On the curvature of warped product Finsler spaces and the Laplacian of the Sasaki–Finsler metrics

As an opening, we prove that a warped product Finsler space F=_F1×fF2$F=F_1{\times }_f{F}_2$ is of constant curvature c$c$ if and only if the base space _F1$F_1$ is also of constant curvature c$c$, the fiber space _F2$F_2$ is of some constant curvature α$\alpha$, and five other partial differential equations are satisfied. A rather similar result is proved for the case of warped product Finsler spaces of scalar curvature. Close relationships between the geometry of the warped product Finsler spaces of constant curvature and the spectral theory of the Laplacian (Laplace–Beltrami operator) of the well-known Sasaki–Finsler metrics of the base space _F1$F_1$ is established by detailed investigation of the above mentioned PDEs. We also define a new tensor for warped product Finsler spaces, which we call a warped-Cartan tensor. Using the tensor we define a new class of warped product Finsler spaces, calling them C-Warped spaces, which contain Landsberg, Berwald, locally Minkowski and Riemannian spaces, but not necessarily all of the constant curvature Finsler spaces of warped product type. Several results are obtained and special cases, for example the case of Riemannian, C-Warped and projectively flat spaces are also considered.     

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.     

Einstein gravity in almost Kähler and Lagrange–Finsler variables and deformation quantization

A geometric procedure is elaborated for transforming (pseudo) Riemannian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in turn, can be equivalently represented as almost Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deformation quantization. Such constructions are performed not on tangent bundles, as in usual Finsler geometry, but on spacetimes enabled with nonholonomic distributions defining 2+2$2+2$ splitting with associate nonlinear connection structure. We also show how the Einstein equations can be written in terms of Lagrange–Finsler variables and corresponding almost symplectic structures and encoded into the zero-degree cohomology coefficient for a quantum model of Einstein manifolds.     

The Origin of Phase Transition and the Usual Evolutions of the Unit-Cell Constants of the NASICON Structures of the Solid Solution LiTi2 – xGex(PO4)3

Physics of the Solid State - Ge-doped LiTi2(PO4)3 has been synthesized by a conventional solid-state reaction. Compounds LiM$$_{2}^{{{\text{IV}}}}$$(PO4)3 with LTP-type structure present a...     

The electronic structures of commensurate Ru(0001)–(3 × 3)–4Kr and Ru(0001)–(5 × 5)–Kr using density functional theory

We have calculated the minimum energies for each of three positionings of the adatom unit cells for Ru(0001)–(3 × 3)–4Kr (high Kr coverage) and for Ru(0001)–(5 × 5)–Kr (low Kr coverage). The differences between the results for the low and high-coverage cases may clarify puzzles posed by the experimental results of Narloch and Menzel. The low-coverage solution converges to a structure having Kr in the top site at a height of 3.09 Å above the substrate with the adsorption energy 185 meV. In the high-coverage case, adatom unit cells with a corner Kr at top, fcc hollow, and hcp hollow locations are found to have nearly the same adsorption energy of 175 meV. The height of the corner atom above the substrate is found to be 3.35, 3.54, and 3.50 Å for the top, fcc hollow and hcp hollow sites, respectively. These results are explained by demonstrating that there is an enhancement of the substrate electronic density of states at krypton orbital energies in the low-coverage case.     

A Study of the Structure and Magnetic Properties of FeRh1 – xIrx (x = 0.5–1) Alloys by First-Principles Methods

Physics of the Solid State - The structure and magnetic properties of FeRh1 – xIrx alloys (x = 0.5, 0.625, 0.75, 0.875, and 1) are investigated by first-principles methods...     

