Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices

Two widely used methods for computing matrix exponentials and matrix logarithms are, respectively, the scaling and squaring and the inverse scaling and squaring. Both methods become effective when combined with Padé approximation. This paper deals with the computation of exponentials of skew-symmetric matrices and logarithms of orthogonal matrices. Our main goal is to improve these two methods by exploiting the special structure of skew-symmetric and orthogonal matrices. Geometric features of the matrix exponential and logarithm and extensions to the special Euclidean group of rigid motions are also addressed.     

Open tubular liquid chromatography: Recent advances and future trends

Nano-liquid chromatography (nanoLC) is gaining significant attention as a primary analytical technique across various scientific domains. Unlike conventional high-performance LC, nanoLC utilizes columns with inner diameters (i.ds.) usually ranging from 10 to 150 μm and operates at mobile phase flow rates between 10 and 1000 nl/min, offering improved chromatographic performance and detectability. Currently, most exploration of nanoLC has focused on particle-packed columns. Although open tubular LC (OTLC) can provide superior performance, optimized OTLC columns require very narrow i.ds. (< 10 μm) and demand challenging instrumentation. At the moment, these challenges have limited the success of OTLC. Nevertheless, remarkable progress has been made in developing and utilizing OTLC systems featuring narrow columns (< 2 μm). Additionally, significant efforts have been made to explore larger columns (10–75 μm i.d), demonstrating practical applicability in many situations. Due to their perceived advantages, interest in OTLC has resurged in the last two decades. This review provides an updated outlook on the latest developments in OTLC, focusing on instrumental challenges, achievements, and advancements in column technology. Moreover, it outlines selected applications that illustrate the potential of OTLC for performing targeted and untargeted studies.     

Solvent dependent conformational isomerism and ligand oxidation of novel Ru(II) cyclen complexes

The synthesis of cis-[Ru(II)(cyclen)(L)(x)](n+) (cyclen = 1,4,7,10-tetraazacyclododecane and L = 2,2'-bipyridine (bpy), phenanthroline (phen) or 4-cyanopyridinium (4-NCpyH(+))) is reported. The freshly prepared complexes are stable in aprotic solvents and cyclen undergoes oxidative dehydrogenation reaction at high pH. These compounds also present solvent dependent conformational isomerization.     

Twistor diagrams for spinning massless free fields

A set of simple identities is utilized to build up new projective twistor diagrams for massless free fields of arbitrary spin in real Minkowski space. It is effectively shown that the inner structure of the configurations which arise out of implementing the relevant techniques has characteristics that are different from those of the conventional diagrams associated with the Kirchoff-D'Adhemar-Penrose integral expressions. A nonhomogeneous version of the configurations is also provided.     

Pharmaceutical approaches involving carvedilol characterization,compatibility with different excipients and kinetic studies

This study was performed to investigate the physical–chemical characteristics of carvedilol (CRV), complemented by compatibility studies with a great variety of pharmaceutical excipients. Thermogravimetry and differential scanning calorimetry, supported by diffuse reflectance infrared fourier transform spectroscopy (DRIFT), X-ray powder diffraction, and scanning electron microscopy (SEM) were selected as the solid-state techniques for the intended analyses. In addition, non-isothermal methods were employed to investigate kinetic data of CRV decomposition process under nitrogen and air atmospheres. CRV is characterized by an endothermic sharp event (T _peak = 389.81 K and ΔH _fusion of ?176.28 J g^?1) and a thermal decomposition behavior in two stages, totalizing 98 % of mass loss. The CRV pattern diffraction presents prominent peaks at 2θ: 5.92°, 14.90°, 18.62°, 24.47°, and 26.30°, and the DRIFT spectrum showed the main characteristics bands for CRV chemical functional groups. The SEM photomicrographs demonstrate that CRV is characterized by irregular blocky shaped crystals. Zero order kinetics was determined by Ozawa method in both nitrogen and air atmospheres. The compatibility results showed no evidence of any incompatibility among CRV and all the excipients analyzed.     

Characterization and adsorption capacity of Brazilian kaolin

Journal of Radioanalytical and Nuclear Chemistry - This study has evaluated chemical, radiological composition and determined the cation exchange capacity (CEC) for three commercially available...     

Iridium and Rhodium as Permanent Chemical Modifiers for the Determination of Ag, As, Bi, Cd, and Sb by Electrothermal Atomic Absorption Spectrometry

Performance of graphite platforms coated with Ir, Rh, and a mixture of both, as permanent modifiers for Ag, As, Bi, Cd, and Sb, was evaluated. The coating process is very simple: a solution containing Ir, Rh, or a mixture of both is pipetted on the platform inserted in a graphite tube, and this is submitted to a temperature program. High pyrolysis temperatures are allowed, especially for As and Bi, 1400°C, in the Ir + Rh-coated platform. The sensitivity remains about the same for all analytes with different coatings, except for As in the Ir-coated platform, for which a remarkable gain was obtained in comparison to the other coatings. The lifetimes of the treated tubes were in the range 50 to more than 1000 cycles, being especially long for Sb and Ag in the Rh-coated platform, more than 600 and 1000 cycles, respectively. The Rh coating could not be used for Bi and Cd. Analysis of a certified reference water and of acid oyster tissue digests showed the absence of interference and good precision. Advantages of the permanent coatings are the possibility of low blanks byin situcleaning of the modifier and shorter analysis time.     

Synthesis of modified vermiculite by interaction with aromatic heterocyclic amines

Vermiculite of general formula [Si_6.85Al_1.15][Mg_4.68Al_0.51Fe_0.63]O₂₀(OH)₄Ca_0.128Na_0.032K_0.094 reacted with heteroaromatic amines α-, β-, and γ-picolines from aqueous solution. The products were characterized by elemental analysis, infrared spectroscopy, and X-ray diffraction. The intercalated nanocompounds maintained the crystallinity and changed the original interlayer distance of 1422 pm to 1474, 1456, and 1474 pm, for the sequence of the guest picoline molecules. Natural and intercalated vermiculite can remove copper at the solid/liquid interface; removal 0.40 mmol g⁻¹ was obtained for the original matrix, and 1.10, 0.92, and 1.33 mmol g⁻¹ for the intercalated forms. These values are near the capacity of cation exchange (CEC) of this clay mineral, which can be possibly used as source of copper removal from aqueous solution.     

Heuristic analysis of <Emphasis Type="Italic">Eucalyptus globulus</Emphasis> bark depolymerization via acid-liquefaction

A clear, direct and rapid analysis of the preliminary results concerning the acid liquefaction of Eucalyptus globulus’ bark is herein presented. The results led to a methodology for the selective liquefaction of hemicellulose and amorphous cellulose. Liquefaction was conducted at various temperatures, as well as different reaction times. The process results are heuristically explained in view of the experiments of ATR-FTIR, hydroxyl number, and acid value. The procedure method allows reusing the wastes arising from the paper industry. Valuable products and chemical building blocks from lignocellulosic biomass, mostly based on cellulose can be thus accessed.