An Isoperimetric Theorem Obtained by Elementary Means

1946 ◽  
Vol 30 (288) ◽  
pp. 14-16
Author(s):  
A. D. Booth

It is usually considered that the solution of isoperimetric problems is only to be achieved through the medium of the more or less advanced technique of variation calculus. The following theorem is derived using only the notions of pure geometry and elementary calculus, and is interesting since the method of proof is easily extended to several other problems of the same type.

2008 ◽  
Vol 105 (12) ◽  
pp. 586-595
Author(s):  
M. Dormann ◽  
B. Vanderheyden ◽  
D. Steyls

2021 ◽  
pp. 192-201
Author(s):  
Jessica Fiolin ◽  
Ludwig Andre Powantia Pontoh ◽  
Ismail Hadisoebroto Dilogo

Comprehensive emergency managements and early stabilization are pivotal upon treating complex pelvic and acetabular fractures. A thorough operative strategy is required to determine the best operative approach based on the patient’s general condition, available facilities, and surgeon preferences in such complex fracture configuration. Advanced technique of the fixation is necessary during a skillful execution of surgery in order to achieve good treatment results. An 18-years-old female crushed by a bus upon crossing street, presented with hypovolemic shock with ISS polytrauma score 50 consisting of right acetabular associated both column fracture, bilateral pelvic fracture anteroposterior compression type 3, and coccygeal fracture with bilateral drop foot. She underwent emergency laparotomy, had her ovary, bladder, and intestine primarily sutured, and then we immobilized the pelvic using anterior frame external fixator, which was maintained for 6 days. Upon stable condition, we performed right ilioinguinal approach and modified Stoppa with lateral window for the left side, while Kocher-Langenbeck technique was used to approach the posterior acetabular column. Postoperative radiology showed an adequate internal fixation in both right acetabular columns, successful reconstruction of pelvic ring which was fixated the left ischium, left superior and inferior pubic rami, and full restoration of left sacroiliac joint disruption. Majeed pelvic outcome score was 54, while Hannover pelvic outcome score was good and the patient was able to sit without pain 2 months postoperative. Management of complex pelvic-acetabular-coccygeal fracture requires a holistic chain of treatment by emphasizing the prompt emergency management, accurate preoperative planning, and excellent execution of reconstructive surgical strategy to achieve satisfactory outcome.


Analysis ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Siran Li

AbstractIt is a well-known fact – which can be shown by elementary calculus – that the volume of the unit ball in \mathbb{R}^{n} decays to zero and simultaneously gets concentrated on the thin shell near the boundary sphere as n\nearrow\infty. Many rigorous proofs and heuristic arguments are provided for this fact from different viewpoints, including Euclidean geometry, convex geometry, Banach space theory, combinatorics, probability, discrete geometry, etc. In this note, we give yet another two proofs via the regularity theory of elliptic partial differential equations and calculus of variations.


Langmuir ◽  
2021 ◽  
Vol 37 (4) ◽  
pp. 1365-1371
Author(s):  
Sergei V. German ◽  
Gleb S. Budylin ◽  
Evgeny A. Shirshin ◽  
Dmitry A. Gorin

2022 ◽  
Author(s):  
Domenico Accardo ◽  
Giorgio de Alteriis ◽  
Claudia Conte ◽  
Giancarlo Rufino ◽  
Rosario Schiano Lo Moriello ◽  
...  

Author(s):  
Deepak Kumar ◽  
S. B. Singh

Here, we appraise the reliability for numerous complex structures (series structure, parallel structure and bridge structure) using accuracy and score function under fuzzy environment. The main focus of this effort is to address an advanced technique for fuzzy reliability evaluation of various complex systems having different arrangements by treating reliability of the unit/component as an interval valued intuitionistic hesitant fuzzy element. This technique helps to handle uncertainty and hesitancy in multi-attribute group decision-making related issues, specially when information occurs in interval form in fuzzy set. A numerical illustration is also included to demonstrate the proposed technique.


2017 ◽  
pp. 59-60
Author(s):  
A.A. Dovgan ◽  

The objective: to improve tactics of pregravidare training of women with hysteromyoma. Patients and methods. Under observation there were 100 patients of active and late genesial age (from 22 to 44 years), with the main diagnosis hysteromyoma established on the basis of complex inspection. To all patients the conservative myomectomy by laparotomny that laparoscopic accesses out of pregnancy was made, a course of complex rehabilitational therapy in the early and late postoperative period is conducted, the next and remote results are tracked. Results. Efficiency of pregravidarny training of patients with a hysteromyoma made 67.0%, thus authentically larger frequency of offensive of pregnancy is noted in group of the patients receiving in the postoperative period therapy by agonists of GNRG (73.0%), including at women with genesial problems (52.0%). Besides, purpose of agonists of GNRG after operation allows to reduce number of recurrence of a disease in the remote period. Conclusions. The advanced technique of pregravidarny preparation allows to improve the genesial forecast of women with hysteromyoma. Key words: hysteromyoma, pregravidarny preparation, optimization.


2021 ◽  
Author(s):  
Juan He ◽  
Qinghua Deng ◽  
Zhenping Feng

Abstract Double wall cooling, consisting of internal impingement cooling and external film cooling, is believed to be the most advanced technique in modern turbine blades cooling. In this paper, to improve the uniformity of temperature distribution, a flat plate double wall cooling model with gradient diameter of film and impingement holes was proposed, and the heat transfer and flow characteristics were investigated by solving steady three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations with SST k-ω turbulence model. The influence of gradient diameter on overall cooling effectiveness and total pressure loss was studied by comparing with the uniform pattern at the blowing ratios ranging from 0.5 to 2. For gradient diameter of film hole patterns, results show that −10% film pattern always has the lowest film flow non-uniformity coefficient. The laterally averaged overall cooling effectiveness of uniform pattern lies between that of +10% and −10% film patterns, but the intersection of three patterns moves upstream from the middle of flow direction with the increase of blowing ratio. Therefore, the −10% film pattern exerts the highest area averaged cooling effectiveness, which is improved by up to 1.6% and 1% at BR = 0.5 and 1 respectively compared with a uniform pattern. However, at higher blowing ratios, the +10% film pattern maintains higher cooling effectiveness and lower total pressure loss. For gradient diameter of impingement hole patterns, the intersection of laterally averaged overall cooling effectiveness in three patterns is located near the middle of flow direction under all blowing ratios. The uniform pattern has the highest area averaged cooling effectiveness and the smallest non-uniform coefficient, but the −10% jet pattern has advantages of reducing pressure loss, especially in the laminated loss.


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