Addendum to: “Geometrical and topological aspects of electrostatics on Riemannian manifolds” [J. Geom. Phys. 57 (8) (2007) 1679–1696]

In this note we discuss and solve several open problems posed in our recent paper “Geometrical and topological aspects of electrostatics on Riemannian manifolds”, also published in this journal. Some minor mistakes therein are corrected as well.     

Reply to the comments of M.E. Golmakani and J. Rezatalab,Comment on “Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates” (by R. Aghababaei and J.N. Reddy,Journal of Sound and Vibration 326 (2009) 277–289), Journal of Sound Vibration, 333 (2014) 3831–3835

Golmakani and Rezatalab [1] suggested in their paper that the deflection of a simply supported nonlocal elastic plate under uniform load is not affected by the small length scale terms. They based their proof on the use of Navier?s method using a sinusoidal-based deflection solution. This insensitivity of the deflection solution of a simply supported nonlocal elastic plate with respect to the small length terms of Eringen?s model is not correct, as already detailed in the literature (for example, see [2] for beam problems). In fact, the deflection of the nonlocal plate (in the Eringen sense) is larger than the one of the local case, as shown in many papers available in the literature. We prove in this reply to the authors that the Navier?s method has to be correctly applied for highlighting the specific sensitivity phenomenon of the deflection solution, as compared to exact analytical solution.     

Solid-phase total synthesis of (–)-Phenylhistine and (–)-Aurantiamine. Synthesis of a diverse dehydro-2,5-diketopiperazine library. Part II

The preparation of solid supported glycine phosphonate and its utilization for the total synthesis of two natural products is presented. The proposed protocol combines diversity with accessibility and speed, which makes this scaffold suitable for automated parallel synthesis and combinatorial chemistry. The preparation of a small library of dehydro-2,5-diketopiperazines, combining several natural amino acids with diverse heterocycles (including thiazoles, pyridines, indoles and imidazoles), is also demonstrated.     

Atomic and nanostructures of monolayer c(2 × 2)NiN on Cu(0 0 1)

Structures of monolayer nickel nitride (NiN) on Cu(0 0 1) surface are studied by X-ray photoelectron spectroscopy (XPS), low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). Formations of Ni–N chemical bonds and NiN monolayer at the surface are confirmed by XPS on the N-adsorbed Cu(0 0 1) surfaces after Ni deposition and subsequent annealing to 670 K. A c(2 × 2) structure is always observed in the LEED patterns, which is a quite contrast to the (2 × 2)p4g structure observed usually at the N-adsorbed Ni(0 0 1) surface. Atomic images by STM indicate the mixture of Ni–N and Cu–N structures at the surface. Density of the trenches on the N-saturated surface decreases and the grid pattern on partially N-covered surfaces becomes disordered with increasing the Ni coverage. These results are attributed to the decrease of the surface compressive stress at the N-adsorbed Cu surface by mixing Ni atoms.     

Spectral and Structural Characteristics of Molybdates (Lu1 – xEux)2(MoO4)3

Physics of the Solid State - The structure, the photoluminescence, and IR absorption spectra of solid solutions (Lu1 ‒ xEux)2(MoO4)3 have been studied over a wide range of...     

Spectral and Structural Characteristics of (Lu1 – xEux)2(WO4)3 Tungstates

Physics of the Solid State - The structure, luminescence, and IR absorption spectra of (Lu1 – xEux)2(WO4)3 solid solutions are studied in a wide range of europium...     

Entangled Eigenvectors of Scalar Fields φ1(x) - φ2(x) and П1(x) + П2(x)

We first demonstrate the precise Einstein-Podolsky-Rosen entanglement, which is inherent in quantum mechanics, in the context of quantum theory of complex scalar fields. We explicitly derive the entangled common eigenstates of φ₁(x) - φ₂(x) and П₁(x) + П₂(x) φ₁and φ₂ are two real components of the complex scalar field, and П₁ and П₂ are the corresponding conjugate fields) in the Fock space. The entangled eigenstates span a complete and orthonormal representation.     

