An Extremal Property of p-mean Width

2018 ◽  
Vol 73 (1) ◽  
Author(s):  
Qunli Long ◽  
Songjun Lv
Keyword(s):  
Extremal Property ◽  
Mean Width

An extremal property of the mean width of the simplex

1998 ◽  
Vol 310 (4) ◽  
pp. 685-693 ◽  
Author(s):  
Franck Barthe
Keyword(s):  
Extremal Property ◽  
Mean Width ◽  
The Mean

scholarly journals Ethnic variation in medial orbital wall anatomy and its implications for decompression surgery

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Minhui Amy Chan ◽  
Farah Ibrahim ◽  
Arjunan Kumaran ◽  
Kailing Yong ◽  
Anita Sook Yee Chan ◽  
...  
Keyword(s):  
Relative Position ◽  
Ethmoid Sinus ◽  
Decompression Surgery ◽  
Ethnic Variation ◽  
Sinus Wall ◽  
Orbital Wall ◽  
Mean Width ◽  
Significant Difference ◽  
The Mean ◽  
Medial Orbital Wall

Abstract Background To describe the inter-ethnic variation in medial orbital wall anatomy between Chinese, Malay, Indian and Caucasian subjects. Methods Single-centre, retrospective, Computed Tomography (CT)-based observational study. 20 subjects of each ethnicity, were matched for gender and laterality. We excluded subjects younger than 16 years and those with orbital pathology. OsiriX version 8.5.1 (Pixmeo., Switzerland) and DICOM image viewing software CARESTREAM Vue PACS (Carestream Health Inc., USA) were used to measure the ethmoidal sinus length, width and volume, medial orbital wall and floor angle and the relative position of the posterior ethmoid sinus to the posterior maxillary wall. Statistical analyses were performed using Statistical Package for Social Sciences version 25.0 (IBM, USA). Results There were 12 males (60 %) in each group, with no significant difference in age (p = 0.334–0.994). The mean ethmoid sinus length in Chinese, Malay, Indian and Caucasian subjects, using the Chinese as reference, were 37.2, 36.9, 38.0 and 37.4mm, the mean width was 11.6, 10.5, 11.4 and 10.0mm (p = 0.020) and the mean ethmoid sinus volume were 3362, 3652, 3349 and 3898mm3 respectively. The mean medial orbital wall and floor angle was 135.0, 131.4, 131.0 and 136.8 degrees and the mean relative position of posterior ethmoid sinus to posterior maxillary wall were − 2.0, -0.2, -1.5 and 1.6mm (p = 0.003) respectively. Conclusions No inter-ethnic variation was found in decompressible ethmoid sinus volume. Caucasians had their posterior maxillary sinus wall anterior to their posterior ethmoidal walls unlike the Chinese, Malay and Indians. Awareness of ethnic variation is essential for safe orbital decompression.

scholarly journals Electrochemical treatment of ex vivo human abdominal skin and potential use in scar management: A pilot study

2021 ◽  
Vol 7 ◽  
pp. 205951312098853
Author(s):  
Dana M Hutchison ◽  
Amir A Hakimi ◽  
Avin Wijayaweera ◽  
Soohong Seo ◽  
Ellen M Hong ◽  
...  
Keyword(s):  
Color Change ◽  
Ex Vivo ◽  
Low Cost ◽  
Histological Evaluation ◽  
Ph Change ◽  
Level Of Evidence ◽  
Abdominal Skin ◽  
Electrochemical Therapy ◽  
Mean Width ◽  
Scar Management

Introduction: Scar treatments aim to address pathologic collagen deposition; however, they can be expensive or difficult to control. Electrochemical therapy (ECT) offers a simple alternative treatment. The purpose of this study is to examine the acid-base and histological changes in ex vivo human abdominal skin following ECT. Methods: Forty-two ex vivo human panniculus tissue sections collected from six individuals were tumesced with normal saline. ECT was performed by inserting two platinum needle electrodes connected to a DC power supply into each specimen. Voltage was varied (3–6 V) and applied for 5 minutes. Each specimen was sectioned across both electrode insertion sites and immediately stained with pH sensitive dye. The width of dye color change for each dosimetry pair was calculated. Hematoxylin and eosin staining was used to evaluate samples. Results and Discussion: ECT caused a spatially localised and dose-dependent increased area of acidic and basic pH around the anode and cathode, respectively. A significantly greater mean width of pH change was generated at the cathode compared to the anode in all treatment groups. Histological evaluation displayed broad condensation and hyalinisation of dermal collagen. Conclusion: ECT triggered dermal pH alterations and changed the underlying structural framework of the specimen. This technology may serve as a low-cost, minimally invasive local soft-tissue remodeling technique with potential application in scar management. Level of Evidence: 5 Lay Summary Electrochemical therapy is a novel treatment that causes spatially selective dermal injury in areas of interest. This study measures the effects of electrochemical therapy when applied to abdominal skin. Electrochemical therapy appears to have beneficial effects by causing a highly localised reduction in collagen content or local softening of tissue, which is consistent with other studies on scar therapies, including chemexfoliation, radiofrequency technologies, and lasers. However, electrochemical therapy can be performed at a fraction of the costs of these aforementioned modalities.

