The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

Calcification and ossification of the convexity of the falx cerebri and related subdural space in human cadavers

OBJECTIVE: The present work was planned to report the incidence of calcification and ossification of an isolated cranial dural fold. The form, degree of severity and range of extension of such changes will be described. Involvement of the neighboring brain tissue and blood vessels, whether meningeal or cerebral, will also be determined. The results of this study might highlight the occasional incidence of intracranial calcification and ossification in images of the head and their interpretation, by radiologists and neurologists, to be of dural or vascular origin.

METHODS: Two human formalin-fixed cadavers, one middle-aged female another older male, were investigated at the Anatomy Laboratory, College of Medicine, King Faisal University, Dammam, Kingdom of Saudi Arabia during the period from 2000 to 2003. In each cadaver, the skullcap was removed and the convexity of the cranial dura mater, as well as the individual dural folds, were carefully examined for any calcification or ossification. The meningeal and cerebral blood vessels together with the underlying brain were grossly inspected for such structural changes. Calcified or ossified tissues, when identified, were subjected to histological examination to confirm their construction.

RESULTS: The female cadaver showed a calcified parietal emissary vein piercing the skullcap and projecting into the scalp. The latter looked paler and deficient in hair on its right side. The base of the stump was surrounded by a granular patch of calcification. The upper convex border of the falx cerebri was hardened and it presented granules, plaques and a cauliflower mass, which all proved to be osseous in structure. The meningeal and right cerebral vessels were mottled with calcium granules. The underlying temporal and parietal lobes of the right cerebral hemisphere were degenerated. The male cadaver also revealed a calcified upper border of the falx cerebri and superior sagittal sinus. Osseous granules and plaques, similar to those of the first specimen, were also identified but without gross changes in the underlying brain.

CONCLUSION: Calcification or ossification of an isolated site of the cranial dura mater and the intracranial blood vessels might occur. These changes should be kept in mind while interpreting images of the skull and brain. Clinical assessment and laboratory investigations are required to determine whether these changes are idiopathic, traumatic, or as a manifestation of a generalized disease such as hyperparathyroidism, vitamin D-intoxication, or chronic renal failure.

A Study of Closure and Fuzzy Closure Spaces with Reference to H-Closedness and Convexity

Department of Mathematics, Cochin University of Science and Technology.

Some Problems In Algebra And Topology A Study Of Fuzzy Convexity With Special Reference To Separation Properties

This thesis is a study of abstract fuzzy convexity spaces and fuzzy topology fuzzy convexity spaces No attempt seems to have been made to develop a fuzzy convexity theoryin abstract situations. The purpose of this thesis is to introduce fuzzy convexity theory in abstract situations

Acute shortening and subsequent lengthening of the radius and ulna for the treatment of an infected nonunion in a dog

A 3-year-old, male crossbred dog with osteomyelitis of the radius and ulna was treated using Ilizarov's method. Two centimeters of infected bone was resected, then acute bone shortening and subsequent lengthening of a healthy bone site were performed. The infection was eradicated, but a residual leg-length discrepancy was present.

Convexity of the extreme zeros of Gegenbauer and Laguerre polynomials

Let C-n(lambda)(x), n = 0, 1,..., lambda > -1/2, be the ultraspherical (Gegenbauer) polynomials, orthogonal. in (-1, 1) with respect to the weight function (1 - x(2))(lambda-1/2). Denote by X-nk(lambda), k = 1,....,n, the zeros of C-n(lambda)(x) enumerated in decreasing order. In this short note, we prove that, for any n is an element of N, the product (lambda + 1)(3/2)x(n1)(lambda) is a convex function of lambda if lambda greater than or equal to 0. The result is applied to obtain some inequalities for the largest zeros of C-n(lambda)(x). If X-nk(alpha), k = 1,...,n, are the zeros of Laguerre polynomial L-n(alpha)(x), also enumerated in decreasing order, we prove that x(n1)(lambda)/(alpha + 1) is a convex function of alpha for alpha > - 1. (C) 2002 Published by Elsevier B.V. B.V.

Effect of bovine bone morphogenetic proteins on radius fracture healing in rabbits

OBJETIVO: Investigar a influência de Proteínas Morfogenéticas Ósseas de origem bovina (bBMPs) ligadas a hidroxiapatita mais colágeno na consolidação de fraturas instáveis do rádio. MÉTODOS: em 15 coelhos com aproximadamente 5,5 meses de idade e peso médio de 3,5kg foi realizada uma fratura transversa na porção média da diáfise do rádio de ambos os membros. Na fratura do rádio direito foi aplicada mistura de bBMPs ligadas à hidroxiapatita (bBMP-HA) e colágeno bovino como aglutinante e na do rádio esquerdo, considerada controle, nenhum tratamento foi usado. Os coelhos (cinco por período) foram submetidos à eutanásia aos 30, 60 e 90 dias após a cirurgia para realização do processamento histológico e análise microscópica. RESULTADOS: A análise histológica descritiva revelou que a consolidação foi similar para os membros tratado e controle. Pela análise histomorfométrica, a área de novo osso foi em média 867442,16 mm², 938743.00 mm² e 779621,06 mm² para os membros controles e 841118,47 mm², 788038,76mm² e 618587,24 mm² para os membros tratados, aos 30, 60 e 90 dias, respectivamente. Desta forma, aos 60 dias de pós-operatório a área de novo osso foi 12.17% maior no membro tratado com bBMP-HA/colágeno em relação ao membro controle (p<0.05, teste de Tukey). em ambos os membros a área de novo osso aumentou durante o período experimental até a total consolidação da fratura. CONCLUSÃO: Baseado nos resultados obtidos foi possível concluir que a mistura de bBMP-HA/colágeno induziu pequena, porém significante melhora na consolidação da fratura.

Treatment of radius, ulna and humerus fractures with the aid of a bone morphogenetic protein in a giant anteater (Myrmecophaga tridactyla)

A giant anteater (Myrmecophaga tridactyla) was found with closed comminuted fractures on the fight radius and ulna and left humerus he duration of which was unknown. The animal was unable to use either of he thoracic limbs. The fractures were stabilized with 3.5-mm titanium plates and a commercially available mixture of micro lyophilized bovine cortical osseous and bovine BMP (Gen-tech(R), Baumer, Brazil) was implanted into the fractures sites. Postoperative radiographic evaluations were performed every 30 days and after four months. Bone healing was observed in all of he fractures. The animal was able to be reintroduced into its natural habitat. From his case we conclude that despite he low metabolic fate of the giant anteater, which is an inherent characteristic of this species, he treatment of radius, ulna and humerus fractures by means of plates and screws, associated with BMP on the Myrmecophaga tridactyla, was a success.

Sphere of influence and gravitational capture radius: a dynamical approach

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Measurement of the ratio of inclusive jet cross sections using the anti-k(T) algorithm with radius parameters R=0.5 and 0.7 in pp collisions at root s=7 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)