On the rate of convergence of certain random series in terms of norms of Orlicz spaces

There are obtained conditions for the convergence and estimates of the rate of convergence in terms of norms of Orlicz spaces of random series of the form where f_k(¯t) is an orthonormal system of eigenfunctions of a certain integral equation, k are random variables in an Orlicz space, ¯t Rⁿ.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 6, pp. 841–848, June, 1991.     

Sorption behavior and speciation of AmIII in orthophosphates of rare-earth elements

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Self-Assembly in the Systems MX<Subscript>2</Subscript>–Nicotinic Hydrazide–Pyruvic Acid (М = Со, Ni; X = Cl,CH<Subscript>3</Subscript>COO)

In the course of self-assembly in the systems MX₂–nicotinic hydrazide (HN)–pyruvic acid, where М = Co, Ni; X = Сl, CH₃COO, complexes of composition: [CoCl(HNРv)(H₂O)₂], [Co(HNРv)₂], [Ni(HIРv)₂] have been synthesized. Local atomic structure of the coordination centers was established by the method of X-ray absorption spectroscopy. Thermal stability, electric conductivity, and magnetic susceptibility of the complexes have been determined.     

A Study of Сu(II) Complexes with Pyruvic Acid Nicotinoyl and Isonicotinoyl Hydrazones by EPR and X-ray Absorption Spectroscopy

The composition and structure of the Cu²⁺ coordination cores in the previously synthesized [CuCl(HNPv)] · H₂O, [CuCl(HIPv)] · H₂O, [Cu(AOc)(HNPv)], [Cu(AOc)(HIPv)], [Cu(NO₃)(HNPv)], and [Cu(NO₃)(HIPv)] complexes, where HNPv and HIPv pyruvic acid nicotinoyl and isonicotinoyl hydrazones, respectively, have been determined. The binuclear complex [Cu₂(HNPv)₂(H₂O)2(μ-Cl)] has been synthesized for the first time and characterized by elemental analysis and IR, EPR, and EXAFS spectroscopy. Its dimeric structure has been proved by magnetic susceptibility measurement and EPR.     

Nickel(II) complexes with cytosine and threonine: Synthesis and structure

Mono-and mixed-ligand complexes with the composition [Ni(Cyt)₂(H₂O)₂]Cl₂, [Ni(Thr^–)₂(H₂O)₂] and [Ni(Thr^–)(Cyt)(H₂O)₂]Cl are synthesized and studied. Using IR spectroscopy it is determined that in the complex compounds, cytosine is bidentate (C=O group oxygen and heterocycle N3), threonine interacts with the Ni(II) ion due to amino and carboxyl groups. The models of the atomic structure of the studied compounds are proposed based on the EXAFS and XANES spectroscopy results.     

Products of complexation in the Cu(CH<Subscript>3</Subscript>CОО)<Subscript>2</Subscript>–2-(7-bromo-2-oxo-5-phenyl-3H-1,4-benzodiazepin-1-yl)acetohydrazide–salicylaldehyde–isopropanol system

Copper(II) complexes isolated from the Cu(CH₃COO)₂–2-(7-bromo-2-oxo-5-phenyl-3H-1,4-benzodiazepin-1-yl)acetohydrazide (Hydr)–salicylaldehyde (HSal)–isopropanol system [Cu₂(HydrSal)₂(μ-CH₃COO)] (I), [Cu(HydrSal)₂] (II) (HydrSal (hydrazone)is the condensation product of hydrazide and salicylaldehide) are synthesized and investigated. The complexes are characterized by elemental analysis, electrical conductivity measurements, and IR spectroscopy. The composition and structure of the Cu²⁺ coordination core are determined by ESR spectroscopy (I), magnetic susceptibility measurements and extended X-ray absorption fine structure (EXAFS) spectroscopy (II).     

