Clinical and MRI investigation of temporomandibular joint in major depressed patients

Objective: The aim of the present study was to describe the clinical and MRI findings of the temporomandibular joint (TMJ) in patients with major depressive disorders (MDDs) of the non-psychotic type.Methods: 40 patients (80 TMJs) who were diagnosed as having MDDs were selected for this study. The clinical examination of the TMJs was conducted according to the research diagnostic criteria and temporomandibular disorders (TMDs). The MRIs were obtained bilaterally in each patient with axial, parasagittal and paracoronal sections within a real-time dynamic sequence. Two trained oral radiologists assessed all images. For statistical analyses, Fisher's exact test and chi(2) test were applied (alpha = 0.05).Results: Migraine was reported in 52.5% of subjects. Considering disc position, statistically significant differences between opening patterns with and without alteration (p = 0.00) and between present and absent joint noises (p = 0.00) were found. Regarding muscular pain, patients with and without abnormalities in disc function and patients with and without abnormalities in disc position were not statistically significant (p = 0.42 and p = 0.40, respectively). Significant differences between mandibular pathway with and without abnormalities (p=0.00) and between present and absent joint noises (p=0.00) were observed.Conclusion: Based on the preliminary results observed by clinical and MRI examination of the TMJ, no direct relationship could be determined between MDDs and TMDs. Dentomaxillofacial Radiology (2012) 41, 316-322. doi: 10.1259/dmfr/27328352

Polar Multiplicities and Euler obstruction of the stable types in weighted homogeneous map germs from C-n to C-3 n >= 3

In this article we show that for corank 1, quasi-homogeneous and finitely determined map germs f : (C-n, 0)-> (C-3, 0), n >= 3 one can obtain formulae for the polar multiplicities defined on the following stable types of f, f(Delta(f) and f(Sigma(n-2,1)(f), in terms of the weights and degrees of f. As a consequence we show how to compute the Euler obstruction of such stable types, also in terms of the weights and degrees of f.

Chebyshev-Laurent polynomials and weighted approximation

Let (a, b) subset of (0, infinity) and for any positive integer n, let S-n be the Chebyshev space in [a, b] defined by S-n:= span{x(-n/2+k),k= 0,...,n}. The unique (up to a constant factor) function tau(n) is an element of S-n, which satisfies the orthogonality relation S(a)(b)tau(n)(x)q(x) (x(b - x)(x - a))(-1/2) dx = 0 for any q is an element of Sn-1, is said to be the orthogonal Chebyshev S-n-polynomials. This paper is an attempt to exibit some interesting properties of the orthogonal Chebyshev S-n-polynomials and to demonstrate their importance to the problem of approximation by S-n-polynomials. A simple proof of a Jackson-type theorem is given and the Lagrange interpolation problem by functions from S-n is discussed. It is shown also that tau(n) obeys an extremal property in L-q, 1 less than or equal to q less than or equal to infinity. Natural analogues of some inequalities for algebraic polynomials, which we expect to hold for the S-n-pelynomials, are conjectured.

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Pre-weighted homogeneous map germs finite determinacy and topological triviality

In this paper we introduce the notion of G-pre-weighted homogeneous map germ, (G is one of Mather's groups A or K.) and show that any G-pre-weighted homogeneous map germ is G-finitely determined. We also give an explicit order, based on the Newton polyhedron of a pre-weighted homogeneous germ of function, such that the topological structure is preserved after perturbations by terms of higher order.