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EN
The aim of the study was to assess the usefulness of isometric torque (IT) and peak torque (PT) of the hamstring to quadriceps muscles ratio (H/Q ratio) in monitoring the effectiveness of physiotherapy (PH) in males after ACLR. Hypothesis: The H/Q ratio is a diagnostic tool for monitoring of the effectiveness of the 6- month PH after ACLR. Methods: Twenty males 6 months after ACLR (ACLR group) and 20 male controls underwent IT and PT (60°/s and 180°/s) bilateral measurements of H and Q muscles. The IT and PT were normalized to body mass, and expressed as relative IT (RIT) and relative PT (RPT). The RIT and RPT H/Q ratios, and Limb Symmetry Index (LSI) were calculated. Results: In the ACLR group, the RIT for the H and Q, the RIT for the H/Q ratio and most of the RPT, as well as the H/Q ratio, ROM and LSI values of the operated knee, were not significantly different (NSD) than those of the non-operated side (NOS) or the control group. The between-group comparison of the H/Q ratio for RIT and RPT weren’t NSD. The isokinetic test at 180 °/s showed lower RPT, H/Q ratio and LSI values for the Q muscle than those of the NOS (p = 0.042, p = 0.001). Conclusions: The H/Q ratio, in combination with the RIT, RPT and LSI, is a useful diagnostic tool for monitoring the effectiveness of 6-month PH after ACLR. Restoring the correct H/Q ratio can reduce the risk factor for ACL graft rupture.
EN
Important basic transformations, implemented in CAD systems, are congruence transformations, so-called isometries, which preserve the distance of points. Logic of CAD software bases on the reflection, translation, rotation, and similarity. This fact is the important desideratum in the teaching of Descriptive Geometry. The paper includes a proposal for a teaching from the scope of isometries on the plane and in three-dimensional space.
PL
Ważnymi przekształceniami zaimplementowanymi w oprogramowaniu CAD, są izometrie, czyli przekształcenia zachowujące odległość punktów. Logika tych systemów opiera się gównie na pojęciu symetrii, translacji i obrotu. Ważną jeszcze rolę odgrywa podobieństwo. Uwzględnienie tego faktu w nauczaniu geometrii wykreślnej jest ważnym dezyderatem dydaktycznym. Praca zawiera propozycję dydaktyczną z zakresu zastosowania izometrii na płaszczyźnie i w przestrzeni.
3
Content available remote Multiplication operators on Cesàro sequence spaces
EN
In this paper we characterize the compact, invertible and Fredholm multiplication operators on Cesàro sequence spaces.
4
Content available remote Mappings preserving some distances
EN
We deal with mappings which preserve unit (some positive) distance, as well as with mappings contracting (expanding) some distance. In particular, we show that a mapping preserving three positive distances is an isometry.
EN
Let Y be a Banach lattice and X a strictly monotone sublattice of Y. Every isometric copy of an L1-space in X is 1-complemented in Y (Theorem l). This is an extension of the classical result of Pełczyński for Y = X = L1(my), and of Dor for Y = X being q-concave. We also study the consequences of the existence of isometric copies of l1 in strictly monotone E[phi](my)-spaces, where E[phi](my) denotes the ideal of an Orlicz space L[phi](my) of the elements with absolutely continuous norm.
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