Optically Anomalous Crystals

The optical symmetry of many crystals is lower than would be expected from their external form and X-ray diffraction data. Recently such optical anomalies have been attributed to nonequilibrium structures resulting from kinetically controlled crystal growth. Impurities are incorporated to different extents at various surface sites that would otherwise have become symmetry-related within the bulk crystal. After their discovery by Brewster in 1815, optically anomalous crystals were the subject of lively debate throughout the 19th century among some of the most distinguished contributors to the development of crystallography including Biot, Berzelius, Herschel, Mitscherlich, Frankenheim, Pasteur, Mallard, Klein, Groth, Wyrouboff, Barlow, Brauns, Rinne, Pockels, and Friedel. From a sea of wild speculation two conflicting postulates emerged: that the symmetric form resulted from accidental twinning of segments with lower symmetry, or that the optical peculiarities resulted from stress due to impurities or external perturbations. Neither postulate expresses the present view. Interest in this research waned at the turn of the century, and after 1917 no one pursued Tammann's alternative correct insight. The problem of anomalous double refraction attracted no attention for more than half a century until its recent solution. This review discusses both mineral and organic systems with particular emphasis on the phyllosilicate apophyllite and on 1,5-dichloro-2,3-dinitrobenzene. These nonequilibrium structures relate to questions of crystal order, crystal growth, molecular recognition, and the design of new materials. The review provides a reminder of the enduring value of the polarizing microscope as a research tool in chemistry.     

Synthesis of 2D Germanane (GeH): a New,Fast, and Facile Approach

Germanane (GeH), a germanium analogue of graphane, has recently attracted considerable interest because its remarkable combination of properties makes it an extremely suitable candidate to be used as 2D material for field effect devices, photovoltaics, and photocatalysis. Up to now, the synthesis of GeH has been conducted by substituting Ca by H in a β‐CaGe₂ layered Zintl phase through topochemical deintercalation in aqueous HCl. This reaction is generally slow and takes place over 6 to 14 days. The new and facile protocol presented here allows to synthesize GeH at room temperature in a significantly shorter time (a few minutes), which renders this method highly attractive for technological applications. The GeH produced with this method is highly pure and has a band gap (E_g) close to 1.4 eV, a lower value than that reported for germanane synthesized using HCl, which is promising for incorporation of GeH in solar cells.     

On Weaknesses of Non–surjective Round Functions

We propose a new attack on Feistel ciphers with a non-surjective round function such as the CAST cipher family and LOKI91. We extend the attack towards block ciphers that use a non-uniformly distributed round function and apply the extended attack to the CAST family. This attack demonstrates that the round function of a Feistel cipher with six to eight rounds needs to be surjective and sufficiently uniform.     

Logarithmic residues, generalized idempotents, and sums of idempotents in Banach algebras

In a commutative Banach algebraB the set of logarithmic residues (i.e., the elements that can be written as a contour integral of the logarithmic derivative of an analyticB-valued function), the set of generalized idempotents (i.e., the elements that are annihilated by a polynomial with non-negative integer simple zeros), and the set of sums of idempotents are all the same. Also, these (coinciding) sets consist of isolated points only and are closed under the operations of addition and multiplication. Counterexamples show that the commutativity condition onB is essential. The results extend to logarithmic residues of meromorphicB-valued functions.     

Isospectral surfaces with distinct covering spectra via Cayley graphs

The covering spectrum is a geometric invariant of a Riemannian manifold, more generally of a metric space, that measures the size of its one-dimensional holes by isolating a portion of the length spectrum. In a previous paper we demonstrated that the covering spectrum is not a spectral invariant of a manifold in dimensions three and higher. In this article we give an example of two isospectral Cayley graphs that admit length space structures with distinct covering spectra. From this we deduce the existence of infinitely many pairs of Sunada-isospectral surfaces with unequal covering spectra.     

How To Play Two-Player Restricted Quantum Games with 10 Cards

We show that it is possible to play ‘restricted’ two-player quantum games proposed originally by Marinatto and Weber (Phys. Lett. A 272:291–303, 2000) by purely macroscopic means, in the simplest case having as the only equipment a pack of 10 cards. Our example shows also that some apparently ‘genuine quantum’ results, even those that emerge as a consequence of dealing with entangled states, can be obtained by suitable application of Kolmogorovian probability calculus and secondary-school mathematics, without application of the ‘Hilbert space machinery’.     

Experimental realization of linear-optical partial swap gates

We present a linear-optical implementation of a class of two-qubit partial SWAP gates for polarization states of photons. Different gate operations, including the SWAP and entangling sqrt[SWAP], can be obtained by changing a classical control parameter, namely, the path difference in the interferometer. Reconstruction of output states, full quantum process tomography, and an evaluation of entanglement of formation prove very good performance of the gates.     

Ultrasonics in heterogeneous metal catalysis: sonochemical chemo- and enantioselective hydrogenations over supported platinum catalysts

Sonochemical chemo- and enantioselective hydrogenations over supported platinum catalysts are described. We disclose our results with respect to a sonochemical modification of the chemoselective hydrogenation of cinnamaldehyde over supported platinum catalysts, and the asymmetric hydrogenation of ethyl pyruvate promoted by various ultrasonic pretreatments. The ultrasonic pretreatment of the supported platinum catalysts was found to be highly beneficial in almost every case, improving both the catalytic activity and selectivity. The effect of additional experimental variables, such as hydrogen pressure, catalyst support, temperature and the ultrasonic insonation time were also studied. The enantioselectivity of the hydrogenation of ethyl pyruvate increased up to 97.1% ee. In the case of cinnamaldehyde hydrogenation, the selective preparation of cinnamyl alcohol became possible. The theoretical aspects of the working mechanisms in comparison with 'silent' reactions will also be provided.