A theorem on products of matrices

A new result on products of matrices is proved in the following theorem: let M_i (i=1,2,…) be a bounded sequence of square matrices, and K be the l.u.b. of the spectral radii ρ(M_i). Then for any positive number ε there is a constant A and an ordering p(j) (j = 1,2,…) of the matrices such that

$\text{∏}\text{j=1}\text{n}\text{M}{}_{\mathrm{p(j)}}\text{?A·(K+ε)}{}^{\mathrm{n}}\text{(n = 1,2,…)}$

. The ordering is well defined by p(j), a one-to-one mapping on the set of positive integers. In general the inequality does not hold for any ordering p(j) (a counterexample is provided); however, some sufficient conditions are given for the result to remain true irrespective of the order of the matrices.     

An improved synthesis of cyclopropanes from stabilized phosphonates and 1,2-dioxines

Addition of stabilized Horner-Wadsworth-Emmons (HWE) phosphonates to substituted 1,2-dioxines leads to diastereomerically pure di- and trisubstituted cyclopropanes in high yields and represents a viable alternative to ylides in the cyclopropanation reaction involving 1,2-dioxines. While yields are comparable, reaction times with these stabilized phosphonates were accelerated and the diastereoselectivity for this cyclopropanation reaction was significantly greater than for the previously reported examples employing ylides.     

Interactions magnétiques dans des groupements binucléaires du Ruthénium +V

The cationic ordering in the $\text{Ba}\text{M}{}_{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{Ru}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{O}{}_3\text{(M =}\text{Mg, Ca, Cd, Sr}\text{)}$ oxides which crystallize with the 6H structure gives rise to Ru⁵⁺Ru⁵⁺ pairs in (Ru₂O₉) clusters. The magnetic properties have been analyzed on the basis of the Heisenberg-Dirac-Van Vleck model: The d electrons are localized on each Ru⁵⁺ ion and interact strongly through antiferromagnetic exchange. The susceptibility curves agree with the H.D.V.V. model. The values of the exchange integrals have been determined by fitting the experimental values.     

Amine-terminated dendrimers as biomimetic templates for silica nanosphere formation

In diatoms, silica synthesis occurs by use of complex posttranslationally modified peptides, termed silaffins, and highly complex biological polyamine structures. Silaffin peptides have lysine residues that are modified to long-chain polyamine moieties of N-methyl derivatives of polypropylenimine to drive silica synthesis at slightly acidic pH conditions. Using polypropylenimine (PPI) and PAMAM amine-terminated dendrimers as a biomimetic analogue of the polyamine modifications of silaffins, we have demonstrated the condensation of silica nanospheres. We have shown that the dendrimers react in an amine concentration-dependent fashion yielding silica nanospheres with a distinct size distribution reminiscent of the structures produced from both the modified and nonmodified peptides extracted from diatoms. Additionally, the templates were encapsulated by the growing nanospheres and precipitated from solution in a manner similar to that previously described for the bioactive peptides and polyamines.     

The Yellow Polymorphs of Mercuric Iodide (HgI2)

HgI₂ crystallizes under ambient conditions from various solvents and by sublimation into three concomitant polymorphs whose colors are red, orange, and yellow. The orange and yellow phases are metastable and transform into the red phase when touched. A phase transition from red to yellow occurs at 400 K. The reverse transition from yellow to red shows a huge hysteresis. We established that the structures of the metastable yellow^M phase (determined by single‐crystal X‐ray diffraction) and the high‐temperature yellow^HT phase (determined by powder synchrotron X‐ray diffraction and second‐harmonic generation) are different, albeit closely related. Both show analogous packings of I? Hg? I molecules, which are straight in the first and bent with an angle of ca. 160° in the second. The red and orange phases are tetrahedral semiconductor structures that sublime even at room temperature. The growth of the yellow^M phase from 2‐chloroethanol and the kinetics of the reconstructive phase transition red to yellow^HT and back were studied by optical microscopy, Raman spectroscopy in solution, luminescence, and powder synchrotron X‐ray diffraction as a function of time at various temperatures. Both yellow phases grow by accretion of HgI₂ molecules, present in the solution or liberated from the red crystals, on the surface of the crystal. In contrast, the reverse transformation from yellow to red occurs in the bulk of the crystal, presumably by migration of Hg in the packing of I and subsequent rearrangement of I. The displacement parameters of Hg in both structures are considerably larger than those of I and apparently not dominated by disorder effects.     

Absolute line intensity measurements of hot bands for carbonyl sulfide at 12 microm

Using diode-laser spectroscopy, the intensities of 58 lines of the v(1) + v(1/2) - v(1/2) band and 36 lines of the 2v(1) - v(1) band of OCS have been measured. The corresponding band strengths S(0)(v) and the vibrational transition dipoles micro(v) have been derived through least squares fitting of these individual intensities. The band strengths values have been determined with a precision better than 2.5%.     

