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In the spirit of work of Kerman and Sawyer, a condition is given that is necessary and sufficient for the Fourier transform norm inequality


On Bernstein's Inequality and Kahane's Ultraflat Polynomials


We prove a trigonometric inequality of Ingham's type for nonharmonic Fourier series when the gap condition between frequencies does not hold any more.


An important example is the MoserTrudinger inequality where limiting Sobolev behavior for critical exponents provides significant understanding of geometric analysis for conformal deformation on a Riemannian manifold [5, 6].


It is proved that in the rectangle, the function h satisfies the followingfunctional inequality: where c is an absolute positive constant.

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 From 1979 to 1983, onestage lengthening of femur was done in 12 cases of lower extremity (due to inequality from infantile paralysis). The age of the patients ranged from 18 to 25 years. Lengthgain ranged from 8 to 6 cm; averaged 4.34cm. Callus could be secured through roentgenograph in all cases 2 months after the operation. The patients could walk postoperatively on crutch in 3 months. Cmplications occurred in 8 cases:(1.transient paralysis of the common peroneal nerve; 2. stiffness of the knee joint... From 1979 to 1983, onestage lengthening of femur was done in 12 cases of lower extremity (due to inequality from infantile paralysis). The age of the patients ranged from 18 to 25 years. Lengthgain ranged from 8 to 6 cm; averaged 4.34cm. Callus could be secured through roentgenograph in all cases 2 months after the operation. The patients could walk postoperatively on crutch in 3 months. Cmplications occurred in 8 cases:(1.transient paralysis of the common peroneal nerve; 2. stiffness of the knee joint and 3. splitting fracture of the distal fragment). But no sequela persisted. The soft tissues on the lateral side of the thigh should bereleased adequatly to overcome the resistance encountered during distraction.(Satisfactory anesthesia and proper positioning were inportant as well.) The enlargement of intermedullary canal had to be carried out beforehand and then the use of intermedullary nail of proper size favoured the procedure of lengthening and prevented the nail from fracture, Periosteous decorication technique in association with autogenous iliac grafting without infection would avoid completely the disunion of bones. Traditional chinese medicine used postoperatively perhaps had some effect to accelerate the healing of hones.  本文报告1979年至今共进行12例股骨一次延长术。延长长度最长6cm,最短3cm,平均4.34cm,全部病例均获成功。对术中出现的3例并发症进行了讨论,阐述了如何扩大骨髓腔、防止断钉、解决骨延长阻力等问题,为防止骨不连接和促进骨痂生长等,提出了作者的看法。  Nineteen cases of postpolio lower extremities inequality were operated upon. by transiliac lengthening. The disparity between legs was 2.59cm, average 4.6cm. After operation the legs were lengthened 2.5—3.0cm, averaged 2.9cm, but during followup (531 months, average 13 months) the lengthening was reduced to 2.5cm in average. It took 812 weeks, average 9.1 weeks, to get bony union. All the cases were improved apparently, with stable hip during weight bearing and good gait.  本文报道经骨盆截骨下肢延长术治疗脊髓灰质炎后遗症19例,术中骨延长高度2.5～3.0cm,平均2.9cm。骨愈合时间8～12周,平均9.1周。随访5个月至2年7个月,平均13月,随访时骨延长高度平均2.5cm。双下肢不等长明显改善或纠正。对本手术的优点、适应证和并发症,及其预防措施进行了讨论。  This report presents 23 cases of lower leg inequality resulting from sequelae of infantile paralysis, etc, treated with epiphyseal catatasis elongation, from January 1983 to May 1987. The site of incision were the proximal tibia and fibula in 19 cases and distal femor in 2 cases. Two Kirschner's wires were inserted into the epiphysis and another two into the diaphysis of the shortened bone. All the wires were connected with a distractionfixation apparatus and lengthened 1mm under strict control everyday.... This report presents 23 cases of lower leg inequality resulting from sequelae of infantile paralysis, etc, treated with epiphyseal catatasis elongation, from January 1983 to May 1987. The site of incision were the proximal tibia and fibula in 19 cases and distal femor in 2 cases. Two Kirschner's wires were inserted into the epiphysis and another two into the diaphysis of the shortened bone. All the wires were connected with a distractionfixation apparatus and lengthened 1mm under strict control everyday. Two cases failed to be extended and tibial transection across the lower part of epiphyseal plate was performed.All the cases' legs were elongated 4.5～10cm successfully and healed except healing in 1 case. Postoperatively, 4 cases showed early epiphyseal occlusion.  自1983年1月～1987年5月止,对脊髓灰质炎后遗症等疾病引起的下肢不等长的23例患者;采用骨骺牵伸延长治疗,均达到延长目的,延长长度在4.5～10cm。股骨远端骨骺牵伸延长2例,胫骨和腓骨的近端骨骺同时牵仲无需腓骨切骨延长19例。另2例骨骺未能牵脱而改用手术,在骺板下部位横断胫骨。以上除1例延期愈合外均达到骨性愈合。术后观察,4例骺板早闭。   << 更多相关文摘 
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