Essential oil composition of endemic Tanacetum zahlbruckneri (Nab.) and Tanacetum tabrisianum (Boiss.) Sosn. and Takht. from Turkey

In this study, water-distilled essential oils from the flowers of Tanacetum zahlbruckneri and flowers and stems of Tanacetum tabrisianum from Turkey were analysed by gas chromatography (GC) and gas chromatography-mass spectrometry (GC-MS). The flower oil of T. zahlbruckneri was characterised by the sesquiterpenes germacrene D (29.7%) and spathulenol (12%). Flower (A) and stem (B) oil of T. tabrisianum was characterised by 1,8-cineole: 17.6% (A), 22.5% (B), hexadecanoic acid: 10.3% (A), 8% (B), decanoic acid: 5.8% (A) and trans-linalooloxide acetate: 5.3% (A), 4% (B). Unlike a previous report on the essential oil composition of T. tabrisianum, in this study a 1,8-cineole and hexadecanoic acid-rich oil with a low percentage of caryophyllene oxide and spathulenol was obtained. The composition of the essential oil of endemic T. zahlbruckneri was investigated for the first time.     

Phenyliodine(III) bis(trifluoroacetate) (PIFA)-promoted synthesis of Bodipy dimers displaying unusual redox properties

Phenyliodine(III) bis(trifluoroacetate) (PIFA) in conjunction with a Lewis acid promotes C-C coupling of Bodipy monomers leading to mixtures of various oligomers. When a single position is blocked with an iodo or phenyl group, formation of the dimer is favored. These dimers display two successive oxidation and two reduction waves separated on average by 260 and 130 mV, respectively, corresponding to each Bodipy subunit.     

Nanoscopic optical sensors based on functional supramolecular hybrid materials

This review highlights how the combination of supramolecular principles and nanoscopic solid structures enables the design of new hybrid sensing ensembles with improved sensitivity and/or selectivity and for the targeting of analytes for which selectivity is hard to achieve by conventional methods. Such ideas are bridging the gap between molecules, materials sciences and nanotechnology. Relevant examples will be detailed, taking into account functional aspects such as (1) enhanced coordination of functionalized solids, (2) enhanced signalling through preorganization, (3) signalling by assembly–disassembly of nanoscopic objects, (4) biomimetic probes utilizing discrimination by polarity and size and (5) distinct switching and gating protocols. These strategies are opening new prospects for sensor research and signalling paradigms at the frontier between nanotechnology, smart materials and supramolecular chemistry.     

On the Nagumo uniqueness theorem

By a convenient reparametrization of the integral curves of a nonlinear ordinary differential equation (ODE), we are able to improve the conclusions of a recent generalization of Nagumo’s uniqueness theorem. In this way, we establish a flexible uniqueness criterion for ODEs without Lipschitz-like nonlinearities.     

An efficient computational method for a stochastic dynamic lot-sizing problem under service-level constraints

We provide an efficient computational approach to solve the mixed integer programming (MIP) model developed by Tarim and Kingsman [8] for solving a stochastic lot-sizing problem with service level constraints under the static-dynamic uncertainty strategy. The effectiveness of the proposed method hinges on three novelties: (i) the proposed relaxation is computationally efficient and provides an optimal solution most of the time, (ii) if the relaxation produces an infeasible solution, then this solution yields a tight lower bound for the optimal cost, and (iii) it can be modified easily to obtain a feasible solution, which yields an upper bound. In case of infeasibility, the relaxation approach is implemented at each node of the search tree in a branch-and-bound procedure to efficiently search for an optimal solution. Extensive numerical tests show that our method dominates the MIP solution approach and can handle real-life size problems in trivial time.     

Geometric invariant theory and Einstein–Weyl geometry

In this article, we give a survey of geometric invariant theory for Toric Varieties, and present an application to the Einstein-Weyl geometry. We compute the image of the Minitwistor space of the Honda metrics as a categorical quotient according to the most efficient linearization. The result is the complex weighted projective space CP_1,1,2. We also find and classify all possible quotients.     

A collocation approach for the numerical solution of certain linear retarded and advanced integrodifferential equations with linear functional arguments

This article presents a Taylor collocation method for the approximate solution of high‐order linear Volterra‐Fredholm integrodifferential equations with linear functional arguments. This method is essentially based on the truncated Taylor series and its matrix representations with collocation points. Some numerical examples, which consist of initial and boundary conditions, are given to show the properties of the technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

On constructing total orders and solving vector optimization problems with total orders

In this paper, we introduce a construction method of total ordering cone on \mathbbRⁿ{\mathbb{R}^n} . It is shown that any total ordering cone on \mathbbRⁿ{\mathbb{R}^n} is isomorphic to the cone \mathbbRⁿ_lex{\mathbb{R}^n_{lex}} . Existence of a total ordering cone that contain given cone with a compact base is shown. By using this cone, a solving method of vector and set valued optimization problems is presented.     

How much do we “pay” for using default parameters?

This paper explores the potential benefit of using tuned parameter settings for integer programming instances. Three metrics are considered for selecting parameters: Time-to-Optimality, Proven-Gap and Best-Integer-Solution. Good parameter settings for each metric are found using the open-source software tool Selection Tool for Optimization Parameters. Computational tests are presented using CPLEX solver (version 9.0) on MIPLIB test instances, showing substantial improvements over the default parameter setting. Although the benefit of a tuned parameter setting on an individual instance is outweighed by the cost of identifying the tuned setting, these results indicate that substantial benefit may be achieved in cases where the cost of tuning parameter settings is justified.     

Manganese(III) Acetate Catalyzed Oxidative Radical Additions of α‐Dicarbonyl Compounds to 1‐ and 2‐Phenylcyclohepta‐1,3,5‐triene

Manganese(III) acetate catalyzed oxidative radical‐addition reactions of α‐dicarbonyl compounds such as methyl acetoacetate ( 6 ), acetylacetone ( 7 ), and dimedone ( 8 ) to the mixture of 1‐ and 2‐phenylcyclohepta‐1,3,5‐triene ( 4 and 5 ) were investigated (Scheme 1). The 1‐phenylcyclohepta‐1,3,5‐triene ( 4 ) formed mainly [2+3] and [4+3] dihydrofuran addition products derived from cycloheptatriene and [2+3] dihydrofuran addition products derived from the norcaradiene structure. The 2‐phenylcyclohepta‐1,3,5‐triene ( 5 ) formed mainly [6+3] dihydrofuran addition products derived from cycloheptatriene and [4+3] dihydrofuran addition products derived from the norcaradiene structure. The structures of isolated products were established by their spectroscopic data (IR, ¹H‐ and ¹³C‐NMR, MS, and elemental analysis) and comparison with literature data. The formation mechanism of the products is discussed.