Asymptotic exactness of an a posteriori error estimator based on the equilibrated residual method

In this paper we analyze an a posteriori error estimator based on the equilibrated residual method. We prove that this estimator is asymptotically exact in the energy norm for regular solutions and meshes. Numerical examples are included to illustrate the theoretical results.     

Quaternionic monopoles

We present the simplest non-abelian version of Seiberg-Witten theory: Quaternionic monopoles. These monopoles are associated withSpin ^h (4)-structures on 4-manifolds and form finite-dimensional moduli spaces. On a Kähler surface the quaternionic monopole equations decouple and lead to the projective vortex equation for holomorphic pairs. This vortex equation comes from a moment map and gives rise to a new complex-geometric stability concept. The moduli spaces of quaternionic monopoles on Kähler surfaces have two closed subspaces, both naturally isomorphic with moduli spaces of canonically stable holomorphic pairs. These components intersect along a Donaldson instanton space and can be compactified with Seiberg-Witten moduli spaces. This should provide a link between the two corresponding theories.Partially supported by: AGE-Algebraic Geometry in Europe, contract No ERBCHRXCT940557 (BBW 93.0187), and by SNF, nr. 21-36111.92     

Optically active Babinet planar metamaterial film for terahertz polarization manipulation

A planar Babinet‐inverted dimer metamaterial possessing strong optical activity is proposed and characterized. An original fabrication method to produce large area (up to several cm²) freely suspended flexible metallic membranes is implemented to fabricate the metamaterial. Its optical properties are characterized by terahertz time‐domain spectroscopy, revealing anisotropic transmission with high optical activity. A simple coupled resonator model is applied to explain the principal optical features of the dimers, with predictive power of positions and number of resonances through a parametrical model. The model is validated for correct polarization‐dependent quantitative results on the optical activity in transmission spectra. The fabrication method presented in this work as well as the slit dimer design has great potential for exploitation in terahertz optics.     

Non-Birational Twisted Derived Equivalences in Abelian GLSMs

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kähler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kähler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov’s ‘homological projective duality.’ Along the way, we shall see how ‘noncommutative spaces’ (in Kontsevich’s sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.     

Analog of Formula of Total Probability for Quantum Observables Represented by Positive Operator Valued Measures

We represent Born’s rule as an analog of the formula of total probability (FTP): the classical formula is perturbed by an additive interference term. In this note we consider practically the most general case: generalized quantum observables given by positive operator valued measures and measurement feedback on states described by atomic instruments. This representation of Born’s rule clarifies the probabilistic structure of quantum mechanics (QM). The probabilistic counterpart of QM can be treated as the probability update machinery based on the special generalization of classical FTP. This is the essence of the Växjö interpretation of QM: statistical realist contextual and local interpretation. We analyze the origin of the additional interference term in quantum FTP by considering the contextual structure of the two slit experiment which was emphasized by R. Feynman.     

3,5‐Di­fluoro‐4‐nitro­pyridine N‐oxide and 3,5‐di­amino‐4‐nitro­pyridine N‐oxide monohydrate

The mol­ecule of 3,5‐di­fluoro‐4‐nitro­pyridine N‐oxide, C₅H₂F₂N₂O₃, is twisted around the C—NO₂ bond by 38.5 (1)°, while the 3,5‐di­amino analogue, 3,5‐di­amino‐4‐nitro­pyridine N‐oxide monohydrate, C₅H₆N₄O₃·H₂O, adopts a planar conformation stabilized by intramolecular hydrogen bonds, with a significant redistribution of π electrons.     

Defining the nucleotide binding sites of P2Y receptors using rhodopsin-based homology modeling

Ongoing efforts to model P2Y receptors for extracellular nucleotides, i.e., endogenous ADP, ATP, UDP, UTP, and UDP-glucose, were summarized and correlated for the eight known subtypes. The rhodopsin-based homology modeling of the P2Y receptors is supported by a growing body of site-directed mutagenesis data, mainly for P2Y₁ receptors. By comparing molecular models of the P2Y receptors, it was concluded that nucleotide binding could occur in the upper part of the helical bundle, with the ribose moiety accommodated between transmembrane domain (TM) 3 and TM7. The nucleobase was oriented towards TM1, TM2, and TM7, in the direction of the extracellular side of the receptor. The phosphate chain was oriented towards TM6, in the direction of the extracellular loops (ELs), and was coordinated by three critical cationic residues. In particular, in the P2Y₁, P2Y₂, P2Y₄, and P2Y₆ receptors the nucleotide ligands had very similar positions. ADP in the P2Y₁₂ receptor was located deeper inside the receptor in comparison to other subtypes, and the uridine moiety of UDP-glucose in the P2Y₁₄ receptor was located even deeper and shifted toward TM7. In general, these findings are in agreement with the proposed binding site of small molecules to other class A GPCRs.     

Signatures of beta-sheet secondary structures in linear and two-dimensional infrared spectroscopy

Using idealized models for parallel and antiparallel beta sheets, we calculate the linear and two-dimensional infrared spectra of the amide I vibration as a function of size and secondary structure. The model assumes transition-dipole coupling between the amide I oscillators in the sheet and accounts for the anharmonic nature of these oscillators. Using analytical and numerical methods, we show that the nature of the one-quantum vibrational eigenstates, which govern the linear spectrum, is, to a large extent, determined by the symmetry of the system and the relative magnitude of interstrand interactions. We also find that the eigenstates, in particular their trends with system size, depend sensitively on the secondary structure of the sheet. While in practice these differences may be difficult to distinguish in congested linear spectra, we demonstrate that they give rise to promising markers for secondary structure in the two-dimensional spectra. In particular, distinct differences occur between the spectra of parallel and antiparallel beta sheets and between beta hairpins and extended beta sheets.     

Kinetics and Mechanism of Cr(VI) Reduction in a Water Cathode Induced by Atmospheric Pressure DC Discharge in Air

The process of reduction of Cr⁶⁺ ions (solution of potassium dichromate, K₂Cr₂O₇) in a water cathode was studied during a DC discharge in air. The concentration range of Cr⁶⁺ was (5.7–19) ×10^?5 mol/l and discharge current range was 20–80 mA. Cr⁶⁺ ions were shown to be reversibly reduced under a discharge action. The equilibrium degree of reduction increased with increasing initial concentration of the solution at fixed discharge current. At fixed initial concentration the reduction degree increased with increasing discharge current. The reduction degrees so obtained were 0.34–0.84. A kinetic scheme of the processes taking place in a solution was proposed. The calculated data obtained as a result of application of this scheme described well the experimental results on Cr⁶⁺ kinetics. The main processes of Cr⁶⁺ reduction and Cr³⁺ oxidation were revealed. HO ₂ ^· radicals and hydrogen peroxide were shown to be responsible for Cr⁶⁺ reduction whereas ^·OH radicals and O₂ molecules provide the reverse process of Cr³⁺ oxidation to Cr⁶⁺. The mechanism of action of phenol additives improving the process efficiency is discussed. The efficiency of phenol action as a radical scavenger was shown to be determined with its mass-transfer to the reaction area rather than chemical reaction rate.