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Opis: An essential aspect of jumping performance is the ability to control impact forces. One of the key measures of this ability is the damping ratio, a dimensionless parameter that quantifies the rate at which oscillations decay following a disturbance. This study aims to assess the intra-session and inter-session reliability of damping ratios at different lower-limb anatomical landmarks and evaluate their sensitivity in detecting differences between various repetitive jumping forms, with an emphasis on establishing a specific methodological approach. Twenty-three physically active male and female students performed maximal countermovement jumps (CMJs) and bilateral (BL) and unilateral (UL) hopping (HOP). Ten wireless inertial measurement units recorded inertial data of five bilateral lower-limb anatomical landmarks. Results showed that the damping ratios during CMJ and HOPUL demonstrated good reliability, whereas in HOPBL were moderately reliable. The damping ratios of nearly all the anatomical landmarks differed between the jumping forms. CMJ had the highest values, HOPBL the lowest, and HOPUL values in between, likely due to variations in joint stiffness and amplitude displacement, as well as stretch‒shortening cycle reliance. Methodologically, using 20 repetitions in an intra-session trial and averaging left and right sides for inter-session reliability and inter-jump sensitivity, damping ratios are acceptably reliable and sufficiently sensitive for biomechanical analysis of different repetitive jumping forms. This metric could potentially be a valuable tool in developing theoretical nonlinear multibody mass‒spring‒damper models and could enhance biomechanical analysis with practical applications in sports training and rehabilitation.
Ključne besede: stretch–shortening cycle, stiffness, impact absorption, oscillation, intraclass, correlation coefficient
Objavljeno v RUP: 13.04.2026; Ogledov: 267; Prenosov: 9
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Opis: It is known that smallest counterexamples to the Cycle Double Cover Conjecture and Berge-Fulkerson Conjecture (if they exist) are cyclically 4- and 5-edge-connected, respectively. We further analyse small cycle separating cuts in possible counterexamples. We prove that if a smallest counterexample G to the CDC Conjecture contains a cycle separating 4-cut S, then the behaviour of the admissible CDC coverings along the dangling edges of the two 4-poles induced by S is uniquely determined among more than 2 a priori possibilities. Similarly, for the Berge-Fulkerson Conjecture, we prove that among more than 2 a priori possibilities, there are only 13 pairs of admissible sets that could occur along the dangling edges of a 5-cut in a smallest counterexample.
Ključne besede: snark, cyclic connectivity, cycle double cover, Berge-Fulkerson conjecture
Objavljeno v RUP: 03.03.2026; Ogledov: 407; Prenosov: 13
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Opis: One of the fundamental results in graph minor theory is that for every planar graph $H$, there is a minimum integer $f(H)$ such that graphs with no minor isomorphic to $H$ have treewidth at most $f(H)$. A lower bound for $f(H)$ can be obtained by considering the maximum integer $k$ such that $H$ contains $k$ vertex-disjoint cycles. There exists a graph of treewidth $\Omega(k\log k)$ which does not contain $k$ vertex-disjoint cycles, from which it follows that $f(H) = \Omega(k\log k)$. In particular, if $f(H)$ is linear in $\lvert V(H) \rvert$ for graphs $H$ from a subclass of planar graphs, it is necessary that $n$-vertex graphs from the class contain at most $\lvert V(H) \rvert$ vertex-disjoint cycles. We ask whether this is also a sufficient condition, and demonstrate that this is true for classes of planar graphs with bounded component size. For an $n$-vertex graph $H$ which is a disjoint union of $r$ cycles, we show that ${f(H) \leq 3n/2 + O(r^2 \log r)}$, and improve this to $f(H)$≤$n$+O(√$n$) when $r$=2. In particular this bound is linear when $r$=O(√$n$/logn). We present a linear bound for $f(H)$ when $H$ is a subdivision of an $r$-edge planar graph for any constant~$r$. We also improve the best known bounds for $f(H)$ when $H$ is the wheel graph or the 4×4 grid, obtaining a bound of 160 for the latter.
Ključne besede: graph minor, treewidth, cycle packing
Objavljeno v RUP: 05.01.2026; Ogledov: 827; Prenosov: 2
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Opis: Endpoint indicators for social life cycle analysis (S-LCA) are still less consolidated than those for environmental LCA. There is a broad consensus that human well-being should be the overarching goal of social sustainability and therefore also of S-LCA. However, to date the two major databases for S-LCA are restricted to a multiplication of working hours with a quality- or risk-adjusted factor. This paper aims to evaluate the congruence between this technical pragmatism and well-established findings of happiness research. The analysis starts with the argument that evidence and consequentiality are necessary criteria for any variables used. It is then shown that some of the variables such as poverty are not consequential, while the unit of working hours lacks any evidence about a relationship with subjective well-being. The analysis concludes that a simple pointbased endpoint indicator would be more appropriate for S-LCA than the current hour-based indicator.
Ključne besede: social sustainability, life cycle analysis, indicators, endpoint
Objavljeno v RUP: 18.12.2025; Ogledov: 432; Prenosov: 0
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Opis: In 1965, Erdős and Pósa proved that there is an (approximate) duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold for odd cycles, and Dejter and Neumann-Lara asked in 1988 to find all pairs (l, z) of integers where such a duality holds for the family of cycles of length l modulo z. We characterise all such pairs, and we further generalise this characterisation to cycles in graphs labelled with a bounded number of abelian groups, whose values avoid a bounded number of elements of each group. This unifies almost all known types of cycles that admit such a duality, and it also provides new results. Moreover, we characterise the obstructions to such a duality in this setting, and thereby obtain an analogous characterisation for cycles in graphs embeddable on a fixed compact orientable surface.
Ključne besede: Erdős-Pósa property, cycle packing, group-labelled graph
Objavljeno v RUP: 17.11.2025; Ogledov: 683; Prenosov: 9
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