On V-semirings and Semirings All of Whose Cyclic Semimodules Are Injective

In this article, we introduce and study V- and CI-semirings—semirings all of whose simple and cyclic, respectively, semimodules are injective. We describe V-semirings for some classes of semirings and establish some fundamental properties of V-semirings. We show that all Jacobson-semisimple V-semirings are V-rings. We also completely describe the bounded distributive lattices, Gelfand, subtractive, semisimple, and antibounded, semirings that are CI-semirings. Applying these results, we give complete characterizations of congruence-simple subtractive and congruence-simple antibounded CI-semirings which solve two earlier open problems for these classes of CI-semirings.     

Exceptional collections of line bundles on projective homogeneous varieties

We construct new examples of exceptional collections of line bundles on the variety of Borel subgroups of a split semisimple linear algebraic group G$G$ of rank 2 over a field. We exhibit exceptional collections of the expected length for types _A2$A_2$ and _B2=_C2$B_2=C_2$ and prove that no such collection exists for type _G2$G_2$. This settles the question of the existence of full exceptional collections of line bundles on projective homogeneous G$G$-varieties for split linear algebraic groups G$G$ of rank at most 2.     

A Titanium(IV)‐Based Metal–Organic Framework Featuring Defect‐Rich Ti‐O Sheets as an Oxidative Desulfurization Catalyst

While titanium‐based metal–organic frameworks (MOFs) have been widely studied for their (photo)catalytic potential, only a few Ti^IV MOFs have been reported owing to the high reactivity of the employed titanium precursors. The synthesis of COK‐47 is now presented, the first Ti carboxylate MOF based on sheets of Ti^IVO₆ octahedra, which can be synthesized with a range of different linkers. COK‐47 can be synthesized as an inherently defective nanoparticulate material, rendering it a highly efficient catalyst for the oxidation of thiophenes. Its structure was determined by continuous rotation electron diffraction and studied in depth by X‐ray total scattering, EXAFS, and solid‐state NMR. Furthermore, its photoactivity was investigated by electron paramagnetic resonance and demonstrated by catalytic photodegradation of rhodamine 6G.     

Thermal and electrical properties of Ca5Mg4−xZnx(VO4)6 (0 ≤ x ≤ 4)

Calcium vanadates Ca₅Mg_4−xZn_x(VO₄)₆ (0 ≤ x ≤ 4) have been studied for the first time using a set of high-temperature methods of analysis. The onset of melting process determined from differential scanning calorimetry decreases from 1158 to 881 °C (± 1.5 °C) with increasing of x (dopant’s content). CTE temperature dependence is found to show a hysteresis. Electrical transport properties measured by impedance spectroscopy in air of different humidity are also discussed. The value of electrical conductivity does not depend on air humidity. It is found to equal to 1.5 × 10⁻⁶ S cm⁻¹ at 720 °C for Ca₅Mg₄(VO₄)₆ which is specific for garnet-related crystals.

     

Interferometry of non-Abelian anyons

We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach-Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they are distinguishable via monodromy with the probe anyons, which also determines the rate of collapse. We give estimates on the number of probes needed to obtain a desired confidence level for the measurement outcome distinguishing between charges, and explicitly work out a number of examples for some significant anyon models. We apply the same techniques to describe interferometry measurements in a double point-contact interferometer realized in fractional quantum Hall systems. To lowest order in tunneling, these results essentially match those from the Mach-Zehnder interferometer, but we also provide the corrections due to processes involving multiple tunnelings. Finally, we give explicit predictions describing state measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore-Read state at ν=5/2 and Read-Rezayi state at ν=12/5.     

The anomalous spectral dependence of polarization in comets

We have found an anomalous (negative) spectral dependence of polarization for split comet 73P/Schwassmann–Wachmann 3, i.e. polarization degree in the I filter is systematically less (4%) than that in the R filter for both B and C subnuclei of the comet. Earlier we revealed a similar effect for comets 21P/Giacobini–Zinner, C/1999 S4 (LINEAR), and 9P/Tempel 1. Together with comet C/1989 X1 (Austin), for which the similar spectral dependence of polarization was also observed, these comets form a group characterized by some peculiar properties of their dust. Since atypical organic composition is a characteristic feature for all these comets, the anomalous spectral dependence of polarization may indicate specifics of origin of these comets. Really, most of these comets (but not all) originated from the Kuiper Belt. Also, most (but not all) of these comets belong to the group of comets depleted in carbon species in the gas phase, which is typical for comets formed in the giant-planet area of the solar system. On the other hand, all of the comets with negative spectral gradient of polarization have the dust dominated by large particles and most of them belong to the Jupiter family. This may indicate that anomalous spectral dependence of their polarization is a result of their evolution. To identify the reason of anomalous polarization, systematic spectropolarimetric observations of Jupiter-family comets are necessary.     

Deformations of the constraint algebra of Ashtekar's Hamiltonian formulation of general relativity

We show that the constraint algebra of Ashtekar's Hamiltonian formulation of general relativity can be nontrivially deformed by allowing the cosmological constant to become an arbitrary function of the (Weyl) curvature. Our result implies that there is not one but infinitely many (parametrized by an arbitrary function) four-dimensional generally covariant local gravity theories propagating 2 degrees of freedom.     

Universal properties of bulk viscosity near the QCD phase transition

We extract the bulk viscosity of hot quark–gluon matter in the presence of light quarks from the recent lattice data on the QCD equation of state. For that purpose we extend the sum rule analysis by including the contribution of light quarks. We also discuss the universal properties of bulk viscosity in the vicinity of a second-order phase transition, as it might occur in the chiral limit of QCD at fixed strange quark mass and most likely does occur in two-flavor QCD. We point out that a chiral transition in the O(4)$O(4)$ universality class at zero baryon density as well as the transition at the chiral critical point which belongs to the Z(2)$Z(2)$ universality class both lead to the critical behavior of bulk viscosity. In particular, the latter universality class implies the divergence of the bulk viscosity, which may be used as a signature of the critical point. We discuss the physical picture behind the dramatic increase of bulk viscosity seen in our analysis, and devise possible experimental tests of related phenomena.