argument). I show that all three arguments fail to convince.

Extrapolation Problem for Continuous Time Periodically Correlated Isotropic Random Fields

The problem of optimal linear estimation of functionals depending on the unknown values of a random fieldζ(t,x), which is mean-square continuous periodically correlated with respect to time argumenttє R and isotropic on the unit sphere Sn with respect to spatial argumentxєSn. Estimates are based on observations of the fieldζ(t,x) +Θ(t,x) at points (t,x) :t< 0;xєSn, whereΘ(t,x) is an uncorrelated withζ(t,x) random field, which is mean-square continuous periodically correlated with respect to time argumenttє R and isotropic on the sphereSnwith respect to spatial argumentxєSn. Formulas for calculating the mean square errors and the spectral characteristics of the optimal linear estimate of functionals are derived in the case of spectral certainty where the spectral densities of the fields are exactly known. Formulas that determine the least favourable spectral densities and the minimax (robust) spectral characteristics are proposed in the case where the spectral densities are not exactly known while a class of admissible spectral densities is given.

Real tense and real aspect in mirativity

The goal of this paper is an account of the role of tense and aspect in mirative constructions in Spanish. I propose that the past tense morphology and the imperfect/perfect morphology in Spanish miratives contribute their standard meanings to the semantics of mirativity. I define mirativity as the clash between the speaker’s previous beliefs and the current state of affairs asserted by the proposition. I propose a M operator that relates the speaker’s beliefs and the proposition by ranking the worlds in which the proposition doesn’t hold in the speaker’s previous beliefs as better ones. The past tense is interpreted outside the proposition, and constitutes the time argument of the modal base (doxastic domain). Aspect gets its usual interpretation in the proposition but also in the alternative propositions that order the worlds in the modal base. This way, differences regarding the imperfect mirative and the pluperfect one are accounted for. Finally, the paper also discusses stative miratives, which apparently challenge part of the analysis. I claim that these are not counter examples, but rather confirmation of the analysis, once we account for the interaction between miratives, statives and lifetime effects.