Construction of position and momentum operators and Hamiltonians by embedding and submersion

Extrinsic position and momentum operators are defined on a manifold M via an embedding i: M→(R _n , g _n ) and, via a submersion, π: R _n →M. A Hamiltonian , describing free dynamics on M, is constructed as an intrinsic property of M by the embedding i and an associated Riemannian geodesic submersion.     

Quantum and Classical Disparity and Accord

Discrepancies and accords between quantum (QM) and classical mechanics (CM) related to expectation values and periods are generally found for both the harmonic oscillator (SHO) and a free particle in a box (FPB), which may apply generally. These indicate non-locality is expected throughout QM. The FPB energy states violate the Correspondence Principle. Previously unexpected accords are found and proven that 〈x ²〉 _CM =〈x ²〉 _QM and τ _CM =τ _QMb (beat period i.e. beats between the phases for adjoining energy states) for the SHO for all quantum numbers, n. However, for the FPB the beat periods differ at small n. It is shown that a particle’s velocity in an infinite square well varies, no matter how wide the box, nor how far the particle is from the walls. The quantum free particle variances share an indirect commonality with the Aharonov-Bohm and Aharonov-Casher effects in that there is a quantum action in the absence of a force. The concept of an “Expectation Value over a Partial Well Width” is introduced. This paper raises the question as to whether these inconsistencies are undetectable, or can be empirically ascertained. These inherent variances may need to be fixed, or nature is manifestly more non-classical than expected.     

Accuracy and repeatability of QRAPMASTER and MRF-vFA

Our purpose is to evaluate bias and repeatability of the quantitative MRI sequences QRAPMASTER, based on steady-state imaging, and variable Flip Angle MRF (MRF-VFA), based on the transient response.Both techniques are assessed with a standardized phantom and five volunteers on 1.5 T and 3 T clinical scanners. All scans were repeated eight times in consecutive weeks.In the phantom, the mean bias±95% confidence interval for T1 values with QRAPMASTER was 10 ± 10% on 1.5 T and 4 ± 13% on 3.0 T. The mean bias for T1 values with MRF-vFA was 21 ± 17% on 1.5 T and 9 ± 9% on 3.0 T. For T2 values the mean bias with QRAPMASTER was 12 ± 3% on 1.5 T and 23 ± 1% on 3.0 T. For T2 values the mean bias with MRF-vFA was 17 ± 1% on 1.5 T and 19 ± 2% on 3.0 T. QRAPMASTER estimated lower T1 and T2 values than MRF-vFA. Repeatability was good with low coefficients of variation (CoV). Mean CoV ± 95% confidence interval for T1 were 3.2 ± 0.4% on 1.5 T and 4.5 ± 0.8% on 3.0 T with QRAPMASTER and 2.7% ± 0.2% on 1.5 T and 2.5 ± 0.2% on 3.0 T with MRF-vFA. For T2 were 3.3 ± 1.9% on 1.5 T and 3.2 ± 0.6% on 3.0 T with QRAPMASTER and 2.0 ± 0.4% on 1.5 T and 5.7 ± 1.0% on 3.0 T with MRF-vFA.The in-vivo T1 and T2 are in the range of values previously reported by other authors.The in-vivo mean CoV ± 95% confidence interval in gray matter were for T1 1.7 ± 0.2% using QRAPMASTER and 0.7 ± 0.5% using MRF-vFA and for T2 were 0.9 ± 0.4% using QRAPMASTER and 2.4 ± 0.5% using MRF-vFA. In white matter were for T1 0.9 ± 0.3% using QRAPMASTER and 1.3 ± 1.1% using MRF-vFA and for T2 were 0.7 ± 0.4% using QRAPMASTER and 2.4 ± 0.4% using MRF-vFA. A GLM analysis showed that the variations in T1 and T2 mainly depend on the field strength and the subject, but not on the follow-up repetition in different days. This confirms the high repeatability of QRAPMASTER and MRF-vFA.In summary, QRAPMASTER and MRF-vFA on both systems were highly repeatable with moderate accuracy, providing results comparable to standard references. While repeatability was similar for both methods, QRAPMASTER was more accurate. QRAPMASTER is a tested commercial product but MRF-vFA is 4.77 times faster, which would ease the inclusion of quantitative relaxometry.     

