Detailed nuclear structure studies far from stability

State-of-the-art spectroscopy of nuclei far from stability has achieved an extraordinary level of sophistication and detail in the last ten years. In principle, if a state can be populated, it can be characterized by its energy, spin, parity, and major decay paths. Sometimes its lifetime can be measured. In practice, one is confronted with enormous complexity. To convert raw spectroscopic data into nuclear structure data involves a complex process of disentangling gamma rays and conversion electrons into decay schemes. Specifically, coincidence techniques, especially coincidence intensities, play a crucial role in this process. Recent examples and methods from work done at UNISOR are presented.     

Cyclic trihydroxamic acid derivatives

In the crystal structures of two cyclic trihydroxamic acid derivatives containing the same substructure unit, viz. 1,3,5‐trihydroxy‐1,3,5‐triazinane‐2,4,6‐trione dihydrate, C₃H₃N₃O₆·2H₂O, (I), and 1,3,5‐benz­yloxy‐1,3,5‐triazinane‐2,4,6‐trione, C₂₄H₂₁N₃O₆, (II), there is no significant difference in the geometric parameters. In (I), there are 11 hydrogen bonds of the O—H⋯O type inter­connecting the mol­ecules in a three‐dimensional network, while in (II) there are only two weak C—H⋯O hydrogen bonds. The results of IR spectroscopic analysis are in good agreement with the crystallographic study.     

Mercury(II) complex with terpyridine: structure of the 2∶1 solvate of [Hg(terpy)2](CF3SO3)2 with acetone

[Hg(terpy)₂](CF₃SO₃)₂·0.5(CH₃)₂CO crystallizes in the triclinic space group witha=14.631(6),b=15.258(4),c=18.785(7) Å, =69.66(2), =70.72(1), =88.55(1)°. The crystal structure consists of two independent [Hg(terpy)₂]²⁺ cations, four trifluoromethanesulfonate anions and an acetone molecule in the asymmetric unit. Each mercury atom is coordinated by two tridentate terpyridine ligands forming an irregular six-coordination polyhedron. The Hg–N bond lengths range from 2.27(2) to 2.53(2) Å.     

Direct Potentiometric Study of Cationic and Nonionic Surfactants in Disinfectants and Personal Care Products by New Surfactant Sensor Based on 1,3-Dihexadecyl−1H-benzo[d]imidazol−3-ium

A novel, simple, low-cost, and user-friendly potentiometric surfactant sensor based on the new 1,3-dihexadecyl−1H-benzo[d]imidazol−3-ium-tetraphenylborate (DHBI–TPB) ion-pair for the detection of cationic surfactants in personal care products and disinfectants is presented here. The new cationic surfactant DHBI-Br was successfully synthesized and characterized by nuclear magnetic resonance (NMR), Fourier transform infrared (FTIR) spectrometry, liquid chromatography–mass spectrometry (LC–MS) and elemental analysis and was further employed for DHBI–TPB ion-pair preparation. The sensor gave excellent response characteristics for CTAB, CPC and Hyamine with a Nernstian slope (57.1 to 59.1 mV/decade) whereas the lowest limit of detection (LOD) value was measured for CTAB (0.3 × 10⁻⁶ M). The sensor exhibited a fast dynamic response to dodecyl sulfate (DDS) and TPB. High sensor performances stayed intact regardless of the employment of inorganic and organic cations and in a broad pH range (2−11). Titration of cationic and etoxylated (EO)-nonionic surfactant (NSs) (in Ba²⁺) mixtures with TPB revealed the first inflexion point for a cationic surfactant and the second for an EO-nonionic surfactant. The increased concentration of EO-nonionic surfactants and the number of EO groups had a negative influence on titration curves and signal change. The sensor was successfully applied for the quantification of technical-grade cationic surfactants and in 12 personal care products and disinfectants. The results showed good agreement with the measurements obtained by a commercial surfactant sensor and by a two-phase titration. A good recovery for the standard addition method (98–102%) was observed.     

The Langlands classification for non-connected -adic groups II: Multiplicity one

For a non-connected reductive -adic group, we prove that the Langlands subrepresentation appears with multiplicity one in the representation parabolically induced from the corresponding Langlands data.

     

Requirements in mathematics textbooks: a five-dimensional analysis of textbook exercises and examples

Mathematics textbooks play a very important role in mathematics education and textbook tasks are used by students for practice to a large extent. Since the nature of the tasks may influence the way students think it is important that the textbooks provide a balance of a variety of tasks. The analyses of the requirements in textbook tasks contain the usual dimensions of content, cognitive demands, question type and contextual features. The aim of this study is to embed a new fifth dimension into the framework: mathematical activities. This addresses the question of what a student should do in a particular textbook task: to represent, to compute, to interpret or to use argumentation. The analysis encompassed more than 22,000 tasks from the most commonly used Croatian mathematics textbooks in the 6th, 7th and 8th grade. The results show that the textbooks do not provide a full range of task types. There is an emphasis on computation, while argumentation and interpretation activities, reflective thinking and open answer tasks are underrepresented. The study revealed that incorporating mathematical activities into the multidimensional framework of textbook tasks may help to better understand the opportunities to learn which are afforded students by using mathematics textbooks.     

Improving the Accuracy of Small-Molecule Crystal Structures Solved from Powder X-Ray Diffraction Data by Using External Sources

Structural analysis using powder X-ray diffraction data has overcome many obstacles and nowadays is readily applicable for structural analysis of all types of compounds and materials. Being less straightforward than single crystal diffraction, it requires significant users’ input and consequently, implementation of standardized tools to assess the accuracy of crystal structures. This article discusses potential errors in crystal structure solution and refinement of small-molecule structures obtained from PXRD data. Moreover, it proposes how accuracy of these structures can be improved by using high-quality PXRD data, complementary external analytical techniques, knowledge stored in crystal structure databases, as well as an approach to search the parameter space to avoid local minima in testing different sets of geometry restraints.     

Nonionic surfactant-selective electrode and its application for determination in real solutions

A liquid membrane nonionic surfactant sensitive electrode has been prepared, based on a new barium pseudocationic complex of a highly ethoxylated fatty alcohol polyglycol ether and tetraphenylborate as sensing material. The complex has been incorporated into the plasticized PVC-membrane and used as sensing material.The electrode exhibited positive linear non-Nernstian response toward different nonionic surfactants and sub-Nernstian response toward tetraphenylborate with the lower detection limit of 3.3 × 10⁻⁷ mol dm⁻³ in barium chloride solution.The interfering effect of some alkaline, alkaline earth, and heavy metal cations, has been demonstrated by displaying their calibration curves compared with that of Triton X-100.The electrode has been used as an end-point indicator for potentiometric titration of analytical and technical grade polyethoxylated nonionic surfactants, modelled detergent products, and commercial detergents.