Preparation of terminal alkenic esters by an oxidative radical reaction

A general method is described for the conversion of(mono)alkenic esters with the double bond at the n^th C atom to terminal alkenic esters of (n?1) C atoms in length, with the double bond at n?2. Ozonolysis, either in methanol or in light petroleum, is followed by reaction with a mixture of ferrous and cupric salts. Methyl 10-undecenoate, methyl oleate (methyl (Z)-9-octadecenoate) and methyl erucate (methyl (Z)-13-docosenoate) were converted to methyl 8-nonenoate, methyl 7-octenoate and methyl 11-dodecenoate respectively. An improved preparation of 5-hexenoic acid is also described.     

Synthesis of pH‐ and thermoresponsive poly(2‐n‐propyl‐2‐oxazoline) based copolymers

Polymers that possess lower critical solution temperature behavior such as poly(2‐alkyl‐2‐oxazoline)s (PAOx) are interesting for their application as stimulus‐responsive materials, for example in the biomedical field. In this work, we discuss the scalable and controlled synthesis of a library of pH‐ and temperature‐sensitive 2‐n‐propyl‐2‐oxazoline P(nPropOx) based copolymers containing amine and carboxylic acid functionalized side chains by cationic ring opening polymerization and postpolymerization functionalization strategies. Using turbidimetry, we found that the cloud point temperature (CP) is strongly dependent on both the polymer concentration and the polymer charge (as a function of pH). Furthermore, we observed that the CP decreased with increasing salt concentration, whereas the CP increased linearly with increasing amount of carboxylic acid groups. Finally, turbidimetry studies in PBS‐buffer indicate that CPs of these polymers are close to body temperature at biologically relevant polymer concentrations, which demonstrates the potential of P(nPropOx) as stimulus‐responsive polymeric systems in, for example, drug delivery applications. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1573–1582     

Combinatorial Integer Labeling Theorems on Finite Sets with Applications

Tucker’s well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {±1,±2,…,±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits a 1-dimensional simplex whose two vertices have opposite labels. In this paper, we are concerned with an arbitrary finite set D of integral vectors in the n-dimensional Euclidean space and an integer labeling that assigns to each element of D a label from the set {±1,±2,…,±n}. Using a constructive approach, we prove two combinatorial theorems of Tucker type. The theorems state that, under some mild conditions, there exists two integral vectors in D having opposite labels and being cell-connected in the sense that both belong to the set {0,1} ⁿ +q for some integral vector q. These theorems are used to show in a constructive way the existence of an integral solution to a system of nonlinear equations under certain natural conditions. An economic application is provided.     

An algorithm for computing the nucleolus of disjunctive non-negative additive games with an acyclic permission structure

A cooperative game with a permission structure describes a situation in which players in a cooperative TU-game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. In this paper we consider non-negative additive games with an acyclic permission structure. For such a game we provide a polynomial time algorithm for computing the nucleolus of the induced restricted game. The algorithm is applied to a market situation where sellers can sell objects to buyers through a directed network of intermediaries.     

Anisotropic X-ray magnetic linear dichroism Its importance for the analysis of soft x-ray spectra of magnetic oxides

Using spectroscopic information for x ray magnetometry and magnetic microscopy requires detailed theoretical understanding of spectral shape and magnitude of dichroism signals. We have shown unambiguously that – contrary to common belief—spectral shape and magnitude of x ray magnetic linear dichroism (XMLD) are not only determined by the relative orientation of magnetic moments and x ray polarization, but also their orientations relative to the crystallographic axes must be taken into account for accurate interpretation of XMLD data.