The University of Zielona Góra was founded on 1 September 2001 as a result of a merger between Zielona Góra's Pedagogical University, which was founded in 1971 and Technical University, which was founded in 1965. It is one of the newer universities in Poland. Main buildings are located in two campuses: "A" on Podgórna street and "B" on Wojska Polskiego street. The President's office is located near the Old Town on Licealna Street.
This paper is concerned with abnormal geodesics on the Carnot group with growth vector (2,3,5,8,14) . Because of a large number of symmetries, this problem reduces to an analysis of the five-dimensional flow. Using the Kovalevskaya method, integrable cases of the resulting system are identified. For these cases, first integrals and explicit solutions are found. It is shown that in the general case the system admits no additional meromorphic first integrals. The paper concludes by discussing some problems regarding the abnormal geodesics on Lie groups.
We introduce the Lyapunov Integrability Test (LIT), a new numerical framework for exploring integrability in nonlinear dynamical systems. The main idea is inspired by the role of the Mandelbrot set in complex dynamics: instead of identifying parameter values associated with stable periodic orbits, the LIT seeks parameter regions that may correspond to integrable dynamics. The method is based on a global analysis of Lyapunov exponents across parameter space and provides a simple and efficient way to visualize candidate integrable regimes. Its performance is demonstrated on several benchmark systems, including the ABC flow, the heavy top, quantum dots, a helically symmetric Hamiltonian system with three degrees of freedom, and the classical double pendulum. The results demonstrate that the LIT is an effective and computationally efficient framework for the global exploration of parameter space and the identification of candidate integrable regimes.
Geopolymer concrete (GC), which is produced from industrial by-products rich in aluminosilicates such as fly ash, ground granulated blast furnace slag, and silica fume, serves as an environmentally sustainable substitute for conventional Portland cement-based concrete. Fracture toughness is vital for GC, as its brittle matrix is prone to crack initiation and propagation, affecting structural safety. Enhancing fracture resistance ensures reliable performance under various loading modes. Coir and flax fibers were chosen for their availability, sustainability, and ability to bridge cracks and improve post-crack energy absorption, providing insights for optimizing natural fiber reinforcement. Researchers have turned to natural fibers such as coir and flax to overcome the limited ductility and mechanical shortcomings typical of geopolymer composites. These fibers were specifically chosen for their potential to enhance both toughness and post-cracking energy absorption in the matrix. This investigation focused on how different aspect ratios of coir and flax fibers affected the fracture properties of GC when exposed to various loading modes: Mode I, Mode III, and their combination. To ensure a controlled comparison, GC specimens were cast with fiber lengths set at 20 mm, 40 mm, and 60 mm, while maintaining a fixed fiber volume fraction of 0.5
We study the integrability of a two-dimensional Hamiltonian system with a gyroscopic term and a non-homogeneous potential composed of two homogeneous components of different degrees. The model describes the motion of a particle in a plane under the combined influence of a central (Kepler-type) potential, a uniform magnetic field, and a superposition of homogeneous forces. By combining the Levi–Civita regularization with the so-called coupling constant metamorphosis transformation, and employing differential Galois theory, we derive analytical necessary conditions for integrability in the Liouville sense. They put restrictions on the degrees of homogeneity of the potential terms and their values in particular points. The obtained results encompass and generalize several classical galactic and astrophysical models, including the generalized Hill model, the Hénon–Heiles and Armbruster–Guckenheimer–Kim systems, providing a unified framework for studying non-homogeneous Hamiltonians. We demonstrate the effectiveness of the derived integrability obstructions by proving the non-integrability of these models in the presence of a uniform rotational field. The numerical analysis via the Poincaré cross-sections further confirms the analytical results, illustrating the transition from regular to chaotic dynamics as the rotational and non-homogeneous terms are introduced. Moreover, we show that, without the Kepler-type term, a generalized non-homogeneous extension of the exceptional potential remains integrable. The explicit forms of the first integrals are given.
The Istanbul metropolitan mayoral election in 2019 provided a suitable way to study the subtle and apparent shifts in the Turkish political landscape. For the first time in recent history, opposition gained ground in this main commercial and population hub. So far, Istanbul local politics were treated from an aspatial perspective. Here, we employ spatial econometrics to understand the subtle groundswell in Istanbul’s political geography. This paper maps the electoral change that took place in the 84 days between two elections using 31 thousand ballot data based on 782 districts in Istanbul. In addition to the change in voting patterns we also employ two different datasets to better situate the change of public opinion. The first database is the socioeconomic status indexing of Istanbul’s districts. The second database comes from the author’s own work employing python-based datamining the online database of for sale properties in Istanbul on the verge of the 2019 election. An OLS regression analysis and a spatial-lag regression is applied on the datasets. The results are contrary to the political punditry and points to a newly emerging middle-class coalition.
