On an integral equation of the third type

Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 3, pp. 308–314, July–September, 1995.     

Some open categorical problems inTop

In this paper, a pendant to a recent survey paper, the authors discuss several open problems in categorical topology. The emphasis is on topology-oriented problems rather than on more general category-oriented ones. In fact, most problems deal with full subconstructs or superconstructs of the constructTop of topological spaces and continuous maps.     

Reply to the Comment on¶Low temperature specific heat of blue bronze K0.30MoO3

Eur. Phys. J. B 24, 315 (2001) In our Reply to the Comment [#!1!#] we refute the “straightforward” interpretation of the excess low-temperature specific heat, C_p, contribution we have measured in our study of CDW systems K_0.3MoO₃ and (TaSe₄)₂I [#!2!#] as originating solely from normal phonon modes. The specific sensitivity of the bump in C _p / T ³ at low temperatures to the impurity content is consistent with the increased value of the phason pinning gap while the dispersion of normal phonons remains unaffected. We ascribe at least this part of the anomaly to the phason contribution. As stated in reference [3] that the phonon density of states extracted from neutron scattering measurements is the least reliable in this energy range (<0.5 meV), we conclude that C_p measurements are more accurate for detecting the phason contribution. Received 17 April 2002 Published online 19 July 2002     

Modulational instability in one-dimensional saturable waveguide arrays: Comparison with Kerr nonlinearity

Discrete modulational instability within the first band of uniform one-dimensional waveguide arrays possessing a saturable self-defocusing nonlinearity is investigated in detail within the coupled mode approach. Explicit analytical results for both the threshold and the maximal gain of instability are compared with the corresponding data from waveguide arrays exhibiting Kerr nonlinearity. We find that saturation bounds the interval of existence of discrete modulational instability, stabilizes the frequency region of perturbations around ±π/2 and decreases both gain and critical spatial frequency of perturbations.     

Study of glassy microporous filters in the sodium borosilicate glasses with appropriate carriers

Summary DúThe aim of this work is to prepare a porous filter composed of two porous layers: macro-porous carrier and micro-porous sodium borosilicate (NBS) glass with TiO₂ additive (NBST glass), a Vycor-type glass. In the present work we prepared the macroporous support from the same material (NBST glass) as the upper microporous layer and then by sintering both parts to produce the required composite. This work introduces the results of experiments in the preparation of micro-porous filter on NBST glass base, laid on macro-porous carrier. After sintering of scrap NBST glass, porous samples were prepared to be used as carriers for micro-porous samples of phase-separated NBST glass. In other cases, the following carrier materials were used: a) frita SIMAX, b) Al₂O₃. The properties of the NBST glass and the changes in the glass structure with temperature were studied in order to determine the optimal sintering temperature of the prepared glasses. For the development of the sintered glasses, valuable information was obtained from heating microscopy (HM) and scanning electron microscopy (SEM) studies. The combination of the HM and SEM results with the measurements of the micro-hardness and density directed to the further study of the phase separated NBST glasses.     

The radiation of polarized matter in a wave-guide of general cross-section with many dielectrics I

In this first part a straight general wave-guide with a perfectly conducting outer wall and several dielectrics, excited by an electrically generally polarized matter is considered and the electromagnetic field is determined.     

The Green–Kubo Formula for Locally Interacting Fermionic Open Systems

We consider a model describing finitely many free Fermi gas reservoirs coupled by local interactions and prove the Green–Kubo formulas and the Onsager reciprocity relations for heat and charge fluxes generated by temperature and chemical potential differentials. Submitted: September 2, 2006. Accepted: November 21, 2006.     

On a model for quantum friction,II. Fermi's golden rule and dynamics at positive temperature

We investigate the dynamics of anN-level system linearly coupled to a field of mass-less bosons at positive temperature. Using complex deformation techniques, we develop time-dependent perturbation theory and study spectral properties of the total Hamiltonian. We also calculate the lifetime of resonances to second order in the coupling.