Lower bounds of the Laplacian graph eigenvalues

In this paper we prove that all positive eigenvalues of the Laplacian of an arbitrary simple graph have some positive lower bounds. For a fixed integer k 1 we call a graph without isolated vertices k-minimal if its kth greatest Laplacian eigenvalue reaches this lower bound. We describe all 1-minimal and 2-minimal graphs and we prove that for every k 3 the path P_k+1 on k + 1 vertices is the unique k-minimal graph.     

On the Seneta Sequences

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.     

On a problem connected with zeros of ζ(s) on the critical line

The existence of zeros ofZ ^(k)(t) in short intervals of the type [T, T+H] is established, whereHT ^a(k)logT, . Hitherto the sharpest bounds for the constanta(k) are obtained by employing a certain exponential averaging technique and the estimation of the relevant exponential sums. Bounds for are also derived, under the assumption that orZ(t) does not vanish in certain short intervals.     

Polarographic study of the dipropyldithiophosphinate complexes of Pd(II), Pb(II), Cd(II), and Zn(II) ions

The complexes of the dithiophosphinic acids with Pd(II), Pb(II), Cd(II), and ZN(II) in a toluene-ethanol medium produce single polarographic waves. The half-wave potential is a linear function of the ligand concentration. The stabilities of these chelates, which are characterized by a sulphur-metal bond, are in the order: Pd(II) > Pb(II) > Cd(II) > Zn(II).     

Investigation on the TeO2–MoO3–V2O5 System. II. Properties of the obtained glasses

Some of the properties of glasses obtained in the systems TeO₂–MoO₃ and TeO₂–MoO₃–V₂O₅ had been studied. A good correlation between the properties and the phase diagram of the TeO₂–MoO₃ system was established. The glass resistance-composition function varied between 6.85 · 10⁹ ohm · cm and 2.93 · 10¹⁰ ohm · cm. The isolines of the properties (softening temperature, density, resistance at room and higher temperatures and activation energy) of the glasses obtained from the TeO₂–MoO₃–V₂O₅ system were ploted. The electrical resistance is influenced by the concentration of V₂O₅ and MoO₃ and by temperature. The glass absorption characteristics of thin layers were determined in the visible range.     

Ab initio Study of the Keto-Enol Equilibriumof Malonaldehyde

 The mechanism of the keto-enol tautomerism of malonaldehyde was studied by ab initio methods using 6-21G^** and 6-311G^** basis functions at the HF level. Two separate mechanisms were examined: through-space proton transfer in the ω-shaped form and through-space proton transfer in a sickle-shaped form obtained from the ω form by rotation. The transition state structure of the ω form is non-planar, whereas that of the sickle form is planar. The sickle form is connected with a 2^nd order saddle, indicating that there should exist a lower energy barrier, i.e. that the through-bond mechanism may be preferred. The calculated energy barriers of keto-enol tautomerism for the sickle form is twice as high as those for the omega form.     

CEMS and DCEMS investigations of Al-implanted iron

-Fe surfaces were implanted with a nominal dose of 5×10¹⁷ Al ions/cm² at 50 keV and a current density of about 3.7 A/cm². Samples of different shapes and thicknesses have been used in order to test the influence of heat flow from specimen to target holder during implantation. Integral and energy differential (depth-selective)⁵⁷Fe conversion electron Mössbauer spectroscopy (CEMS and DCEMS) were employed. The spectra indicated a magnetic phase characterised by a broad hyperfine field distributionP(B _hf), a non-magnetic phase, and -Fe. The relative intensity of the non-magnetic phase was enhanced if the thermal contact during implantation became worse. An energy dependence of DCEM spectra in the L-electron range was observed. Model calculations using L-electron weight functions and experimental concentration profiles obtained by secondary neutral mass spectroscopy (SNMS) yielded fair agreement between calculated and experimental phase signals. The results demonstrate that the non-magnetic Fe-Al alloy phase with high Al concentration is located closer to the surface than the magnetic alloy phase, which extends to much larger depth than expected.     

Flow-injection analysis with a small cylindrical wire type electrode

An amperometric detector with a small thin mercury film electrode is described. The device demonstrates advantageous operational characteristics such as small dispersion (D<2) and “memory effect” (me<0.6%), extensive maximum sample frequency (msf −200 samples/h), and high sensitivity. It has been proven useful in flow-injection analysis at a constant potential under hydrodynamic conditions.