High Blocking Temperature of Magnetization and Giant Coercivity in the Azafullerene Tb2@C79N with a Single‐Electron Terbium–Terbium Bond

The azafullerene Tb₂@C₇₉N is found to be a single‐molecule magnet with a high 100‐s blocking temperature of magnetization of 24 K and large coercivity. Tb magnetic moments with an easy‐axis single‐ion magnetic anisotropy are strongly coupled by the unpaired spin of the single‐electron Tb?Tb bond. Relaxation of magnetization in Tb₂@C₇₉N below 15 K proceeds via quantum tunneling of magnetization with the characteristic time τ_QTM=16 462±1230 s. At higher temperature, relaxation follows the Orbach mechanism with a barrier of 757±4 K, corresponding to the excited states, in which one of the Tb spins is flipped.     

Tailoring thermal development of gamma alumina sorbents material using combustion synthesis: the effect of amino acids (G,A, N) and equivalence ratio

Using a combustion synthesis, the range of achievable textures is broader than using conventional synthesis methods and can be controlled more successfully. As a tool allowing the achievement and control of desired textures, here we bring about wet chemistry synthesis using aluminium nitrate nonahydrate (ANN) precursor systematically combined with different fuels (amino acids). The amino acids; glycine (G), alanine (A) and asparagine (N) have been specifically selected in order to show the role of gradual increase in their: (1) molar mass, (2) enthalpy of combustion, (3) amine groups content and (4) ratio to ANN. Detailed (micro) structural and thermal characterisations confirm that the nanocrystalline character and thermomechanical stability were not diminished in the course of this synthesis. The conditions leading to development of different morphologies from gels to powders were found to be heavily under the influence of fuel/oxygen ratio, i.e. of the smouldering versus flaming mechanism of the combustion. Higher content of nitrates (predominately from amino-rich amino acids) strongly promoted auto-combustion behaviour. As-derived alumina precursors have been thermally treated at various temperatures (quenched and soaked), to monitor γ- and α-alumina crystallisation, with respect to the development of morphology. Different texture types have been observed, such as porous wormhole, porous and porous expanded flakes. Higher fuel levels promote specific surface increase. This combustion synthesis allows facile tailoring of nanocrystalline γ-alumina with different morphological features, whereas samples having optimal parameters were suitable for catalyst support application on behalf of rapid sorption performance.

     

Editable machine learning models? A rule-based framework for user studies of explainability

Advances in Data Analysis and Classification - So far, most user studies dealing with comprehensibility of machine learning models have used questionnaires or surveys to acquire input from...     

Phase Transition in Vertex-Reinforced Random Walks on {\mathbb{Z}} with Non-linear Reinforcement

Vertex-reinforced random walk is a random process which visits a site with probability proportional to the weight w _k of the number k of previous visits. We show that if w _k ∼ k ^α, then there is a large time T ₀ such that after T ₀ the walk visits 2, 5, or ∞ sites when α < 1, = 1, or > 1, respectively. More general results are also proven.      

Tomographic probability representation for quantum fermion fields

Tomographic probability representation is introduced for fermion fields. The states of the fermions are mapped onto the probability distribution of discrete random variables (spin projections). The operators acting on the fermion states are described by fermionic tomographic symbols. The product of the operators acting on the fermion states is mapped onto the star-product of the fermionic symbols. The kernel of the star-product is obtained. The antisymmetry of the fermion states is formulated as a specific symmetry property of the tomographic joint probability distribution associated with the states.     

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space with the resolvent norm that is constant in a neighbourhood of zero.      

Test of the Duh-Haymet-Henderson theory for mixtures: cavity correlation functions and excess volumes

The accuracy of the Duh-Haymet-Henderson (DHH) integral equation theory for predicting the cavity correlation functions of mixtures has been tested by comparison with molecular simulations. We have compared the cavity correlation functions, internal energies, and pressures computed for Lennard-Jones model mixtures of Ar/Kr, Ar/Ne, and Ar/Xe with these same quantities computed from the DHH theory and also, for reference, the Percus-Yevick (PY) integral equation theory. We found that DHH gave much better accuracy than PY at high densities. At low densities DHH and PY give essentially identical predictions. We have computed excess volumes for Ar/Kr mixtures at two pressures (10 and 20?MPa) at 132.32?K, for which experimentally derived data are available. The DHH theory predicts the correct trends and is quantitatively more accurate than the PY theory for predicting the excess volumes. We have tested the local optimality of the DHH theory for pure fluids by adding two adjustable parameters to the DHH bridge function expression to see if it is possible to improve the DHH predictions of the cavity correlation function empirically, holding the form of the bridge function constant. We found that no single set of adjustable parameter values could improve the accuracy of DHH over multiple different isotherms. Furthermore, perturbing DHH leads to a decrease in accuracy of the predictions of both the pressure and energy, although small improvements in the cavity correlation functions were achieved. Thus, the DHH theory is locally optimal, given the form of the bridge function.     

A new trust region technique for the maximum weight clique problem

A new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of other stationary points of the program. We formulate and prove a condition when a Motzkin-Straus optimum coincides with such a point. The developed method has complexity O(n³), where n is the number of vertices of the graph. It was implemented in a publicly available software package QUALEX-MS.Computational experiments indicate that the algorithm is exact on small graphs and very efficient on the DIMACS benchmark graphs and various random maximum weight clique problem instances.     

The first entry to pyrrolo[2,3-c]quinoline-2,4(3aH,5H)-diones

Wittig olefination of 3-aminoquinoline-2,4(1H,3H)-diones 1 with ethyl (triphenylphosphoranylidene)acetate (Ph₃PCHCO₂Et) afforded (E)-3-amino-4-ethoxycarbonylmethylene-1,2,3,4-tetrahydro-2-quinolones (E)-2 and pyrrolo[2,3-c]quinoline-2,4(3aH,5H)-diones 3. An alternative approach for the synthesis of 3 via 3-bromoacetamidoquinoline-2,4(1H,3H)-diones 7, their corresponding triphenylphosphonium salts 8, and ylides A that undergo intramolecular Wittig reaction, was investigated. Under the applied reaction conditions, the phosphonium salts 8 and ylides A are so unstable that they partly decompose to 3-acetamidoquinoline-2,4(1H,3H)-diones 9 during the synthesis of 3.     

Effect of interactions on molecular fluxes and fluctuations in the transport across membrane channels

Transport of molecules across membrane channels is investigated theoretically using exactly solvable one-dimensional discrete-state stochastic models. An interaction between molecules and membrane pores is modeled via a set of binding sites with different energies. It is shown that the interaction potential strongly influences the particle currents as well as fluctuations in the number of translocated molecules. For small concentration gradients, the attractive sites lead to largest currents and fluctuations, while the repulsive interactions yield the largest fluxes and dispersions for large concentration gradients. Interaction energies that lead to maximal currents and maximal fluctuations are the same only for locally symmetric potentials, where transition states are equally distant from the neighboring binding sites, while they differ for the locally asymmetric potentials. The conditions for the most optimal translocation transport with maximal current and minimal dispersion are discussed. It is argued that, in this case, the interaction strength is independent of local symmetry of the potential of mean forces. In addition, the effect of the global asymmetry of the interaction potential is investigated, and it is shown that it also strongly affects the particle translocation dynamics. These phenomena can be explained by analyzing the details of the particle entering and leaving the binding sites in the channel.