Differences in insulin response between the meal replacements occurred, and prolongation of satiety after the LMR, based on time to request additional food, was observed. We speculate that the prolonged satiety associated with low GI foods may prove an effective method for reducing caloric intake and achieving long-term weight control.

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Let L be a finite extension of Q p , and ρ L be an n-dimensional semi-stable non crystalline p-adic representation of Gal L with full monodromy rank. Via a study of Breuil's (simple) L-invariants, we attach to ρ L a locally Q p -analytic representation Π(ρ L ) of GL n (L), which carries the exact information of the Fontaine-Mazur simple L-invariants of ρ L . When ρ L comes from an automorphic representation of G(A F + ) (for a unitary group G over a totally real filed F + which is compact at infinite places and GL n at p-adic places), we prove under mild hypothesis that Π(ρ L ) is a subrerpresentation of the associated Hecke-isotypic subspaces of the Banach spaces of p-adic automorphic forms on G(A F + ). In other words, we prove the equality of Breuil's simple L-invariants and Fontaine-Mazur simple L-invariants.

Let ρ p be a 3-dimensional p-adic semi-stable representation of Gal(Q p /Q p ) with Hodge-Tate weights (0, 1, 2) (up to shift) and such that N 2 = 0 on D st (ρ p ). When ρ p comes from an automorphic representation π of G(A F + ) (for a unitary group G over a totally real field F + which is compact at infinite places and GL 3 at p-adic places), we show under mild genericity assumptions that the associated Hecke-isotypic subspaces of the Banach spaces of p-adic automorphic forms on G(A ∞ F + ) of arbitrary fixed tame level contain (copies of) a unique admissible finite length locally analytic representation of GL 3 (Q p ) of the form considered in [4] which only depends on and completely determines ρ p .

Let F℘ be a finite extension of Qp. By considering partially de Rham families, we establish a Colmez-Greenberg-Stevens formula (on Fontaine-Mazur L-invariants) for (general) 2-dimensional semi-stable non-crystalline Gal(Qp/F℘)-representations. As an application, we prove local-global compatibility results for completed cohomology of quaternion Shimura curves, and in particular the equality of Fontaine-Mazur L-invariants and Breuil's L-invariants, in critical case. Contents 4. Local-global compatibility 17 4.1. Setup and notations 17 4.2. Completed cohomology and eigenvarieties 18 4.3. Local-global compatibility 25 Appendix A. Partially de Rham trianguline representations 33 References 36