Promotion of the self-ignition of fuel–air mixtures with mechanoactivated Al (Mg)–MoO<Subscript>3</Subscript> particles

The ignition delay times of heptane–air and diesel oil–air mixtures with and without additives of mechanoactivated Mg–MoO³, Al–MoO³, and Mg–fluoroplastic nanopowders are measured using a rapid-mixture-injection setup. At temperatures below a certain threshold value, the metal–MoO³ additives produce practically no effect on the ignition delay time, whereas at higher temperatures, these additives sharply reduce the ignition delay time, down to the resolution time of the experimental method. The promoting efficiency of the small heterogeneous additives tested is many times superior to that of the known homogeneous promoters. Magnesium–fluoroplastic additives are demonstrated to produce no promoting effect on the ignition of the fuel–air mixtures studied. The mechanism of the action of the heterogeneous additives on the gasphase self-ignition of fuels is discussed.     

Concept of an Electron–Positron Collider for Production and Study of the (μ<Superscript>+</Superscript>μ<Superscript>–</Superscript>) Bound State

The possibility of producing and studying thus far unobserved dimuonium atoms (μ⁺μ^?) using low-energy colliding е⁺е^? beams is considered. Possible collider implementations are discussed, processes affecting its efficiency are investigated, and its parameters are estimated. The collider can probably also be used for high-luminosity experiments on the study of π^± and η mesons.     

Parametric Model of the Optical Constant Spectra of Hg1 – xCdxTe and Determination of the Compound Composition

Optics and Spectroscopy - A parametric model describing the spectra of optical constants n(λ) and k(λ) of a Hg1&nbsp;–&nbsp;xCdxTe (MCT) solid solution for the x values in...     

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&nbsp;–&nbsp;xEux)2(WO4)3 solid solutions are studied in a wide range of europium...     

Bond properties of the chalcopyrite and stannite phases in the Cu–(In,Ga)–Se system

Bond properties of the chalcopyrite and (defect) stannite phases in the Cu–(In,Ga)–Se system are compared in view of the bond overlap population calculated by the molecular orbital calculation of the DV-Xα method. Bond stretching force constant α is estimated for the stannite phases through the bond Ovlp. The Cu–Se and In(Ga)–Se bonds in defect stannite structure are considered to be mechanically weakened by the 2b-site vacancies. We estimate the weakened force constants to be 60–70% of those in the chalcopyrite structure. On the other hand, in In(Ga)-rich stannite, In(Ga)_4d–Se_8i and In(Ga)_2b–Se_8i bonds are estimated to be tighter by 23–25 and 8–9%, respectively, than In(Ga)_4b–Se_8d bond in the chalcopyrite structure. The Γ₁ frequencies of the stannite phases are also calculated using the estimated force constants. Characteristic Raman signals peaked at 160–175 cm⁻¹ observed for the Cu(In_1−xGa_x)₃Se₅ system are explained by the Cu-rich phase for the Cu–In–Se system, and the phase combination of Cu-rich and Ga_2aV_2b types for the Cu–Ga–Se system from these calculations.     

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&nbsp;‒&nbsp;xEux)2(MoO4)3 have been studied over a wide range of...     

More on the renormalization of the horizon function of the Gribov–Zwanziger action and the Kugo–Ojima Green function(s)

In this paper we provide strong evidence that there is no ambiguity in the choice of the horizon function underlying the Gribov–Zwanziger action. We show that there is only one correct possibility which is determined by the requirement of multiplicative renormalizability. As a consequence, this means that relations derived from other horizon functions cannot be given a consistent interpretation in terms of a local and renormalizable quantum field theory. In addition, we also discuss that the Kugo–Ojima functions u(p ²) and w(p ²) can only be defined after renormalization of the underlying Green function(s).     

Correlated development of a (2 × 2) reconstruction and a charge accumulation layer on the InAs(111)–Bi surface

We have studied the formation of a Bi-induced (2 × 2) reconstruction on the InAs(111)B surface. In connection to the development of the (2 × 2) reconstruction, a two dimensional charge accumulation layer located at the bottom of the InAs conduction band appears as seen through a photoemission structure at the Fermi level. Not well ordered Bi layers do not induce a charge accumulation. The Bi-induced reconstruction reduces the polarization of the pristine surface and changes the initial charge distribution. InAsBi alloying occurs below the surface where Bi acts as charge donor leading to the charge accumulation layer.     

