On inclusion theorems for absolute matrix summability methods, corrections: [J. Math. Anal. Appl. 238 (1999) 82-90]

We modify some of the conditions of the theorem to make it more applicable.     

Approximation by Nörlund means of double fourier series to continuous functions in two variables

We study the rate of uniform approximation by Nörlund means of the rectangular partial sums of double Fourier series of continuous functionsf(x, y), 2π-periodic in each variable. The results are given in terms of the modulus of symmetric smoothness defined by $$\begin{gathered} \omega _2 \left( {f,\delta _1 ,\delta _2 } \right) = \mathop {\sup }\limits_{x,y} \mathop {\sup }\limits_{\left| u \right| \leqslant \delta _1 ,\left| v \right| \leqslant \delta _2 } \left| {f\left( {x + u,y + v} \right)} \right. + f\left( {x + u,y - v} \right) + f\left( {x - u,y + v} \right) \hfill \\ + \left. {f\left( {x - u,y - v} \right) + 4f\left( {x,y} \right)} \right| for \delta _1 ,\delta _2 \geqslant 0. \hfill \\ \end{gathered} $$ As a special case we obtain the rate of uniform approximation to functionsf(x,y) in Lip({α, β}), the Lipschitz class, and inZ({α, β}), the Zygmund class of ordersα andβ, 0<α,β ≤ l, as well as the rate of uniform approximation to the conjugate functions \(\tilde f^{(1,0)} (x,y), \tilde f^{(0,1)} (x,y)\) and \(\tilde f^{(1,1)} (x,y)\) .     

Hexadentate hydroxypyridonate iron chelators based on TREN-Me-3,2-HOPO: variation of cap size

TREN-Me-3,2-HOPO, TR322-Me-3,2-HOPO, TR332-Me-3,2-HOPO, and TRPN-Me-3,2-HOPO correspond to stepwise replacement of ethylene by propylene bridges. A series of tripodal, hexadentate hydroxypyridinone ligands are reported. These incorporate 1-methyl-3,2-hydroxypyridinone (Me-3,2-HOPO) bidentate chelating units for metal binding. They are varied by systematic enlargement of the capping scaffold which connects the binding units. The series of ligands and their iron complexes are reported. Single crystal X-ray structures are reported for the ferric complexes of all four tripodal ligands: FeTREN-Me-3,2-HOPO.0.375C(4)H(10)O.0.5CH(2)Cl(2) [P2(1)/n (No. 14), Z = 8, a = 20.478(3) A, b = 12.353(2) A, c = 27.360(3) A; beta = 91.60(1) degrees ]; FeTR322-Me-3,2-HOPO.CHCl(3).0.5C(6)H(14).CH(3)OH.0.5H(2)O [P2(1)/n (No. 14), Z = 4, a = 12.520(3) A, b = 22.577(5) A, c = 16.525(3) A; beta = 111.37(3) degrees ]; FeTR332-Me-3,2-HOPO.3.5CH(3)OH [C2/c (No. 15), Z = 8, a = 13.5294(3) A, b = 19.7831(4) A, c = 27.2439(4) A; beta = 101.15(3) degrees ]; FeTRPN-Me-3,2-HOPO.C(3)H(7)NO.2C(4)H(10)O [P1 (No. 2), Z = 2, a = 11.4891(2) A, b = 12.3583(2) A, c = 15.0473(2) A; alpha = 86.857(1) degrees, beta = 88.414(1) degrees, gamma = 70.124(1) degrees ]. The structures show the importance of intermolecular hydrogen bonds and the effect of cap enlargement to the stability and geometry of the metal complexes throughout the series. All protonation and iron complex formation constants have been determined from solution thermodynamic studies. The TREN-capped derivative is the most acidic, with a cumulative protonation constant, log beta(014), of 25.95. Corresponding values of 26.35, 26.93, and 27.53 were obtained for the TR322, TR332, and TRPN derivatives, respectively. The protonation constants and NMR spectroscopic data are interpreted as being due to the influence of specific hydrogen-bond interactions. The incremental enlargement of ligand size results in a decrease in iron-chelate stability, as reflected in the log beta(110) values of 26.8, 26.2, 26.42, and 24.48 for the TREN, TR322, TR332, and TRPN derivatives, respectively. The metal complex formation constants are also affected by the acidity of a proximal (non-metal-binding) amine in the complexes, a trend consistent with the effects of internal hydrogen bonding. The ferric complexes display reversible reduction potentials (measured relative to the normal hydrogen electrode (NHE)) between -0.170 and -0.223 V.     

