arXiv subjects

M. Klimek

Publications and source records attributed to M. Klimek.

4 recordsLinked to original sources

arXiv2025

Disruption Management in Airline Operations: A Solver-based Approach using Time-Space Network Optimization

This paper presents AIRS, a day-of-operations disruption-recovery system. AIRS.ACR models integrated aircraft-crew recovery on a Time-Space Network (TSN) and solves a mixed-integer linear program (MILP) that enforces rotation continuity, crew legality, maintenance windows, slot capacities, and multi-leg integrity via flow-balance constraints; disruption-aware search-space construction and warm starts control combinatorial growth. A companion module, AIRS.PaxR, performs rapid passenger re-accommodation using greedy assignment and lightweight evolutionary search while preserving aircraft-crew feasibility. Across realistic evaluations, AIRS meets operational decision windows and reduces recovery costs relative to manual or sequential methods, providing a scalable, extensible decision-support capability for operations control centers.

cs.OH↗

arXiv2001

Stationarity-conservation laws for certain linear fractional differential equations

The Leibniz rule for fractional Riemann-Liouville derivative is studied in algebra of functions defined by Laplace convolution. This algebra and the derived Leibniz rule are used in construction of explicit form of stationary-conserved currents for linear fractional differential equations. The examples of the fractional diffusion in 1+1 and the fractional diffusion in d+1 dimensions are discussed in detail. The results are generalized to the mixed fractional-differential and mixed sequential fractional-differential systems for which the stationarity-conservation laws are obtained. The derived currents are used in construction of stationary nonlocal charges.

math-ph↗

arXiv2000

Conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces

The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general method include equations on quantum plane, supersymmetric equations for chiral and antichiral supermultiplets as well as auxiliary equations of integrable models - principal chiral model and various cases of nonlinear Toda lattice equations.

math-ph↗

arXiv1997

Conservation laws for linear equations on quantum Minkowski spaces

The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved currents are given. The proposed procedure can be simplified for *-invariant equations. The derived method is then applied to Klein-Gordon, Dirac and wave equations on different classes of Minkowski spaces. In the examples also symmetry operators for these equations are obtained. They include quantum deformations of classical symmetry operators as well as an additional operator connected with deformation of the Leibnitz rule in non-commutative differential calculus.

hep-th↗