On the lower Markov spectrum

C. Hightower found two infinite sequences of gaps in the Markov spectrum, ( _n , _n ) and ( _n , _n ) with _n and _n both Markov elements, converging to . This paper exhibits Markov elements _n ^* and _n ^* such that, for alln 1, ( _n ^* , _n ) and ( _{n n} ^* ) are gaps in the Markov spectrum. Other results include showing that, for alln 1, _n is completely isolated, while the other endpoints of the gaps are limit points in the Markov spectrum.     

Accumulation points of the Lagrange and Markov spectra

In this note several conditions are developed which together guarantee that an element of the Markov spectrum is an accumulation point of the Lagrange spectrum. Every known limit point of the Lagrange spectrum which is the Markov value of an attained non-completely periodic sequence satisfies these criteria. Examples are given to show that the removal of any one of the conditions can result in an element of the Markov spectrum which is not a limit point of the Lagrange spectrum. New elements of the Markov spectrum satisfying these conditions have been included.     

Preparation of inorganic crystalline compounds induced by ionizing,UV and laser radiations

Results on preparation of nickel, zinc, yttrium, aluminum and cobalt oxides, zinc peroxide and hydroxide, yttrium and lutetium aluminum garnets and cobalt(II) aluminate via irradiation of aqueous solutions containing soluble metal salts and radical scavengers (formate anion or propan-2-ol) are summarized in this paper. Various physico-chemical and structural properties of prepared compounds (e.g. crystallinity, specific surface area, particle size) are also reported.All used variants of radiation method are rather convenient and simple, and yield nano-scale powder materials with interesting characteristics. Prepared materials generally have high chemical purity, high specific surface area and narrow distribution of particle size (ranging in tens of nm).Generally, accelerated electrons, gamma, and UV radiation yield materials with comparable properties and structural characteristics, but UV-radiation seems to be the most convenient for preparation of intricate compounds such as synthetic garnets and spinels, while ionizing radiation is better for preparation of compounds doped with foreign ions.Among discussed compounds, only zinc oxide, peroxide and hydroxide were prepared directly via irradiation. For preparation of other crystalline oxidic compounds, mild heat treatment of amorphous or weakly crystalline solid phase was necessary.     

Properties of ZnO nanocrystals prepared by radiation method

Zinc oxide nanoparticles were prepared by irradiation of aqueous solutions containing zinc(II) ions, propan-2-ol, polyvinyl alcohol, and hydrogen peroxide. Zinc oxide was found in solid phase either directly after irradiation, or after additional heat treatment. Various physicochemical parameters, including scintillation properties of prepared materials, were studied. After decomposition of impurities and annealing of oxygen vacancies, the samples showed intensive emission in visible spectral range and well-shaped exciton luminescence at 390–400 nm. The best scintillating properties had zinc oxide prepared from aqueous solutions containing zinc formate as initial precursor and hydrogen peroxide. Size of the crystalline particles ranged from tens to hundreds nm, depending on type of irradiated solution and post-irradiation thermal treatment.     

Phase conjugation with random fields and with deterministic and random scatterers

The theory of distortion correction by phase conjugation, developed since the discovery of this phenomenon many years ago, applies to situations when the field that is conjugated is monochromatic and the medium with which it interacts is deterministic. In this Letter a generalization of the theory is presented that applies to phase conjugation of partially coherent waves interacting with either deterministic or random weakly scattering nonabsorbing media.     

Phase singularities of the coherence functions in Young's interference pattern

We analyze the coherence properties of a partially coherent field emerging from two pinholes in an opaque screen and show that the spectral degree of coherence possesses phase singularities on certain surfaces in the region of superposition. To our knowledge, this is the first illustration of the singular behavior of the spectral degree of coherence, and the results extend the field of singular optics to the study of phase singularities of correlation functions.     

Energy spectra for decaying 2D turbulence in a bounded domain

We use results derived in the framework of the replica approach to study the liquid-glass thermodynamic transition. The main results are derived without using replicas and applied to the study of the Lennard-Jones binary mixture introduced by Kob and Andersen. We find that there is a phase transition due to the entropy crisis. We compute both analytically and numerically the value of the phase transition point T(K) and the specific heat in the low temperature phase.     

The Gouy phase of Airy beams

The phase behavior of Airy beams is studied, and their Gouy phase is defined. Analytic expressions for the idealized, infinite-energy type beam are derived. They are shown to be excellent approximations for finite-energy beams generated under typical experimental conditions.     

Scattering of light from particles with semisoft boundaries

A three-dimensional multi-Gaussian function, being a finite sum of Gaussian functions, is adopted for modeling of a spherically symmetric scatterer with a semisoft boundary, i.e. such that has continuous and adjustable drop in the index of refraction. A Gaussian sphere and a hard sphere are the two limiting cases when the number of terms in multi-Gaussian distribution is one and infinity, respectively. The effect of the boundary's softness on the intensity distribution of the scattered wave is revealed. The generalization of the model to random scatterers with semisoft boundaries is also outlined.     

Reduction of turbulence-induced scintillation by nonuniformly polarized beam arrays

We have explored a method to reduce turbulence-induced scintillation by using an incoherent beam array composed of beamlets with nonuniform polarization. It is shown that significant scintillation reduction of such an incoherent beam array can be obtained by using nonuniformly polarized beamlets whose scintillation properties are optimized.