STICKELBERGER SERIES AND IWASAWA MAIN CONJECTURE FOR FUNCTION FIELDS

Let F be a global function \ufb01eld in characteristic p>0. There exists many di\ufb00erent types of L-functions that can be associated to F, such as the Artin L-functions, the Goss Zeta function or the p-adic L-functions. In this work i have investigated the correlations between these analytic objects and the Stickelberger series, which is a formal power series whose coe\ufb03cients lie in a suitable Galois algebra. In the second part of this work i have studied the Iwasawa extension generated by the p-torsion of a Hayes module and i have used the Stickelberger series to prove a "main conjecture" for the p-part of the class group

Dispersion engineering of highly nonlinear chalcogenide suspended-core fibers

Chalcogenide optical fibers are currently undergoing intensive investigation with the aim of exploiting the excellent glass transmission and nonlinear characteristics in the near- and mid-infrared for several applications. Further enhancement of these properties can be obtained, for a particular application, with optical fibers specifically designed that are capable of providing low effective area together with a properly tailored dispersion, matching the characteristics of the laser sources used to excite nonlinear effects. Suspended-core photonic crystal fibers are ideal candidates for nonlinear applications, providing small-core waveguides with large index contrast and tunable dispersion. In this paper, the dispersion properties of As2S3 suspended-core fibers are numerically analyzed, taking into account, for the first time, all the structural parameters, including the size and the number of the glass bridges. The results show that a proper design of the cladding struts can be exploited to significantly change the fiber properties, altering the maximum value of the dispersion parameter and shifting the zero-dispersion wavelengths over a range of 400 nm

Modeling thermo-optic effect in large mode area double cladding photonic crystal fibers

The impact of thermally-induced refractive index changes on the single-mode (SM) properties of large mode area (LMA) photonic crystal fibers are thoroughly investigated by means of a full-vector modal solver with integrated thermal model. Three photonic crystal fiber designs are taken into account, namely the 19-cell core fiber, the large-pitch fiber (LPF) and the distributed modal filtering (DMF) fiber, to assess the effects of the interplay between thermal effects and the high-order mode (HOM) suppression mechanisms exploited in order to obtain effectively SM guiding. The results have shown significant differences in the way the SM regime is changed by the increase of heat load, providing useful hints for the design of LMA fibers for high power lasers

Insulin metabolism is a major factor responsible for high or low peripheral insulin levels in response to oral glucose loading in the healthy man

In the present study we evaluated C-peptide peripheral levels after an oral glucose load in 30 healthy subjects (18 females, 12 males, aged from 15 to 55) with high or low insulin response to glucose challenge in order to clarify whether or not their beta-cell secretion rate keeps pace with peripheral insulin levels. Moreover, by the study of the relations between C-peptide and insulin in peripheral blood, we had an insight into the extent of insulin metabolism. On the basis of an insulin incremental area higher or lower than the mean +/- 1 SD after a 100-gram oral glucose load, 6 subjects were classified as 'high insulin responders' and 6 other subjects as 'low insulin responders'. Their insulin incremental area after glucose averaged 0.25 +/- 0.01 nmol X 1-1 X min and 0.078 +/- 0.005 nmol X 1-1 X min, respectively (p less than 0.001). The two groups were matched for sex, age and body weight. The glycemic profile after oral glucose load was higher in low insulin responders than in high insulin responders. C-peptide concentrations after glucose load were similar in the two groups, as well as C-peptide incremental areas (0.92 +/- 0.12 vs. 0.74 +/- 0.08 nmol X l-1 X min in high insulin responders and low insulin responders, respectively). The molar ratios of C-peptide to insulin after oral glucose load, as well as the relations between the incremental areas of the two peptides, were significantly lower in high insulin responders than in low insulin responders.(ABSTRACT TRUNCATED AT 250 WORDS

Secretion and hepatic removal of insulin in female obese subjects with reactive hypoglycemia

In the present study insulin and C-peptide responses to oral glucose as well as C-peptide to insulin ratios and relations were evaluated in 10 nondiabetic obese female subjects with reactive hypoglycemia and in 10 age- and weight-matched controls. Insulin levels and incremental areas did not differ significantly in the two groups, whereas C-peptide concentrations and incremental areas were significantly higher in the obese group with reactive hypoglycemia. C-peptide to insulin molar ratio increments after glucose load as well as relations between incremental areas of the two peptides were significantly higher in obese subjects with reactive hypoglycemia than in controls. Our results suggest that B-cell response to oral glucose as well as insulin uptake by the liver in obese subjects with reactive hypoglycemia are greater than in controls

Relationship between insulin resistance, insulin secretion and insulin metabolism in simple obesity

The study was designed to evaluate whether the correlation occurring in simple obesity between insulin resistance and peripheral hyperinsulinemia corresponds to a relationship between insulin resistance and insulin overproduction by the pancreas. In addition, the study investigated the relation existing in simple obesity between insulin resistance and insulin metabolism. For these purposes, we measured and correlated: (1) insulin sensitivity, estimated by glucose disappearance rate from plasma after intravenous insulin injection; (2) insulin secretion by the pancreas, estimated by fasting C-peptide levels in peripheral blood; (3) insulin metabolism, estimated by means of C-peptide: insulin molar ratio in peripheral blood. Twenty-five subjects (20 females, five males) aged 21 to 59 years were studied. All were obese and had a normal glucose tolerance. Glucose disappearance rate from plasma after i.v. insulin injection averaged 3.65 +/- 0.42 mg/dl/min (mean +/- s.e.m.). Fasting C-peptide was 0.90 +/- 0.09 nmol/l. Fasting C-peptide: insulin molar ratio averaged 5.94 +/- 0.48. Negative correlations were found between glucose disappearance rates after i.v. insulin injection, ie, insulin sensitivity, and fasting concentrations of both insulin (r = -0.806, P less than 0.001) and C-peptide (r = -0.525, P less than 0.01). A positive relationship was found between glucose disappearance rate from plasma after i.v. insulin injection and fasting C-peptide: insulin molar ratio, ie, insulin metabolism (r = 0.707, P less than 0.001). We conclude that in simple obesity insulin overproduction by the pancreas is negatively related to insulin resistance, and insulin resistance and impaired insulin metabolism are strictly related phenomena