Ab initio study of Yb on the Ge(111)–(3 × 2) and Si(111)–(3 × 2) surfaces

The surface reconstruction, 3 × 2, induced by Yb adsorption on a Ge (Si)(111) surface has been studied using first principles density-functional calculation within the generalized gradient approximation. The two different possible adsorption sites have been considered: (i) H₃ (this site is directly above a fourth-layer Ge (Si) atom) and (ii) T₄ (directly above a second-layer Ge (Si) atom). We have found that the total energies corresponding to these binding sites are nearly the same, indeed for the Yb/Ge (Si)(111)–(3 × 2) structure the T₄ model is slightly energetic by about 0.01 (0.08) eV/unitcell compared with the H₃ model. In particular for the Ge sublayer, the energy difference is small, and therefore it is possible that the T₄, H₃, or T₄H₃ (half of the adatoms occupy the T₄ adsorption site and the rest of the adatoms are located at the H₃ site) binding sites can coexist with REM/Ge(111)–(3 × 2). In contrast to the proposed model, we have not determined any buckling in the Ge = Ge double bond. The electronic band structures of the surfaces and the corresponding natures of their orbitals have also been calculated. Our results for both substrates are seen to be in agreement with the recent experimental data, especially that of the Yb/Si(111)–(3 × 2) surface.     

First principles total energy calculations of the adsorption of germane and digermane on Si(0 0 1)-c(2 × 4)

First principles total energy studies are performed to investigate the energetics, and the atomic structure of the adsorption of germane (GeH₄), and digermane (Ge₂H₆) on the Si(0 0 1)-c(2 × 4) surface. It has been observed experimentally that adsorption of Ge₂H₆ is a dissociative process, which first yields GeH₃ and then GeH₂ fragments as products. We first study the adsorption of GeH₂ considering two different models; the intra-row and the on-dimer geometries. Our results show that the on-dimer site is more stable than the intra-row geometry by 0.44 eV. This is not a surprise since in the absence of H atoms, adsorption in the on-dimer site leaves no dangling bonds. In contrast, when the GeH₂ fragment is considered together with two H atoms, the intra-row geometry is favored energetically as compared with the on-dimer site, in good agreement with experiment. Similar results have been previously obtained for the adsorption of SiH₂ on Si(0 0 1). Digermane adsorption is explored according to two different geometries. In the first one, we have considered the adsorption as two GeH₃ fragments, while in the second, we have considered the adsorption as two GeH₂ fragments plus 2 H fragments. In good agreement with experiments, it is found that the latter geometry is energetically more favorable.     

Reply to: “Comment on: ‘Exposed-key weakness of αη’ [Phys. Lett. A 370 (2007) 131]” [Phys. Lett. A 372 (2008) 7091]

We present simulations countering the claims in [R. Nair, H.P. Yuen, Phys. Lett. A 372 (2008) 7091] that the approximation given in [C. Ahn, K. Birnbaum, Phys. Lett. A 370 (2007) 131, quant-ph/0612058] for the eavesdropper's entropy on the encrypted key cannot be valid, and additionally discuss ways in which our views on security requirements differ from those given in [R. Nair, H.P. Yuen, Phys. Lett. A 372 (2008) 7091].     

Investigation of the reconstructive phase transition between metastable (α) and stable (β) modifications of the NH<Subscript>4</Subscript>LiSO<Subscript>4</Subscript> crystal

Crystals of ammonium lithium sulfate NH₄LiSO₄ in α and β modifications are studied, and conditions of their nucleation and growth are determined. The α modification of NH₄LiSO₄ and α → β phase transitions are investigated using polarized light microscopy, x-ray diffraction, and differential scanning calorimetry in the temperature range 80–530 K. It is found that, depending on the conditions of growth and storage, there exist two temperature ranges (T_{α → β} ≈ 340–350 and ≈440–450 K) in which the crystals can undergo an α → β reconstructive phase transition. The enthalpy of this transformation depends on the symmetry of the final phase. In the former case (340–350 K), the reconstructive phase transition leads to rapid destruction of the sample. In the latter case (440–450 K), the crystal structure undergoes a slow transformation (recrystallization) without noticeable distortions. The results obtained indicate that no structural phase transition occurs in the α modification of NH₄LiSO₄ at 250 K.     

