Typical Martingale Diverges at a Typical Point

We investigate convergence of martingales adapted to a given filtration of finite \(\sigma \)-algebras. To any such filtration, we associate a canonical metrizable compact space \(K\) such that martingales adapted to the filtration can be canonically represented on \(K\). We further show that (except for trivial cases) typical martingale diverges at a comeager subset of \(K\). ‘Typical martingale’ means a martingale from a comeager set in any of the standard spaces of martingales. In particular, we show that a typical \(L^1\)-bounded martingale of norm at most one converges almost surely to zero and has maximal possible oscillation on a comeager set.     

Superchiral Pd3L6 Coordination Complex and Its Reversible Structural Conversion into Pd3L3Cl6 Metallocycles

Large, non‐symmetrical, inherently chiral bispyridyl ligand L derived from natural ursodeoxycholic bile acid was used for square–planar coordination of tetravalent Pd^II, yielding the cationic single enantiomer of superchiral coordination complex 1 Pd₃ L ₆ containing 60 well‐defined chiral centers in its flower‐like structure. Complex 1 can readily be transformed by addition of chloride into a smaller enantiomerically pure cyclic trimer 2 Pd₃ L ₃Cl₆ containing 30 chiral centers. This transformation is reversible and can be restored by the addition of silver cations. Furthermore, a mixture of two constitutional isomers of trimer, 2 and 2′ , and dimer, 3 and 3′ , can be obtained directly from L by its coordination to trans‐ or cis‐N‐pyridyl‐coordinating Pd^II. These intriguing, water‐resistant, stable supramolecular assemblies have been thoroughly described by ¹H DOSY NMR, mass spectrometry, circular dichroism, molecular modelling, and drift tube ion‐mobility mass spectrometry.     

Synthesis and microstructure investigation of heterogeneous metal-plasma polymer Ag/HMDSO nanoparticles

Metal-polymer nanocomposites have gained increasing attention due to the wide potential applications field. Synthesis of nanoparticles from the gas phase is an intensively studied alternative to the chemical preparation methods. We present a one-step procedure that combines magnetron-based gas aggregation cluster source of silver nanoparticles and simultaneous plasma-enhanced chemical vapour deposition of hexamethyldisiloxane (HMDSO). The key parameter of the process, significantly influencing the morphology and microstructure of studied nanoparticles, was found to be the amount of HMDSO added to the deposition chamber as witnessed by small angle X-ray scattering and X-ray diffraction methods combined with transmission electron microscopy and UV–Vis spectrophotometry. The presence of HMDSO in the chamber leads to changes in the size distribution and also in the architecture of prepared nanoparticles. The increasing amount of HMDSO induces the formation of individual core-shell nanoparticles, chains of core-shell nanoparticles, and for the highest concentration of HMDSO, the synthesis of multi-core-shell nanoparticles. The size of crystallites in the silver cores of nanoparticles decreases with addition of HMDSO, which prevents further aggregation.     

Quantum graph vertices with permutation-symmetric scattering probabilities

Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix U. Observing that if U has at most two eigenvalues, then the scattering matrix S(k) of the vertex is a linear combination of the identity matrix and a fixed Hermitian unitary matrix, we construct vertex couplings with this property: For all momenta k, the transmission probability from the j-th edge to ?-th edge is independent of (j,?), and all the reflection probabilities are equal. We classify these couplings according to their scattering properties, which leads to the concept of generalized δ- and δ^′-couplings.     

Photochemistry of HI on argon and water nanoparticles: hydronium radical generation in HI·(H2O)n

Photochemistry of HI molecules on large Ar(n) and (H(2)O)(n), n ～ 100-500, clusters was investigated after excitation with 243 nm and 193 nm laser radiation. The measured H-fragment kinetic energy distributions pointed to a completely different photodissociation mechanism of HI on water than on argon clusters. Distinct features corresponding to the fragment caging (slow fragments) and direct exit (fast fragments) were observed in the spectra from HI photodissociation on Ar(n) clusters. On the other hand, the fast fragments were entirely missing in the spectrum from HI·(H(2)O)(n) and the slow-fragment part of the spectrum had a different shape from HI·Ar(n). The HI·(H(2)O)(n) spectrum was interpreted in terms of the acidic dissociation of HI on (H(2)O)(n) in the ground state, and hydronium radical H(3)O formation following the UV excitation of the ionically dissociated species into states of a charge-transfer-to-solvent character. The H(3)O generation was proved by experiments with deuterated species DI and D(2)O. The experiment was complemented by ab initio calculations of structures and absorption spectra for small HI·(H(2)O)(n) clusters, n = 0-5, supporting the proposed model.     

