Proximal Point Subgradient Algorithm

2021 ◽  
pp. 103-173
Author(s):  
Alexander J. Zaslavski
Keyword(s):  
Proximal Point ◽  
Subgradient Algorithm

Recurrent varicose veins below the knee after varicose vein surgery

Phlebologie ◽  
2007 ◽  
Vol 36 (03) ◽  
pp. 132-136
Author(s):  
M. W. de Haan ◽  
J. C. J. M. Veraart ◽  
H. A. M. Neumann ◽  
P. A. F. A. van Neer
Keyword(s):  
Varicose Vein ◽  
Varicose Veins ◽  
Varicose Vein Surgery ◽  
Proximal Point ◽  
Perforating Veins ◽  
Recurrent Varicose Veins ◽  
Below The Knee ◽  
Duplex Imaging ◽  
Additional Value

SummaryThe objectives of this observational study were to investigate whether varicography has additional value to CFDI in clarifying the nature and source of recurrent varicose veins below the knee after varicose vein surgery and to investigate the possible role of incompetent perforating veins (IPV) in these recurrent varicose veins. Patients, material, methods: 24 limbs (21 patients) were included. All patients were assessed by a preoperative clinical examination and CFDI (colour flow duplex imaging). Re-evaluation (clinical and CFDI) was done two years after surgery and varicography was performed. Primary endpoint of the study was the varicographic pattern of these visible varicose veins. Secondary endpoint was the connection between these varicose veins and incompetent perforating veins. Results: In 18 limbs (75%) the varicose veins were part of a network, in six limbs (25%) the varicose vein appeared to be a solitary vein. In three limbs (12.5%) an incompetent sapheno-femoral junction was found on CFDI and on varicography in the same patients. In 10 limbs (41%) the varicose veins showed a connection with the persistent below knee GSV on varicography. In nine of these 10 limbs CFDI also showed reflux of this below knee GSV. In four limbs (16%) the varicose veins showed a connection with the small saphenous vein (SSV). In three limbs this reflux was dtected with CFDI after surgery. An IPV was found to be the proximal point of the varicose vein in six limbs (25%) and half of these IPV were detected with CFDI as well. Conclusion: Varicography has less value than CFDI in detecting the source of reflux in patients with recurrent varicose veins after surgery, except in a few cases where IPV are suspected to play a role and CFDI is unable to detect these IPV.

STRONG AND Δ - CONVERGENCE THEOREMS USING MODIFIED PROXIMAL POINT ALGORITHM IN CAT(0) SPACES

2018 ◽  
Vol 7 (2) ◽  
pp. 8
Author(s):  
KUMAR DAS APURVA ◽  
DHAR DIWAN SHAILESH ◽  
DASHPUTRE SAMIR ◽  
◽  
◽  
...  
Keyword(s):  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Convergence Theorems

scholarly journals Effect of synthetic bone replacement material of different size on shear stress resistance within impacted native and thermodisinfected cancellous bone: an in vitro femoral impaction bone grafting model

2021 ◽  
Author(s):  
C. Fölsch ◽  
P. Sahm ◽  
C. A. Fonseca Ulloa ◽  
G. A. Krombach ◽  
M. Kampschulte ◽  
...  
Keyword(s):  
Cancellous Bone ◽  
Bone Grafting ◽  
Shear Force ◽  
Distal Region ◽  
Impaction Bone Grafting ◽  
Proximal Point ◽  
Local Antibiotics ◽  
Joint Replacements ◽  
Native Bone

