A New Martingale Representation Theorem (Discrete Time)

In this paper, we prove a new theorem concerning representation of discrete time martingales, which is based on solving a specially chosen problem of optimal control with random sequences. We establish a relationship between the solution of the Bellman equation and the martingale representation. We illustrate the results with an example of calculating a European type option.     

Luminescence of heavily Ce-doped alkaline-earth fluorides

The spectral and kinetic parameters of M_1−xCe_xF_2+x (x=0.35, M=Ca, Sr, Ba) crystals luminescence have been studied. These characteristics are compared to the luminescence of solution base hosts: MF₂:Ce and CeF₃. The emission bands of heavily Ce-doped alkali earth fluorides are closed to the spectrum of perturbed Ce-center in CeF₃ at T=9 K. Luminescence of M_0.65Ce_0.35F_2.35 crystals reveals the efficient excitation in the UV and VUV ranges. The main feature of the emission and excitation spectra of Ce³⁺ luminescence is the displacement to the low-energy range according to the bandgap decrease in the Ca-, Sr- and Ba-based fluorides, respectively. Small Stokes shift leads to the reabsorption and light yield decrease. Luminescence peculiarities of M_1−xCe_xF_2+x solid solution and the role of Ce-enriched inclusions are discussed.     

Luminescence of Pr-doped LiCaAlF6 and LiSrAlF6 crystals

The spectral and kinetic parameters of LiCaAlF₆:Pr and LiSrAlF₆:Pr single crystals are studied at LHeT and room temperature (RT). Photon cascade emission (PCE), i.e., ¹S₀→¹I₆ and ³P₀→³H_j, ³F_j transitions after Pr³⁺ excitation via 4f²→4f 5d absorption results in the conversion of the vacuum ultraviolet photon to two visible photons. The excitation and photoemission spectra as well as decay times have been measured and compared with those for CaF₂:Pr and SrF₂:Pr crystals. X-ray luminescence was measured to study the emission origin from both ¹S₀ and ³P₀ states of Pr³⁺. An intense phosphorescence of LiSrAlF₆:Pr was observed in the visible range after X-irradiation at RT, contrary to LiCaAlF₆:Pr.     

Perturbed Motion of a Centrally Symmetric Point Vortex System

The types of motion in a system of point vortices initially located at the vertices of a 2n-sided regular polygon, produced by a spatially periodic perturbation, in the presence of which the vortices are positioned at the corners of two regular concentric n-sided polygons, are described.     

Synthesis of 3-acetamidoindole derivatives

2-Carbethoxy-3-phenylazoindoles, which are reduced to 2-carbethoxy-3-acetamidoindoles, were obtained by diazo coupling of 2-carbethoxyindoles with benzene diazonium chloride. Some transformations of these compounds were studied.     

Pulling CsI(Na) single crystals from melt by continuous method without plastic deformation

It is established that bromine impurity in CsI(Na) crystals not only facilitates the homogeneous incorporation of an activator into the lattice and prevents complex activator clusters from forming, but it also significantly hinders (at certain concentrations) the action of the primary and secondary dislocation slip systems. It is shown that the automatic pulling of large CsI-based crystals can be provided by the introduction of a single Br impurity into the charge; this impurity, to a large extent, strengthens only the top part of the crystal. The absence of plastic deformation in CsI-CsBr(Na) crystals with a diameter Ø300 mm and height h = 600 mm (grown by the continuous method) and Ø500 mm and h = 200 mm (grown by the automatic Kiropulos method) has been experimentally confirmed.     

