Interval versions of Milne’s multistep methods

In the literature, most known sequence transformations can be written as a ratio of two determinants. But, it is not always this case. One exception is that the sequence transformation proposed by Brezinski, Durbin, and Redivo-Zaglia cannot be expressed as a ratio of two determinants. Motivated by this, we will introduce a new algebraic tool—pfaffians, instead of determinants in the paper. It turns out that Brezinski–Durbin–Redivo-Zaglia’s transformation can be expressed as a ratio of two pfaffians. To the best of our knowledge, this is the first time to introduce pfaffians in the expressions of sequence transformations. Furthermore, an extended transformation of high order is presented in terms of pfaffians and a new convergence acceleration algorithm for implementing the transformation is constructed. Then, the Lax pair of the recursive algorithm is obtained which implies that the algorithm is integrable. Numerical examples with applications of the algorithm are also presented.     

Planarity of heteroaryldithiocarbazic acid derivatives showing tuberculostatic activity. III. Mono‐ and diesters of 3‐(pyrazin‐2‐ylcarbonyl)dithiocarbazic acid

Methyl 2‐(pyrazin‐2‐ylcarbonyl)hydrazinecarbodithioate, C₇H₈N₄OS₂, (E1), N′‐[bis(methylsulfanyl)methylidene]pyrazine‐2‐carbohydrazide, C₈H₁₀N₄OS₂, (F1), N′‐[bis(methylsulfanyl)methylidene]‐6‐methoxypyrazine‐2‐carbohydrazide, C₉H₁₂N₄O₂S₂, (F2), and methyl 1‐methyl‐2‐(pyrazin‐2‐ylcarbonyl)hydrazinecarbodithioate, C₈H₁₀N₄OS₂, (G1), can be considered as derivatives of classical (thio)amide‐type tuberculostatics, and all are moderately active against Mycobacterium tuberculosis. This study was undertaken in a search for relationships between activity and specific intramolecular interactions, especially conjugations and hydrogen‐bond contacts, and the molecular structures were compared with respective amine analogues, also active against the pathogen. Despite the differences between the amine and carbonyl groups with opposite functions in the hydrogen bond, the two types of structure show a surprisingly similar planar geometry, mostly due to the conjugations aided by the bifurcated intramolecular hydrogen‐bond contact between the N—H group of the central hydrazide group as donor and a pyrazine N atom and an S atom of the dithio function as acceptors. Planarity was suggested to be crucial for the tuberculostatic activity of these compounds. The N‐methylated derivative (G1) showed a significant twist at the N—N bond [torsion angle = −121.9 (3)°] due to the methyl substitution, which precludes an intramolecular N—H...S contact and the planarity of the whole molecule. Nonetheless, the compound shows moderate tuberculostatic activity.     

Effect of Li<Superscript>+</Superscript> stabilization on smectite intercalate properties

Smectites are widely used minerals whose structure and properties can be modified and controlled. The aim of this study was to improve the sorption capacity and accessibility of interlayer (interpacket) spaces by reducing the pillar density in Chmielnik smectite. The micropore volume increases by increasing one of their dimensions, which is determined as the distance between pillars. This aim was achieved by lowering the resultant packet charge. Changes in intercalate structure and microporosity were studied using X-ray diffractometry and Ar sorption at–196°C. The Li/Na smectite ratio is crucial for modifying the smectite properties, particularly those associated with mineral microporosity. The behavior of the samples with the same interlayer cation composition exhibited two distinct trends. The first one is a decrease in the specific surface value (volume of micropores) accompanied by an increase in the amount of Li in the ion interlayer composition. The second one is a decline in the specific surface (volume of micropores) when the calcination temperature rises.     

A convenient method for the synthesis of 2-[(5-benzyl-1,3-thiazol-2-yl)imino]-1,3-thiazolidin-4-one derivatives

It was found that the reaction of 2-chloroacetamido/chloropropioamido-5-benzylthiazole with potassium thiocyanate gave, via rearrangement, 2-[(5-benzyl-1,3-thiazol-2-yl)imino]-1,3-thiazolidin-4-ones.     

Water-window microscopy using a compact, laser-plasma SXR source based on a double-stream gas-puff target

We report on a compact, desktop size, laboratory type microscopy setup, based on a short wavelength gas puff target soft X-ray source, which emits incoherent radiation in “water-window” spectral range. The microscope employs a Wolter type I reflective objective and allows capturing magnified images of objects with ~1-μm spatial resolution and exposure time as low as 5 s. A detailed characterization and optimization of both the source and the microscope setups are presented and discussed.     

Onsite hybridization between Ce 4f and 5d states as the indicator of the transition from Kondo insulator to metallic state in CeRhSb

We discuss and determine the conditions under which a Kondo-insulator phase is stable. We show for CeRhSb that the dependence of the onsite hybridization energy Vdf between the Ce 5d and Ce 4f states on the number of valence electrons or the unit cell volume is decisive for the hybridization Kondo gap formation. We also propose the method for determining the energy Vdf from the ab initio calculations. This approach supplies an accurate Kondo-insulator-metal transition in agreement with the recent experimental data.