Bogomolov restriction theorem for Higgs bundles

Let (E,θ) be a stable Higgs bundle of rank r on a smooth complex projective surface X equipped with a polarization H. Let C⊂X be a smooth complete curve with [C]=n⋅H. If where , then we prove that the restriction of (E,θ) to C is a stable Higgs bundle. This is a Higgs bundle analog of Bogomolov's restriction theorem for stable vector bundles.     

Visibility with One Reflection

We extend the concept of the polygon visible from a source point S in a simple polygon by considering visibility with two types of reflection, specular and diffuse. In specular reflection a light ray reflects from an edge of the polygon according to the rule: the angle of incidence equals the angle of reflection. In diffuse reflection a light ray reflects from an edge of the polygon in all inward directions. Several geometric and combinatorial properties of visibility polygons under these two types of reflection are described, when at most one reflection is permitted. We show that the visibility polygon Vs(S) under specular reflection may be nonsimple, while the visibility polygon Vd(S) under diffuse reflection is always simple. We present a Θ(n ² ) worst-case bound on the combinatorial complexity of both Vs(S) and Vd(S) and describe simple O(n ² log ² n) time algorithms for constructing the sets. Received September 27, 1995, and in revised form October 24, 1997.     

On symmetric incidence matrices of projective planes

We investigate the incidence matrix of a finite plane of ordern which admits a (C, L)-transitivityG. The elation groupG affords a generalized Hadamard matrixH=(h _ij ) of ordern and an incidence matrix for the plane is completely determined by the matrixR(H)=(R(h _ij )), whereR(g) denotes the regular permutation matrix forgG. We prove that in the caseR(H) is symmetric thatG is an elementary abelian 2-group or elseG is a nonabelian group andn is a square. Results are obtained in the abelian case linking the roots of the incidence matrixR(H) to the roots of the complex matrix (H), a nontrivial character ofG.     

Ternary complexes of copper(II), nickel(II) and zinc(II) with nitrilotriacetic acid as a primary ligand and some phenolic acids as secondary ligands

Summary The formation of ternary complexes of the MAL^3– type [where M = Cu^II, Ni^II and Zn^II ; A = nitrilotriacetic acid (NTA); L = 1-hydroxy-2-naphthoic acid (1,2 HNA) and 2-hydroxy-1-naphthoic acid (2,1 HNA)] have been studied potentiometrically in 50% v/v aqueous — ethanol (25° and µ = 0.1). Under identical conditions the binary complexes of the 1,2- and 2,1-HNA ligands have also been examined. The values of mixed ligand formation constants K_MAL have been found to be lower than K_ML (first step formation constant of binary complexes) and even less than (second step formation constant of binary complexes).     

A novel nitrate-selective electrode based on precipitated nitron nitrate

Summary A nitrate-selective electrode based on precipitated nitron nitrate in an epoxy resin matrix has been prepared. The lower detection limit is 10^–5 M, the optimum pH range is 2.0–8.5, and the response time is 1 min. The electrode is selective in presence of CH₃COO^–, SO₄ ^2–, C₂O₄ ^2–, PO₄ ^3–, NO₂ ^–, Cl^– and Br^–, but I^– interferes. Results for nitrate in soil samples were in agreement with values obtained spectrophotometrically.

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Eine neue nitrat-spezifische Elektrode auf der Basis gefällten Nitronnitrats

Zusammenfassung Eine nitrat-spezifische Elektrode auf der Basis gefällten Nitronnitrats in einer Epoxyharz-Matrix wurde hergestellt. Die untere Nachweisgrenze ist 10^–5 M, das pH-Optimum liegt zwischen 2,0 und 8,5, die Reaktionszeit beträgt 1 Minute. Die Elektrode ist selektiv in Gegenwart von Acetat, Sulfat, Oxalat, Phosphat, Nitrit, Chlorid und Bromid; aber Jodid stört. Ergebnisse der Nitratbestimmung in Bodenproben stimmen mit spektrophotometrischen Resultaten überein.

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Presented at the 8th International Microchemical Symposium, Graz, August 25–30, 1980.     

Sequential Co-Sparse Factor Regression

In multivariate regression models, a sparse singular value decomposition of the regression component matrix is appealing for reducing dimensionality and facilitating interpretation. However, the recovery of such a decomposition remains very challenging, largely due to the simultaneous presence of orthogonality constraints and co-sparsity regularization. By delving into the underlying statistical data-generation mechanism, we reformulate the problem as a supervised co-sparse factor analysis, and develop an efficient computational procedure, named sequential factor extraction via co-sparse unit-rank estimation (SeCURE), that completely bypasses the orthogonality requirements. At each step, the problem reduces to a sparse multivariate regression with a unit-rank constraint. Nicely, each sequentially extracted sparse and unit-rank coefficient matrix automatically leads to co-sparsity in its pair of singular vectors. Each latent factor is thus a sparse linear combination of the predictors and may influence only a subset of responses. The proposed algorithm is guaranteed to converge, and it ensures efficient computation even with incomplete data and/or when enforcing exact orthogonality is desired. Our estimators enjoy the oracle properties asymptotically; a non-asymptotic error bound further reveals some interesting finite-sample behaviors of the estimators. The efficacy of SeCURE is demonstrated by simulation studies and two applications in genetics. Supplementary materials for this article are available online.     

Operational issues and network effects in vaccine markets

One of the most important concerns for managing public health is the prevention of infectious diseases. Although vaccines provide the most effective means for preventing infectious diseases, there are two main reasons why it is often difficult to reach a socially optimal level of vaccine coverage: (i) the emergence of operational issues (such as yield uncertainty) on the supply side, and (ii) the existence of negative network effects on the consumption side. In particular, uncertainties about production yield and vaccine imperfections often make manufacturing some vaccines a risky process and may lead the manufacturer to produce below the socially optimal level. At the same time, negative network effects provide incentives to potential consumers to free ride off the immunity of the vaccinated population. In this research, we consider how a central policy-maker can induce a socially optimal vaccine coverage through the use of incentives to both consumers and the vaccine manufacturer. We consider a monopoly market for an imperfect vaccine; we show that a fixed two-part subsidy is unable to coordinate the market, but derive a two-part menu of subsidies that leads to a socially efficient level of coverage.     

Spectral editing in solid-state MAS NMR of quadrupolar nuclei using selective satellite inversion

A sensitivity enhancement method based on selective adiabatic inversion of a satellite transition has been employed in a (pi/2)CT-(pi)ST1-(pi/2)CT spectral editing sequence to both enhance and resolve multisite NMR spectra of quadrupolar nuclei. In addition to a total enhancement of 2.5 times for spin 3/2 nuclei, enhancements up to 2.0 times is reported for the edited sites in a mixture of rubidium salts.