Complementarity forms of theorems of Lyapunov and Stein, and related results

The well-known Lyapunov's theorem in matrix theory / continuous dynamical systems asserts that a (complex) square matrix A is positive stable (i.e., all eigenvalues lie in the open right-half plane) if and only if there exists a positive definite matrix X such that AX+XA^* is positive definite. In this paper, we prove a complementarity form of this theorem: A is positive stable if and only if for any Hermitian matrix Q, there exists a positive semidefinite matrix X such that AX+XA^*+Q is positive semidefinite and X[AX+XA^*+Q]=0. By considering cone complementarity problems corresponding to linear transformations of the form I−S, we show that a (complex) matrix A has all eigenvalues in the open unit disk of the complex plane if and only if for every Hermitian matrix Q, there exists a positive semidefinite matrix X such that X−AXA^*+Q is positive semidefinite and X[X−AXA^*+Q]=0. By specializing Q (to −I), we deduce the well known Stein's theorem in discrete linear dynamical systems: A has all eigenvalues in the open unit disk if and only if there exists a positive definite matrix X such that X−AXA^* is positive definite.     

Impurity profile of macitentan in tablet dosage form using a stability-indicating high performance liquid chromatography method and forced degradation study

Macitentan (MAC) is a pulmonary arterial hypertension (PAH) drug marketed as a tablet and often has stability issues in the final dosage form. Quantitative determination of MAC and its associated impurities in tablet dosage form has not been previously reported. This study quantified impurities present in Macitentan tablets using a binary solvent-based gradient elution method using reversed phase-high performance liquid chromatography. The developed method was validated per International Conference on Harmonization (ICH) guidelines and the drug product was subjected to forced degradation studies to evaluate stability. The developed method efficiently separated the drug and impurities (48 min) without interference from solvents, excipients, or other impurities. The developed method met all guidelines in all characteristics with recoveries ranging from 85%-115%, linearity with r² ≥ 0.9966, and substantial robustness. The stability-indicating nature of the method was evaluated using stressed conditions (hydrolysis:1 N HCl at 80℃/15 min; 1 N NaOH at 25℃/45 min; humidity stress (90% relative humidity) at 25℃ for 24 h, oxidation:at 6% (v/v) H₂O₂, 80℃/15 min, thermolysis:at 105℃/16 h and photolysis:UV light at 200 Wh/m²; Fluorescent light at 1.2 million luxh). Forced degradation experiments showed that the developed method was effective for impurity profiling. All stressed samples were assayed and mass balance was>96%. Forced degradation results indicated that MAC tablets were sensitive to hydrolysis (acid and alkali) and thermal conditions. The developed method is suitable for both assay and impurity determination, which is applicable to the pharmaceutical industry.     

Non-isothermal crystallization kinetics and degradation kinetics studies on barium thioglycolate end-capped poly(ε-caprolactone)

Journal of Thermal Analysis and Calorimetry - The poly(ε-caprolactone) (PCL) was synthesized by ring-opening polymerization at 160 °C under nitrogen atmosphere for 2 h...     

Discovery of a Novel Mycobacterial F-ATP Synthase Inhibitor and its Potency in Combination with Diarylquinolines

The F₁F_O-ATP synthase is required for growth and viability of Mycobacterium tuberculosis and is a validated clinical target. A mycobacterium-specific loop of the enzyme's rotary γ subunit plays a role in the coupling of ATP synthesis within the enzyme complex. We report the discovery of a novel antimycobacterial, termed GaMF1, that targets this γ subunit loop. Biochemical and NMR studies show that GaMF1 inhibits ATP synthase activity by binding to the loop. GaMF1 is bactericidal and is active against multidrug- as well as bedaquiline-resistant strains. Chemistry efforts on the scaffold revealed a dynamic structure activity relationship and delivered analogues with nanomolar potencies. Combining GaMF1 with bedaquiline or novel diarylquinoline analogues showed potentiation without inducing genotoxicity or phenotypic changes in a human embryonic stem cell reporter assay. These results suggest that GaMF1 presents an attractive lead for the discovery of a novel class of anti-tuberculosis F-ATP synthase inhibitors.     

Rearrangements in Scholl Reaction

Rearrangements in Scholl reaction are mostly serendipitous. The design of molecular precursors is what seems to guide the course of rearrangement. This review consolidates different classes of precursors used in Scholl reaction and their accompanying rearrangements that include aryl migration, migration followed by cyclization and skeletal rearrangements involving ring expansion, ring contraction and both, under the reaction conditions. The attempt in collating heretofore-reported examples in this review is to guide designing appropriate precursors to predictably achieve complex molecular structures or nanographenes or defect-nanographenes via rearrangement.     

Coloring Quasicrystals with Prescribed Symmetries and Frequencies

We show how to color the tiles in a heirarchical tiling system so that the resulting system is not only repetitive (i.e., has the local isomorphism property) but has prescribed color symmetries as well. Received March 9, 1998, and in revised form August 3, 1998.     

Deformations of Algebras Constructed using Quantum Stochastic Calculus

Deformations of associative algebras in which time is the deformation parameter are constructed using quantum stochastic flows in which the usual multiplicativity requirement is replaced by multiplicativity with respect to the deformed multiplication. The theory is restricted by a commutativity requirement on the structure maps of the flow, but examples which can be constructed in this way include the noncommutative torus and the Weyl–Moyal deformation.     

金催化肌酸酐与靛红的加成反应:一种可持续的绿色方法用于非对映选择合成3-取代的3-羟基靛红

报道了水介质中金催化肌酸酐与不同靛红之间的醛醇缩合反应.该法无需繁杂的溶剂萃取和柱色谱技术,只需简单的过滤即可将产物分离出来,因而操作简单.通过较宽范围的靛红衍生物的反应,均可高产率并完全地制取相应的顺式醛醇缩合产物,因此该法表现出较高的通用性.还将该合成策略进一步拓展至靛红,肌酸酐和丙二腈的串联反应,可高产率、完全的制取反式多组分产物.采用分光光度法测定了合成产物的抗氧化性能,结果表明,与标准物相比,含有卤素原子的三个化合物(2c,2d和2e)表现出最高的活性.