Synthesis and Reactivity of Mg(II)–Fe(II)–Fe(III) Hydroxycarbonates

Green rust-like compounds (GRs) were discovered as natural minerals in various hydromorphic soils, where anoxic conditions allow their stability. They may control some redox processes in aquifers and participate to the transformation of various pollutants. Since Mg(II) cations are present in the fields where GRs were discovered, a partial substitution of Mg(II) to Fe(II) leading to intermediate compounds between GRs and usual Mg(II)–Fe(III) hydroxysalts is suspected. Mg(II)–Fe(II)–Fe(II) hydroxycarbonates can be obtained as intermediate oxidation products of (Mg, Fe)(OH)₂ in carbonate-containing aqueous media obeying to [Fe^II _4(1–x)Mg^II _4x Fe^III ₂(OH)₁₂]²⁺ [CO₃ ^2– nH₂O]^–2. TMS spectra at 12 K are similar to those of GRs, i.e., two quadrupole doublets, one due to Fe(II) with a large isomer shift =1.29 mms^–1 (with respect to -iron at room temperature) and quadrupole splitting E _Q=2.76 mms^–1, the other one due to Fe(III) with smaller hyperfine parameters =0.49 mms^–1 and E _Q=0.44 mms^–1. Fe(II) ions oxidise rapidly into Fe(III) with dissolved O₂. The reactivity is similar to that of Fe(II)–Fe(III) hydroxysalts GR, and thus the potential of Mg(II)–Fe(II)–Fe(III) compounds for reducing pollutants.     

Europium-sensitized Chemiluminescence of System Tetracycline–H<Subscript>2</Subscript>O<Subscript>2</Subscript>–Fe(II)/(III) and Its Application to the Determination of Tetracycline

Chemiluminescence (CL) of the reaction system tetracycline–H₂O₂–Fe(II)/(III)–Eu(III) was used for the determination of tetracycline hydrochloride in water, pharmaceutical preparations, and honey. The CL spectrum registered for this system shows emission bands typical of Eu(III) ions, with a maximum at λ ∼ 600 nm, corresponding to the electronic transitions of ⁵D₀ → ⁷F₁ and ⁵D₀ → ⁷F₂. A strong chemiluminescence intensity characteristic of europium(III) ions in the system tetracycline–H₂O₂–Fe(II)/(III)–Eu(III), as contrasted to the emission of the system tetracycline–H₂O₂–Fe(II)/(III) without Eu(III), proves that the Eu(III) ion plays the role of a chemiluminescence sensitizer, accompanying tetracycline oxidation in the Fenton system (H₂O₂–Fe(II)/(III)). A linear dependence was observed for the integrated CL light intensity on the tetracycline concentration in the range of 2 × 10⁻⁷ to 3 × 10⁻⁵ mol l⁻¹ with the detection limit of 5 × 10⁻⁸ mol l⁻¹ in aqueous solution.     

To the Problem of the Water Transparency Bandwidth (1.8–11.2 eV) and Hydrogen Bonds

It is experimentally detected the gravity center of theOHband of Raman scattering (RS) of picosecond pulses in water shifts by ~40 cm^?1 (~0.005 eV) to the high-frequency wing due to shortening the time of observation of the hydrogen bond restructuring in comparison with RS of nanosecond pulses. It was shown that declarative negation of hydrogen bonds and the introduction of the water transparency window half-width (5 eV) or (11.2 eV as seen in Fig. 1 of the paper by V. G. Artemov [Bulletin of the Lebedev Physics Institute 42, 187-191 (2015)] should be regarded as incorrect. These values multiply exceed the well known half-width in the range of 650–360 nm (~1.8 eV [1] which is defined by the fundamental absorption region and OH stretching vibration band overtones from the side of UV and IR regions, respectively.