Abstract:
the evolution of iodine nutrition in chilean school age children belonging to 4 censorial areas is described. the excesive urinary iodine excretion, in spite that food sanitary regulations decreased iodine concentration in salt from 100 to a range of 20 to 60 ppm, is noted. we were interested in studying why iodine in urine did not decreased. iodine content in bread was measured due to its high intake in chile (250 ug/day). iodine concentration in different types of breads was around 0.5 ug/g, a value 10 times the determinations done in england and spain. however it was estimated that bread consumption in chile contributed around 130 ug i/ day, which does not explain completely current high urinary iodine excretions. it is important continue searching the cause of this high intake to avoid posible complications.

Abstract:
Se describe la evolución de la nutrición de yodo en el escolar chileno perteneciente a 4 zonas censorias del país, destacando la excesiva excreción urinaria de yodo a pesar que el Reglamento Sanitario de los Alimentos disminuyó el a o 2000 la concentración de yodo en la sal de 100 ppm a un rango de 20 a 60 ppm. Nos interesó estudiar porque no disminuyeron las yodurias en los escolares. Para ello se midió el contenido de yodo en el pan, por tener un alto consumo en Chile (en promedio 250 g por día). En diferentes tipos de pan se determinó la concentración de yodo que fue alrededor de 0.5 ug /g, valor 10 veces mas alta que en mediciones efectuadas en Inglaterra y Espa a. Sin embargo se estimó que el consumo de pan en Chile aportaría alrededor de 130 ug I/día, lo que no explicaría totalmente las altas cifras de excreción de yodo actuales. De importancia es continuar indagando las causas de este alto consumo para evitar sus posibles complicaciones The evolution of iodine nutrition in chilean school age children belonging to 4 censorial areas is described. The excesive urinary iodine excretion, in spite that Food Sanitary regulations decreased iodine concentration in salt from 100 to a range of 20 to 60 ppm, is noted. We were interested in studying why iodine in urine did not decreased. Iodine content in bread was measured due to its high intake in Chile (250 ug/day). Iodine concentration in different types of breads was around 0.5 ug/g, a value 10 times the determinations done in England and Spain. However it was estimated that bread consumption in Chile contributed around 130 ug I/ day, which does not explain completely current high urinary iodine excretions. It is important continue searching the cause of this high intake to avoid posible complications.

A case of
anatomical variation of the hyoid bone in a girl is presented. Over-extended
bending of the elongated and curved right side of the hyoid bone, may project
to the lumen of the supraglottic area as the patient presented. She had a
foreign body sensation in her throat, and on fiber optic laryngeal examination, a bulge’s appearance as a “third arythenoid”
was seen. We present the clinical finding and the picture of a “third arythenoid” with literature review.

Abstract:
Let $p:R^n\to R$ be a polynomial map. Consider the complex $S'\Omega^*(\RR^n)$ of tempered currents on $R^n$ with the twisted differential $d_p=d-dp$ where $d$ is the usual exterior differential and $dp$ stands for the exterior multiplication by $dp$. Let $t\in R$ and let $F_t=p^{-1}(t)$. In this paper we prove that the reduced cohomology $\tilda H^k(F_t;C)$ of $F_t$ is isomorphic to $H^{k+1}(S'\Omega^*(\RR^n),d_p)$ in the case when $p$ is homogeneous and $t$ is any positive real number. We conjecture that this isomorphism holds for any polynomial $p$, for $t$ large enough (we call the $F_t$ for $t >> 0$ the remote fiber of $p$) and we prove this conjecture for polynomials that satisfy certain technical condition. The result is analogous to that of A. Dimca and M. Saito, who give a similar (algebraic) way to compute the reduced cohomology of the generic fiber of a complex polynomial.

Abstract:
We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc. For elliptic differential graded algebra we construct a complete set of deformations. We show that for several deformation problems the existence of a formal power series solution guarantees the existence of an analytic solution.