Synthesis,structure, and photoluminescence properties of 4-methyl-<Emphasis Type="Italic">N</Emphasis>-{2-([1-alkyl-2-[2-(<Emphasis Type="Italic">p</Emphasis>-tolylsulfonylamino)phenyl]benzimidazol-5-yl]iminomethyl)phenyl}benzenesulfonamides and their zinc complexes

4-Methyl-N-{2-([1-alkyl-2-[2-(p-tolylsulfonylamino)phenyl]benzimidazol-5-yl]iminomethyl)phenyl}-benzenesulfamides (H₂L) and zinc complexes on their basis Zn₂L₂ have been synthesized. The structure of the ligands and complexes has been studied by IR, UV, ¹Н NMR spectroscopy, X-ray absorption spectroscopy, and X-ray diffraction analysis.     

Copper,cobalt, and nickel complexes of azomethine compounds containing phenylazo group in the amine fragment: Syntheses,structures, and magnetic properties

The Cu, Ni, and Со complexes based on the following new azomethine compounds containing azobenzene groups in the ortho- or para-positions of the amine fragment are synthesized: 2-allyl-6-[(E)-[4-(E)-phenylazophenyl]iminomethyl]phenol (HL¹), 2-allyl-6-[(E)-[4-methyl-2-[(E)-phenylazo]-p-tolylazo] iminomethyl]phenol (HL²), 5-methoxy-2-[(E)-[4-[(E)-phenylazo]phenyl]iminoethyl]phenol (HL³), and 5-methoxy-2-[(E)-[4-methyl-2-[(E)-p-tolylazo]phenyl]iminomethyl]phenol (HL⁴). The structures of the complexes are determined by the data of IR and ¹Н NMR spectroscopy (for the azomethine compounds), X-ray absorption spectroscopy, and magnetochemistry. The coordination centers of all Cu complexes have a distorted square structure. A direct dependence of the geometry of the coordination polyhedron on the position of azobenzene groups in the amine fragments of the ligands is found for the Ni and Co complexes. The octahedral environment of the nickel and cobalt ions takes place in the case of the ortho-position of the amine fragment, whereas the square environment for the Ni complexes or the tetrahedral environment for the Co complexes is observed at the para-position. The molecular structures of two azomethines HL¹ and HL⁴ are determined by X-ray diffraction analysis (CIF files CCDC nos. 1552836 (HL¹) and 1552837 (HL⁴)).     

Self-assembling in the systems МХ<Subscript>2</Subscript>–2-(7-bromo-2-oxo-5-phenyl-2,3-dihydro-1<Emphasis Type="Italic">Н</Emphasis>-1,4-benzdiazepin-1-yl)acetohydrazide–salicyl aldehyde (М = Сo,Ni, Zn; X = Cl,CH<Subscript>3</Subscript>COO)

By self-assembling in the systems MX₂–2-(7-bromo-2-oxo-5-phenyl-2,3-dehydro-1Н-1,4-benzdiazepin-1-yl)acetohydrazide (Hydr)–salicyl aldehyde (HSal) (М = Co, Ni, Zn; X = Cl, CH₃COO) the complexes of composition [Co(HydrSal)₂], [Ni(HydrSal)₂], [Zn(HydrHSal)Cl₂], [Zn(HydrSal)(CH₃COO)(H₂O)] have been synthesized. The local atomic structure of the coordination unit was determined by the method of X-ray absorption spectroscopy. Thermal stability, electroconductivity, and magnetic susceptibility of the complexes have been studied.     

Highly Luminescent,Water‐Soluble Lanthanide Fluorobenzoates: Syntheses,Structures and Photophysics,Part I: Lanthanide Pentafluorobenzoates

Highly luminescent, photostable, and soluble lanthanide pentafluorobenzoates have been synthesized and thoroughly characterized, with a focus on Eu^III and Tb^III complexes as visible emitters and Nd^III, Er^III, and Yb^III complexes as infrared emitters. Investigation of the crystal structures of the complexes in powder form and as single crystals by using X‐ray diffraction revealed five different structural types, including monomeric, dimeric, and polymeric. The local structure in different solutions was studied by using X‐ray absorption spectroscopy. The photoluminescence quantum yields (PLQYs) of terbium and europium complexes were 39 and 15 %, respectively; the latter value was increased almost twice by using the heterometallic complex [Tb_0.5Eu_0.5(pfb)₃(H₂O)] (Hpfb=pentafluorobenzoic acid). Due to the effectively utilized sensitization strategy (pfb)^?→Tb→Eu, a pure europium luminescence with a PLQY of 29 % was achieved.