On the possible multi-valuedness of quantum wavefunctions

A theorem generalizing a result due to Schrödinger on the possible multi-valuedness of quantum wavefunctions is proved. Relevant examples show that double-valued wavefunctions do exist, at least in problems of a theoretical interest.     

Reducing-difference infrared spectral analysis of cis- and trans-configurated lactams

The conventional (non-polarized) and linear-polarized IR-spectra of 2-pyrrolidone and laurolactam as typical representatives of lactams with cis- and trans-amide configuration, respectively, were studied by means of difference IR-spectroscopy. The application of this method to treatment of the non-polarized IR-spectra permits additional conclusions about the likely self-associates of these compounds dissolved in aprotic solvents. By means of the difference linear-dichroic IR-spectroscopy, a more precise assignment of the characteristic bands of the lactam cis- and trans-peptide forms as well as their stereo structures were accomplished. A comparative analysis with the linear-dichroic IR-spectra of epsilon-caprolactam and caprylolactam, as similar compounds, with cis- and trans-conformation, respectively, was also carried out.     

Motzkin decomposition of closed convex sets

Theodore Motzkin proved, in 1936, that any polyhedral convex set can be expressed as the (Minkowski) sum of a polytope and a polyhedral convex cone. This paper provides five characterizations of the larger class of closed convex sets in finite dimensional Euclidean spaces which are the sum of a compact convex set with a closed convex cone. These characterizations involve different types of representations of closed convex sets as the support functions, dual cones and linear systems whose relationships are also analyzed in the paper. The obtaining of information about a given closed convex set F and the parametric linear optimization problem with feasible set F from each of its different representations, including the Motzkin decomposition, is also discussed.     

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".