A total order in [0,1] defined through a 'next' operator

A `next' operator, s, is built on the set R1=(0,1]-{ 1-1/e} defining a partial order that, with the help of the axiom of choice, can be extended to a total order in R1. Besides, the orbits {sn(a)}nare all dense in R1 and are constituted by elements of the samearithmetical character: if a is an algebraic irrational of degreek all the elements in a's orbit are algebraic of degree k; if a istranscendental, all are transcendental. Moreover, the asymptoticdistribution function of the sequence formed by the elements in anyof the half-orbits is a continuous, strictly increasing, singularfunction very similar to the well-known Minkowski's ?(×) function.

Les adénocarcinomes kystiques de la glande lacrymale [Cystic adenocarcinomas of the lacrymal gland]

Adenoid cystic carcinoma of the lacrimal gland. BACKGROUND: Adenoid cystic carcinoma is the most frequent epithelial tumour of the lacrimal gland. It represents 1.6 % of the orbital tumours. The aim of this study is to present a series of such patients who were followed up in our clinic and to discuss their clinical management in order to achieve a better life prognosis. MATERIALS AND METHODS: The cases we followed up in our department were presented, the treatment modalities were discussed, and conclusions were drawn. RESULTS: Six patients with this pathology were examined, 3 men and 3 women, aged 31 to 69 years. A large excision was performed in 5 patients (exenteration alone or extended exenteration with complementary radiotherapy) and in 1 patient with excision of the tumour followed by radiotherapy. One patient died due to carcinoma six years after the first surgery. The median follow-up period of our cases is 25 months. CONCLUSION: Adenoid cystic carcinoma of the lacrimal gland is a malignant tumour with a reserved prognosis. Various treatments were proposed to improve the mortality rate of the disease. At present radical surgery with or without complementary therapy seems to give the best chances of healing, at least with short or mid-term follow-up.

RAX and anophthalmia in humans: Evidence of brain anomalies.

PURPOSE: To report the clinical and genetic study of two families of Egyptian origin with clinical anophthalmia. To further determine the role of the retina and anterior neural fold homeobox gene (RAX) in anophthalmia and associated cerebral malformations. METHODS: Three patients with clinical anophthalmia and first-degree relatives from two consanguineous families of Egyptian origin underwent full ophthalmologic, general and neurologic examination, and blood tests. Cerebral magnetic resonance imaging (MRI) was performed in the index cases of both families. Genomic DNA was prepared from venous leukocytes, and direct sequencing of all the exons and intron-exon junctions of RAX was performed after PCR amplification. RESULTS: Clinical bilateral anophthalmia was observed in all three patients. General and neurologic examinations were normal; obesity and delay in psychomotor development were observed in the isolated case. Orbital MRI showed a hypoplastic orbit with present but rudimentary extraocular muscles and normal lacrimal glands. Cerebral MRI showed agenesis of the optic nerves, optic tracts, and optic chiasma. In the index case of family A, the absence of the frontal and sphenoidal sinuses was also noted. In the index case of family B, only the sphenoidal sinus was absent, and there was significant cortical atrophy. The three patients carried a novel homozygous c.543+3A>G mutation (IVS2+3A>G) in RAX. Parents were healthy heterozygous carriers. No mutations were detected in orthodenticle homeobox 2 (OTX2), ventral anterior homeobox 1 (VAX1), or sex determining region Y-box 2 (SOX2). CONCLUSIONS: This is the first report of a homozygous splicing RAX mutation associated with autosomal recessive bilateral anophthalmia. To our knowledge, only two isolated cases of anophthalmia, three null and one missense case affecting nuclear localization or the DNA-binding homeodomain, have been found to be caused by compound heterozygote RAX mutations. A novel missense RAX mutation was identified in three patients with bilateral anophthalmia and a distinct systemic and neurologic phenotype. The mutation potentially affects splicing of the last exon and is thought to result in a protein that has an aberrant homeodomain and no paired-tail domain. Functional consequences of this change still need to be characterized.

Management of diplopia secondary to neurosurgical injury of the orbital roof

BACKGROUND: Diplopia related to neurosurgical procedures is often consecutive to oculomotor nerve lesions. We hereby report an oculomotor dysfunction secondary to an orbital roof effraction and its treatment. HISTORY AND SIGNS: Following surgery for a left anterior communicating artery aneurysm, a 45-year-old woman reported vertical diplopia associated with a left orbital hematoma. The diagnosis of third cranial nerve palsy was excluded by orbital imaging which revealed an orbital roof defect with incarceration of the levator palpebrae and superior rectus. THERAPY AND OUTCOME: As neurosurgeons advised against muscle adhesiolysis, diplopia was corrected by a two-step procedure on the oculomotor muscles. We first corrected horizontal and torsional deviations by operating on the healthy eye, before correcting the vertical deviation on the fellow eye. This two-step extraocular muscle surgery allowed restoration of binocular single vision in a useful field of gaze. CONCLUSIONS: Diplopia can occur as a rare orbital complication during neurosurgical procedures. Surgery of extraocular muscles can provide good functional results