Separation of Rare-Earth Elements from Nitrate Solutions by Solvent Extraction Using Mixtures of Methyltri-n-octylammonium Nitrate and Tri-n-butyl Phosphate

The article presents data on the solvent extraction separation of rare-earth elements (REEs), such as La(III), Ce(III), Pr(III), and Nd(III), using synergic mixtures of methyltrioctylammonium nitrate (TOMANO₃) with tri-n-butyl phosphate (TBP) from weakly acidic nitrate solutions. Specifically, experimental results on separation of REEs, for the pair Ce(III)/Pr(III) for quaternary mixtures of REEs (La(III), Ce(III), Pr(III), Nd(III)) and for the pair La(III)/Pr(III) for solutions containing La(III), Pr(III), and Nd(III), are presented. It was shown that effective separation for the pair Ce(III)/Pr(III) from a solution containing 219 g Ce(III)/L, 106 g La(III)/L, 20 g Pr(III)/L, 55 g Nd(III)/L, and 0.1 mol/L HNO₃, was achieved using 56 steps of a multistage, counter-current solvent extraction cascade with scrubbing, at an organic-to-aqueous phase volume ratio (O/A) equal to 2/1 on the extraction section and O/A equal to 4/1 on the scrubbing section, using 3.3 mol/L solutions of the mixture TOMANO₃-TBP with molar ratio 0.15:0.85 in dodecane. Separation for the pair La(III)/Pr(III) could be achieved using a solvent extraction cascade with scrubbing in 32 steps at O/A equal to 2/1 on the extraction section and O/A equal to 2.8/1 on the scrubbing section of the solvent extraction cascade from a solution containing 258 g La(III)/L, 58 g Pr(III)/L, 141 g Nd(III)/L, and 0.1 mol/L HNO₃ with 3.0 mol/L solution of the mixture TOMANO₃-TBP with molar ratio 0.2:0.8 in dodecane.     

Peculiarities of cascade photon emission and energy storage in M1−xPrxF2+x (M=Ca,Sr, Ba,x≈0.35) crystals

Peculiarities of cascade photon emission (CPE) and energy storage in M_1?xPr_xF_2+x (M=Ca, Sr, Ba, x≈0.35) crystals were studied. The investigation of lattice parameters revealed that these solid solutions belong to the fluorite structure type with the lattice constant noticeably different from that of MF₂ crystals. Absorption, emission and excitation spectra of M_0.65Pr_0.35F_2.35 were measured at LHeT and RT. As it turned out the typical for 4f²→4f² transition in Pr³⁺ emission lines are broadened as compared with the PrF₃ crystal. The analysis of the excitation spectra broadening does not allow bringing out the type of the superlattice, which is inherent to the material, but it indicates clearly the simultaneous presence of different types of the Pr centers in mixed crystals. Yet another specific feature is the higher radiation sensitivity of these fluorides relatively PrF₃, MF₂ and Pr-doped MF₂ crystals. Coloration efficiency enhances in direction Ca→Sr→Ba, and the positions of induced absorption band depend on composition of the solid solution. Colorization, thermo-stimulated luminescence and afterglow of the M_1?xPr_xF_2+x crystals denote high radiation sensitivity as compared with M_1?xCe_xF_2+x.     

Radiation stability of M1 − xPrxF2 + x (M = Ca,Sr, Ba) crystals

The radiation stability of the mixed crystals M_1 ? xR_xF_2 + x (M = Ca, Sr, Ba) depends on types of the alkaline-earth and rare-earth ions. Different to Eu- and Ce-containing systems, M_1 ? xPr_xF_2 + x solid solutions have a low radiation resistance, which may be associated with hole trapping on praseodymium ion according to the reaction Pr³⁺ → Pr⁴⁺ which is typical for praseodymium. The coloration efficiency of M_1 ? xPr_xF_2 + x crystals grows in the row Ca → Sr → Ba, which is explained satisfactorily within the model of rare-earth clusters, the structure of which is determined by the ratio of the base alkaline-earth cation to the praseodymium ion radii.     

Reaction of 3-aminoindole-2-carboxylic acids with diethyl acetylenedicarboxylate

-Carboline and indolo--carboline derivatives were obtained by reaction of the potassium salts of 3-aminoindole-2-carboxylic acids with diethyl acetylenedicarboxylate. A difference in the behavior of 3-aminoindole derivatives in the Michael reaction due to the nature of the substituent in the 5 position of the indole ring was established.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 82–84, January, 1977.