AbstractAntibiotic carrier particles of variable size might influence mechanic properties within impacted thermodisinfected and native cancellous bone different. Herafill®G containing calciumsulfate and calciumcarbonate provides high local concentrations of gentamicin being important for revision surgery in infected joint replacements. Native and thermodisinfected cancellous bone derived from 6 to 7 months old piglets was used for in vitro impaction bone grafting and supplemented each with Herafill®G granules of two different sizes. Micromovement of implants related to shear force was measured in 29 specimens distributed in 6 groups. Thermodisinfected cancellous bone revealed a significant higher shear force resistance than native bone with a mean difference of 423.8 mdeg/Nm (p < 0.001) ranging within 95% confidence interval from 181.5 to 666.0 mdeg/Nm. Adding small granules to thermodisinfected bone did not reduce shear force resistance significantly since adding large granules to native bone improved it by 344.0 mdeg/Nm (p < 0.003). Shear force resistance was found higher at the distal region of the implant compared to a proximal point of measurement throughout all specimens. Less impaction impulses were necessary for thermodisinfected bone. Thermodisinfected cancellous bone might achieve a higher degree of impaction compared with native bone resulting in increased resistance against shear force since impaction was found increased distally. Supplementation of thermodisinfected bone with small granules of Herafill®G might be considered for application of local antibiotics. Large granules appeared more beneficial for supplementation of native bone. Heterogeneity of bone graft and technical aspects of the impaction procedure have to be considered regarding the reproducibility of femoral impaction bone grafting.

scholarly journals Analysis of the subcapital two-part humerus fracture by fluoroscopy: objective criteria for classification and decision making

2021 ◽  
Author(s):  
Nicolas Bless ◽  
Nicola Keller ◽  
Amir Steinitz ◽  
Thibaut Klein ◽  
Daniel Rikli
Keyword(s):  
Decision Making ◽  
Proximal Humerus ◽  
Image Intensifier ◽  
Anatomical Landmarks ◽  
Proximal Point ◽  
Level Of Evidence ◽  
Lesser Tuberosity ◽  
Varus Angulation ◽  
Exact Degree ◽  
Humerus Fractures

Abstract Background Surgical decision making in the treatment of proximal humerus fractures (PHFx) is primarily based on fracture classification using standard radiographs. Due to the lack of objective criteria, this classification process is associated with high interobserver variation. In this study, we investigate the fluoroscopic analysis of humerus fractures through the surgical neck using a semi-quantitative determination of distinct angulation patterns of the proximal humerus as they appear in the image intensifier. Methods Using a saw bone model, defined subcapital 2-part fracture configurations were generated and assessed radiographically. Anatomical landmarks—including the greater and lesser tuberosity as well as anatomical neck—were identified using an image converter, and the exact degree of fracture displacement with 10° up to 70° (in 10° increments) of posterior, varus or combined posterior-varus angulation was compared to nondisplaced controls. From the resultant series of radiographs, the appearance of these angulations in anteroposterior (AP) and scapular Y-views were also visualized and defined. Results An angulation of 50° or more of any given 2-part fracture through the surgical neck is present when the greater tuberosity becomes the most proximal point in AP view (varus and combined posterior-varus angulation) or a bimodal form is found for the superior contour of the head with the lesser tuberosity being the most proximal point in the Y-view (posterior angulation). Conclusion The radiological appearance of various PHFx constellations can be well visualized using the saw bone shoulder model. The presence of angulation in accordance with the Neer classification for group III fractures can be adequately determined by analyzing the relative position of the greater or lesser tuberosity to the humeral head calotte. This can assist the surgeon’s decision on whether to operate or opt for a conservative approach. Level of evidence Basic Science, Anatomy Study, Imaging.

scholarly journals Some Proximal Methods for Solving Mixed Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Muhammad Aslam Noor ◽  
Zhenyu Huang
Keyword(s):  
Variational Inequalities ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Proximal Methods ◽  
Proximal Point ◽  
Equivalent Formulation ◽  
New Methods ◽  
Special Cases ◽  
Mixed Variational Inequalities

It is well known that the mixed variational inequalities are equivalent to the fixed point problem. We use this alternative equivalent formulation to suggest some new proximal point methods for solving the mixed variational inequalities. These new methods include the explicit, the implicit, and the extragradient method as special cases. The convergence analysis of these new methods is considered under some suitable conditions. Our method of constructing these iterative methods is very simple. Results proved in this paper may stimulate further research in this direction.

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