Structural characterization of cardiolipin by tandem quadrupole and multiple-stage quadrupole ion-trap mass spectrometry with electrospray ionization

We report negative-ion electrospray tandem mass spectrometric methods for structural characterization of cardiolipin (CL), a four-acyl-chain phospholipid containing two distinct phosphatidyl moieties, of which structural assignment of the fatty acid residues attached to the glycerol backbones performed by low-energy CAD tandem mass spectrometry has not been previously described. The low-energy MS2-spectra of the [M - H]- and [M - 2H]2- ions obtained with ion-trap or with tandem quadrupole instrument combined with ion-trap MS3-spectra or with source CAD product-ion spectra provide complete structural information for CL characterization. The MS2-spectra of the [M - H]- ions contain two sets of prominent fragment ions that comprise a phosphatidic acid, a dehydrated phosphatidylglycerol, and a (phosphatidic acid + 136) anion. The substantial differences in the abundances of the two distinct phosphatidic anions observed in the MS2-spectra of the [M -H]- ions lead to the assignment of the phosphatidyl moieties attached to the 1' or 3' position of central glycerol. Upon further collisional dissociation, the MS3-spectra of the phosphatidic anions provide information to identify the fatty acyl substituents and their position in the glycerol backbone. The MS2-spectra of the [M - 2H]2- ions obtained with TSQ or ITMS contain complementary information to confirm structural assignment. The applications of the above methods in the differentiation of cardiolipin isomers and in the identification of complex cardiolipin species consisting of multiple molecular structures are also demonstrated.     

Branching spin chain dynamics

We study the dynamics of various branched spin chain systems. In such systems entanglement can be generated and distributed, providing an essential resource for teleportation or distributed quantum processing. We show in detail how simple operations can be employed at chosen times to change the subsequent dynamics of the branched spin chains, rendering the distributed entanglement more accessible.     

Non-anticipative representations of Banach space valued gaussian processes with respect to brownian motion

Necessary and sufficient conditions are found for the equivalence of the measures associated with (i) a Banach space valued Gaussian process, with mean 0, and (ii) a Bach space valued Brownian motion. The notion of a non-anticipative representation of (i) with respect to (ii) is defined and in the case of equivalence of the measures it is shown that such a representation exists and has an explicit stochastic integral form which is invertible. Theorems of Ershov on absolute continuity of measures associated with diffusion processes are extended to Banach space. Applications to infinite-dimensional filtering are considered.     

Levels of mineral nutrients in fresh- and frozen bulk hydrated biological specimens: A comparison of EDS data collected in the environmental SEM and a conventional cryo-SEM

Energy-dispersive X-ray microanalysis (EDS) was compared in fresh- and frozen bulk hydrated tissues using the Environmental SEM (ESEM) and conventional cryo-SEM, respectively. Analyses of globoid inclusions of Eucalyptus calophylla seed from two soil types demontsrated that higher levels of cations (K, Ca, Mg, Al, Fe, Mn, Cu, Zn) occurred in seeds from soils containing higher levels of Al, while EDS-detectable levels of S and P were dependent upon the techniques utilised. Cumulative changes in ESEM-EDS-detectable levels of S and P were characterised by collecting cumulative spectra from nutrient standards and compared with those for K. Progressive increases in K occurred and were consistent with an enriching effect. Levels of S and P increased during early analysis (40–60 sec live time) and decreased thereafter. The semi-conductive nature of biological samples, the loss of anions and gain of cations from the net negatively-charged electron interaction volume contributed to an electrochemical bias. These local modifications in fluid chemistry were reversible. Dehydration effects also occurred in stable, “wet‘ samples. These differences indicated that EDS in ESEM may be limited to cations rather than anions, and that changes in fluid electrochemistry and dehydration may affect the level and distribution of elements.     

Plasma Photocathodes

Plasma wakefield accelerators offer accelerating and focusing electric fields three to four orders of magnitude larger than state-of-the-art radiofrequency cavity-based accelerators. Plasma photocathodes can release ultracold electron populations within such plasma waves and thus open a path toward tunable production of well-defined, compact electron beams with normalized emittance and brightness many orders of magnitude better than state-of-the-art. Such beams will have far-reaching impact for applications such as light sources, but also open up new vistas on high energy and high field physics. This paper reviews the innovation of plasma photocathodes, and reports on the experimental progress, challenges, and future prospects of the approach. Details of the proof-of-concept demonstration of a plasma photocathode in 90° geometry at SLAC FACET within the E-210: Trojan Horse program are described. Using this experience, alongside theoretical and simulation-supported advances, an outlook is given on future realizations of plasma photocathodes such as the upcoming E-310: Trojan Horse-II program at FACET-II with prospects toward excellent witness beam parameter quality, tunability, and stability. Future installations of plasma photocathodes also at compact, hybrid plasma wakefield accelerators, will then boost capacities and open up novel capabilities for experiments at the forefront of interaction of high brightness electron and photon beams.