Search results for "Lacunary function"
showing 6 items of 6 documents
Synthesis, Characterization, and Catalysis of β3-[(CoIIO4)W11O31(O2)4],10- the First Keggin-Based True Heteropoly Dioxygen (Peroxo) Anion. Spectrosco…
1999
Reactions of hydrogen peroxide with several lacunary polyoxometalates of the 1:11 series, XW11O39m- (X = Co3+, Ga3+, Fe3+, Si4+, and P5+), are reported. Synthetic pathways to new polyoxotungstates incorporating dioxygen moieties (peroxo and/or superoxo) are developed. The key step involves treating lacunary precursors with H2O2 in strongly buffered aqueous solutions. Upon reaction of H2O2 with α-[Co3+W11O39],9- (a) the central tetrahedral Co3+ is reduced to Co2+ and (b) each of the four unshared oxygens surrounding the vacancy are replaced by a peroxide group, yielding salts of the tetraperoxide anion β3-[(Co2+O4)W11O31(O2)4]10- (1). These results are unequivocally established by a combinat…
On lacunary Toeplitz determinants
2014
By using Riemann--Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants $\det_N\big[ c_{\ell_a-m_b}[f] \big]$ generated by holomorhpic symbols, where $\ell_a=a$ (resp. $m_b=b$) except for a finite subset of indices $a=h_1,\dots, h_n$ (resp. $b=t_1,\dots, t_r$). In addition to the usual Szeg\"{o} asymptotics, our answer involves a determinant of size $n+r$.
Comparative study of the arterial and lacunary systems of the ventricular myocardium of elasmobranch and teleost fishes.
1983
The typical fish heart has a spongy trabeculated ventricular myocardium (spongiosa) supplied by the venous blood of the intertrabecular spaces (lacunae); hence it is called a "venous heart." However, in some fishes a more complex ventricular muscle is found (mixed type), in which the spongiosa is covered by an outer layer of densely arranged myocardial bundles (compacta). The compacta receives oxygenated blood from the coronary vessels. The objective of this study was to investigate relations between myoarchitecture and blood supply with an emphasis on the hitherto unexplored, putative vascular connections between the arterial and the lacunary circuits. Using histological methods combined w…
Synthesis and Characterization of New Keggin-Based Structure Tungstocobaltates: K9[Co3+W11O39] and its Vanadium Derivatives, K8[Co2+W11V4+O40], K7[Co…
1995
Abstract Good yield synthesis of the potassium salts of four new interrelated : olyoxometalates, [Co3+W11O39]9-(I), [Co2+W11V4+O4]8-(II), [Co2+W11V5+O40]7-(III), and [Co3+W11V5+O40]6-(IV), are reported. The title compounds have been characterized by IR and UV-Vis.-NIR spectroscopies, cyclic voltammetry and magnetic measurements. IR spectra confirm that I has the lacunary structure of an undecatungstate anion, while II through IV have a substituted α-Keggin structure with the vanadium atom located at an octahedral site replacing one tungsten atom. Optical data confirm the oxidation states for both, the Co and V atoms, as formulated for I through IV.
Lacunary Bifurcation of Multiple Solutions of Nonlinear Eigenvalue Problems
1991
In order to describe the type of nonlinear eigenvalue problems we are going to discuss, consider a densely defined closed linear operator T in a real Hilbert space H and let H1 be the Hilbert space which consists of the domain of T together with the graph norm. Also, let H 1 * be the dual space of H1 and denote the dual operator corresponding to T: H1 → H by T’:H → H 1 * . Since H1 is dense in H, we may view H as a subspace of H1, and then the scalar product (·,·) on H and the dual pairing on H1 × H 1 * coincide on H1 × H.
Monolacunary Keggin polyoxometalates connected to ten 4d or 4f metal atoms.
2013
The rational self-assembly of mono-lacunary Keggin clusters with 4d and 4f metal salts via a conventional method has yielded two novel polyoxometalate-based 4d-4f heterometallic compounds containing lacunary Keggin anions connected to ten metal atoms: {[Ag{Ag2(H2O)4}{Ln(H2O)6}2H ⊂ {SiW11Ln(H2O)4O39}2]·nH2O (Ln = Ce and n = 7 for 1, Ln = Pr and n = 3 for 2). Their structures were determined by single crystal X-ray diffraction analyses and further characterized by elemental analyses, IR spectra, and thermogravimetric (TG) analyses. A structural feature in 1 and 2 is that each [SiW11O39](8-) cluster (SiW11) is connected to ten metals (five Ag(+) and five Ln(3+) cations), representing the highe…