Wigner Measures in Noncommutative Quantum Mechanics

We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner measure, for a Gaussian to be a noncommutative Wigner measure, and derive certain properties of the marginal distributions which are not shared by ordinary Wigner measures. Moreover, we derive the Robertson-Schrödinger uncertainty principle. Finally, we show explicitly how the set of noncommutative Wigner measures relates to the sets of Liouville and (commutative) Wigner measures.     

Cycloparaphenylene (CPP) series are molecular models for graphene armchair edges: trends in their aromaticity and cyclic conjugation are evaluated

Cycloparaphenylene ([r]CPP) and cyclacene ([r]CA) series are models for short carbon nanotubes. It is shown that armchair edges in model cycloparaphenylenes possess greater aromaticity and cyclic conjugation than do zigzag edges in model cyclacenes. According to Aihara’s bond resonance energy (BRE) and Bosanac and Gutman energy effect (ef) measurements, cycloparaphenylenes are twice as aromatic as cyclacenes. The general solution of all eigenvalues of all members of the cycloparaphenylene series is given. The origin of the recurrence of some eigenvalues are determined.     

Multidimensional Continued Fractions,Dynamical Renormalization and KAM Theory

The disadvantage of ‘traditional’ multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis we describe a simple algorithm based on the dynamics of flows on the homogeneous space (the space of lattices of covolume one) that indeed yields best possible approximations to any irrational vector. The algorithm is ideally suited for a number of dynamical applications that involve small divisor problems. As an example, we explicitly construct a renormalization scheme for the linearization of vector fields on tori of arbitrary dimension.     

Noninvasive Temperature Measurement in Dental Materials Using Nd3+, Yb3+ Doped Nanoparticles Emitting in the Near Infrared Region

In this work, the application of near infrared (NIR)-emitting NaYbF₄:1%Tm³⁺@NaLuF₄:30%Nd³⁺ core–shell nanoparticles is reported for noninvasive probing and monitoring the temperature during photopolymerization of dental materials. When excited at 808 nm, the synthesized nanoparticles emit NIR photoluminescence (PL) with two distinctive peaks at 865 and 980 nm which correspond to radiative transitions from the doped Nd³⁺ and Yb³⁺ ions, respectively. Luminescence intensity ratio between these two bands is found to vary with temperature due to temperature-dependent electronic excitation energy transfer between Nd³⁺ and Yb³⁺ ions at the core/shell interface. This finding allows luminescence ratiometric evaluation of the in situ temperature during photopolymerization of resin cement (doped with nanoparticles) in a veneer placement procedure. In addition, the NIR emission also enables PL imaging of the distribution of the adhesive under the veneer. The results highlight that rare-earth ions–doped nanoparticles with both excitation and emission in the NIR spectral range are advantageous for both PL-based nanothermometry and imaging due to the reduced attenuation of NIR light by dental ceramics.     

Search for singlet-triplet bistability or biradicaloid properties in polycyclic conjugated hydrocarbons: a valence-bond analysis

Two classes of molecules displaying singlet-triplet biradical bistability (i.e. species having significant biradicaloid properties) can be designed as follows. Alternant conjugated polycyclic hydrocarbons with numerous fixed double bonds (double bonds that remain unchanged in all its Kekulé resonance structures), a large number of Dewar resonance structures which measures the corresponding diradical resonance, and a small HOMO-LUMO band gap which measures the ease of thermal spin inversion are candidates for singlet triplet biradical bistability. Chichibabin's hydrocarbon ( 1 ) is an example. In addition, in the search for candidate molecules having singlet triplet bistability, one should also examine polycyclic conjugated systems having nonalternant induced spin frustration. Spin frustrated nonalternant polycyclic conjugated hydrocarbons will display singlet-triplet bistability (biradicaloid properties) and are generated from alternant valence-bond diradicals or Hückel molecular orbital diradicals having classical Kekulé structures by appropriate intramolecular joining of two starred or nonstarred positions with bonds, respectively.     

Experimental NMR and MS study of benzoylguanidines. Investigation of E/Z isomerism

Molecules containing the guanidinic nuclei possess several pharmacological applications, and knowing the preferred isomers of a potential drug is important to understand the way it operates pharmacologically. Benzoylguanidines were synthesized in satisfactory to good yields and characterized by NMR, Electrospray Ionization Mass Spectrometry (ESI‐MS) and Fourrier Transform InfraRed Spectroscopy techniques (FTIR). E/Z isomerism of the guanidines was studied and confirmed by NMR analysis in solution (¹H‐¹³C Heteronuclear Single Quantum Coherence (HSQC) and Heteronuclear Multiple‐Bond Correlation (HMBC), ¹H‐¹⁵N HMBC, ¹H‐¹H Correlation Spectroscopy (COSY) and Nuclear Overhauser Effect Spectroscopy (NOESY) experiments) at low temperatures. Compounds with p‐Cl and p‐Br aniline moiety exist mainly as Z isomer with a small proportion of E isomer, whereas compounds with p‐NO2 moiety showed a decrease in proportion of isomer Z. The results are important for the application of these molecules as enzymatic inhibitors. Copyright © 2013 John Wiley & Sons, Ltd.     

Determination of Pb,Zr, Ti,Sr, Cr,Nb and La in lead zirconate titanate ceramics by particle‐induced X‐ray emission

A particle‐induced X‐ray emission (PIXE) technique has been used in the determination of the principal components Pb, Zr and Ti and the substituting elements Sr, Cr, Nb and La in lead zirconate titanate ceramics. In general, precision of analysis was concentration dependent from each element under study. For Pb, precision varied between 0.13% and 0.16%, at higher concentration of 59.32–64.5%. It was around 6–9% for Sr, Cr and Nb at concentrations of 1% or lower. Particular attention was devoted to the estimation of the analysis trueness. With this purpose, three methods were applied: (1) comparison of PIXE and inductively coupled plasma optical emission spectrometry concentrations, (2) recovery study and (3) comparison with a laboratory standard. Trueness of analysis was around 100 ± 10% for the evaluated elements Pb, Zr, Ti, Sr and Cr. The expected stoichiometry and elemental composition homogeneity of a wide group of produced ceramics were confirmed by the PIXE technique. Copyright © 2012 John Wiley & Sons, Ltd.