Infrared and Raman spectra and vibrational assignments of diiodomethane and its deuterated analogs

The infrared (from 4000 to 100 cm^?1) and Raman spectra of CH₂I₂ and CD₂I₂ have been recorded in the liquid and gaseous phases. Assignments have been made for all observed bands and, in the case of CH₂I₂, compared with those previously reported. Some bands appearing in the CD₂I₂ spectrum have been attributed to the presence of CHDI₂. The wavenumbers of the fundamental bands of CHDI₂ have been calculated from those of CH₂I₂ and CD₂I₂ using Brodersen and Langseth's rule, and compared with those observed in the CD₂I₂ spectrum.     

Energy gap and transition temperature of highly disordered and amorphous thallium- and indium-films

Thin and pure Tl-films and In-films with different impurities (Ag, Te, Ge, Sb) are condensed onto a cooled substrate at 4 K. Measurements of the energy gap by means of the tunnel effect and the transition temperature of the weak-coupling superconductor thallium are carried out as a function of the degree of disorder of the films. The ratioα=2Δ ₀/kT _c increases proportional to the reciprocal mean free path from 3.5 for the annealed film up to 3.8 for the highly disordered film. For In-films condensed by quenching with impurity additions, one finds a linear relation between energy gap and transition temperature. In-films with Sb-additive are obtained in an amorphous phase with a ratioα=2Δ ₀/kT _c of 4.4. The amorphous state of the In/Sb-films is confirmed by measurements of the electric conductivity and the Hall-effect.     

Adsorption and solution of H2 and N2 by Ta and Nb

The condensation and desorption kinetics of H₂ and N₂ on polycrystalline wires of Ta and Nb are examined for solute concentrations between 0.1 and 100 monolayers. Accurate comparisons of adsorbate densities and sticking coefficients on Ta, Nb, Mo and W are obtained by making simultaneous measurements on all four substrates in the same vacuum system. Desorption exhibits second order kinetics for all substrates at all coverages. Desorption activation energies are higher on Ta and Nb than on W and Mo for both gases. Diffusion limited desorption is observed for H₂ at high heating rates. Solution of H₂ occurs at measurable rates (s ? 0.01) in Ta and Nb even at 78 °K while for N₂ no solution is observed for T < 600 °K.     

Experimental and modeling study on the pyrolysis and oxidation of n-decane and n-dodecane

High pressure n-decane and n-dodecane shock tube experiments were conducted to assist in the development of a Jet A surrogate kinetic model. Jet A is a kerosene based jet fuel composed of hundreds of hydrocarbons consisting of paraffins, olefins, aromatics and naphthenes. In the formulation of the surrogate mixture, n-decane or n-dodecane represent the normal paraffin class of hydrocarbons present in aviation fuels like Jet A. The experimental work on both n-alkanes was performed in a heated high pressure single pulse shock tube. The mole fractions of the stable species were determined using gas chromatography and mass spectroscopy. Experimental data on both n-decane and n-dodecane oxidation and pyrolysis were obtained for temperatures from 867 to 1739 K, pressures from 19 to 74 atm, reaction times from 1.15 to 3.47 ms, and equivalence ratios from 0.46 to 2.05, and ∞. Both n-decane and n-dodecane oxidation showed that the fuel decays through thermally driven oxygen free decomposition at the conditions studied. This observation prompted an experimental and modeling study of n-decane and n-dodecane pyrolysis using a recently submitted revised n-decane/iso-octane/toluene surrogate model. The surrogate model was extended to n-dodecane in order to facilitate the study of the species and the 1-olefin species quantified during the pyrolysis of n-dodecane and n-decane were revised with additional reactions and reaction rate constants modified with rate constants taken from literature. When compared against a recently published generalized n-alkane model and the original and revised surrogate models, the revised (based on our experimental work) and extended surrogate model showed improvements in predicting 1-olefin species profiles from pyrolytic and oxidative n-decane and n-dodecane experiments. The revised and extended model when compared to the published generalized n-alkane and surrogate models also showed improvements in predicting species profiles from flow reactor n-decane oxidation experiments, but similarly predicted n-decane and n-dodecane ignition delay times.     

