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Quantum Markov States on Cayley treesFeb 08 2019It is known that any locally faithful quantum Markov state (QMS) on one dimensional setting can be considered as a Gibbs state associated with Hamiltonian with commuting nearest-neighbor interactions. In our previous results, we have investigated quantum ... More

Phase transitions for Quantum Markov Chains associated with Ising type models on a Cayley treeMay 15 2016The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered ... More

Phase Transitions for quantum Ising model with competing XY -interactions on a Cayley treeFeb 08 2019The main aim of the present paper is to establish the existence of a phase transition for the quantum Ising model with competing XY interactions within the quantum Markov chain (QMC) scheme. In this scheme, we employ the $C^*$-algebraic approach to the ... More

On the perturbation of the electromagnetic energy due to the presence of inhomogeneities with small diametersMay 31 2007We consider solutions to the time-harmonic Maxwell problem in $\R^3$. For such solution we provide a rigorous derivation of the asymptotic expansions in the practically interesting situation, where a finite number of inhomogeneities of small diameter ... More

Recovery of small electromagnetic inhomogeneities from boundary measurements in time-dependent Maxwell's equationsJun 01 2007We consider for the time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic measurements of the tangential component ... More

Asymptotic behaviors for eigenvalues and eigenfunctions associated to Stokes operator in the presence of small boundary perturbationsSep 07 2015Feb 09 2016We consider the Stokes eigenvalue problem in a bounded domain of R3 with Dirich- let boundary conditions. The aim of this paper is to advance the development of high-order terms in the asymptotic expansions of the boundary perturbations of eigen- values, ... More

Determination of small linear perturbations in the diffusion coefficient from partial dynamic boundary measurementsFeb 07 2016This work deals with an inverse boundary value problem arising from the equation of heat conduction. We reconstruct small perturbations of the (isotropic) heat conductivity distribution from partial (on accessible part of the boundary) dynamic boundary ... More

Identification of the theory of multidimensional orthogonal polynomials with the theory of symmetric interacting Fock spaces with finite dimensional one particle spaceMar 10 2014Sep 01 2016The identification mentioned in the title allows a formulation of the multidi mensional Favard Lemma different from the ones currently used in the literature and which exactly parallels the original one dimensional formulation in the sense that the positive ... More

Inverse Conduction Problem for a Parabolic Equation using a Boundary Integral MethodMay 05 2008In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary measurements ... More

Identifying of the refractive index for the acoustic equation at fixed frequencyApr 16 2008In this paper we determine a formula for calculating the refractive index ${\bf n}$ for the acoustic equation from the partial Dirichlet to Neumann map(DN) associated to ${\bf n}$. We apply these results to identify locations and values of small volume ... More

Designing a Framework for Smart IoT AdaptationsSep 25 2017The Internet of Things (IoT) is the science of connecting multiple devices that coordinate to provide the service in question. IoT environments are complex, dynamic, rapidly changing and resource constrained. Therefore, proactively adapting devices to ... More

Elastic Properties of FeC and FeN MartensitesJul 31 2015Single crystal elastic constants of bcc iron and bct FeC and FeN alloys, martensites, have been evaluated by ab initio calculations based on the density functional theory. The energy of a strained crystal has been computed using the supercell method at ... More

A Lagrangian model of copepod dynamics: Clustering by escape jumps in turbulenceJan 07 2016Apr 26 2016Planktonic copepods are small crustaceans that have the ability to swim by quick powerful jumps. Such an aptness is used to escape from high shear regions, which may be caused either by flow per- turbations, produced by a large predator (i.e., fish larvae), ... More

The Gathering Problem for Two Oblivious Robots with Unreliable CompassesNov 07 2011Anonymous mobile robots are often classified into synchronous, semi-synchronous and asynchronous robots when discussing the pattern formation problem. For semi-synchronous robots, all patterns formable with memory are also formable without memory, with ... More