We investigate existence and structure of solutions to quadratic control problems with semi-explicit differential algebraic constraints. By means of an equivalent index-1 formulation we identify conditions for the unique existence of optimal solutions. Knowing of the existence of an optimal input we provide a representation of the associated feedback-law via a Riccatilike decoupling that is for...

This paper is devoted to some fundumental calculation on 2-dimensional smoothable semi-log-terminal singularities. If we study minimal or canonical models of one parameter degeneration of algebraic surfaces, we must treat singularities that appear in the central fiber. Smoothable semi-log-terminal singularities are the singularities of the central fiber of the minimal model of degeneration, and...

The semi-topological nature of the eta-invariant of a self-adjoint elliptic differential operator derives from a relative identification with a Chern character. This remarkable semi-locality property of the eta-invariant can be seen in spectral flow formulae and many other applications [APS2, APS3, BC1, DZ1, L1]. In this paper we prove two geometric index theorems for a family of first-order el...

Abbreviations: C, carbon; N, nitrogen; BD, soil bulk d mass; BGB, belowground biomass; SL, semi-decomposit carbon pool;Np, soil nitrogenpool; SOC, soil organic carbo content; FG, fenced grassland with grazing exclusion; GG index; H, Shannon–Wiener diversity index; E, Evenness in ⁎ Corresponding author at: State Key Laboratory of Soil E the Loess Plateau, Institute of Soil and Water Conservati Y...

We study the most general conditions under which the computations of the index of a perturbed Dirac operator Ds = D + sZ localize to the singular set of the zeroth order operator Z in the semi-classical limit s → ∞. We use Witten’s method to compute the index of D by doing a combinatorial computation involving local data at the nondegenerate singular points of the operator Z. The paper contains...

We study the most general conditions under which the computations of the index of a perturbed Dirac operator Ds = D + sZ localize to the singular set of the zeroth order operator Z in the semi-classical limit s → ∞. We use Witten’s method to compute the index of D by doing a combinatorial computation involving local data at the nondegenerate singular points of the operator Z. The paper contains...

Let H0 and H be self-adjoint operators in a Hilbert space. We consider the spectral projections of H0 and H corresponding to a semi-infinite interval of the real line. We discuss the index of this pair of spectral projections and prove an identity which extends the Birman-Schwinger principle onto the essential spectrum. We also relate this index to the spectrum of the scattering matrix for the ...

OBJECTIVE To analyze the relationship between dietary glycemic index (GI) and retinal microvasculature in adults. METHODS This was a cross-sectional study of 300 subjects from the EVIDENT II study. Dietary GI was calculated using a validated, semi-quantitative food frequency questionnaire. Retinal photographs were digitized, temporal vessels were measured in an area 0.5-1 disc diameter from t...