Abstract:
Let g be a semisimple Lie algebra over an algebraically closed field k of characteristic 0. Let V be a simple finite-dimensional g-module and let y\in V be a highest weight vector. It is a classical result of B. Kostant that the algebra of functions on the closure of the orbit of y under the simply connected group which corresponds to g is quadratic (i.e. the closuree of the orbit is a quadratic cone). In the present paper we extend this result of Kostant to the case of the quantized universal enveloping algebra U_q(g). The result uses certain information about spectrum of braiding operators for U_q(g) due to Reshetikhin and Drinfeld.

Abstract:
Let F be a flat vector bundle over a compact Riemannian manifold M and let f be a Morse function. Let g be a smooth Euclidean metric on F, let g_t=e^{-2tf}g and let \rho(t) be the Ray-Singer analytic torsion of F associated to the metric g_t. Assuming that the vector field grad(f) satisfies the Morse-Smale transversality conditions, we provide an asymptotic expansion for \log(\rho(t)) for t\to +\infty of the form a_0+a_1t+b\log\left(\frac t\pi\right)+o(1), where the coefficient b is a half-integer depending only on the Betti numbers of F. In the case where all the critical values of f are rational, we calculate the coefficients a_0 and a_1 explicitly in terms of the spectral sequence of a filtration associated to the Morse function. These results are obtained as an applications of a theorem by Bismut and Zhang.

Abstract:
Consider a flat vector bundle F over compact Riemannian manifold M and let f be a self-indexing Morse function on M. Let g be a smooth Euclidean metric on F. Set g_t=exp(-2tf)g and let \rho(t) be the Ray-Singer analytic torsion of F associated to the metric g_t. Assuming that the vector field $grad f$ satisfies the Morse-Smale transversality conditions, we provide an asymptotic expansion for log(\rho(t)) for t\to\infty of the form a_0+a_1t+b log(t)+o(1). We present explicit formulae for coefficients a_0,a_1 and b. In particular, we show that b is a half integer.

Abstract:
Let $D$ be a (generalized) Dirac operator on a non-compact complete Riemannian manifold $M$ acted on by a compact Lie group $G$. Let $v:M --> Lie(G)$ be an equivariant map, such that the corresponding vector field on $M$ does not vanish outside of a compact subset. These data define an element of $K$-theory of the transversal cotangent bundle to $M$. Hence a topological index of the pair $(D,v)$ is defined as an element of the completed ring of characters of $G$. We define an analytic index of $(D,v)$ as an index space of certain deformation of $D$ and we prove that the analytic and topological indexes coincide. As a main step of the proof, we show that index is an invariant of a certain class of cobordisms, similar to the one considered by Ginzburg, Guillemin and Karshon. In particular, this means that the topological index of Atiyah is also invariant under this class of non-compact cobordisms. As an application we extend the Atiyah-Segal-Singer equivariant index theorem to our non-compact setting. In particular, we obtain a new proof of this theorem for compact manifolds.

Abstract:
For a semi-simple simply connected algebraic group G we introduce certain parabolic analogues of the Nekrasov partition function (introduced by Nekrasov and studied recently by Nekrasov-Okounkov and Nakajima-Yoshioka for G=SL(n)). These functions count (roughly speaking) principal G-bundles on the projective plane with a trivialization at infinity and with a parabolic structure at the horizontal line. When the above parabolic subgroup is a Borel subgroup we show that the corresponding partition function is basically equal to the Whittaker matrix coefficient in the universal Verma module over certain affine Lie algebra - namely, the one whose root system is dual to that of the affinization of Lie(G). We explain how one can think about this result as the affine analogue of the results of Givental and Kim about Gromov-Witten invariants (more precisely, equivariant J-functions) of flag manifolds. Thus the main result of the paper may considered as the computation of the equivariant J-function of the affine flag manifold associated with G (in particular, we reprove the corresponding results for the usual flag manifolds) via the corresponding "Langlands dual" affine Lie algebra. As the main tool we use the algebro-geometric version of the Uhlenbeck space introduced by Finkelberg, Gaitsgory and the author. The connection of these results with the Seiberg-Witten prepotential will be treated in a subsequent publication.