Muonium states and dynamics in phosphorus and sulphur

Magnetic properties of single crystal Ba₂Cu₃O₄Cl₂ with Cu₃O₄ planes were investigated by temperature‐ and magnetic‐field‐dependent anisotropic magnetization M(T,H) and zero‐field‐μSR. Muon spin precession was observed below as well as above T=32 K where an anomaly in M(T) appears. At this temperature the frequency of the precession changes and the damping of it diverges. This is an evidence for a magnetic transition. We also found the temperature dependence of the H‐linear component of M(H) shows a maximum around T=80 K, which is similar to the behavior of low‐dimensional magnets with an antiferromagnetic interaction. This revised version was published online in July 2006 with corrections to the Cover Date.     

Sonochemical preparation of SnS and SnS2 nano- and micropowders and their characterization

Sonochemical production of tin(II) and tin(IV) sulfides is investigated. Different conditions of syntheses are examined: used solvent (ethanol or ethylenediamine), source of tin (SnCl₂ or SnCl₄), the molar ratio of thioacetamide to the tin source, and time of sonication. The obtained powders are characterized by the X-ray diffraction method (PXRD), scanning electron microscopy (SEM), scanning transmission electron microscopy (STEM), energy-dispersive X-ray spectroscopy (EDX), and the Tauc method. Raman and FT-IR measurements were performed for the obtained samples, which additionally confirmed the crystallinity and phase composition of the samples. The influence of experimental conditions on composition (is it SnS or SnS₂), morphology, and on the bandgap of obtained products is elucidated. It was found that longer sonication times favor more crystalline product. Each of bandgaps is direct and most of them show typical values – c.a. 1.3 eV for SnS and 2.4 eV for SnS₂. However, there are some exceptions. Synthesized powders show a variety of forms such as needles, flower-like, rods, random agglomerates (SnS₂) and balls (SnS). Using ethanol as a solvent led to powders of SnS₂ independently of which tin chloride is used. Sonochemistry in ethylenediamine is more diverse: this solvent protects Sn²⁺ cations from oxidation so mostly SnS is obtained, while SnCl₄ does not produce powder of SnS₂ but Sn(SO₄)₂ instead or, at a higher ratio of thioacetamide to SnCl₄, green clear mixture.     

Synthesis and hydrolysis of octacalcium phosphate and its characterization by electron microscopy and X-ray diffraction

Octacalcium phosphate (OCP) powder was produced by precipitating 250 mL Ca(CH₃COO)₂ 0.04 M into 750 L of phosphate solution (5 mmol Na₂HPO₄ and 5 mmol NaH₂PO₄) at a constant temperature of 60 °C and pH 5, which resulted in a dry white powder. X-ray diffraction (XRD), transmission electron microscopy (TEM) analysis, and the electron diffraction pattern (SAED) all showed only OCP. Hydroxyapatite (HAP) was directly obtained through hydrolysis of the powder. The total transformation of OCP into HAP was registered over a period of 6 h. During the first 30 min of hydrolysis both phases coexisted. The two phases and the OCP-HAP interface were structurally analyzed through XRD and TEM. OCP parameters (calculated by the Rietveld method) are a=19.70, b=9.50, c=6.85 Å; α=90.03°, β=92.48°, γ=108.32° (triclinic P-1) with average crystal size of 13.5±0.2 nm, while HAP parameters were a=9.45, c=6.87 Å (hexagonal P6₃/m) with average crystal size of 16.9±0.2 nm.     

