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 \(\tilde f^{(1,1)} (x,y)\) .     

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.     

Synthesis,characterization and antioxidant,antibacterial activity Zn2+, Cu2+, Ni2+ and Co2+, complexes of ligand [2-(thiophen-2-yl)-1-(thiophen-2-ylmethyl)-1H-benzo[d]imidazole]

New metal complexes of (Zn(II), Co(II), Ni(II) and Cu(II)) based on the ligand 2-(thiophen-2-yl)-1-(thiophen-2-ylmethyl)-1H-benzo[d]imidazole] were synthesized, whose structures were determined with the different spectroscopic techniques ¹H NMR,¹³C NMR, FT-IR, UV–Visible and by mass spectrometry. The thermal analysis was performed by TG-DTA. The antioxidant activity of the ligand and its complexes was evaluated by DPPH (2,2-diphenyl-1-picrylhydrazyl) method, in comparison with the synthetic antioxidant, ascorbic acid. The results obtained showed that the antioxidant activity of the ligand and its complexes is moderate and that the copper complex has a high activity that exceeds that of ascorbic acid. Antimicrobial activity of the ligand and its metal complexes was studied against two Gram-positive bacteria: Bacillus subtilis ILP1428B, Staphylococcus aureus CIP543154 and two Gram-negative bacteria: Pseudomonas aeruginosa ATCC27653, Escherichia coli CIP5412 (American Type Culture Collection)the activity data show that the metal complexes are more potent than the free ligand.     

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.     

Allostery in a disordered protein: oxidative modifications to α-synuclein act distally to regulate membrane binding

Both oxidative stress and aggregation of the protein α-synuclein (aS) have been implicated as key factors in the etiology of Parkinson's disease. Specifically, oxidative modifications to aS disrupt its binding to lipid membranes, an interaction considered critical to its native function. Here we seek to provide a mechanistic explanation for this phenomenon by investigating the effects of oxidative nitration of tyrosine residues on the structure of aS and its interaction with lipid membranes. Membrane binding is mediated by the first ～95 residues of aS. We find that nitration of the single tyrosine (Y39) in this domain disrupts binding due to electrostatic repulsion. Moreover, we observe that nitration of the three tyrosines (Y125/133/136) in the C-terminal domain is equally effective in perturbing binding, an intriguing result given that the C-terminus is not thought to interact directly with the lipid bilayer. Our investigations show that tyrosine nitration results in a change of the conformational states populated by aS in solution, with the most prominent changes occurring in the C-terminal region. These results lead us to suggest that nitration of Y125/133/136 reduces the membrane-binding affinity of aS through allosteric coupling by altering the ensemble of conformational states and depopulating those capable of membrane binding. While allostery is a well-established concept for structured proteins, it has only recently been discussed in the context of disordered proteins. We propose that allosteric regulation through modification of specific residues in, or ligand binding to, the C-terminus may even be a general mechanism for modulating aS function.     

On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its fourier series

In a recent paper Lal and Yadov [4] obtained a theorem on the degree of approximation for a function belonging to the Lipschitz class Lipα using the product of the Cesàro and Euler means of order one of its Fourier series. In this paper we extend this result to any regular Hausdorff matrix for the same class of functions.