Rzeszów University of Technology

In the paper we introduce the concept of the Kuratowski distance between nonempty and bounded subsets of a Banach space. We show that the Kuratowski measure of noncompactness of a nonempty and bounded subset of a Banach space is equal to the Kuratowski distance of that subset to the family of all nonempty and relatively compact subsets of the mentioned Banach space.

With the growing share of distributed energy sources and energy storage, the problem of high-voltage line overloads is becoming one of the key challenges of modern power systems. This paper proposes a method to eliminate transmission line overloads by coordinating power changes among selected generation units, loads, and energy storage units, with network reconfiguration as needed. A key element of the proposed approach is identifying the controllable elements most strongly associated with overload patterns in post-contingency scenarios. These elements were identified using statistical correlation coefficients describing the relationship between line loading levels and the power generated, consumed, or stored at individual buses. Correlation analysis was used to determine a subset of candidate elements most relevant to the observed overload patterns, thereby reducing the dimension of the control problem. The proposed approach enables effective overload reduction while simultaneously reducing the problem's dimensionality. The results indicate that it can be a useful tool supporting network management under conditions of high generation and load variability.

Entropic uncertainty relations are universal quantifiers of fundamental uncertainties of quantum measurements and are widely discussed in the quantum metrology literature. Quantum memory is a phenomenon related to the specific type of quantum correlations that allows for reducing fundamental uncertainties of quantum measurements. In the present work, the modified concept of quantum memory for time-dependent problems is proposed. We compare the time-dependent formulation of quantum memory with the out-of-time-ordered correlator (OTOC). Quantum memory is a rigorous mathematical concept that requires demanding calculations. Thus, until now, quantum memory has been discussed mainly for simple model systems and stationary problems. In the present work, we demonstrate that quantum memory can also be studied for realistic and physically relevant systems, e.g., the atomic helical spin chain, as well as the emergence and propagation of quantum correlations in time. We found that quantum memory manifests faster oscillations in time than OTOC and does not equilibrate. Furthermore, an artificial neural network is trained and asked to predict results for OTOC and quantum memory. These results show that quantum memory is more sensitive than OTOC in terms of broken inversion symmetry and the nonreciprocal effect.

This paper evaluates the robustness and structural invariance of hybrid population-based metaheuristics under various objective space transformations. A light-weight plug-and-play hybridization operator is applied to nineteen state-of-the-art algorithms - including differential evolution, particle swarm optimization, and recent bio-inspired methods - without modifying their internal logic. Benchmarking on the CEC-2017 suite across four dimensions (10, 30, 50, 100) is performed under five transformation types: baseline, translation, scaling, rotation, and constant shift. Statistical comparisons based on Wilcoxon and Friedman tests, Bayesian dominance analysis, and convergence trajectory profiling consistently show that differential-based hybrids (e.g., hybrid improved multi-operator differential evolution, hybrid success-history adaptive differential evolution, hybrid double mutational salp swarm algorithm) maintain high accuracy, stability, and invariance across all tested deformations. In contrast, classical algorithms - especially particle swarm optimization- and Harris hawks optimization - based variants -exhibit significant performance degradation under non-separable or distorted landscapes. The findings confirm the superiority of adaptive, structurally resilient hybrids for real-world optimization tasks subject to domain-specific transformations. However, the evidence is based on deterministic, continuous, bound-constrained single-objective CEC-2017 functions. The experiments use a fixed budget and five predefined transformations. Therefore, the conclusions should be interpreted within this controlled setting and may not directly generalize to nonlinear constrained, noisy, dynamic, or multi-objective problems without dedicated protocols. To partially bridge to practice, we also include a constrained helical compression spring design case study evaluated with the same methodology.

We study the thermodynamics of the recently proposed superconducting Josephson junction diode, in particular its specific heat capacity. Its low temperature behavior is determined by the interplay of two intrinsic energy scales of the microscopic Hamiltonian, associated with the superconducting gap and tunneling amplitude of conventional electrons through the junction. If the latter is large enough to overcome the former, the specific heat decays linearly with temperature, reflecting the presence of a current through the diode. In the opposite case, the specific heat decays exponentially and the diode becomes non-conducting. In the intermediate regime, where both scales are equally large, the specific heat exhibits a non-trivial power-law behavior in terms of the temperature. It is demonstrated, that switching on and off of the device is possible by changing the phase of the superconducting condensate only, which is accessible via an external magnetic field. Having magnetic textures hosting magnetic defects, such as skyrmions, antiskyrmions or domain walls as sources of such magnetic field leaves behind unique defect specific footprints in the specific heat.