The popliteal cyst

A popliteal cyst, originally called Baker's cyst, is a synovial fluid-filled mass located in the popliteal fossa. The most common synovial popliteal cyst is considered to be a distension of the bursa located beneath the medial head of the gastrocnemius muscle. Usually, in an adult patient, an underlying intra-articular disorder is present. In children, the cyst can be isolated and the knee joint normal. The anatomy, etiopathogenesis, clinical presentation, differential diagnosis, imaging and treatment modalities of the popliteal cyst are presented. The authors try to answer some questions dealing with this condition. Is the cyst isolated, can it be treated as such, is its origin always well-defined and does surgical excision provide a permanent cure

The First Self-Assembled Trimetallic Lanthanide Helicates Driven by Positive Cooperativity

The segmental tris-tridentate ligand L7 reacts with stoichiometric quantities of Ln(III) (Ln=La-Lu) in acetonitrile to give the complexes [Ln(2)(L7)(3)](6+) and [Ln(3)(L7)(3)](9+). Formation constants point to negligible size-discriminating effects along the lanthanide series, but Scatchard plots suggest that the self-assembly of the trimetallic triple-stranded helicates [Ln(3)(L7)(3)](9+) is driven to completion by positive cooperativity, despite strong intermetallic electrostatic repulsions. Crystallization provides quantitatively [Ln(3)(L7)(3)](CF(3)SO(3))(9) (Ln=La, Eu, Gd, Tb, Lu) and the X-ray crystal structure of [Eu(3)(L7)(3)](CF(3)SO(3))(9).(CH(3)CN)(9).(H(2)O)(2) (Eu(3)C(216)H(226)N(48)O(35)F(27)S(9), triclinic, P1, Z=2) shows the three ligand strands wrapped around a pseudo-threefold axis defined by the three metal ions rigidly held at about 9 A. Each metal ion is coordinated by nine donor atoms in a pseudo-trigonal prismatic arrangement, but the existence of terminal carboxamide units in the ligand strands differentiates the electronic properties of the terminal and the central metallic sites. Photophysical data confirm that the three coordination sites possess comparable pseudo-trigonal symmetries in the solid state and in solution. High-resolution luminescence analyses evidence a low-lying LMCT state affecting the central EuN(9) site, so that multi-metal-centered luminescence is essentially dominated by the emission from the two terminal EuN(6)O(3) sites in [Eu(3)(L7)(3)](9+). New multicenter equations have been developed for investigating the solution structure of [Ln(3)(L7)(3)](9+) by paramagnetic NMR spectroscopy and linear correlations for Ln=Ce-Tb imply isostructurality for these larger lanthanides. NMR spectra point to the triple helical structure being maintained in solution, but an inversion of the magnitude of the second-rank crystal-field parameters, obtained by LIS analysis, for the LnN(6)O(3) and LnN(9) sites with respect to the parameters extracted for Eu(III) from luminescence data, suggests that the geometry of the central LnN(9) site is somewhat relaxed in solution

Arithmetic Operations in the Polynomial Modular Number System

Arithmetic Operations in the Polynomial Modular Number Syste

Improving Euclidean Division and Modular Reduction for Some Classes of Divisors

International audienceModular arithmetic is becoming an area of major importance for many modern applications; RNS is widely used in digital signal processing, and most public-key cryptographic algorithms require very fast modular multiplication , and exponentiation. When such an arithmetic is required, specific values such as Fermat or Mersenne numbers are often chosen since they allow for very efficient implementations. However, there are cases where only very few of those numbers are available. We present an algorithm for the Euclidean division with remainder and we give the classes of divisors for which our algorithm is particularly efficient compared to commonly used method