Cluster Categories Coming from Cyclic Posets

Cyclic posets are generalizations of cyclically ordered sets. In this article, we show that any cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The stable category of a Frobenius category is always triangulated and has a cluster structure in many cases. The continuous cluster categories of [14 Igusa , K. , Todorov , G. ( 2013 ). Continuous Frobenius categories . Proceedings of the Abel Symposium 2011 : 115 – 143 .[Crossref] , [Google Scholar]], the infinity-gon of [12 Holm , T. , Jøot rgensen , P. ( 2012 ). On a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon . Math. Z. 270 : 277 – 295 .[Crossref], [Web of Science ®] , [Google Scholar]], and the m-cluster category of type A _∞ (m ≥ 3) [13 Holm , T. , Jøot rgensen , P. ( 2015 ). Cluster tilting vs. weak cluster tilting in Dynkin type A infinity . Forum Math. 27 : 1117 – 1137 .[Crossref], [Web of Science ®] , [Google Scholar]] are examples of this construction as well as some new examples such as the cluster category of ?². An extension of this construction and further examples are given in [16 Igusa, K., Todorov, G. Continuous Cluster Categories of Type D. arXiv:1309.7409 . [Google Scholar]].     

Power variation from second order differences for pure jump semimartingales

We introduce power variation constructed from powers of the second-order differences of a discretely observed pure-jump semimartingale processes. We derive the asymptotic behavior of the statistic in the setting of high-frequency observations of the underlying process with a fixed time span. Unlike the standard power variation (formed from the first-order differences of the process), the limit of our proposed statistic is determined solely by the jump component of the process regardless of the activity of the latter. We further show that an associated Central Limit Theorem holds for a wider range of activity of the jump process than for the standard power variation. We apply these results for estimation of the jump activity as well as the integrated stochastic scale.     

Constraint qualifications in linear vector semi-infinite optimization

Linear vector semi-infinite optimization deals with the simultaneous minimization of finitely many linear scalar functions subject to infinitely many linear constraints. This paper provides characterizations of the weakly efficient, efficient, properly efficient and strongly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The global constraint qualifications are illustrated on a collection of selected applications.     

Synthesis and characterization of novel (9H‐fluoren‐9‐ylamino) carbonylaminomethylphosphonic acid

The new α‐aminophosphonic acids are synthesized, reacting (9H‐fluoren‐9‐yl)urea with formaldehyde and phosphorus trichloride. (9H‐Fluoren‐9‐yl)urea was prepared from spiro(fluoren‐9,4′‐imidazolidine)‐2′,5′‐dione by alkaline hydrolysis with Ba(OH)₂. The structure of the title compounds was proved by means of IR, ¹H, ¹³C, and ³¹P NMR spectroscopy. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:719–722, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20500     

Cyclic posets and triangulation clusters

Triangulated categories coming from cyclic posets were originally introduced by the authors in a previous paper as a generalization of the constructions of various triangulated categories with cluster structures.We give an overview, and then analyze "triangulation clusters" which are those corresponding to topological triangulations of the 2-disk. Locally finite nontriangulation clusters give topological triangulations of the "cactus space" associated to the "cactus cyclic poset".     

Generalized Cohomologies and the Physical Subspace of the SU(2) WZNW Model

The zero modes of the monodromy extended SU(2) WZNW model give rise to a gauge theory with a finite-dimensional state space. A generalized BRS operator A such that being the height of the current algebra representation) acts in -dimensional indefinite metric space of quantum group invariant vectors. The generalized cohomologies Ker are 1-dimensional. Their direct sum spans the physical subquotient of .     

Synthese und Metallierung des Diaminosiloxans O(SiiPr2NH2)2

Synthesis and Metalation of the Diaminosiloxane O(SiiPr₂NH₂)₂ The 1,3‐diaminoldisiloxane O(SiiPr₂NH₂)₂ ( 1 ) was obtained from the reaction of O(SiiPr₂Cl)₂ with NH₃. The reactions of 1 with AlEt₃ or GaEt₃ produced the compounds [O{SiiPr₂N(H)MEt₂}{SiiPr₂NMEt}]₂ ( 2 : M = Al; 3 : M = Ga). The crystal structures of 2 and 3 were determined by single crystal X‐ray diffraction, showing a polycyclic M₄N₄Si₄O₂ core structure of these molecules.     

QUASI: a novel method for simultaneous superposition of multiple flexible ligands and virtual screening using partial similarity

The structure of many receptors is unknown, and only information about diverse ligands binding to them is available. A new method is presented for the superposition of such ligands, derivation of putative receptor site models and utilization of the models for screening of compound databases. In order to generate a receptor model, the similarity of all ligands is optimized simultaneously taking into account conformational flexibility and also the possibility that the ligands can bind to different regions of the site and only partially overlap. Ligand similarity is defined with respect to a receptor site model serving as a common reference frame. The receptor model is dynamic and coevolves with the ligand alignment until an optimal self-consistent superposition is achieved. When ligand conformational flexibility is permitted, different superposition models are possible and consistent with the data. Clustering of the superposition solutions is used to obtain diverse models. When the models are used to screen a database of compounds, high enrichments are obtained, comparable to those obtained in docking studies.     

Synthesis,Structure, and Properties of the High‐Pressure Modification of CePdSn – a 5 K Antiferromagnet

The high‐pressure (HP) modification of CePdSn was synthesized under multianvil high‐pressure (10.5 GPa) high‐temperature (1100 °C) conditions from the normal‐pressure (NP) modification. The structures of both modifications were studied by X‐ray powder and single crystal diffraction: TiNiSi type, Pnma, a = 754.1(2), b = 470.6(1), c = 798.4(3) pm, wR2 = 0.0333, 945 F² values, 20 variables for NP‐CePdSn and ZrNiAl type, , a = 760.03(5), c = 416.06(3) pm, wR2 = 0.0443, 248 F² values, 13 variables for HP‐CePdSn. The structural chemistry of both modifications is goverened by platinum centered trigonal prisms. The platinum and tin atoms in NP‐CePdSn and HP‐CePdSn build up a three‐dimensional [PdSn] network in which the cerium atoms fill channels. Susceptibility measurements on HP‐CePdSn reveal an experimental magnetic moment of 2.55(1) μ_B/Ce atom in the paramagnetic region. At 5 K a paramagnetic‐to‐antiferromagnetic transition is evident from magnetization and specific heat measurements.