An extremal property of the hypersphere

1951 ◽  
Vol 47 (1) ◽  
pp. 245-247 ◽  
Author(s):  
A. M. Macbeath
Keyword(s):  
Convex Body ◽  
Extremal Property ◽  
Plane Case ◽  
Simple Application ◽  
Plane Convex ◽  
Plane Convex Body

It was shown by Sas (1) that, if K is a plane convex body, then it is possible to inscribe in K a convex n-gon occupying no less a fraction of its area than the regular n-gon occupies in its circumscribing circle. It is the object of this note to establish the n-dimensional analogue of Sas's result, giving incidentally an independent proof of the plane case. The proof is a simple application of the Steiner method of symmetrization.

scholarly journals Convex Bodies of Minimal Volume, Surface Area and Mean Width with Respect to Thin Shells

2008 ◽  
Vol 60 (1) ◽  
pp. 3-32 ◽  
Author(s):  
Károly Böröczky ◽  
Károly J. Böröczky ◽  
Carsten Schütt ◽  
Gergely Wintsche
Keyword(s):  
Unit Ball ◽  
Surface Area ◽  
Convex Bodies ◽  
Extreme Points ◽  
Thin Shells ◽  
Minimal Volume ◽  
Asymptotic Formulae ◽  
Mean Width

AbstractGiven r > 1, we consider convex bodies in En which contain a fixed unit ball, and whose extreme points are of distance at least r from the centre of the unit ball, and we investigate how well these convex bodies approximate the unit ball in terms of volume, surface area and mean width. As r tends to one, we prove asymptotic formulae for the error of the approximation, and provide good estimates on the involved constants depending on the dimension.

Cervical and High Thoracic Ligamentum Flavum Frequently Fails to Fuse in the Midline

2003 ◽  
Vol 99 (6) ◽  
pp. 1387-1390 ◽  
Author(s):  
Philipp Lirk ◽  
Christian Kolbitsch ◽  
Guenther Putz ◽  
Joshua Colvin ◽  
Hans Peter Colvin ◽  
...  
Keyword(s):  
Ligamentum Flavum ◽  
Epidural Needle ◽  
Complete Fusion ◽  
Thoracic Epidural ◽  
Loss Of Resistance ◽  
Ligamenta Flava ◽  
Mean Width ◽  
Human Cadavers ◽  
The Mean ◽  
High Thoracic Epidural

Background Cervical and high thoracic epidural anesthesia and analgesia have gained increasing importance in the treatment of painful conditions and as components of anesthetics for cardiac and breast surgery. In contrast to the hanging-drop technique, the loss-of-resistance technique is thought to rely on the penetration of the ligamentum flavum. However, the exact morphology of the ligamentum flavum at different vertebral levels remains controversial. Therefore, the aim of this study was to investigate the incidence and morphology of cervical and high thoracic ligamentum flavum mid-line gaps in embalmed cadavers. Methods Vertebral column specimens were obtained from 52 human cadavers. On each dissected level, ligamentum flavum mid-line gaps were recorded and evaluated with respect to shape and size. Results The following variations were encountered: complete fusion in the mid-line, mid-line fusion with a gap in the caudal part, mid-line gap, and mid-line gap with widened caudal end. The incidence of mid-line gaps at the following levels was: C3-C4: 66%, C4-C5: 58%, C5-C6: 74%, C6-C7: 64%, C7-T1: 51%, Th1-Th2: 21%, Th2-Th3: 11%, Th3-Th4: 4%, Th4-Th5: 2%, and Th5-Th6: 2%. The mean width of mid-line gaps was 1.0 +/- 0.3 mm. Conclusions In conclusion, the present study shows that gaps in the ligamenta flava are frequent at cervical and high thoracic levels but become rare at the T3/T4 level and below, such that one cannot always rely on the ligamentum flavum as a perceptible barrier to epidural needle placement at these levels.

scholarly journals Radiographic Measurement of Cochlear in Sudanese Population using High Resolution Computed Tomography (HRCT)

2021 ◽  
Vol 29 (2) ◽  
Author(s):  
Lubna Bushara ◽  
Mohamed Yousef ◽  
Ikhlas Abdelaziz ◽  
Mogahid Zidan ◽  
Dalia Bilal ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Hearing Loss ◽  
High Resolution ◽  
Temporal Bone ◽  
Healthy Subjects ◽  
Cochlear Nerve ◽  
High Resolution Computed Tomography ◽  
Mean Width ◽  
The Mean ◽  
The Right

This study aimed to determine the measurements of the cochlea among healthy subjects and hearing deafness subjects using a High Resolution Computed Tomography (HRCT). A total of 230 temporal bone HRCT cases were retrospectively investigated in the period spanning from 2011 to 2015. Three 64-slice units were used to examine patients with clinical complaints of hearing loss conditions at three Radiology departments in Khartoum, Sudan. For the control group (A) healthy subjects, the mean width of the right and left cochlear were 5.61±0.40 mm and 5.56±0.58 mm, the height were 3.56±0.36 mm and 3.54±0.36 mm, the basal turn width were 1.87±0.19 mm and 1.88 ±0.18 mm, the width of the cochlear nerve canal were 2.02±1.23 and 1.93±0.20, cochlear nerve density was 279.41±159.02 and 306.84±336.9 HU respectively. However, for the experimental group (B), the mean width of the right and left cochlear width were 5.38±0.46 mm and 5.34±0.30 mm, the height were 3.53±0.25 mm and 3.49±0.28mm, the basal turn width were 1.76±0.13 mm, and 1.79±0.13 mm, the width of the cochlear nerve canal were 1.75±0.18mm and 1.73±0.18mm, and cochlear nerve density were 232.84±316.82 and 196.58±230.05 HU, respectively. The study found there was a significant difference in cochlea’s measurement between the two groups with a p-value < 0.05. This study had established baseline measurements for the cochlear for the healthy Sudanese population. Furthermore, it found that HRCT of the temporal bone was the best for investigation of the cochlear and could provide a guide for the clinicians to manage congenital hearing loss.

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