How to Cope with Division Problems under Interval Uncertainty of Claims?

The paper deals with division situations where individual claims can vary within closed intervals.Uncertainty of claims is removed by compromising in a consistent way the upper and lower bounds of the claim intervals.Deterministic division problems with compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to e .cient and reasonable rules for division problems under interval uncertainty of claims.uncertainty;claims;division problems

How to Cope with Division Problems under Interval Uncertainty of Claims?

The paper deals with division situations where individual claims can vary within closed intervals.Uncertainty of claims is removed by compromising in a consistent way the upper and lower bounds of the claim intervals.Deterministic division problems with compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to e .cient and reasonable rules for division problems under interval uncertainty of claims.

How to Cope with Division Problems under Interval Uncertainty of Claims?

The paper deals with division situations where individual claims can vary within closed intervals.Uncertainty of claims is removed by compromising in a consistent way the upper and lower bounds of the claim intervals.Deterministic division problems with compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to e .cient and reasonable rules for division problems under interval uncertainty of claims

Linear programming approach for solving stochastic control problem on networks with discounted transition costs

Секция 10. Теоретическая информатикаThe infinite horizon stochastic control problem on network with expected total discounted cost optimization criterion is studied. A linear programming approach for solving this problem on networks is developed. Moreover, a polynomial tim

Adiabatic Pair Creation

We give here the proof that pair creation in a time dependent potentials is possible. It happens with probability one if the potential changes adiabatically in time and becomes overcritical, that is when an eigenvalue enters the upper spectral continuum. The potential may be assumed to be zero at large negative and positive times. The rigorous treatment of this effect has been lacking since the pioneering work of Beck, Steinwedel and Suessmann in 1963 and Gershtein and Zeldovich in 1970.Comment: 53 pages, 1 figure. Editorial changes on page 22 f

Everything Hits at Once: How Remote Rainfall Matters for the Prediction of the 2021 North American Heat Wave

In June 2021, Western North America experienced an intense heat wave with unprecedented temperatures and far-reaching socio-economic consequences. Anomalous rainfall in the West Pacific triggers a cascade of weather events across the Pacific, which build up a high-amplitude ridge over Canada and ultimately lead to the heat wave. We show that the response of the jet stream to diabatically enhanced ascending motion in extratropical cyclones represents a predictability barrier with regard to the heat wave magnitude. Therefore, probabilistic weather forecasts are only able to predict the extremity of the heat wave once the complex cascade of weather events is captured. Our results highlight the key role of the sequence of individual weather events in limiting the predictability of this extreme event. We therefore conclude that it is not sufficient to consider such rare events in isolation but it is essential to account for the whole cascade over different spatiotemporal scales

Optical lattice quantum simulator for QED in strong external fields: spontaneous pair creation and the Sauter-Schwinger effect

Spontaneous creation of electron-positron pairs out of the vacuum due to a strong electric field is a spectacular manifestation of the relativistic energy-momentum relation for the Dirac fermions. This fundamental prediction of Quantum Electrodynamics (QED) has not yet been confirmed experimentally as the generation of a sufficiently strong electric field extending over a large enough space-time volume still presents a challenge. Surprisingly, distant areas of physics may help us to circumvent this difficulty. In condensed matter and solid state physics (areas commonly considered as low energy physics), one usually deals with quasi-particles instead of real electrons and positrons. Since their mass gap can often be freely tuned, it is much easier to create these light quasi-particles by an analogue of the Sauter-Schwinger effect. This motivates our proposal of a quantum simulator in which excitations of ultra-cold atoms moving in a bichromatic optical lattice represent particles and antiparticles (holes) satisfying a discretized version of the Dirac equation together with fermionic anti-commutation relations. Using the language of second quantization, we are able to construct an analogue of the spontaneous pair creation which can be realized in an (almost) table-top experiment.Comment: 21 pages, 10 figure

Derivation of the cubic NLS and Gross-Pitaevskii hierarchy from manybody dynamics in d=3d=3 based on spacetime norms

We derive the defocusing cubic Gross-Pitaevskii (GP) hierarchy in dimension $d=3$, from an $N$-body Schr\"{o}dinger equation describing a gas of interacting bosons in the GP scaling, in the limit $N\rightarrow\infty$. The main result of this paper is the proof of convergence of the corresponding BBGKY hierarchy to a GP hierarchy in the spaces introduced in our previous work on the well-posedness of the Cauchy problem for GP hierarchies, \cite{chpa2,chpa3,chpa4}, which are inspired by the solutions spaces based on space-time norms introduced by Klainerman and Machedon in \cite{klma}. We note that in $d=3$, this has been a well-known open problem in the field. While our results do not assume factorization of the solutions, consideration of factorized solutions yields a new derivation of the cubic, defocusing nonlinear Schr\"odinger equation (NLS) in $d=3$.Comment: 44 pages, AMS Late