On one master integral for three-loop on-shell HQET propagator diagrams with mass

An exact expression for the master integral I_2 arising in three-loop on-shell HQET propagator diagrams with mass is derived and its analytical expansion in the dimensional regularization parameter epsilon is given.Comment: 6 pages, 1 figure; v3: completely re-written, 2 new authors, many new results, additional reference

On Epsilon Expansions of Four-loop Non-planar Massless Propagator Diagrams

We evaluate three typical four-loop non-planar massless propagator diagrams in a Taylor expansion in dimensional regularization parameter $\epsilon=(4-d)/2$ up to transcendentality weight twelve, using a recently developed method of one of the present coauthors (R.L.). We observe only multiple zeta values in our results.Comment: 3 pages, 1 figure, results unchanged, discussion improved, to appear in European Physical Journal

Size effect in the oxidation-reduction processes of platinum particles supported onto silicon dioxide

The interaction of the Pt/SiO2 model catalysts as thin films on the surface of tantalum supports with a mixture of NO + O2 (1: 1) was studied by X-ray photoelectron spectroscopy. The pressure of the reaction mixture was varied from 6 to 64 mbar, and the temperature was varied from room temperature to 500°C. Two types of the catalysts, in which the Pt/Si atomic ratios were ~0.1 and ~0.3 (0.1-Pt/SiO2 and 0.3-Pt/SiO2, respectively) according to the XPS data, were studied. In 0.1-Pt/SiO2, the particles of platinum predominantly had a size from 1 to 2.5 nm; a wide Pt particle size distribution in a range from 1 to 15 nm with a maximum at ~4 nm was characteristic of 0.3-Pt/SiO2. The interaction of all of the samples with NO + O2 at room temperature led to the dissolution of oxygen atoms in the bulk of platinum metal particles. As the reaction temperature was increased, PtO x platinum oxide particles were formed: from small Pt particles in 0.1-Pt/SiO2 at 300°C and from larger particles in 0.3-Pt/SiO2 at 400-500°C. It was established that the reactivity of platinum oxide particles toward hydrogen also depended on the particle size. The small particles of platinum oxide were converted into platinum metal under the action of hydrogen (16 mbar) at 300°C. The coarse particles of PtO x in the samples of 0.3-Pt/SiO2 were reduced much more easily starting with room temperature. © 2015 Pleiades Publishing, Ltd

O(\alpha \alpha_s) correction to the pole mass of the t-quark within the Standard Model

We have calculated the O(\alpha \alpha_s) contributions to the relationship between the MS-mass and the pole of the t-quark propagator in the Standard Model in the limit of a diagonal CKM matrix and for a massless b-quark. Analytical results for the so far unknown master-integrals appearing in the calculation are also given.Comment: 23 pages, LaTeX, 5-eps figures; In v.2 the typos in Eqs.(4.41), (5.54), (5.56), (5.57) and Fifure 4 corrected. New references are adde

MS vs. Pole Masses of Gauge Bosons: Electroweak Bosonic Two-Loop Corrections

The relationship between MS and pole masses of the vector bosons Z and W is calculated at the two-loop level in the Standard Model. We only consider the purely bosonic contributions which represents a gauge invariant subclass of diagrams. All calculations were performed in the linear $R_\xi$ gauge with three arbitrary gauge parameters utilizing the method of asymptotic expansions. The results are presented in analytic form as series in the small parameters $\sin^2\theta_W$ and mass ratio $m_Z^2/m_H^2$. As a byproduct we obtain the bosonic two-loop contributions to the renormalization of the weak mixing parameter $\sin^2\theta_W$ and of the Fermi constant. The running of Fermi constant will become important at high energy colliders.Comment: LaTeX, 36 p., 10 fig.; in v3 more technical details about renormalization procedure are adde

Planck scale effects in neutrino physics

We study the phenomenology and cosmology of the Majoron (flavon) models of three active and one inert neutrino paying special attention to the possible (almost) conserved generalization of the Zeldovich-Konopinski-Mahmoud lepton charge. Using Planck scale physics effects which provide the breaking of the lepton charge, we show how in this picture one can incorporate the solutions to some of the central issues in neutrino physics such as the solar and atmospheric neutrino puzzles, dark matter and a 17 keV neutrino. These gravitational effects induce tiny Majorana mass terms for neutrinos and considerable masses for flavons. The cosmological demand for the sufficiently fast decay of flavons implies a lower limit on the electron neutrino mass in the range of 0.1-1 eV.Comment: 24 pages, 1 figure (not included but available upon request), LaTex, IC/92/196, SISSA-140/92/EP, LMU-09/9

Planck-Scale Physics and Neutrino Masses

We discuss gravitationally induced masses and mass splittings of Majorana, Zeldovich-Konopinski-Mahmoud and Dirac neutrinos. Among other implications, these effects can provide a solution of the solar neutrino puzzle. In particular, we show how this may work in the 17 keV neutrino picture.Comment: 10 pages, IC/92/79, SISSA-83/92/EP, LMU-04/92 (the preprint number has been corrected; no other changes

About higher order epsilon-expansion of some massive two- and three-loop master-integrals

For certain dimensionally-regulated massive two- and three-loop propagator-type diagrams the higher order epsilon-expansion is constructed.Comment: 17 pages, LaTeX, 1-eps figure; v3: journal version; new references added; some unessential typos correcte

Digitalization of housing and communal services using the example of apartment buildings

The possibility of digitalization of housing and communal services is mathematically considered using the example of apartment buildings. The approaches discussed in the paper can be used in the construction of new apartment complexes, as well as in the overhaul of the existing housing stock. In addition, the applied approaches can be easily adapted for use in office buildings and business centers