The quantum theory of the Liouville model with imaginary field is considered using the Quantum Inverse Scattering Method. An integrable structure with nontrivial spectral parameter dependence is developed for lattice Liouville theory by scaling the L-matrix of lattice sine-Gordon theory. This L-matrix yields Bethe Ansatz equations for Liouville theory, by the methods of the algebraic Bethe Ansa...

The doping effects of Al2O3 on SiO2 ( -cristobalite) have been studied by first principles calculations, with emphasis on the structural, electronic and optical properties. Compared to pure SiO2 crystal, the electronic density of states (DOS) of the Al2O3 doped SiO2 show significant changes. The electron energy states corresponding to the newly emerged sharp DOS peaks are found to exhibit local...

Current multi-analytes chips are limited with requiring numbers of sensors, complex synthesis and compounds screen. It is expected to develop new principles and techniques to achieve high-performance multi-analytes testing with facile sensors. Here, we investigated the correlative multi-states properties of a photochromic sensor (spirooxazine), which is capable of a selective and cross-reactive...

We consider a class of identification algorithms for distributed parameter systems. Utilizing stochastic optimization techniques, sequences of estimat.ors are constructed by minimizing appropriate functionals. The main effort is to devel<?p weak and strong invariance principles for the underlying algorithms. By means of weak convergence methods, a functional central limit theorem is established...

We investigate the interactions between two identical magnetic impurities substituted into a graphene superlattice. Using a first-principles approach, we calculate the electronic and magnetic properties for transition-metal substituted graphene systems with varying spatial separation. These calculations are compared for three different magnetic impurities, manganese, chromium, and vanadium. We ...

The effective on-site Coulomb interaction (Hubbard U) between localized electrons at crystal surfaces is expected to be enhanced due to the reduced coordination number and reduced subsequent screening. By means of first principles calculations employing the constrained random-phase approximation we show that this is indeed the case for simple metals and insulators but not necessarily for transi...

The principles of sustainable economic development are formulated on the basis developed concept description systems. Mathematical algorithms for finding equilibrium states were built and conditions complete clearing markets found. definition phenomenon recession is given theorems established that formulate existence a in system. depth parameter introduced. For input-output production model, ne...