Linear impulsive dynamic systems on time scales

The purpose of this paper is to present the fundamental concepts of the basic theory for linear impulsive systems on time scales. First, we introduce the transition matrix for linear impulsive dynamic systems on time scales and we establish some properties of them. Second, we prove the existence and uniqueness of solutions for linear impulsive dynamic systems on time scales. Also we give some sufficient conditions for the stability of linear impulsive dynamic systems on time scales

Qualitative aspects of Volterra integro-dynamic system on time scales

This paper deals with the resolvent, asymptotic stability and boundedness of the solution of time-varying Volterra integro-dynamic system on time scales in which the coefficient matrix is not necessarily stable. We generalize at time scale some known properties about asymptotic behavior and boundedness from the continuous case. Some new results for discrete case are obtained

Dirac states with knobs on: interplay of external parameters and the surface electronic properties of 3D topological insulators

Topological insulators are a novel materials platform with high applications potential in fields ranging from spintronics to quantum computation. In the ongoing scientific effort to demonstrate controlled manipulation of their electronic structure by external means, stoichiometric variation and surface decoration are two effective approaches that have been followed. In ARPES experiments, both approaches are seen to lead to electronic band structure changes. Such approaches result in variations of the energy position of bulk and surface-related features and the creation of two-dimensional electron gases.The data presented here demonstrate that a third manipulation handle is accessible by utilizing the amount of illumination a topological insulator surface has been exposed to under typical experimental ARPES conditions. Our results show that this new, third, knob acts on an equal footing with stoichiometry and surface decoration as a modifier of the electronic band structure, and that it is in continuous competition with the latter. The data clearly point towards surface photovoltage and photo-induced desorption as the physical phenomena behind modifications of the electronic band structure under exposure to high-flux photons. We show that the interplay of these phenomena can minimize and even eliminate the adsorbate-related surface band bending on typical binary, ternary and quaternary Bi-based topological insulators. Including the influence of the sample temperature, these data set up a framework for the external control of the electronic band structure in topological insulator compounds in an ARPES setting. Four external knobs are available: bulk stoichiometry, surface decoration, temperature and photon exposure. These knobs can be used in conjunction to tune the band energies near the surface and consequently influence the topological properties of the relevant electronic states.Comment: 16 pages, 8 figure

High genetic diversity of measles virus, World Health Organization European region, 2005-2006

During 2005-2006, nine measles virus (MV) genotypes were identified throughout the World Health Organization European Region. All major epidemics were associated with genotypes D4, D6, and B3. Other genotypes (B2, D5, D8, D9, G2, and H1) were only found in limited numbers of cases after importation from other continents. The genetic diversity of endemic D6 strains was low; genotypes C2 and D7, circulating in Europe until recent years, were no longer identified. The transmission chains of several indigenous MV strains may thus have been interrupted by enhanced vaccination. However, multiple importations from Africa and Asia and virus introduction into highly mobile and unvaccinated communities caused a massive spread of D4 and B3 strains throughout much of the region. Thus, despite the reduction of endemic MV circulation, importation of MV from other continents caused prolonged circulation and large outbreaks after their introduction into unvaccinated and highly mobile communities

Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus

The aim of this paper is to correct some ambiguities and inaccuracies in Agarwal et al. (Commun. Nonlinear Sci. Numer. Simul. 20(1): 59-73, 2015; Adv. Differ. Equ. 2013: 302, 2013, doi:10.1186/1687-1847-2013-302) and to present new ideas and approaches for fractional calculus and fractional differential equations in nonreflexive Banach spaces