Ziziphus nummularia: A Comprehensive Review of Its Phytochemical Constituents and Pharmacological Properties

Ziziphus nummularia, a small bush of the Rhamnaceae family, has been widely used in traditional folk medicine, is rich in bioactive molecules, and has many reported pharmacological and therapeutic properties. Objective: To gather the current knowledge related to the medicinal characteristics of Z. nummularia. Specifically, its phytochemical contents and pharmacological activities in the treatment of various diseases such as cancer, diabetes, and cardiovascular diseases, are discussed. Methods: Major scientific literature databases, including PubMed, Scopus, ScienceDirect, SciFinder, Chemical Abstracts, Medicinal and Aromatic Plants Abstracts, Henriette’s Herbal Homepage, Dr. Duke’s Phytochemical and Ethnobotanical Databases, were searched to retrieve articles related to the review subject. General web searches using Google and Google scholar were also utilized. The search period covered articles published between 1980 and the end of October 2021.The search used the keywords ‘Ziziphus nummularia’, AND (‘phytochemical content’, ‘pharmacological properties, or activities, or effects, or roles’, ‘anti-inflammatory’, ‘anti-drought’, ‘anti-thermal’, ‘anthelmintic’, ‘antidiabetic’,’ anticancer’, ‘anticholinesterase’, ‘antimicrobial’, ‘sedative’, ‘antipyretic’, ‘analgesic’, or ‘gastrointestinal’). Results: This plant is rich in characteristic alkaloids, especially cyclopeptide alkaloids such as nummularine-M. Other phytochemicals, including flavonoids, saponins, glycosides, tannins, and phenolic compounds, are also present. These phytochemicals are responsible for the reported pharmacological properties of Z. nummularia, including anti-inflammatory, antioxidant, antimicrobial, anthelmintic, antidiabetic, anticancer, analgesic, and gastrointestinal activities. In addition, Z. nummularia has anti-drought and anti-thermal characteristics. Conclusion: Research into the phytochemical and pharmacological properties of Z. nummularia has demonstrated that this plant is a rich source of novel bioactive compounds. So far, Z. nummularia has shown a varied pharmacological profile (antioxidant, anticancer, anti-inflammatory, and cardioprotective), warranting further research to uncover the therapeutic potential of the bioactives of this plant. Taken together, Z. nummularia may represent a new potential target for the discovery of new drug leads.     

Origanum syriacum Phytochemistry and Pharmacological Properties: A Comprehensive Review

Herbal medicine has been gaining special interest as an alternative choice of treatment for several diseases, being generally accessible, cost-effective and safe, with fewer side-effects compared to chemically synthesized medicines. Over 25% of drugs worldwide are derived from plants, and surveys have shown that, when available, herbal medicine is the preferred choice of treatment. Origanum syriacum (Lamiaceae) is a widely used medicinal plant in the Middle East, both as a home and a folk remedy, and in the food and beverage industry. Origanum syriacum contains numerous phytochemical compounds, including flavonoids, phenols, essential oils, and many others. Because of its bioactive compounds, O. syriacum possesses antioxidant, antimicrobial, and antiparasitic capacities. In addition, it can be beneficial in the treatment of various diseases such as cancer, neurodegenerative disorders, and peptic ulcers. In this review, the chemical compositions of different types of extracts and essential oils from this herb will first be specified. Then, the pharmacological uses of these extracts and essential oils in various contexts and diseases will be discussed, putting emphasis on their efficacy and safety. Finally, the cellular and molecular mechanisms of O. syriacum phytochemicals in disease treatment will be described as a basis for further investigation into the plant’s pharmacological role.     

Folding Free Energy Determination of an RNA Three-Way Junction Using Fluctuation Theorems

Nonequilibrium work relations and fluctuation theorems permit us to extract equilibrium information from nonequilibrium measurements. They find application in single-molecule pulling experiments where molecular free energies can be determined from irreversible work measurements by using unidirectional (e.g., Jarzynski’s equality) and bidirectional (e.g., Crooks fluctuation theorem and Bennet’s acceptance ratio (BAR)) methods. However, irreversibility and the finite number of pulls limit their applicability: the higher the dissipation, the larger the number of pulls necessary to estimate ΔG within a few kBT. Here, we revisit pulling experiments on an RNA three-way junction (3WJ) that exhibits significant dissipation and work-distribution long tails upon mechanical unfolding. While bidirectional methods are more predictive, unidirectional methods are strongly biased. We also consider a cyclic protocol that combines the forward and reverse work values to increase the statistics of the measurements. For a fixed total experimental time, faster pulling rates permit us to efficiently sample rare events and reduce the bias, compensating for the increased dissipation. This analysis provides a more stringent test of the fluctuation theorem in the large irreversibility regime.     

Effects of Two Natural Bisbenzylisoquinolines,Curine and Guattegaumerine,Extracted from Isolona hexaloba on Rhodamine Efflux by Abcb1b from Rat Glycocholic-Acid-Resistant Hepatocarcinoma Cells

To develop new therapeutic molecules, it is essential to understand the biological effects and targets of clinically relevant compounds. In this article, we describe the extraction and characterization of two alkaloids from the roots of Isolona hexaloba—curine and guattegaumerine. The effect of these alkaloids on the multidrug efflux pump ABCB1 (MDR1/P-Glycoprotein) and their antiproliferative properties were studied. Compared to verapamil, a widely used inhibitor of P-gp, curine and guattegaumerine were found to be weak inhibitors of MDR1/P-Glycoprotein. The highest inhibition of efflux produced by verapamil disappeared in the presence of curine or guattegaumerine as competitors, and the most pronounced effect was achieved with curine. Altogether, this work has provided new insights into the biological effects of these alkaloids on the rat Mdr1b P-gp efflux mechanism and would be beneficial in the design of potent P-gp inhibitors.