The radial distribution function of worm-like chains

Thermal conformations of semiflexible macromolecules are generically described by the worm-like chain model. The end-to-end distance distribution, a fundamental quantity of the model, is not yet known in closed form. We provide a solution to the practical problem of choosing an appropriate approximation. First, a comprehensive review of existing approximations and exact limiting results is given. We then propose an explicit expression which interpolates between all relevant limiting cases. We show that it accurately reproduces, at no computational cost, high-precision Monte Carlo data, covering a wide range from stiff to flexible chains and from looped to fully stretched configurations. Using this result we quantify the enhancement of short worm-like loop formation by (protein) bridges.     

The Structure of a Non-Symmetric Disordered Tetramer: A Crystallographic and Solid State Multinuclear NMR Study of the Properties of 3(5)-Ethyl-5(3)-Phenyl-1H-Pyrazole

The X-ray structure and the solid-state NMR measurements, mainly ¹⁵N CPMAS of the labelled compound, allow to determine the static and dynamic properties of 3(5)-ethyl-5(3)-phenyl-1H-pyrazole. The compound is a tetramer formed by three 5-ethyl-3-phenyl-1H-pyrazole and one 3-ethyl-5-phenyl-1H-pyrazole tautomers in dynamic equilibrium with the complementary situation.     

Intermolecular spin–spin coupling constants between P atoms

This paper reports the study by NMR spectroscopy and ab initio methods of the structure of 3,4-dimethyl-1-cyanophosphole and its dimer. The dimer presents a P···P interaction of the pnictogen type due to the presence of σ-holes. NMR of the monomer was recorded in CDCl₃ solution while NMR of the dimer corresponds to the solid state (CPMAS) experiments. The ^2pJ_PP spin–spin coupling constant has not been measured, but calculated at the B3LYP level. AIM, NBO and ELF methodologies have been used to describe the electronic structure of the dimer.     

Gas chromatography–triple-quadrupole mass spectrometry for analysis of selected polyhalogenated pollutants in plants. Comparison of extraction methods

Different extraction methods, followed by gas chromatography coupled to triple quadrupole mass spectrometry, were evaluated for simultaneous extraction of seven polychlorinated biphenyls (PCBs) and six polybrominated diphenyl ethers (PBDEs) from common weeds. Pressurized liquid extraction (PLE) with in-cell clean-up, ultrasound-assisted extraction (UAE) with in-column clean-up, and UAE with dispersive solid-phase extraction (dSPE) clean-up were evaluated and compared. In-cell clean-up with 4 g Florisil and 0.5 g graphitized carbon black (GCB) and two extraction cycles of 10 min with n-hexane–ethyl acetate 80:20 (v/v) at 60 °C were used for the PLE procedure. UAE with in-column clean-up was conducted under conditions similar to those reported for the PLE method whereas in UAE with dSPE clean-up purification of the extract was performed after extraction using primary and secondary amine sorbent (PSA) and GCB. Recovery from 82 to 104 % was obtained for all the compounds by PLE whereas, in general, lower extraction efficiency was obtained by UAE with in-column clean-up (especially for BDE-17 and BDE-183, for which recovery was 70 and 41 %, respectively) and by UAE with dSPE clean-up, for which the main drawback is that BDE-183 cannot be extracted. Finally, PLE was used for analysis of PCBs and PBDEs in different plants (Lolium rigidum, Lactuca serriola, Malva sylvestris, and Verbascum thapsus) collected from residential and/or rural areas of Madrid (Spain). Several of the analyzed compounds were detected at low levels in these plants, but only PCB-153 could be quantified.

Microwave‐Assisted Synthesis and Antiprotozoal Activity of Pyridazines Carrying Polyfluoro Substituents

A number of 4,5‐dichloro‐ and 4,5‐dibromopyridazin‐3‐ones and ‐3,6‐diones with polyfluoro substituents at position 2 were obtained in good yields by microwave‐assisted method. The oxopyridazines as well as their respective 5‐dimethylaminoethylamino derivatives were tested for antibacterial, antiviral, and antiprotozoal activity.     

Towards a quaternionic function theory linked with the Lamé's wave functions

Over the past few years, considerable attention has been given to the role played by the Lamé's Wave Functions (LWFs) in various problems of mathematical physics and mechanics. The LWFs arise via the method of separation of variables for the wave equation in ellipsoidal coordinates. The present paper introduces the Lamé's Quaternionic Wave Functions (LQWFs), which extend the LWFs to a non‐commutative framework. We show that the theory of the LQWFs is determined by the Moisil‐Theodorescu type operator with quaternionic variable coefficients. As a result, we explain the connections between the solutions of the Lamé's wave equation, on one hand, and the quaternionic hyperholomorphic and anti‐hyperholomorphic functions on the other. We establish analogues of the basic integral formulas of complex analysis such as Borel‐Pompeiu's, Cauchy's, and so on, for this version of quaternionic function theory. We further obtain analogues of the boundary value properties of the LQWFs such as Sokhotski‐Plemelj formulae, the ‐hyperholomorphic extension of a given Hölder function and on the square of the singular integral operator. We address all the text mentioned earlier and explore some basic facts of the arising quaternionic function theory. We conclude the paper showing that the spherical, prolate, and oblate spheroidal quaternionic wave functions can be generated as particular cases of the LQWFs. Copyright © 2015 John Wiley & Sons, Ltd.