Frobenius morphisms and stability conditions

We generalize Deng-Du's folding argument, for the bounded derived category $\mathcal{D}(Q)$ of an acyclic quiver $Q$, to the finite dimensional derived category $\mathcal{D}(\Gamma Q)$ of the Ginzburg algebra $\Gamma Q$ associated to $Q$. We show that the $F$-stable category of $\mathcal{D}(\Gamma Q)$ is equivalent to the finite dimensional derived category $\mathcal{D}(\Gamma\mathbb{S})$ of the Ginzburg algebra $\Gamma\mathbb{S}$ associated to the species $\mathbb{S}$, which is folded from $Q$. If $(Q,\mathbb{S})$ is of Dynkin type, we prove that $\operatorname{Stab}\mathcal{D}(\mathbb{S})$ (resp. the principal component $\operatorname{Stab}^\circ\mathcal{D}(\Gamma\mathbb{S})$) of the space of the stability conditions of $\mathcal{D}(\mathbb{S})$ (resp. $\mathcal{D}(\Gamma\mathbb{S})$) is canonically isomorphic to $\operatorname{FStab}\mathcal{D}(Q)$ (resp. the principal component $\operatorname{FStab}^\circ\mathcal{D}(\Gamma Q)$) of the space of $F$-stable stability conditions of $\mathcal{D}(Q)$ (resp. $\mathcal{D}(\Gamma Q)$). There are two applications. One is for the space $\operatorname{NStab}\mathcal{D}(\Gamma Q)$ of numerical stability conditions in $\operatorname{Stab}^\circ\mathcal{D}(\Gamma Q)$. We show that $\operatorname{NStab}\mathcal{D}(\Gamma Q)$ consists of $\operatorname{Br} Q/\operatorname{Br} \mathbb{S}$ many connected components, each of which is isomorphic to $\operatorname{Stab}^\circ\mathcal{D}(\Gamma\mathbb{S})$, for $(Q,\mathbb{S})$ is of type $(A_3, B_2)$ or $(D_4, G_2)$. The other is that we relate the $F$-stable stability conditions to the Gepner type stability conditions.Comment: Update versio

Reconnection Electric Field and Hardness of X-Ray Emission of Solar Flares

Magnetic reconnection is believed to be the prime mechanism to trigger solar flares and accelerate electrons up to energies of MeV. In the classical two-dimensional reconnection model, the separation motion of chromospheric ribbons manifests the successive reconnection that takes place higher up in the corona. Meanwhile, downward traveling energetic electrons bombard the dense chromosphere and create hard X-ray (HXR) emissions, which provide a valuable diagnostic of electron acceleration. Analyses of ribbon dynamics and HXR spectrum have been carried out separately. In this Letter, we report a study of the comparison of reconnection electric field measured from ribbon motion and hardness (spectral index) of X-ray emission derived from X-ray spectrum. Our survey of the maximum average reconnection electric field and the minimum overall spectral index for 13 two-ribbon flares show that they are strongly anti-correlated. The former is also strongly correlated with flare magnitude measured using the peak flux of soft X-ray emissions. These provide strong support for electron acceleration models based on the electric field generated at reconnecting current sheet during flares.Comment: 5 pages, 2 figures. Accepted to Astrophysical Journal Letters 2009 Mar 2

clues: An R Package for Nonparametric Clustering Based on Local Shrinking

Determining the optimal number of clusters appears to be a persistent and controversial issue in cluster analysis. Most existing R packages targeting clustering require the user to specify the number of clusters in advance. However, if this subjectively chosen number is far from optimal, clustering may produce seriously misleading results. In order to address this vexing problem, we develop the R package clues to automate and evaluate the selection of an optimal number of clusters, which is widely applicable in the field of clustering analysis. Package clues uses two main procedures, shrinking and partitioning, to estimate an optimal number of clusters by maximizing an index function, either the CH index or the Silhouette index, rather than relying on guessing a pre-specified number. Five agreement indices (Rand index, Hubert and ArabieâÂÂs adjusted Rand index, Morey and AgrestiâÂÂs adjusted Rand index, Fowlkes and Mallows index and Jaccard index), which measure the degree of agreement between any two partitions, are also provided in clues. In addition to numerical evidence, clues also supplies a deeper insight into the partitioning process with trajectory plots.

7-Phenyl-7H-dinaphtho­[2,1-b:1′,2′-d]phosphole 7-oxide

In the title compound, C26H17OP, the naphthyl ring systems are bent away from each other [dihedral angle = 30.81 (8)°]. In the crystal, weak inter­molecular C—H⋯O inter­actions link the mol­ecules into helical chains along the 21 screw axis

2-Isopropyl-5-methyl­cyclo­hexyl diphenyl­phospho­namidate

In the title compound, C22H30NO2P, the P atom has an irregular tetra­hedral geometry. In the crystal, mol­ecules are connected by N—H⋯O hydrogen-bonding inter­actions, giving rise to a chain along the b axis. The phenyl ring of the anilino group is twisted by 77.40 (16)° relative to the other phenyl ring. The absolute configuration of phospho­rus is S p

Factorization for hadronic heavy quarkonium production

We briefly review several models of heavy quarkonium production in hadronic collisions, and discuss the status of QCD factorization for these production models.Comment: 8 pages, 12 figures, Talk presented at the 2nd International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions, Asilomar Conference Grounds, Pacific Grove, California, 9-16 June, 200