To realisation of chromatic polynomial calculation algorithm

We calculate chromatic polynomial of an undirected graph using the fundamental reduction theorem and reducing to complete graphs. We also find the chromatic number using the chromatic polynomial. The C++ program was created, the result is obtained in the form of falling factorials and afterwards by the powers of x, the applications of chromatic polynomial are given

Ab initio and nuclear inelastic scattering studies of Fe3_3Si/GaAs heterostructures

The structure and dynamical properties of the Fe$_3$Si/GaAs(001) interface are investigated by density functional theory and nuclear inelastic scattering measurements. The stability of four different atomic configurations of the Fe$_3$Si/GaAs multilayers is analyzed by calculating the formation energies and phonon dispersion curves. The differences in charge density, magnetization, and electronic density of states between the configurations are examined. Our calculations unveil that magnetic moments of the Fe atoms tend to align in a plane parallel to the interface, along the [110] direction of the Fe$_3$Si crystallographic unit cell. In some configurations, the spin polarization of interface layers is larger than that of bulk Fe$_3$Si. The effect of the interface on element-specific and layer-resolved phonon density of states is discussed. The Fe-partial phonon density of states measured for the Fe$_3$Si layer thickness of three monolayers is compared with theoretical results obtained for each interface atomic configuration. The best agreement is found for one of the configurations with a mixed Fe-Si interface layer, which reproduces the anomalous enhancement of the phonon density of states below 10 meVComment: 14 pages, 9 figures, 4 table

Origin of a Simultaneous Suppression of Thermal Conductivity and Increase of Electrical Conductivity and Seebeck Coefficient in Disordered Cubic Cu2ZnSnS4

The parameters governing the thermoelectric efficiency of a material, Seebeck coefficient, electrical, and thermal conductivities, are correlated and their reciprocal interdependence typically prevents a simultaneous optimization. Here, we present the case of disordered cubic kesterite Cu$_{2}$ZnSnS$_{4}$, a phase stabilized by structural disorder at low temperature. With respect to the ordered form, the introduction of disorder improves the three thermoelectric parameters at the same time. The origin of this peculiar behavior lies in the localization of some Sn lone pair electrons, leading to “rattling” Sn ions. On one hand, these rattlers remarkably suppress thermal conductivity, dissipating lattice energy via optical phonons located below 1.5 THz; on the other, they form electron-deficient Sn—S bonds leading to a p-type dopinglike effect and highly localized acceptor levels, simultaneously enhancing electrical conductivity and the Seebeck coefficient. This phenomenon leads to a 3 times reduced thermal conductivity and doubling of both electrical conductivity and the Seebeck coefficient, resulting in a more than 20 times increase in figure of merit, although still moderate in absolute terms

Near-Earth space plasma modelling and forecasting

In the frame of the European COST 296 project (Mitigation of Ionospheric Effects on Radio Systems, MIERS)in the Working Package 1.3, new ionospheric models, prediction and forecasting methods and programs as well as ionospheric imaging techniques have been developed. They include (i) topside ionosphere and meso-scale irregularity models, (ii) improved forecasting methods for real time forecasting and for prediction of foF2, M(3000)F2, MUF and TECs, including the use of new techniques such as Neurofuzzy, Nearest Neighbour, Cascade Modelling and Genetic Programming and (iii) improved dynamic high latitude ionosphere models through tomographic imaging and model validation. The success of the prediction algorithms and their improvement over existing methods has been demonstrated by comparing predictions with later real data. The collaboration between different European partners (including interchange of data) has played a significant part in the development and validation of these new prediction and forecasting methods, programs and algorithms which can be applied to a variety of practical applications leading to improved mitigation of ionosphereic and space weather effects.Published255-2713.9. Fisica della magnetosfera, ionosfera e meteorologia spazialeJCR Journalope

Near-Earth space plasma modelling and forecasting

In the frame of the European COST 296 project (Mitigation of Ionospheric Effects on Radio Systems, MIERS)in the Working Package 1.3, new ionospheric models, prediction and forecasting methods and programs as well as ionospheric imaging techniques have been developed. They include (i) topside ionosphere and meso-scale irregularity models, (ii) improved forecasting methods for real time forecasting and for prediction of foF2, M(3000)F2, MUF and TECs, including the use of new techniques such as Neurofuzzy, Nearest Neighbour, Cascade Modelling and Genetic Programming and (iii) improved dynamic high latitude ionosphere models through tomographic imaging and model validation. The success of the prediction algorithms and their improvement over existing methods has been demonstrated by comparing predictions with later real data. The collaboration between different European partners (including interchange of data) has played a significant part in the development and validation of these new prediction and forecasting methods, programs and algorithms which can be applied to a variety of practical applications leading to improved mitigation of ionosphereic and space weather effects

Lattice dynamics of endotaxial silicide nanowires

Self-organized silicide nanowires are considered as main building blocks of future nanoelectronics and have been intensively investigated. In nanostructures, the lattice vibrational waves (phonons) deviate drastically from those in bulk crystals, which gives rise to anomalies in thermodynamic, elastic, electronic, and magnetic properties. Hence, a thorough understanding of the physical properties of these materials requires a comprehensive investigation of the lattice dynamics as a function of the nanowire size. We performed a systematic lattice dynamics study of endotaxial FeSi$_2$ nanowires, forming the metastable, surface-stabilized $\alpha$-phase, which are in-plane embedded into the Si(110) surface. The average widths of the nanowires ranged from 24 to 3 nm, their lengths ranged from several $\mu$m to about 100 nm. The Fe-partial phonon density of states, obtained by nuclear inelastic scattering, exhibits a broadening of the spectral features with decreasing nanowire width. The experimental data obtained along and across the nanowires unveiled a pronounced vibrational anisotropy that originates from the specific orientation of the tetragonal $\alpha$-FeSi$_2$ unit cell on the Si(110) surface. The results from first-principles calculations are fully consistent with the experimental data and allow for a comprehensive understanding of the lattice dynamics of endotaxial silicide nanowires.Comment: 9 pages, 7 figures, 3 table