Preparation and Crystal Structure of a New Uranyl Sulfate Templated by a Bis-isothiouronium Cation

Crystals of a new uranyl sulfate (C₂N₄H₈S₂)[UO₂(SO₄)₂] · 0.3H₂O ( 1 ) templated by a relatively rare bis-isothiouronium cation, were formed upon evaporation of aqueous solutions containing uranyl acetate, thiourea, and excess sulfuric acid. The new compound is orthorhombic, P2₁2₁2₁, a = 6.928(2) Å, b = 13.398(3) Å, c = 15.225(3) Å, Z = 2. Its crystal structure is comprised of [UO₂(SO₄)₂] moieties linked by hydrogen bonds formed between the template cations and terminal oxygen atoms of the sulfate tetrahedra. The C₂N₄H₈S₂²⁺ template is most likely formed in situ during a redox reaction between uranyl cation and thiourea in a strongly acidic medium, with UO₂²⁺ partially reduced to U⁴⁺.     

Engineering Platinum–Oxygen Dual Catalytic Sites via Charge Transfer towards Highly Efficient Hydrogen Evolution

A dual‐site catalyst allows for a synergetic reaction in the close proximity to enhance catalysis. It is highly desirable to create dual‐site interfaces in single‐atom system to maximize the effect. Herein, we report a cation‐deficient electrostatic anchorage route to fabricate an atomically dispersed platinum–titania catalyst (Pt₁^O1/Ti_1?xO₂), which shows greatly enhanced hydrogen evolution activity, surpassing that of the commercial Pt/C catalyst in mass by a factor of 53.2. Operando techniques and density functional calculations reveal that Pt₁^O1/Ti_1?xO₂ experiences a Pt?O dual‐site catalytic pathway, where the inherent charge transfer within the dual sites encourages the jointly coupling protons and plays the key role during the Volmer–Tafel process. There is almost no decay in the activity of Pt₁^O1/Ti_1?xO₂ over 300 000 cycles, meaning 30 times of enhancement in stability compared to the commercial Pt/C catalysts (10 000 cycles).     

Higher spin $${{\mathfrak {s}}}{{\mathfrak {l}}}_2$$ s l 2 R-matrix from equivariant (co)homology

Letters in Mathematical Physics - We compute the rational $${{\mathfrak {s}}}{{\mathfrak {l}}}_2$$ R-matrix acting in the product of two spin- $$\ell \over 2$$ ( $${\ell \in {\mathbb {N}}}$$ )...     

From Quantum Probabilities to Quantum Amplitudes

The task of reconstructing the system’s state from the measurements results, known as the Pauli problem, usually requires repetition of two successive steps. Preparation in an initial state to be determined is followed by an accurate measurement of one of the several chosen operators in order to provide the necessary “Pauli data”. We consider a similar yet more general problem of recovering Feynman’s transition (path) amplitudes from the results of at least three consecutive measurements. The three-step histories of a pre- and post-selected quantum system are subjected to a type of interference not available to their two-step counterparts. We show that this interference can be exploited, and if the intermediate measurement is “fuzzy”, the path amplitudes can be successfully recovered. The simplest case of a two-level system is analysed in detail. The “weak measurement” limit and the usefulness of the path amplitudes are also discussed.     

Metastable ion study of substituted cyclopentadienylmanganese cations in the gas phase

The behavior of some substituted cyclopentadienylmanganese ions has been studied by tandem mass spectrometry. This metastable ion study showed that only C₅H₅Mn⁺ and (C₅H₄CN)Mn⁺ ions retain their nido-cluster structure (1), which is characterized by a simple metal-ligand bond cleavage. Other substituted ions, RXC₅H₄Mn⁺, rearrange to a different extent, depending on the nature of the substituent. The first rearrangement step is R radical migration to the central metal atom, leading to RMnC₅H₄X⁺-type ions (2). These ions decompose by elimination of X (for X=CO) or with formation of RMnX⁺, but further rearrangements can also occur. These are the reverse migration of R from the metal atom to the π-ligand (for R=H, Ph) and cyclopentadienyl ring expansion (for X=CH₂). Collisional activation mass spectra contained an Mn⁺ ion peak, which can indicate the existence of stable type 1 structures for most cyclopentadienylmanganese ions. Carboxyl and hydroxymethyl derivatives exist, presumably as ions of type 2. The neutralization-reionization mass spectra of RXC₅H₄Mn⁺ ions are also discussed.     

Density functional and spectroscopic studies of nitrogen inversion in substituted dizocilpines

While developing a synthesis towards tagged dizocilpine (MK‐801) analogues, we observed highly restricted inversion of a nitrogen centre in a number hydroxylamines obtained as key intermediates. These compounds are shown to possess some of the structural elements which are expected to significantly hinder the nitrogen inversion, potentially leading to hydroxylamines with a chiral nitrogen centre. Free energy barriers (ΔG^≠) of the nitrogen inversion were estimated to be ca. 22 kcal mol^?1 at temperatures near 420 K using variable temperature NMR measurements in DMSO‐d₆. Further density functional studies of a number model systems were undertaken in order to better rationalize the measured inversion barriers and follow the role of various structural factors in raising the barrier height of the nitrogen inversion process. Copyright © 2008 John Wiley & Sons, Ltd.     

Area Spaces: First Steps

We show that a Riemannian manifold of dimension at least 3 can be recovered from the space of boundaries of rectifiable integral 2-currents (the “lcycles”) equipped with the filling area distance, and discuss possible approaches to “spaces with area structures”.     

Optimal control for reinitialization in finite element level set methods

A new optimal control problem that incorporates the residual of the Eikonal equation into its objective is presented. The formulation of the state equation is based on the level set transport equation but extended by an additional source term, correcting the solution so as to minimize the objective functional. The method enforces the constraint so that the interface cannot be displaced at least in the continuous setting. The system of first‐order optimality conditions is derived, linearized, and solved numerically. The control also prevents numerical instabilities, so that no additional stabilization techniques are required. This approach offers the flexibility to include other desired design criteria into the objective functional. The methodology is evaluated numerically in three different examples and compared with other PDE‐based reinitialization techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

Pseudoinstantons in Metric-Affine Field Theory

In abstract Yang–Mills theory the standard instanton construction relies on the Hodge star having real eigenvalues which makes it inapplicable in the Lorentzian case. We show that for the affine connection an instanton-type construction can be carried out in the Lorentzian setting. The Lorentzian analogue of an instanton is a spacetime whose connection is metric compatible and Riemann curvature irreducible (pseudoinstanton). We suggest a metric-affine action which is a natural generalization of the Yang–Mills action and for which pseudoinstantons are stationary points. We show that a spacetime with a Ricci flat Levi-Civita connection is a pseudoinstanton, so the vacuum Einstein equation is a special case of our theory. We also find another pseudoinstanton which is a wave of torsion in Minkowski space. Analysis of the latter solution indicates the possibility of using it as a model for the neutrino.     

Nonlocal anomaly of the axial-vector current for bound states

We argue that the amplitude does not vanish in the limit of zero quark masses. This represents a new kind of violation of the classical equation of motion for the axial current and should be interpreted as the axial anomaly for bound states. The anomaly emerges in spite of the fact that the one loop integrals are ultraviolet finite as guaranteed by the finite size of bound-state wave functions. As a result, the amplitude behaves like approximately 1/p(2) in the limit of a large momentum p of the current. The observed effect requires the modification of the classical equation of motion of the axial-vector current by nonlocal operators.