Growth and characterization of DyP/GaAs and DyAs/GaAs-based heterostructures and superlattices

Details of the structural and electrical properties of epitaxial DyP/GaAs and DyAs/GaAs is reported. DyP is lattice matched to GaAs, with a room temperature mismatch of less than 0.01%. DyAs, on the other hand, has a mismatch of nearly 2.4%. Both DyP and DyAs have been grown by solid source MBE using custom designed group V thermal cracker cells and group III high-temperature effusion cells. High-quality DyP and DyAs epilayers, as determined by XRD, TEM, and AFM analysis, were obtained for growth temperatures ranging from 500°C to 600°C with growth rates between 0.5 and 0.7 μm/h. The DyP epilayers are n-type with measured electron concentrations of the order of 3×10²⁰ to 4×10²⁰ cm⁻³, with room temperature mobilities of 250–300 cm²/V s, and with a barrier height of 0.75 eV to GaAs. The DyAs epilayers are also n-type with concentration of 1×10²¹ to 2×10²¹ cm⁻³, with mobilities between 25 and 40 cm²/V s. DyP is stable in air with no apparent oxidation taking place, even after months of ambient exposure to untreated air.     

q-Deformed orthogonal and pseudo-orthogonal algebras and their representations

Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting according to Gel'fand-Tsetlin-type formulas. Unitary representations of the q-deformed algebras U _q (so _n,1) are found.     

Infrared and raman studies on neodymium pentaphosphate and metaphosphates

The infrared and Raman spectra of crystalline samples of NdP₅O₁₄, NaNdP₄O₁₂ and KNdP₄O₁₂ are recorded. The spectra are analysed on the basis of vibrations of P=O, P-O, PO₂ and P-O-P groups. The P₄O ₁₂ ⁴⁻ ion has cyclic structures both in NaNdP₄O₁₂ and KNdP₄O₁₂ crystals. It has been inferred that the P-O-P bridges are stronger in metaphosphates.     

Liberations and twists of real and complex spheres

We study the 10 noncommutative spheres obtained by liberating, twisting, and liberating +twisting the real and complex spheres $S_{\mathbb{R}}^{N-1},S_{\mathbb{C}}^{N-1}$. At the axiomatic level, we show that, under very strong axioms, these 10 spheres are the only ones. Our main results concern the computation of the quantum isometry groups of these 10 spheres, taken in an affine real/complex sense. We formulate as well a proposal for an extended formalism, comprising 18 spheres.     

Photo- and electro-production of mesons on nucleons and nuclei

In these lectures I will show some results obtained with the chiral unitary approach applied to the photo- and electro-production of mesons. The results for the photo-production of ηπ⁰p and K⁰π⁰Σ⁺, together with related reactions will be shown, having with common denominator the excitation of the Δ(1700) resonance which is one of those dynamically generated in the chiral unitary approach. Then I will show the results obtained for the e⁺e⁻→?f₀(980) reaction which reproduce the bulk of the data except for a pronounced peak, giving support to a new mesonic resonance, X(2175). Results will also be shown for the electromagnetic form factors of the N^∗(1535) resonance, also dynamically generated in this approach. Finally, I will show some results on the photo-production of the ω in the nuclei, showing that present experimental results claiming a shift of the ω mass in the medium are tied to a particular choice of background and are not conclusive. On the other hand, the same experimental results show unambiguously a huge increase of the ω width in the nuclear medium.     

Covering and gluing of algebras and differential algebras

Extending work of Budzyński and Kondracki, we investigate coverings and gluings of algebras and differential algebras. We describe in detail the gluing of two quantum discs along their classical subspace, giving a C^*-algebra isomorphic to a certain Podleś sphere, as well as the gluing of U_q^1/2(sl₂)-covariant differential calculi on the discs.