Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories

We show an accurate procedure to obtain a Fourier transform (FT) with no dc term using a commercial twisted-nematic liquid-crystal display. We focus on the application to holographic storage of binary data pages, where a drastic decrease of the dc term in the FT is highly desirable. Two different codification schemes are considered: binary pi radians phase modulation and hybrid ternary modulation. Any deviation in the values of the amplitude and phase shift generates the appearance of a strong dc term. Experimental results confirm that the calculated configurations provide a FT with no dc term, thus showing the effectiveness of the proposal.     

The Ghirlanda-Guerra Identities

If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.     

Micro-Raman investigations of the formaldehyde-ice system

Rapidly frozen aqueous solutions containing variable amounts of dissolved formaldehyde (0.1, 5, 7, 10, 15, and 20 mol %) have been analyzed by micro-Raman spectroscopy at ambient pressure and low temperature. The importance of the formladehyde-ice system has been repeatedly quoted in various contexts, such as atmospheric and snowpack chemistry and interstellar and cometary ices. Understanding and characterizing the effects of freezing and the interactions of formaldehyde with ice are therefore of relevant interest. In this study, the distinct vibrational signatures of the oligomers present in the solution and in the frozen ice mixtures have been identified in the 120-4000 cm(-1) spectral range. From the subtle changes of the bands assigned to the CO and CH group frequencies, at least two distinct crystalline phases (pI and pII) are found to coexist with ice at different temperatures. Depending on the cooling-rewarming protocol, pI is found to crystallize in the 163-213 K temperature range. Above approximately 213 K, pI gets transformed irreversibly into pII which is stable up to approximately 234 K. pII is found to interact more strongly with ice than pI, as revealed, for example, by the drop in frequency of the bands assigned to the O-H stretching as pI transforms into pII. It is suggested that pII consists of a hydrogen-bonded network of oligomers and water molecules. On the other hand, it is suggested that the oligomers mainly present in pI interact through weak forces with the surrounding water molecules.     

Characterization of the time dependence of polarization mode dispersion

We elaborate on a recently proposed model of the temporal dependence of polarization mode dispersion in long fiber links. We evaluate the probability that a channel of a wavelength-division multiplexed system never incurs an outage, and the range of frequency over which the parameters that characterize the temporal statistics of the differential group delay are correlated.     

Ruthenium‐Catalyzed Functionalization of Pyrroles and Indoles with Propargyl Alcohols

Several ruthenium‐catalyzed atom‐economic transformations of propargyl alcohols with pyrroles or indoles leading to alkylated, propargylated, or annulated heteroaromatics are reported. The mechanistically distinct reactions are catalyzed by a single ruthenium(0) complex containing a redox‐coupled dienone ligand. The mode of activation regarding the propargyl alcohols determines the reaction pathway and depends on the alcohols’ substitution pattern. Secondary substrates form alkenyl complexes by a 1,2‐hydrogen shift, whereas the transformation of tertiary substrates involves allenylidene intermediates. 1‐Vinyl propargyl alcohols are converted by a cascade allylation/cyclization sequence. The environmentally benign processes are of broad scope and allow the selective synthesis of highly functionalized pyrroles and indoles generating water as the only waste product.     

Optimizing control of simulated moving bed separations of mixtures subject to the generalized Langmuir isotherm

Simulated moving bed (SMB) is a cost-efficient separation technique that offers high productivity and low solvent consumption. SMB has gained importance in the pharmaceutical and fine chemical industry to perform complex separation tasks. However, an open and challenging problem is the optimal, robust operation of the SMB process. We have developed a control scheme that integrates the optimization and control of the SMB unit. A significant feature of the controller is that only minimal information of the system has to be provided, i.e. the linear adsorption behavior of the mixture to be separated and the average void fraction of the columns. Therefore, a full characterization of the adsorption behavior of the mixture and the columns is no longer required. In this ‘cycle to cycle’ control scheme, the measurements, optimization and control actions are performed once in every cycle. This paper presents simulation results of the control scheme applied to the separation of binary mixtures characterized by generalized Langmuir isotherms. The results are presented and analyzed in the frame of the triangle theory that has been recently extended to encompass these types of isotherms. Besides, online optimum performance of the SMB unit is compared with off-line optimization carried out using genetic algorithm. The results show that the controller fulfills the product and process specifications while operating the SMB unit optimally, regardless of the different types of Langmuir isotherms that the systems exhibit.     

