Phase diagrams of the mixed spin-1 and spin-1/2 Ising-Heisenberg model on the diamond-like decorated Bethe lattice

The ground-state and finite-temperature behavior of the mixed spin-1 and spin-1/2 Ising-Heisenberg model on the diamond-like decorated Bethe lattice is investigated within the framework of two rigorous methods: the decoration-iteration transformation and exact recursion relations. The model under consideration describes a hybrid classical-quantum system consisting of the Ising and Heisenberg spins, which interact among themselves either through the Ising or XXZ Heisenberg nearest-neighbor interaction. Both sublattice magnetizations of the Ising and Heisenberg spins are exactly calculated with the aim to examine phase diagrams, thermal variations of the total and sublattice magnetizations. The finite-temperature phase diagrams form continuous (second-order) phase transition lines only, which exhibit a small reentrant region if the diamond-like decorated Bethe lattice with a sufficiently high coordination number is considered.     

False Vacuum Decay with Gravity in a Critical Case

The vacuum decay in a de Sitter universe is studied for the class of effective inflaton potentials that curvature at the top is less than as well as greater than a critical value determined previously. By comparing the actions of the Hawking - Moss instanton and the Coleman - de Luccia instanton(s) the mode of vacuum decay is determined in this critical situation.     

Electrical conductivity of chromate conversion coating on electrodeposited zinc

For certain applications of galvanized steel protected with conversion coatings it is important that the surface is electrically conductive. This is especially important with mating surfaces for electromagnetic compatibility. This paper addresses electrical conductivity of chromate conversion coatings. A cross-matrix study using different zinc plating techniques by different labs showed that the main deciding factor is the type of zinc-plating bath used rather than the subsequent chromating process. Thus, chromated zinc plate electrodeposited from cyanide baths is non-conductive while that from alkaline (non-cyanide) and acid baths is conductive, even though the plate from all the bath types is conductive before conversion coating. The results correlate well with the microscopic structure of the surfaces as observed with scanning electron microscopy (SEM) and could be further corroborated and rationalized using EDX and Auger spectroscopies.     

Mass separator for radioactive isotopes

A new isotope separator has been designed, constructed, and put into routine operation for separation of ¹³³Xe providing a major advancement and significant cost reduction in preparation of this radioactive isotope. The design features and advantages are discussed that expedite high purity separation of relatively small quantities of this isotope. These advantages could be easily used to expedite separation of other shorter-lived radioactive isotopes.     

Some results on linear nabla Riemann-Liouville fractional difference equations

In this paper, we establish some criteria for boundedness, stability properties, and separation of solutions of autonomous nonlinear nabla Riemann-Liouville scalar fractional difference equations. To derive these results, we prove the variation of constants formula for nabla Riemann-Liouville fractional difference equations.     

ОПРЕДЕЛЕНИЕ ВРЕМЕНИ ЖИЗНИ μ-МЕЗОНОВ ПО АНОМАЛЬНОМУ ПОГЛ0Щ ЕНИЮ МЕТОДОМ ЯДЕРНЫХ ЭМУЛЬСИЙ

- ;- . ( ) . , - .     

Real

The famous problem involves applying two maps: and to positive integers. If is even, one applies , if it is odd, one applies . The conjecture states that each trajectory of the system arrives to the periodic orbit . In this paper, instead of choosing each time which map to apply, we allow ourselves more freedom and apply both and independently of . That is, we consider the action of the free semigroup with generators and on the space of positive real numbers. We prove that this action is minimal (each trajectory is dense) and that the periodic points are dense. Moreover, we give a full characterization of the group of transformations of the real line generated by and .

     

Rotating an interval and a circle

We compare periodic orbits of circle rotations with their counterparts for interval maps. We prove that they are conjugate via a map of modality larger by at most 2 than the modality of the interval map. The proof is based on observation of trips of inhabitants of the Green Islands in the Black Sea.

     

The precision of DCE-MRI using the tissue homogeneity model with continuous formulation of the perfusion parameters

The present trend in dynamic contrast-enhanced MRI is to increase the number of estimated perfusion parameters using complex pharmacokinetic models. However, less attention is given to the precision analysis of the parameter estimates. In this paper, the distributed capillary adiabatic tissue homogeneity pharmacokinetic model is extended by the bolus arrival time formulated as a free continuous parameter. With the continuous formulation of all perfusion parameters, it is possible to use standard gradient-based optimization algorithms in the approximation of the tissue concentration time sequences. This new six-parameter model is investigated by comparing Monte-Carlo simulations with theoretically derived covariance matrices. The covariance-matrix approach is extended from the usual analysis of the primary perfusion parameters of the pharmacokinetic model to the analysis of the perfusion parameters derived from the primary ones. The results indicate that the precision of the estimated perfusion parameters can be described by the covariance matrix for signal-to-noise ratio higher than ~ 20 dB. The application of the new analysis model on a real DCE-MRI data set is also presented.