Influence of isotopic substitution on spectral and structural parameters of an isolated [F(HF)<Subscript>2</Subscript>]— complex. Substitution of a proton by a kaon and a triton

This paper continues the theoretical study (see V. P. Bulychev and M. V. Buturlimova, J. Mol. Struct. 928, 32 (2009)) of the isotopic effects in the H-bonded anionic complex [F(HF)₂]-. Isotopomers of the complex with significant differences between the masses of the light atoms are considered. The four-dimensional anharmonic vibrational problem are solved by the variational method for the symmetric complex [F(KaF)₂]-, in which both protons are substituted by a positive kaon (positive K-meson), and for the asymmetric complex [FKaFTF]-. Variables related to the changes in the lengths of molecular fragments LF (L = Ka and T) and the distances between the F^- anion and the centers of mass of LF are used as the vibra-tional coordinates. The potential energy surfaces are calculated in the MP2/6-311++G(3df,3pd) approximation taking into account the basis set superposition error. The vibrational energy levels, frequencies, and absolute intensities for spectral transitions are determined. To study the isotope effect on the geometrical parameters of the complex, the values of internuclear separations and the asymmetry parameter of the F^-…L-F bridge averaged over the ground state and several excited vibrational states are calculated, as well as their standard deviations. The calculated results are compared to the data obtained previously for the symmetric complexes [F(HF)₂]^-, [F(DF)₂]^-, and [F(TF)₂]^-.     

Total asymmetric synthesis of (–)-Phenylhistine, (–)-Aurantiamine and related compounds. Part I

A new general, short, and efficient strategy for the construction of dehydro-diketopiperazines was developed. Horner–Emmons type coupling between a phosphinyl glycine ester and a formyl heterocycle is the key coupling reaction, which proceeds in good-to-excellent yields on several sterically-hindered substrates. Moreover, racemization of the parent L-amino acids is avoided as a result of the mild basic conditions used. The selection of the NH protective group of the formyl heterocycle was crucial. N-tosylated heterocycles proved ideal for this reaction sequence. Thus, the title compounds, (–)-Phenylhistine and (–)-Aurantiamine, were prepared in high yield (four steps, 47% overall) and optical purity. Furthermore, the synthesis of unnatural derivatives including an indole analogue was successfully completed.     

Reply to the Comment by F. Kožíšek et al. on “Evidence for the existence of stable-water-clusters at room temperature and normal pressure” [Phys. Lett. A 373 (2009) 3872]

After discussing various points raised in a recent comment by F. Ko?íšek et al., who claim that our Letter “Evidence for the existence of stable-water-clusters at room temperature and normal pressure” (Phys. Lett. A 373 (2009) 3872) is unclear and the evidence is scant, we conclude that their arguments are wrong.     

Addendum to: “Ricci-flat holonomy: A classification” [J. Geom. Phys. 57 (6) 1457–1475]: The case of spin(10)

This note fills a hole in the author’s previous paper “Ricci-flat holonomy: A classification”, by dealing with irreducible holonomy algebras that are subalgebras or real forms of C⊕spin(10,C)$\mathbb{C}\oplus \mathfrak{s}\mathfrak{p}\mathfrak{i}\mathfrak{n}(10,\mathbb{C})$. These all turn out to be of Ricci type.     

Adsorption and decomposition of γ-butyrolactone on Pd(1 1 1) and Pt(1 1 1)

The adsorption and thermal chemistry of γ-butyrolactone (GBL) on the (1 1 1) surface of Pd and Pt has been investigated using a combination of high resolution electron energy loss spectroscopy (HREELS) and temperature programmed desorption (TPD). HREELS results indicate that GBL adsorbs at 160 K on both surfaces through its oxygenate functionality. On Pd(1 1 1), adsorbed GBL undergoes ring-opening and decarbonylation by 273 K to produce adsorbed CO and surface hydrocarbon species. On Pt(1 1 1), very little dissociation is observed using HREELS, with almost all of the GBL simply desorbing. TPD results are consistent with decarbonylation and subsequent dehydrogenation reactions on Pd(1 1 1), although small amounts of CO₂ are also detected. TPD results from Pt(1 1 1) indicate that a small proportion of adsorbed GBL (perhaps on defect sites) does undergo ring-opening to produce CO, CO₂, and H₂. These results suggest that the primary dissociation pathway for GBL on Pd(1 1 1) is through O-C scission at the carbonyl position. Through comparisons with previously published studies of cyclic oxygenates, these results also demonstrate how ring strain and functionality affect the ring-opening rate and mechanism.     

