How ∗ not ∗ to solve a Sudoku

We prove the NP-hardness of a consistency checking problem that arises in certain elimination strategies for solving Sudoku-type problems.     

Description of the viscosity of honeys in the supercooled regime

For several honeys from different countries, we study the dependence of the Logarithmic Shift Factor (LSF$LSF$) with temperature that obeys the Williams–Landel–Ferry equation. We find that the LSF$LSF$ may be expressed in terms of a linear equation. On the other hand, the viscosities of different honeys present a corresponding state behavior through a master plot in terms of an adimensional temperature. This kind of behavior has been reported for other glass formers.     

A Morita Context and Galois Extensions for Quasi-Hopf Algebras

If H is a finite dimensional quasi-Hopf algebra and A is a left H-module algebra, we show that there is a Morita context connecting the smash product A#H and the subalgebra of invariants A ^H . We define also Galois extensions and prove the connection with this Morita context, as in the Hopf case.     

Galois Extensions for Coquasi-Hopf Algebras

In this article, we consider categories of all semimodules over semirings which are p-Schreier varieties, i.e., varieties whose projective algebras are all free. Among other results, we show that over a division semiring R all semimodules are projective iff R is a division ring, prove that categories of all semimodules over proper additively π-regular semirings are not p-Schreier varieties (in particular, this result solves Problem 1 of Katsov [8 Katsov , Y. ( 2004 ). Toward homological characterization of semirings: Serre's conjecture and Bass's perfectness in a semiring context . Algebra Universalis 52 : 197 – 214 .[Crossref], [Web of Science ®] , [Google Scholar]]), as well as prove that categories of all semimodules over cancellative division semirings are, in contrast, p-Schreier varieties.     

On the hydroperoxyl radical scavenging activity of two Edaravone derivatives: mechanism and kinetics

The free radical scavenging activity of two Edaravone (EDA) derivatives (C1 and D1) has been studied in aqueous and lipid solutions using the Density Functional Theory. Different mechanisms of reaction have been considered, as well as the acid/base equilibrium in aqueous solution. The studied compounds were found to be rather poor ^?OOH scavengers in non‐polar environments, but better than the parent molecule, EDA, which suggests that the peroxyl scavenging activity of this kind of compounds in lipid media could be increased via structural modifications. In aqueous solution, at physiological pH, D1 is predicted to be a better peroxyl scavenger than C1, and slightly better than its parent molecule, EDA. Their excellent activity, under such conditions, is attributed to the electron transfer from their anionic forms. D1 was found to be among the best peroxyl scavengers known so far, with a rate constant for its reaction with ^?OOH near the diffusion limit regime (2.3 × 10⁸ M^?1s^?1). Copyright © 2013 John Wiley & Sons, Ltd.     

The Arboreal Jump Number of an Order

Let ${\mathcal P}$ be a partial order and ${\mathcal A}$ an arboreal extension of it (i.e. the Hasse diagram of ${\mathcal A}$ is a rooted tree with a unique minimal element). A jump of ${\mathcal A}$ is a relation contained in the Hasse diagram of ${\mathcal A}$ , but not in the order ${\mathcal P}$ . The arboreal jump number of ${\mathcal A}$ is the number of jumps contained in it. We study the problem of finding the arboreal extension of ${\mathcal P}$ having minimum arboreal jump number—a problem related to the well-known (linear) jump number problem. We describe several results for this problem, including NP-completeness, polynomial time solvable cases and bounds. We also discuss the concept of a minimal arboreal extension, namely an arboreal extension whose removal of one jump makes it no longer arboreal.     

Diurnal variations in the photosynthesis-respiration activity of a cyanobacterial bloom in a freshwater dam reservoir: an isotopic study

The stable isotopic analyses of molecular oxygen dissolved in water (delta18O(DO)) and dissolved inorganic carbon (delta13C(DIC)), supplemented with basic chemical measurements, have been carried out on a diurnal basis to better understand the dynamics of photosynthesis and respiration in freshwater systems. Our observations have been carried out in a lowland dam reservoir, the Sulejow Lake (central Poland), during the summer cyanobacterial bloom. All data obtained, isotopic, hydrochemical, and biological, show a high mutual consistency. Namely, the lowest delta18O(DO) values, obtained at 10:00 and 14:00 (16.0 and 15.5 per thousand, respectively), correspond to the highest amount of cyanobacterial cells observed (66 and 63 mg dm(-3), respectively), whereas the minimum delta13C(DIC) (-10.6 per thousand) obtained at 22:00 corresponds to the maximum content of organic matter (110 mg dm(-3)). This evidence suggests that isotopic assays of delta18O(DO) and delta13C(DIC) are a reliable tool for the quantitative study of biochemical processes in freshwater systems.     

Ring-expansion approaches for the total synthesis of salimabromide

We describe the evolution of a synthetic strategy for the construction of the marine polyketide salimabromide. Combining a bicyclo[3.1.0]hexan-2-one ring-expansion to build up a functionalized naphthalene and an unprecedented rearrangement/cyclization cascade, enabled synthesis of a dearomatized tricyclic subunit of the target compound. Alternatively, an intramolecular keteniminium [2 + 2]-cycloaddition and subsequent Baeyer–Villiger ring-expansion gave access to the sterically encumbered architecture of salimabromide. Sequential oxidation of the carbon framework finally enabled the total synthesis of this unusual natural product.     

Novel 4-azaandrostenes as prostate cancer cell growth inhibitors: Synthesis,antiproliferative effects,and molecular docking studies

In this study, synthesis, structural characterization, molecular docking studies, and antiproliferative effects in four different cell lines of several novel 16-arylidene-4-azaandrost-5-ene compounds are reported. These compounds were prepared by oxidative cleavage of the enone system of androstenedione followed by an azacyclization reaction and an aldol condensation with various aldehydes at C16. In the androgen-dependent LNCaP cells, the most relevant antiproliferative effects were observed with the 16-phenyl, 16-p-tolyl, and 16-p-nitrophenyl derivatives. Compound 16E-[(4-methylphenyl)methylidene]-4-azaandrost-5-ene-3,17-dione was the most potent in these cells (IC₅₀ = 28.28 μM), having lower antiproliferative effects in the androgen-independent PC-3 cells (IC₅₀ = 45.31 μM). In addition, an interesting selectivity toward cancer cell lines was found for all compounds because a generally low cytotoxicity was detected in healthy human fibroblasts. Furthermore, the 16-p-tolylazaandrostene steroid induced a reduction of viability in LNCaP cells similar to that observed with finasteride, a clinically used 5α-reductase inhibitor. Moreover, molecular docking studies predicted that these 4-azaandrostene derivatives can interact with 5β-reductase, which has a high level of similarity to 5α-reductase enzyme, and with other common targets of steroidal drugs, particularly the enzyme 17α-hydroxylase/17,20-lyase.