On the Riesz constants for systems of integer translates

In this paper, one-parameter families of integer translates of the Gaussian and Lorentz functions are studied. For a Lorentz function, we obtain formulas for the coefficients of the series defining node functions and show that the limit value of node functions is given by a sample function. For systems of translates generated by the Gaussian and Lorentz functions as well as by the node functions related to them, we obtain explicit expressions for the Riesz constants and study the parameter-dependent behavior of these constants. While proving some of the results of this paper, we establish the monotonicity of a special ratio of two Jacobi theta functions, a fact which is of interest in itself.     

Synthesis,structure, and ESR spectra of the new heteronuclear complex {Li4(VO)2[(OOC)2C(H)Bu]4(H2O)8}·H2O

The reaction of an aqueous solution of vanadyl sulfate VOSO₄·3H₂O, butylmalonic acid (H₂Bumal = C₄H₁₀(COOH)₂), and lithium carbonate at pH ～4–5 gave crystals of the complex Li₄(VO)₂(Bumal)₄(H₂O)₈]·H₂O (1). The structure of complex 1 was established by X-ray diffraction analysis. The molecule of complex 1 consists of two mononuclear bischelate dianionic units {VO(Bumal)₂(H₂O)} linked by four lithium ions to form the hexanuclear heterometallic {V₂Li₄} structure. The crystals and an ethanolic solution of compound 1 were studied by ESR spectroscopy.     

Polymeric copper(II) complexes with 4-formyl-3-methyl-1-phenylpyrazol-5-one hetarylhydrazones: Synthesis and crystal structures

4-Formyl-3-methyl-1-phenylpyrazol-5-one quinolin-2-yl-(H₂L¹) and benzothiazol-2-ylhydrazones (H₂L²) were synthesized and studied. Quantum-chemical modeling of possible tautomers of the hydrazones was performed. Copper(II) complexes of the general formula [Cu(HL)(ROH)]Y (R = CH₃, C₂H₅; Y=NO₃, ClO₄) were obtained and examined by IR and EPR spectroscopy, magnetochemistry, and X-ray diffraction. Additional coordination through the N atom of the pyrazole ring enables the complex molecules to form zigzag polymer chains linked by intermolecular hydrogen bonds.     

Crystal structure and magnetic properties of a new heterometallic complex of Pd(II)-Cu(II) with 1-aminoethylidene-1,1-diphosphonic acid

A heterometallic complex of Pd(II)-Cu(II) with 1-aminoethylidene-1,1-diphosphonic (AEDP) acid (C₄H₂₂CuN₂O₁₆P₄Pd) _n (I) is synthesized. Single crystals of compound I are obtained; its crystal structure is determined by X-ray crystallography. The crystals are orthorhombic, space group Pbcn, a = 18.366(3) Å, b = 9.7661(17) Å, c = 20.198(4) Å, V = 3622.8(11) ų, Z = 8, d _x = 2.376 g/cm³. The compound crystallizes as a coordination polymer; the square environment of Pd(II) is formed by nitrogen atoms of amino groups and oxygen atoms of phosphonic groups, while at two non-equivalent copper atoms the octahedral environment is formed by oxygen atoms of phosphonic groups and water molecules. The crystal structure of compound I is characterized by the formation of a branched network of hydrogen bonds. Based on the analysis of the temperature dependence of the magnetic susceptibility it is found that for the heterometallic complex of Pd(II)-Cu(II) with AEDP antiferromagnetic interactions between the paramagnetic centers are dominant.     

Modification of chemically and physically obtained Fe3O4 magnetic nanoparticles with l-Lys for cell labeling

Russian Chemical Bulletin - Peculiar features of the modification of Fe3O4 magnetic nanoparticles (MNPs) obtained by co-precipitation from solutions of FeII and FeIII salts (10-nm MNPs) and by the...     

The Role of Singlet and Triplet Dioxygen Molecules in the EPR and 1H NMR Spectrum Line Broadening

In the Mo^(VI)/H₂O₂/H₂O system, the relaxation time (T ₁) of protons in a water molecule and in a CH₃ group decreases 10 to 30 times under conditions of dismutation of H₂O₂ with the formation of ¹O₂(¹_g). It is experimentally found that the overequilibrium concentration of triplet dioxygen cannot be the reason behind a decrease in T ₁ in the ¹H NMR spectra. Neither can it explain the anomalous line broadening in ESR spectra under conditions of ¹O₂(¹_g) formation in the systems V^(V)/H₂O₂/AcOH and Mo^(VI)/H₂O₂/H₂O. Ab initio calculations showed that it is principle possible that the ³O₄(³·^- _g-¹_g) molecule exists in a snake-like form and is formed by the reaction between ³O₂(³·^- _g) and ¹O₂(¹_g), which is the product of H₂O₂ decomposition in the systems V^(V)/H₂O₂/AcOH and Mo^(IV)/H₂O₂/H₂O. The interaction of ¹O₂ with the ·OOH radical is exothermic (Q = 2.30 kcal/mol) and leads to the formation of ·OOOOH. It is assumed that the paramagnetic species of type ·OOOOH or ³O₄(³ A ₁) that is formed in the reaction might be responsible for the spectral effects observed.     

Copper(II), nickel(II), and zinc(II) complexes with <Emphasis Type="Italic">o</Emphasis>-tozylaminobenzaldehyde 4,6-dimethylpyrimidyl hydrazone

o-Tosylaminobenzaldehyde dimethylpyrimidyl hydrazone and its copper(II), nickel(II), and zinc(II) complexesare synthesized and studied. According to the X-ray diffraction data, the zinc(II) complex has the structure of a tetragonal pyramid with the N₃O donor ligand environment. According to EPR and magnetochemistry data, the copper(II) complex has a similar structure of the chelate core. In the nickel(II) complex, the solvent molecule completes the coordination core to an octahedron.