La thérapie actuelle du rhabdomyosarcome orbitaire de l'enfant [Update of orbital rhabdomyosarcoma therapy in children]

INTRODUCTION: Rhabdomyosarcoma is the most frequent primitive orbital malignant tumor in children. If the treatment is started as soon as possible after discovery of the disease, the vital prognosis is considerably better than otherwise. The goal of this paper is to present the new therapeutic protocol and to report our experience in this field. MATERIAL AND METHOD: During the past 35 years, 102 cases of orbital tumors were collected in children under 15 years of age: 5 cases of rhabdomyosarcoma were cared for in our department. At the time of tumor diagnosis, the age of our patients ranged from 3 weeks to 13 years. After a biopsy or excision biopsy, all our cases were treated by chemotherapy with or without radiotherapy. Medication was mostly vincristine, ifosfamide and actinomycine D. When the result of the treatment was not satisfactory, carboplatine and epirubicine, vincristine as well as ifosfamide were given. Radiotherapy was performed only in particular cases or in recurrences. CONCLUSION: Rhabdomyosarcoma is a highly malignant tumor. Although rare, it is the most frequent of malignant tumors in children. It is important to keep it in mind in order to perform a biopsy enabling quick diagnosis and treatment following the modern protocol giving the highest chances of survival to these patients: about 98% in 3 years.

Estudi i primera fase per la implementació del FOFB al Sincrotró ALBA

Aquest treball és la culminació de les pràctiques realitzades al sincrotró ALBA. Situat a Cerdanyola del Vallès, ALBA és un accelerador de 3a generació que permet emmagatzemar un feix d'electrons confinat de fins a 400 mA a 3GeV d'energia, amb l'objectiu d'obtenir llum a partir dels girs provocats al feix. Els sincrotrons moderns com el d'ALBA, el que pretenen és aconseguir un major control i estabilitat de la llum. Per aconseguir-ho, cal que el feix d'electrons que creen la llum estigui controlat al màxim i la seva òrbita sigui estable. Amb aquest objectiu els sincrotrons estant implementant sistemes de Fast Orbit FeedBack (FOFB) o sistemes realimentats de correcció ràpida de l'òrbita, per realitzar correccions d'almenys 100Hz que estabilitzin el feix d'electrons amb menys d'un 10% de l'amplada del feix (5-10μm). El treball exposa el desenvolupament d'una part del sistema de correcció ràpida de l'òrbita dels electrons (FOFB) que s'està duent a terme al sincrotró ALBA. Concretament, s’han revisat els estudis previs realitzats durant la fase de disseny del sincrotró, s’han recalculat funcions de transferència i retards de tots els elements involucrats al sistema. També s’han realitzat simulacions per confirmar la viabilitat del sistema amb les noves dades i finalment s’ha desenvolupat part de la unitat de control determinant el Hardware i s'ha adquirit dades que permetran analitzar el soroll de l'òrbita que en futurs treballs determinaran millor l'algorisme de la unitat de control.

Complete bilateral facial cleft (Tessier 4) with corneal staphyloma: a rare association.

The oro-ocular cleft no. 4 according to the Tessier classification is one of the rarest facial cleft, and to this day, few cases have been reported in the literature. We describe the case of a 9-month-old girl with a complete bilateral facial cleft. On the right cornea protruded a hard lesion, a corneal staphyloma. We describe the 3 primary surgical steps used to restore the possibility of satisfactory feeding, to promote language acquisition, and to protect vision in the nonaffected eye. The psychological and social aspects of severe facial deformities in developing countries are also tackled.

Quasilocal density functional theory and its application within the extended Thomas-Fermi approximation

In this paper we propose a generalization of the density functional theory. The theory leads to single-particle equations of motion with a quasilocal mean-field operator, which contains a quasiparticle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the extended Thomas-Fermi approximation and the ground-state properties of doubly magic nuclei are considered within the framework of this approach. Calculations were performed using the finite-range Gogny D1S forces and the results are compared with the exact Hartree-Fock calculations

Kerr measurements on single-domain SrRuO3 thin films

We report on the magneto-optical measurements of an epitaxial SrRuO3 film grown on SrTiO3 (0 0 1), which previously was determined to be single domain orientated by x-ray diffraction and Raman spectroscopy techniques. Our experiments reveal a large Kerr rotation, which reaches a maximum value of about 0.5° at low temperature. By measuring magnetic hysteresis loops at different temperatures, we determined the temperature dependence of the Kerr rotation in the polar configuration. Values of the anisotropic magnetoresistance ~ 20% have been measured. These values are remarkably higher than those of other metallic oxides such as manganites. This striking difference can be attributed to the strong spin-orbit interaction of the Ru 4d ion in the SrRuO3 compound.

Interplanetary transfer of photosynthesis: an experimental demonstration of a selective dispersal filter in planetary island biogeography.

