Fuzzy measures for profit maximization with fuzzy parameters

Profit maximization is an important issue to the firms that pursue the largest economic profit possible. This paper extends the situation from the deterministic to uncertain, where the coefficients are represented by fuzzy numbers. Intuitively, when the problem has fuzzy parameters, the derived profit value should be a fuzzy number as well. The extension principle is utilized to develop a pair of two-level mathematical programs to calculate the upper and lower bounds of the profit value at α-cuts. Following the duality theorem and a variable separation technique, the two-level mathematical programs are transformed into a class of one-level signomial geometric programs to solve. An example is given to illustrate the idea proposed in this paper.     

A note on geodesic connectedness of Gödel type spacetimes

In this note we reduce the problem of geodesic connectedness in a wide class of Gödel type spacetimes to the search of critical points of a functional naturally involved in the study of geodesics in standard static spacetimes. Then, by using some known accurate results on the latter, we improve previous results on the former.     

Fuzzy closure systems on L—ordered sets

In this paper, notions of fuzzy closure system and fuzzy closure L —system on L —ordered sets are introduced from the fuzzy point of view. We first explore the fundamental properties of fuzzy closure systems. Then the correspondence between fuzzy closure systems (fuzzy closure L —systems) and fuzzy closure operators is established. Finally, we study the connections between fuzzy closure systems and fuzzy Galois connections. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Models of expansions of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb N}$\end{document} with no end extensions

We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of ${\mathbb N}$ such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of ${\mathbb N}$ such that expanding ${\mathbb N}$ by any uncountably many of them suffice. Also we find arithmetically closed ${\mathcal A}$ with no ultrafilter on it with suitable definability demand (related to being Ramsey). © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

On a positive set theory with inequality

We introduce a quite natural Frege‐style set theory, which we call Strong‐Frege‐2 $(\mathsf {SF}_2)$, a sort of simplification of the theory considered in 13 (under the name Strong‐Frege‐3) and 1 (under the name F2). We give a model of a weaker variant of $\mathsf {SF}_2$, called $\mathsf {SF}_2\mathsf {AC}$, where atoms and coatoms are allowed. To construct the model we use an enumeration “almost without repetitions” of the Π¹₁ sets of natural numbers; such an enumeration can be obtained via a classical priority argument much in the style of 5 and 15 . © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

A Short and Efficient Synthesis of a Novel Diarylheptanoid Isolated from Pleuranthodium Racemigerum

The first total synthesis of the linear diarylheptanoid 1‐(4″‐methoxyphenyl)‐7‐(4′‐hydroxyphenyl)‐(E)‐hept‐2‐ene, which has a uniquely nonconjugated olefin, was achieved. The synthetic route employed an olefin cross‐metathesis as a key step. Beginning with commercially available 3‐(4‐hydroxyphenyl)propan‐1‐ol, the final product was made in three steps with a 52% yield.     

The Rearrangement of 2,2‐Diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane to 3,4,4‐Triphenylcyclopent‐1‐ene: a DFT Analysis

A computational study on the rearrangement of 2,2‐diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane ( 1 ) is presented, using density functional theory (DFT), (U)B3LYP with the 6‐31G* basis set (DFT1) and (U)M05‐2X with the 6‐311+G** basis set (DFT2). In agreement with a biradical character of the transition structure (TS) or intermediate, the potential‐energy hypersurface is lowered by the influence of three conjugated Ph groups. Surprisingly, two conformations of the geminal diphenyl group (different twist angles) induce two different minimum‐energy pathways for the rearrangement. Independent of the functional used, the first hypersurface harbors true biradical intermediates, whereas the second energy surface is a flat, slightly ascending slope from the starting material to the TS. The functional (U)M05‐2X with the basis set 6‐311+G** provides realistic energies which seem to be close to experiment. The activation energy for racemization of enantiomers of 1 is lower than that of rearrangement by 2.5 kcal mol^?1, in agreement with experiment.     

neo‐Clerodane Diterpenoids from the Aerial Part of Scutellaria barbata

Three new neo‐clerodane diterpenoids, barbatellarines C–E ( 1 – 3 ), were isolated from the CHCl₃‐soluble fraction of the aerial part of Scutellaria barbata. Their chemical structures were elucidated by detailed analysis of NMR and MS data. Compounds 1 and 2 were C(13) epimers, which was confirmed by an NOE difference experiment and the NOESY spectrum. The relative configuration was determined on the basis of the ¹H‐NMR J‐value and NOE data, while the absolute configuration of the previously isolated analogue, barbatellarine B ( 4 ), as a representative member of the group, was assigned by CD analysis.     

Cork-based activated carbons as supported adsorbent materials for trace level analysis of ibuprofen and clofibric acid in environmental and biological matrices

In this contribution, powdered activated carbons (ACs) from cork waste were supported for bar adsorptive micro-extraction (BAμE), as novel adsorbent phases for the analysis of polar compounds. By combining this approach with liquid desorption followed by high performance liquid chromatography with diode array detection (BAμE(AC)-LD/HPLC-DAD), good analytical performance was achieved using clofibric acid (CLOF) and ibuprofen (IBU) model compounds in environmental and biological matrices. Assays performed on 30 mL water samples spiked at the 25.0 μg L(-1) level yielded recoveries around 80% for CLOF and 95% for IBU, under optimized experimental conditions. The ACs textural and surface chemistry properties were correlated with the results obtained. The analytical performance showed good precision (<15%), suitable detection limits (0.24 and 0.78 μg L(-1) for CLOF and IBU, respectively) and good linear dynamic ranges (r(2)>0.9922) from 1.0 to 600.0 μg L(-1). By using the standard addition methodology, the application of the present approach to environmental water and urine matrices allowed remarkable performance at the trace level. The proposed methodology proved to be a viable alternative for acidic pharmaceuticals analysis, showing to be easy to implement, reliable, sensitive and requiring low sample volume to monitor these priority compounds in environmental and biological matrices.