The structure of decomposition of a triconnected graph

We describe the structure of triconnected graph with the help of its decomposition by 3-cutsets. We divide all 3-cutsets of a triconnected graph into rather small groups with a simple structure, named complexes. The detailed description of all complexes is presented. Moreover, we prove that the structure of a hypertree could be introduced on the set of all complexes. This structure gives us a complete description of the relative disposition of the complexes. Keywords: connectivity, triconneted graphs.Comment: 49 pages, 8 figures. Russian version published in Zap. Nauchn. Sem. POMI v.391 (2011), http://www.pdmi.ras.ru/znsl/2011/v391/abs090.htm

Propaedeutic reliability of didactical models in the professional training of teachers

The article describes the concept of propaedeutic reliability through the example of using of the learning informational modelОписывается принцип пропедевтической достоверности на примере моделирования информационных отношений участников процесса обучени

Local anisotropy and giant enhancement of local electromagnetic fields in fractal aggregates of metal nanoparticles

We have shown within the quasistatic approximation that the giant fluctuations of local electromagnetic field in random fractal aggregates of silver nanospheres are strongly correlated with a local anisotropy factor S which is defined in this paper. The latter is a purely geometrical parameter which characterizes the deviation of local environment of a given nanosphere in an aggregate from spherical symmetry. Therefore, it is possible to predict the sites with anomalously large local fields in an aggregate without explicitly solving the electromagnetic problem. We have also demonstrated that the average (over nanospheres) value of S does not depend noticeably on the fractal dimension D, except when D approaches the trivial limit D=3. In this case, as one can expect, the average local environment becomes spherically symmetrical and S approaches zero. This corresponds to the well-known fact that in trivial aggregates fluctuations of local electromagnetic fields are much weaker than in fractal aggregates. Thus, we find that, within the quasistatics, the large-scale geometry does not have a significant impact on local electromagnetic responses in nanoaggregates in a wide range of fractal dimensions. However, this prediction is expected to be not correct in aggregates which are sufficiently large for the intermediate- and radiation-zone interaction of individual nanospheres to become important.Comment: 9 pages 9 figures. No revisions from previous version; only figure layout is change

Signal amplification in a qubit-resonator system

We study the dynamics of a qubit-resonator system, when the resonator is driven by two signals. The interaction of the qubit with the high-amplitude driving we consider in terms of the qubit dressed states. Interaction of the dressed qubit with the second probing signal can essentially change the amplitude of this signal. We calculate the transmission amplitude of the probe signal through the resonator as a function of the qubit's energy and the driving frequency detuning. The regions of increase and attenuation of the transmitted signal are calculated and demonstrated graphically. We present the influence of the signal parameters on the value of the amplification, and discuss the values of the qubit-resonator system parameters for an optimal amplification and attenuation of the weak probe signal.Comment: 7 pages, 8 figure

GRBs with optical afterglow and known redshift: a statistical study

We present a correlation between two intrinsic parameters of GRB optical afterglows. These are the isotropic luminosity at the maximum of the light curve (Lpeak) and the time-integrated isotropic energy (Eiso) radiated after the observed maximum. We test the correlation between the logarithms of (Eiso) and (Lpeak) and finally we value the effect of the different samples of GRBs in according with the first optical observation reduced to proper time.Comment: To be published in the proceedings of the conference "SWIFT and GRBs: Unveiling the Relativistic Universe", Venice, June 5-9, 200

Muon and Tau Neutrinos Spectra from Solar Flares

Solar neutrino flares and mixing are considered. Most power-full solar flare as the ones occurred on 23th February 1956, September 29th 1989, 28th October and on 2nd-4th November 2003 are sources of cosmic rays, X, gamma and neutrino bursts. These flares took place both on front or in the edge and in the hidden solar disk. The observed and estimated total flare energy should be a source of a prompt secondary neutrino burst originated, by proton-proton-pion production on the sun itself; a more delayed and spread neutrino flux signal arise by the solar charged flare particles reaching the terrestrial atmosphere. Our first estimates of neutrino signals in largest underground detectors hint for few events in correlation with, gamma,radio onser. Our approximated spectra for muons and taus from these rare solar eruption are shown over the most common background. The muon and tau signature is very peculiar and characteristic over electron and anti-electron neutrino fluxes. The rise of muon neutrinos will be detectable above the minimal muon threshold of 113 MeV. The rarest tau appearence will be possible only for hardest solar neutrino energies above 3.471 GeVComment: 14 pages, 4 figures, Vulcano Conference 200

Semiorthogonal decompositions of derived categories of equivariant coherent sheaves

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of bounded derived category of G-equivariant coherent sheaves on X into components, equivalent to derived categories of twisted representations of the group. If the group is finite or reductive over the algebraically closed field of zero characteristic, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.Comment: 28 pages, uses XY-pi