A new inequality for the Riemann-Stieltjes integrals driven by irregular signals in Banach spaces.

We prove an inequality of the Loéve-Young type for the Riemann-Stieltjes integrals driven by irregular signals attaining their values in Banach spaces, and, as a result, we derive a new theorem on the existence of the Riemann-Stieltjes integrals driven by such signals. Also, for any [Formula: see text], we introduce the space of regulated signals [Formula: see text] ([Formula: see text] are real numbers, and W is a Banach space) that may be uniformly approximated with accuracy [Formula: see text] by signals whose total variation is of order [Formula: see text] as [Formula: see text] and prove that they satisfy the assumptions of the theorem. Finally, we derive more exact, rate-independent characterisations of the irregularity of the integrals driven by such signals.

Reliability of MR-Based Volumetric 3-D Analysis of Pelvic Muscles among Subjects with Low Back with Leg Pain and Healthy Volunteers.

AIM: Lately, the diagnostic value of magnetic resonance imaging, Lasègue sign and classic neurological signs have been considered not accurate enough to distinguish the radicular from non-radicular low back with leg pain (LBLP) and a calculation of the symptomatic side muscle volume has been indicated as a probable valuable marker. However, only the multifidus muscle volume has been calculated so far. The main objective of the study was to verify whether LBLP subjects presented symptomatic side pelvic muscle atrophy compared to healthy volunteers. The second aim was to assess the inter-rater reliability of 3-D manual method for segmenting and measuring the volume of the gluteus maximus, gluteus medius, gluteus minimus and piriformis muscles in both LBLP patients and healthy subjects. METHOD: Two independent raters analyzed MR images of LBLP and healthy subjects towards muscle volume of four pelvic muscles, i.e. the piriformis, gluteus minimus, gluteus medius and gluteus maximus. For both sides, the MR images of the muscles without adipose tissue infiltration were manually segmented in 3-D medical images. RESULTS: Symptomatic muscle atrophy was confirmed in only over 50% of LBLP subjects (gluteus maximus (p<0.001), gluteus minimus (p<0.01) and piriformis (p<0.05)). The ICC values indicated that the inter-rater reproducibility was greater than 0.90 for all measurements (LBLP and healthy subjects), except for the measurement of the right gluteus medius muscle in LBLP patients, which was equal to 0.848. CONCLUSION: More than 50% of LBLP subjects presented symptomatic gluteus maximus, gluteus minimus and piriformis muscle atrophy. 3-D manual segmentation reliably measured muscle volume in all the measured pelvic muscles in both healthy and LBLP subjects. To answer the question of what kind of muscle atrophy is indicative of radicular or non-radicular pain further studies are required.