Arrhenius analysis of anisotropic surface self-diffusion on the prismatic facet of ice

We present an Arrhenius analysis of self-diffusion on the prismatic surface of ice calculated from molecular dynamics simulations. The six-site water model of Nada and van der Eerden was used in combination with a structure-based criterion for determining the number of liquid-like molecules in the quasi-liquid layer. Simulated temperatures range from 230 K-287 K, the latter being just below the melting temperature of the model, 289 K. Calculated surface diffusion coefficients agree with available experimental data to within quoted precision. Our results indicate a positive Arrhenius curvature, implying a change in the mechanism of self-diffusion from low to high temperature, with a concomitant increase in energy of activation from 29.1 kJ mol(-1) at low temperature to 53.8 kJ mol(-1) close to the melting point. In addition, we find that the surface self-diffusion is anisotropic at lower temperatures, transitioning to isotropic in the temperature range of 240-250 K. We also present a framework for self-diffusion in the quasi-liquid layer on ice that aims to explain these observations.     

4'-Alkoxy oligodeoxynucleotides: a novel class of RNA mimics

4'-Alkoxy-oligothymidylates were prepared as model compounds to study the influence of a C4'-alkoxy group on hybridisation. The phosphodiester homooligomers (15 units long) containing either a 4'-methoxy or 4'-(2-methoxyethoxy) group were found to display increased hybridisation with both dA(15) and rA(15) complementary counterparts compared to the natural oligothymidylate. In addition, we found their hybridisation behaviour to be similar to that of the regioisomeric 2'-O-methyl-oligothymidylate. The formed complexes (duplexes and triplexes) were studied using UV spectroscopy and polyacrylamide gel electrophoresis (PAGE). Structural background of the hybridization behaviour was examined using NMR and MDS. The favourable hybridisation properties of the 4'-alkoxyoligothymidylates indicated that 4'-alkoxy modified nucleotides are promising compounds for the assembly of chimeric oligonucleotides with tunable properties.     

An explicitly correlated Mukherjee's state specific coupled cluster method: development and pilot applications

This paper reports development of the explicitly correlated variant of Mukherjee's state specific multireference coupled cluster method (MkCC-F12). The current implementation is restricted to conventional single and double excitations and to pseudo-double excitations related to the Slater Type Geminal (STG) correlation factor using the SP ansatz. The performance of the MkCCSD-F12 was tested on calculations of singlet methylene, dissociation curve of the fluorine molecule, and the BeH(2) insertion pathway. As expected, the results of the newly developed method reconfirm the significantly faster convergence with respect to the basis set limit compared to the traditional expansion in Slater determinants. Results prove that treating the correlation factor separately for each reference is appropriate.     

Modified Riemschneider Reaction of 3‐Thiocyanatoquinolinediones

The Riemschneider reaction of 3‐thiocyanatoquinoline‐2,4(1H,3H)‐diones with conc. H₂SO₄ was investigated. Using different reaction conditions, 13 types of reaction products were isolated. Compounds bearing a Me, Et, or Bu group at C(3) afforded mainly [1,3]thiazolo[5,4‐c]quinoline‐2,4‐diones and 1,9b‐dihydro‐9b‐hydroxythiazolo[5,4‐c]quinoline‐2,4‐diones. In the case of the 3‐Bu derivatives of the starting compounds, C‐debutylation was also observed. If a Bn group is present at C(3), rapid C‐debenzylation of the starting thiocyanates occurred, yielding [1,3]oxathiolo[4,5‐c]quinoline‐2,4‐diones, and mixtures of mono‐, di‐, and trisulfides derived from 4‐hydroxy‐3‐sulfanylquinoline‐2‐ones. The reaction mechanism of all of the transformations is discussed. All new compounds were characterized by IR, ¹H‐ and ¹³C‐NMR, and EI and ESI mass spectra, and in some cases, ¹⁵N‐NMR spectra were also used to characterize new compounds.