Crystal and Molecular Structure of [2,6‐(Me2NCH2)2C6H3]2SnF2, an Intramolecularly Coordinated Diorganotin Difluoride

Single‐crystal X‐ray diffraction analysis of [2,6‐(Me₂NCH₂)₂C₆H₃]₂SnF₂ reveals that only one of the two dimethylaminomethyl groups of each pincer‐type ligands [2,6‐(CH₂NMe₂)₂C₆H₃]^? is coordinated to the tin atom at Sn‐N distances of 2.576(2) and 2.470(2) Å, inducing chirality of the latter. The tin atom exhibits a distorted octahedral trans(C,C)cis(N,N)cis(F,F) configuration. Extensive intra‐ and intermolecular C‐H···F hydrogen bonding is observed with the latter giving rise to formation of polymeric chains.     

Unprecedented stereoselective synthesis of catalytically active chiral Mo3CuS4 clusters

Cluster excision of polymeric {Mo3S7Cl4}n phases with chiral phosphane (+)-1,2-bis[(2R,5R)-2,5-(dimethylphospholan-1-yl)]ethane ((R,R)-Me-BPE) or with its enantiomer ((S,S)-Me-BPE) yields the stereoselective formation of the trinuclear cluster complexes [Mo3S4{(R,R)-Me-BPE}3Cl3]+ ([(P)-1]+) and [Mo3S4{(S,S)-Me-BPE}3Cl3]+ ([(M)-1]+), respectively. These complexes possess an incomplete cuboidal structure with the metal atoms defining an equilateral triangle and one capping and three bridging sulfur atoms. The P and M symbols refer to the rotation of the chlorine atoms around the C3 axis, with the capping sulphur atom pointing towards the viewer. Incorporation of copper into these trinuclear complexes affords heterodimetallic cubane-type compounds of formula [Mo3CuS4{(R,R)-Me-BPE}3Cl4]+ ([(P)-2]+) or [Mo3CuS4{(S,S)-Me-BPE}3Cl4]+ ([(M)-2]+), respectively, for which the chirality of the trinuclear precursor is preserved in the final product. Cationic complexes [(P)-1]+, [(M)-1]+, [(P)-2]+, and [(M)-2]+ combine the chirality of the metal cluster framework with that of the optically active diphosphane ligands. The known racemic [Mo3CuS4(dmpe)3Cl4]+ cluster (dmpe = 1,2-bis(dimethylphosphanyl)ethane) as well as the new enantiomerically pure Mo3CuS4 [(P)-2]+ and [(M)-2]+ complexes are efficient catalysts for the intramolecular cyclopropanation of 1-diazo-5-hexen-2-one (3) and for the intermolecular cyclopropanation of alkenes, such as styrene and 2-phenylpropene, with ethyl diazoacetate. In all cases, the cyclopropanation products were obtained in high yields. The diastereoselectivity in the intermolecular cyclopropanation of the alkenes and the enantioselectivity in the inter- or intramolecular processes are only moderate.     

Embedding Quantum Universes in Classical Ones

Do the partial order and ortholattice operations of a quantum logic correspond to the logical implication and connectives of classical logic? Rephrased, How far might a classical understanding of quantum mechanics be, in principle, possible? A celebrated result of Kochen and Specker answers the above question in the negative. However, this answer is just one among various possible ones, not all negative. It is our aim to discuss the above question in terms of mappings of quantum worlds into classical ones, more specifically, in terms of embeddings of quantum logics into classical logics; depending upon the type of restrictions imposed on embeddings, the question may get negative or positive answers.