We launched a cryptoendolithic habitat, made of a gneissic impactite inoculated with Chroococcidiopsis sp., into Earth orbit. After orbiting the Earth for 16 days, the rock entered the Earth's atmosphere and was recovered in Kazakhstan. The heat of entry ablated and heated the rock to a temperature well above the upper temperature limit for life to below the depth at which light levels are insufficient for photosynthetic organisms ( approximately 5 mm), thus killing all of its photosynthetic inhabitants. This experiment shows that atmospheric transit acts as a strong biogeographical dispersal filter to the interplanetary transfer of photosynthesis. Following atmospheric entry we found that a transparent, glassy fusion crust had formed on the outside of the rock. Re-inoculated Chroococcidiopsis grew preferentially under the fusion crust in the relatively unaltered gneiss beneath. Organisms under the fusion grew approximately twice as fast as the organisms on the control rock. Thus, the biologically destructive effects of atmospheric transit can generate entirely novel and improved endolithic habitats for organisms on the destination planetary body that survive the dispersal filter. The experiment advances our understanding of how island biogeography works on the interplanetary scale.

Accuracy and predictability in use of AO three-dimensionally preformed titanium mesh plates for posttraumatic orbital reconstruction: a pilot study.

The aim of this study was to prospectively evaluate the accuracy and predictability of new three-dimensionally preformed AO titanium mesh plates for posttraumatic orbital wall reconstruction.We analyzed the preoperative and postoperative clinical and radiologic data of 10 patients with isolated blow-out orbital fractures. Fracture locations were as follows: floor (N = 7; 70%), medial wall (N = 1; 1%), and floor/medial wall (N = 2; 2%). The floor fractures were exposed by a standard transconjunctival approach, whereas a combined transcaruncular transconjunctival approach was used in patients with medial wall fractures. A three-dimensional preformed AO titanium mesh plate (0.4 mm in thickness) was selected according to the size of the defect previously measured on the preoperative computed tomographic (CT) scan examination and fixed at the inferior orbital rim with 1 or 2 screws. The accuracy of plate positioning of the reconstructed orbit was assessed on the postoperative CT scan. Coronal CT scan slices were used to measure bony orbital volume using OsiriX Medical Image software. Reconstructed versus uninjured orbital volume were statistically correlated.Nine patients (90%) had a successful treatment outcome without complications. One patient (10%) developed a mechanical limitation of upward gaze with a resulting handicapping diplopia requiring hardware removal. Postoperative orbital CT scan showed an anatomic three-dimensional placement of the orbital mesh plates in all of the patients. Volume data of the reconstructed orbit fitted that of the contralateral uninjured orbit with accuracy to within 2.5 cm(3). There was no significant difference in volume between the reconstructed and uninjured orbits.This preliminary study has demonstrated that three-dimensionally preformed AO titanium mesh plates for posttraumatic orbital wall reconstruction results in (1) a high rate of success with an acceptable rate of major clinical complications (10%) and (2) an anatomic restoration of the bony orbital contour and volume that closely approximates that of the contralateral uninjured orbit.

Rehabilitation of orbital cavity after total orbital exenteration using oculofacial prostheses anchored by osseointegrated dental implants posed as a one-step surgical procedure

BACKGROUND: Total orbital exenteration is a radical surgical procedure, which typically involves the removal of the entire contents of the orbit including the periorbita, leaving the patient with a deep orbital deformity and results in devastating cosmetic, functional, and psychological consequences requiring difficult and challenging procedures for oculoplastic surgeons. Oculofacial prostheses retained by endosseous dental implants present an attractive and viable alternative when aesthetic and functional demands are beyond the capacity of local reconstructive efforts. PATIENTS AND METHODS: A 72-year-old woman presenting a malignant melanoma of the right eyelids and a 77-year-old man presenting a sebaceous carcinoma of the left upper eyelid underwent a total exenteration followed by positioning of endosseous implants (Straumann system Dental implants) as an integrated one-step combined surgical procedure. The oculofacial prosthesis was placed after epithelialization of the orbital cavity. RESULTS: The implants were perfectly osseointegrated without any complications, providing sufficient retention of the prostheses. A satisfactory aesthetic outcome has been achieved for both patients. CONCLUSIONS: Oculofacial prostheses anchored by osseointegrated dental implants placed as one-step surgical procedure ensure an adequate aesthetic result as well as a considerably decreased rehabilitation time and present a satisfactory solution when reconstruction is not a suitable option.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.

An Adaptive Remeshing Procedure for Proximity Maneuvering Spacecraft Formations

We consider a methodology to optimally obtain reconfigurations of spacecraft formations. It is based on the discretization of the time interval in subintervals (called the mesh) and the obtainment of local solutions on them as a result of a variational method. Applied to a libration point orbit scenario, in this work we focus on how to find optimal meshes using an adaptive remeshing procedure and on the determination of the parameter that governs it