Convergence of Semigroups of Complex Measures on a Lie Group

A theorem of Siebert in its essential part asserts that if μ _n (t) are semigroups of probability measures on a Lie group G, and P _n are the corresponding generating functionals, then $$\bigl \langle \mu_n(t),f \bigr \rangle \ \xrightarrow[n]{}\ \bigl \langle \mu_0(t),f \bigr \rangle , \quad f\in C_b(G), \ t>0,$$ implies $$\langle \pi_{P_n}u,v\rangle \ \xrightarrow[n]{}\ \langle \pi_{P_0}u,v\rangle ,\quad u\in C^{\infty}(E,\pi), \ v\in E,$$ for every unitary representation π of G on a Hilbert space E, where C ^∞(E,π) denotes the space of smooth vectors for π. The aim of this note is to give a simple proof of the theorem and propose some improvements, the most important being the extension of the theorem to semigroups of complex measures. In particular, we completely avoid employing unitary representations by showing simply that under the same hypothesis $$\langle P_n,f\rangle \ \xrightarrow[n]{}\ \langle P_0,f\rangle ,$$ for bounded twice differentiable functions f. As a corollary, the above thesis of Siebert is extended to bounded strongly continuous representations of G on Banach spaces.     

Antioxidant Activities of Some New Chromonyl-2,4-Thiazolidinediones and Chromonyl-2,4-Imidazolidinediones Having Chromone Cores

The antioxidant properties of 11 new synthesized chromonyl-2,4-thiazolidinediones and chromonyl-2,4-imidazolidinediones (CBs) were investigated. The antioxidant activities and mechanisms of the CBs interaction with reactive oxygen species (ROS) were clarified using various in vitro antioxidant assay methods including superoxide anion radical ( $ \mathrm{O}\overline{{}_2^{\bullet }} $ ), hydroxyl radical (HO^?), 1,1-diphenyl-2-picryl-hydrazyl free radical (DPPH^?) scavenging activity and the iron (II)-ferrozine complex formation. The potassium superoxide/18-crown-6 ether dissolved in dimethylsulfoxide (DMSO) was applied as a source of superoxide anion radical. Hydroxyl radicals were produced in the Fenton-like reaction Fe(II)+H₂O₂. Chemiluminescence, spectrophotometry, and electron paramagnetic resonance (EPR) spectroscopy using 5,5-dimethyl-1-pyrroline-1-oxide (DMPO) as spin trap were applied as the measurement techniques. The CBs examined that exhibited good free radical scavenging activity also showed strong total antioxidant power capacity. Possible mechanisms of antioxidation are proposed to explain the differences in the experimental results between the chromone derivatives with imidazolidine-2,4-dione ring and those with thiazolidine-2,4-dione ring. In conclusion, some of the new CBs are promising to be applied as inhibitors of free radicals.     

Preliminary thermal characterization of natural resins from different botanical sources and geological environments

The preliminary studies on thermal behavior of differently aged natural resins from Russia (Khatanga), Dominican Republic (El Valle), Colombia and Poland (Jantar) were performed. Thermal stability and behavior under elevated temperature were investigated by thermogravimetry (TG) and differential scanning calorimetry (DSC), while the differences in the structure and composition by FT-IR spectroscopy. Analyzed resins show different thermal effects during heating suggesting that possible post-reactions and structural changes occurred. TG results indicated that Dominican, Russian and Colombian resins present relatively high thermal stability under air conditions in the range of 228–300 °C, whereas the mass loss of 5mass% at about 217 °C was observed for Baltic amber. During DSC experiments, the analyzed resins expose thermal events which make impossible determination of glass transition temperature in a raw sample. The results indicate that both TG and DSC cannot be considered as methods for age dating of natural resins and more advanced techniques should be applied. Careful analysis of FT-IR data in the carbonyl region may provide additional information about the composition and history of the natural resin.

     

Is there contextuality for a single qubit?

Cabello and Nakamura have shown [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)10.1103/PhysRevLett.90.190401] that the Kochen-Specker theorem can be applied to two-dimensional systems if one uses positive operator-valued measures (POVM). We show that the contextuality in their models is not of the Kochen-Specker type, but it is rather a result of not keeping track of the whole system on which the measurement is performed. This is connected to the fact that there is no one-to-one correspondence between the POVM elements and projectors on the extended Hilbert space, and the same POVM element has to originate from two different projectors when used in Cabello-Nakamura models. Moreover, we propose a hidden-variable formulation of the above models.     

No-local-broadcasting theorem for multipartite quantum correlations

We prove that the correlations present in a multipartite quantum state have an operational quantum character even if the state is unentangled, as long as it does not simply encode a multipartite classical probability distribution. Said quantumness is revealed by the new task of local broadcasting, i.e., of locally sharing preestablished correlations, which is feasible if and only if correlations are stricly classical. Our operational approach leads to natural definitions of measures for quantumness of correlations. It also reproduces the standard no-broadcasting theorem as a special case.     

Beyond Oxides: Nitride as a Ligand in a Neutral IrIXNO3 Molecule Bearing a Transition Metal at High Oxidation State

Theoretical calculations utilizing relativistic ZORA Hamiltonian point to the conceivable existence of an IrNO₃ molecule in C_3v geometry. This minimum is shown to correspond to genuine nonavalent iridium nitride trioxide, which is a neutral analogue of cationic [IrO₄]⁺ species detected recently. Despite the presence of nitride anion, the molecule is protected by substantial barriers exceeding 200 kJ mol⁻¹ against transformations leading, for example, to global minimum (O=)₂Ir−NO, which contains metal at a lower formal oxidation state.     

Electrochemical studies on novel films consisting of phosphorus-doped multi-walled carbon nanotubes

Ionics - Films consisting of phosphorus-doped multi-walled carbon nanotubes (further denoted as P-MWCNTs) were fabricated by means of chemical vapor deposition technique with decomposition of...     

Large-Scale Synthesis of a Niche Olefin Metathesis Catalyst Bearing an Unsymmetrical N-Heterocyclic Carbene (NHC) Ligand and its Application in a Green Pharmaceutical Context

A large-scale synthesis of known Ru olefin metathesis catalyst VII featuring an unsymmetrical N-heterocyclic carbene (NHC) ligand with one 2,5-diisopropylphenyl (DIPP) and one thiophenylmethylene N-substituent is reported. The optimised procedure does not require column chromatography in any step and allows for preparation of up to 0.5 kg batches of the catalyst from simple precursors. The application profile of the obtained catalyst was studied in environmentally friendly dimethyl carbonate (DMC). Although VII exhibited low efficiency in cross-metathesis (CM) with electron-deficient partners, good to excellent results were noted for substrates featuring easy to isomerise C−C double bonds. This includes polyfunctional substrates of medicinal chemistry interest, such as analogues of psychoactive 5F-PB-22 and NM-2201 and two PDE5 inhibitors—Sildenafil and Vardenafil. Finally, a larger scale ring-closing metathesis (RCM) of a Vardenafil derivative was conducted in DMC, allowing for straightforward isolation of the expected product (23 g) in high yield and with low Ru contamination level (7.7 ppm).