Uhlenbeck–Donaldson compactification for framed sheaves on projective surfaces

We construct a compactification $M^{\mu ss}$ of the Uhlenbeck–Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\gamma :M^{ss} \rightarrow M^{\mu ss}$ , where $M^{ss}$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin–Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.     

Universality at the edge of the spectrum for unitary,orthogonal, and symplectic ensembles of random matrices

We prove universality at the edge of the spectrum for unitary (β = 2), orthogonal (β = 1), and symplectic (β = 4) ensembles of random matrices in the scaling limit for a class of weights w(x) = e^?V(x) where V is a polynomial, V(x) = κ_2mx^2m + · · ·, κ_2m > 0. The precise statement of our results is given in Theorem 1.1 and Corollaries 1.2 and 1.4 below. For the same class of weights, a proof of universality in the bulk of the spectrum is given in [12] for the unitary ensembles and in [9] for the orthogonal and symplectic ensembles. Our starting point in the unitary case is [12], and for the orthogonal and symplectic cases we rely on our recent work [9], which in turn depends on the earlier work of Widom [46] and Tracy and Widom [42]. As in [9], the uniform Plancherel‐Rotach‐type asymptotics for the orthogonal polynomials found in [12] plays a central role. The formulae in [46] express the correlation kernels for β = 1, 4 as a sum of a Christoffel‐Darboux (CD) term, as in the case β = 2, together with a correction term. In the bulk scaling limit [9], the correction term is of lower order and does not contribute to the limiting form of the correlation kernel. By contrast, in the edge scaling limit considered here, the CD term and the correction term contribute to the same order: this leads to additional technical difficulties over and above [49]. © 2006 Wiley Periodicals, Inc.     

Editorial

More than 30 years of scientific endeavor have brought us from programming simple models to impressive simulations of dynamic systems. Lattice models like Potts, percolation, fuse, fiber bundle, and growth models, just to name a few, are the prototypes or godfathers of statistical mechanics. With the availability of more powerful tools it became possible to develop these models and apply them on complex topologies, finding important practical applications in socio-technological systems (e.g., opinion dynamics, traffic, communication networks) and to engineering problems (e.g., fracture phenomena, mass transport). In parallel, particle models evolved from a hand full of interacting discs to three dimensional multibillion particle simulations that successfully describe interesting fracture phenomena, granular flow, and even fluid flow for engineering applications. Prof. Dr. Hans Jürgen Herrmann has dedicated his professional life to this journey.     

The string coupling accelerates the expansion of the universed

Generic cosmological models in non-critical string theory have a time-dependent dilaton background at a late epoch. The cosmological deceleration parameter q ₀ is given by the square of the string coupling, g _s ², up to a negative sign. Hence the expansion of the Universe must accelerate eventually, and the observed value of q ₀ corresponds to g _s ² ∼ 0.6. In this scenario, the string coupling is asymptotically free at large times, but its present rate of change is imperceptibly small. First Award in the 2005 Essay Competition of the Gravity Research Foundation. - Ed.     

Scanning electron microscopy of Ancylostoma spp. dog infective larvae captured and destroyed by the nematophagous fungus Duddingtonia flagrans

The interaction between the nematode-trapping fungus Duddingtonia flagrans (isolate CG768) against Ancylostoma spp. dog infective larvae (L₃) was evaluated by means of scanning electron microscopy. Adhesive network trap formation was observed 6 h after the beginning of the interaction, and the capture of Ancylostoma spp. L₃ was observed 8 h after the inoculation these larvae on the cellulose membranes colonized by the fungus. Scanning electron micrographs were taken at 0, 12, 24, 36 and 48 h, where 0 is the time when Ancylostoma spp. L₃ was first captured by the fungus. Details of the capture structure formed by the fungus were described. Nematophagous Fungus Helper Bacteria (NHB) were found at interactions points between the D. flagrans and Ancylostoma spp. L₃. The cuticle penetration by the differentiated fungal hyphae with the exit of nematode internal contents was observed 36 h after the capture. Ancylostoma spp. L₃ were completely destroyed after 48 h of interaction with the fungus. The scanning electron microscopy technique was efficient on the study of this interaction, showing that the nematode-trapping fungus D. flagrans (isolate CG768) is a potential exterminator of Ancylostoma spp. L₃.     

A Note on Error Bounds for Convex and Nonconvex Programs

Given a single feasible solution and a single infeasible solution of a mathematical program, we provide an upper bound to the optimal dual value. We assume that satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [11] on the distance of a point to a convex set specified by inequalities.     

2-μm high-power multiple-frequency single-mode Q-switched Ho:YLF laser for DIAL application

We report on the development and the demonstration of a two-wavelength single-frequency laser oscillator based on Ho:YLF crystal. This laser is especially suitable for application as a transmitter in differential absorption lidar (DIAL)/integrated path differential absorption (IPDA) measurements of atmospheric carbon dioxide (CO₂) using the R30 CO₂ absorption line at 2,050.967 nm. The oscillator consists in a fiber-coupled and free-space solid-state hybrid system and can be used in high-energy middle-rate or moderate-energy high-rate configurations. The latter produced On and Off sequentially single-frequency laser pulses with 13 mJ of energy at a repetition rate of 2 kHz and pulse duration of 42 ns. The pulse energy and frequency stabilities are specially documented in free-running, single-frequency and two-frequency seeding single-mode operations. Standard deviation is 7.7 % for pulse energy and 2 MHz for frequency stability for the two-wavelength seeding operation. Allan variance plot shows that frequency fluctuations are reduced below 70 kHz for 10 s of averaging which is suitable for accurate CO₂ DIAL or IPDA measurements.     

Ab initio and Monte Carlo studies of phase transitions and magnetic properties of YCrO3: Heisenberg model

By using the density functional theory (DFT) and Monte Carlo simulations (MCS) with the Heisenberg model, we have studied magnetic properties of the bulk perovskite YCrO₃. The exchange couplings of the Heisenberg model and the magnetic anisotropy are investigated. The 110 direction in the crystalline structure of the compound has shown the minimum energy, it is the easy magnetic direction. Using Monte Carlo simulations, the magnetizations behavior, the effects of system parameters and the critical exponents of the compound YCrO₃ are implemented. It is shown that the bulk perovskite YCrO₃ belongs to the 3D Heisenberg universality class.