Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Chemical Profiles and Pharmacological Properties with in Silico Studies on Elatostema papillosum Wedd

The current study attempted, for the first time, to qualitatively and quantitatively determine the phytochemical components of Elatostema papillosum methanol extract and their biological activities. The present study represents an effort to correlate our previously reported biological activities with a computational study, including molecular docking, and ADME/T (absorption, distribution, metabolism, and excretion/toxicity) analyses, to identify the phytochemicals that are potentially responsible for the antioxidant, antidepressant, anxiolytic, analgesic, and anti-inflammatory activities of this plant. In the gas chromatography-mass spectroscopy analysis, a total of 24 compounds were identified, seven of which were documented as being bioactive based on their binding affinities. These seven were subjected to molecular docking studies that were correlated with the pharmacological outcomes. Additionally, the ADME/T properties of these compounds were evaluated to determine their drug-like properties and toxicity levels. The seven selected, isolated compounds displayed favorable binding affinities to potassium channels, human serotonin receptor, cyclooxygenase-1 (COX-1), COX-2, nuclear factor (NF)-κB, and human peroxiredoxin 5 receptor proteins. Phytol acetate, and terpene compounds identified in E. papillosum displayed strong predictive binding affinities towards the human serotonin receptor. Furthermore, 3-trifluoroacetoxypentadecane showed a significant binding affinity for the KcsA potassium channel. Eicosanal showed the highest predicted binding affinity towards the human peroxiredoxin 5 receptor. All of these findings support the observed in vivo antidepressant and anxiolytic effects and the in vitro antioxidant effects observed for this extract. The identified compounds from E. papillosum showed the lowest binding affinities towards COX-1, COX-2, and NF-κB receptors, which indicated the inconsequential impacts of this extract against the activities of these three proteins. Overall, E. papillosum appears to be bioactive and could represent a potential source for the development of alternative medicines; however, further analytical experiments remain necessary.     

Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Donor-acceptor copolymers from cyclopentannulation polymerizations with dicyclopenta[cd,jk]pyrene and dicyclopenta[cd,lm] perylene acceptors

A series of donor-acceptor copolymers with dicyclopenta[cd,jk]pyrene and dicyclopenta[cd,lm]perylene acceptor units was prepared via palladium catalyzed cyclopenta-annulation reactions. The acceptor units were paired with diethynyl containing donor groups based on benzo[1,2-b:4,5-b’]dithiophene, thieno[3,2-b]thiophene, and 4-octyl-4H-dithieno[3,2-b:2′,3′-d]pyrrole to create six polymer variants. The cyclopentannulation polymerization resulted in copolymers with molecular weights (Mn) of 6–14 kDa and broad light absorption in the visible region with band gaps of 1.38–1.85 eV. The synthetic methodology, as well as optoelectronic properties, including thin-film absorption and cyclic voltammetry, of the donor-acceptor copolymers are presented.     

Investigation on Ochratoxin A stability using different extraction techniques

The stability of Ochratoxin A during its extraction using different extraction techniques has been evaluated. Microwave-assisted extraction and pressurised liquid extraction, in addition to two other reference methods of extraction, i.e. ultrasound-assisted and magnetic stirring-assisted extraction, were evaluated. The effect of extraction temperature using the cited techniques was checked.The results show that Ochratoxin A can be extracted using microwave-assisted extraction at temperatures up to 150 °C without degradation. Pressurised liquid extraction can be used at temperatures up to 100 °C, for extraction times of less than 30 min. Further, both ultrasound-assisted extraction and magnetic stirring extraction can be applied at temperatures up to 65 °C.High-performance liquid chromatography combined with fluorescence detection using a Chromolith RP-18e column at a flow rate of 5 mL min⁻¹ was used to quantify the Ochratoxin A. The retention time for the Ochratoxin A was 1.3 min. The limits of detection (LOD) and of quantification (LOQ) were 0.03 and 0.10 μg L⁻¹, respectively.     

Temperature dependence of interband transition energy in InGaAsN strain-compensated quantum-well and ridge-waveguide lasers fabricated with pulsed anodic oxidation

Ridge-waveguide InGaAsN triple-quantum-well strain-compensated lasers grown by metal organic chemical vapor deposition were fabricated with pulsed anodic oxidation. The laser’s output power reached 145 mW in continuous-wave mode at room temperature for a 4-?m -stripe-width laser. Continuous-wave single longitudinal mode operation was maintained at a high injection current level with a wavelength of 1287.3 nm at room temperature. Single longitudinal mode operation at 1317.2 nm was achieved at twice the threshold current at 100 °C. The band gap of InGaAsN in the quantum wells at different temperatures was calculated and compared to the measured temperature-dependent laser wavelength.     

Influence of moisture on the viscoelastic relaxations in long aliphatic chain contained semiaromatic polyamide, (PA9‐T) fiber

The effect of moisture on the mechanical relaxation processes of semiaromatic semicrystalline polyamides synthesized by a long‐chain aliphatic diamine and terephthalic acid was investigated by dynamic viscoelastic analysis (DVA) and differential scanning calorimetry (DSC). Moreover, the implication of moisture with the amorphous and crystalline domains was also examined by temperature‐dependent wide‐angle X‐ray diffraction and Fourier transform infrared spectra. The characteristics of the relaxations such as α, β, γ, and the pronounced peak shoulder appeared at 25–100 °C in DVA tan δ curves were found to be strongly susceptible to the presence of moisture. With moisture evaporation, the peak shoulder of 25–100 °C and the β‐relaxation disappeared. The former is anticipated to originate from to the side group motion of hydrogen‐bonded water, whereas the later one is from the motions of the amide–water complex units. With the disappearance of the β‐relaxation, the γ‐relaxation appeared simultaneously in much lower temperatures and ultimately coupled with the δ‐relaxation. The γ‐relaxation is attributed to be associated with the molecular motion of the amide group and δ‐relaxation with for the motion of the methylene units. The existence of two types of water was identified in the polymer, namely, tightly bound and loosely bound. The tightly bound water is believed to be directly connected by hydrogen bonding with the strong polar groups and the loosely bound water weakly links with those connected water making hydrogen bridges. The moisture acts as a plasticizer in the polymer matrix, which causes quite a large depression in its glass transition temperature (T_g). WAXD and FTIR studies corroborated the existence of water solely in amorphous regions, i.e., no rapport of water with the crystalline parts. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2878–2891, 2003     

Negative ion FAB mass spectroscopy of some ribose alkylated 5'-UMP derivatives

Characteristic fragment ions obtained in Fast atom bombardment (FAB) mass spectroscopy of ribose alkylated Uridine 5'-monophosphate (5'-UMP) derivatives in negative ion mode are described. All the compounds examined exhibited either [M]- or quasimolecular ion [M - H]- the fragmentations can be used to characterize these nucleotides.     

Three new cholinesterase-inhibiting cis-clerodane diterpenoids from Otostegia limbata

Three new tricyclic cis-clerodane type diterpenoids trivially named as limbatolide A (1), limbatolide B (2) and limbatolide C (3) have been isolated from the roots of Otostegia limbata along with two known compounds; oleanic acid and beta-sitosterol. The structure elucidation of the new compounds was based primarily on two-dimensional (2D) NMR techniques. Compounds 1-3 displayed inhibitory potential in a concentration-dependent manner against acetylcholinesterase (AChE; EC 3.1.1.7) and butyrylcholinesterase (BChE; EC 3.1.1.8) enzymes, respectively.