Crystal structure,spectroscopy and magnetism of binuclear complexes of mercury and lanthanides; the Ln(NCS)(HMPA)4(μ-SCN)2HgCl(SCN) type

A series of lanthanide compounds of type Ln(NCS)(HMPA)₄,(μ-SCN)₂HgCl(SCN) (Ln = Pr, Nd, Eu) were synthesized and grown in the form of single crystals.

The crystal structure of the neodymium complex was determined by X-ray diffraction. Its space group is Cc, with the following unit cell parameters; a = 17.338(3) Å, b = 15.795(3) Å, c = 21.828(4) Å, β = 107.65(3)°. The structure has an unexpected architecture in which one Cl^? ion, four SCN^? ions, and four oxygen atoms of HMPA groups are engaged in the metal ion coordination.

The binuclear complex is composed of two types of subunits; seven coordinated Nd (III) and four coordinated Hg (II). The results obtained were compared with the earlier published data on the crystal structures of polynuclear complexes with ions of the IIa group (Zn or Cd). Luminescence, excitation of luminescence and absorption spectra of lanthanide (Pr, Nd, Eu) single crystals, as well as vibrational IR and Raman spectra at 293, 77 and 4K, were recorded. Non-trivial results of reabsorption of the d-level of Pr(III) emission by ³H₄ → ³ P_J, ₁D² transitions were observed with simultaneous detection of emission from the ³P₀ level after excitation in the UV region. The experimental oscillator strengths of the transitions were determined from the absorption spectra and parametrized in terms of the Judd-Ofelt intensity parameters Ω_λ (λ = 2, 4, 6).

Satisfactory results for the calculation with low errors of estimation of the parameters were obtained for a crystal of the Nd-Hg compound, which reproduced the intensities of the electronic transitions well. Positive values of Ω_λ were evaluated for Pr(III) after including the ³H₄ → ³F₂ hypersensitive transition (obeying selection rules δJ = 2, δL = 2) in the calculations.

Based on the above results, the radiative rate constant can be determined. Strong vibronic components were found in the low temperature spectra for both types of ligands involved in metal ion coordination. The vibronic transitions are mainly associated with modes of groups directly coordinated to the metal ions. Electron-phonon coupling including the resonant vibronic effect was analysed based on IR and Raman data.

Magnetic susceptibility measurements were carried out down to 1.7 K. Correlation of the spectra and magnetic properties with details of the structure of the title compound was studied.     

Preparation and magnetic and electrical properties of EuBaMn<Subscript>2</Subscript>O<Subscript>6−δ</Subscript> (δ=0,1)

The EuBaMn₂O₆ composition prepared in air at T=1500°C is shown to be a cubic perovskite exhibiting spin-glass properties below T_f=40 K. The reduced composition, EuBaMn₂O₅, crystallizes in a perovskite-like, YBaCuFeO₅-type layered structure with a tetragonal unit cell. EuBaMn₂O₅ with crystallographically ordered Eu³⁺ and Ba²⁺ ions is a ferromagnet with T_N=160 K. The anomalous behavior of the paramagnetic susceptibility is assumed to be due to a partial ordering of the Mn²⁺ and Mn³⁺ ions. EuBaMn₂O₅ oxidized in air at 900°C to EuBaMn₂O₆ has a magnetic ordering temperature T_M=260 K, near which the magnetoresistance reaches a peak value. X-ray diffraction measurements show the long-range order in the Eu³⁺ and Ba²⁺ ion arrangement to persist in the oxidized EuBaMn₂O₆ sample.