Complete classification of torsion of elliptic curves over quadratic cyclotomic fields

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In a previous paper Najman (in press) [9], the author examined the possible torsions of an elliptic curve over the quadratic fields Q(i) and . Although all the possible torsions were found if the elliptic curve has rational coefficients, we were unable to eliminate some possibilities for the torsion if the elliptic curve has coefficients that are not rational. In this note, by finding all the points of two hyperelliptic curves over Q(i) and , we solve this problem completely and thus obtain a classification of all possible torsions of elliptic curves over Q(i) and .

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Phenolic Profile,Antioxidant, Anti-Enzymatic and Cytotoxic Activity of the Fruits and Roots of Eleutherococcus senticosus (Rupr. et Maxim.) Maxim

Eleutherococcus senticosus (Rupr. et Maxim.) Maxim. is well-known for its adaptogenic properties in traditional Eastern medicine. It has been categorized as an endangered species due to the over-exploitation of the roots. As a result, alternatives must be found, including the usage of renewable aerial parts such as fruits. The goal of this research was to determine the phenolic compounds and the enzymatic, antioxidant, and cytotoxic activities of the intractum gained from the E. senticosus fruits and the mixture of chloroform-methanol roots extract with naringenin (3:7:5). The obtained results showed, that the intractum contained 1.02 mg/g ext. of polyphenols, 0.30 mg/g ext. of flavonoids, and 0.19 mg/g ext. of phenolic acids. In turn, the mixture of chloroform-methanol roots extract with naringenin (3:7:5) contained 159.27 mg/g ext. of polyphenols, 137.47 mg/g ext. of flavonoids, and 79.99 mg/g ext. of phenolic acids. Regarding the anti-enzymatic assay, the IC₅₀ values for tyrosinase and hyaluronidase were equal to 586.83 and 217.44 [μg/mL] for the intractum, and 162.56 and 44.80 [μg/mL] for the mixture, respectively. Both preparations have possessed significant antioxidant activity in the ABTS, DPPH, and ferrozine tests. No cytotoxic effect on the FaDu and HEP G2 cancer cell lines was observed. Our findings support the traditional use of fruits and roots. Moreover, the results indicate also that adaptogens are rather nontoxic for normal and cancer cells, which corresponds with some hypotheses on adaptogens activity.     

Vinylogous Urea—Urethane Vitrimers: Accelerating and Inhibiting Network Dynamics through Hydrogen Bonding

Vinylogous urethane (VU_O) based polymer networks are widely used as catalyst-free vitrimers that show rapid covalent bond exchange at elevated temperatures. In solution, vinylogous ureas (VU_N) undergo much faster bond exchange than VU_O and are highly dynamic at room temperature. However, this difference in reactivity is not observed in their respective dynamic polymer networks, as VU_O and VU_N vitrimers prepared herein with very similar macromolecular architectures show comparable stress relaxation and creep behavior. However, by using mixtures of VU_O and VU_N linkages within the same network, the dynamic reactions can be accelerated by an order of magnitude. The results can be rationalized by the effect of intermolecular hydrogen bonding, which is absent in VU_O vitrimers, but is very pronounced for vinylogous urea moieties. At low concentrations of VU_N, these hydrogen bonds act as catalysts for covalent bond exchange, while at high concentration, they provide a pervasive vinylogous urea - urethane (VU) network of strong non-covalent interactions, giving rise to phase separation and inhibiting polymer chain dynamics. This offers a straightforward design principle for dynamic polymer materials, showing at the same time the possible additive and synergistic effects of supramolecular and dynamic covalent polymer networks.     

Nonresonant ionization of oxygen molecules by femtosecond pulses: plasma dynamics studied by time-resolved terahertz spectroscopy

We show that optical pump-terahertz probe spectroscopy is a direct experimental tool for exploring laser-induced ionization and plasma formation in gases. Plasma was produced in gaseous oxygen by focused amplified femtosecond pulses. The ionization mechanisms at 400- and 800-nm excitation wavelengths differ significantly being primarily of a multiphoton character in the former case and a strong-field process in the latter case. The generation of the plasma in the focal volume of the laser and its expansion on subnanosecond time scale is directly monitored through its density-dependent susceptibility. A Drude model used to evaluate the plasma densities and electron-scattering rates successfully captures the observations for a wide range of pump intensities. In addition, rotational fingerprints of molecular and ionic species were also observed in the spectra.     

HPLC-UV and GC-MS Methods for Determination of Chlorambucil and Valproic Acid in Plasma for Further Exploring a New Combined Therapy of Chronic Lymphocytic Leukemia

High performance liquid chromatography with ultra-violet detection (HPLC-UV) and gas chromatography–mass spectrometry (GC-MS) methods were developed and validated for the determination of chlorambucil (CLB) and valproic acid (VPA) in plasma, as a part of experiments on their anticancer activity in chronic lymphocytic leukemia (CLL). CLB was extracted from 250 µL of plasma with methanol, using simple protein precipitation and filtration. Chromatography was carried out on a LiChrospher 100 RP-18 end-capped column using a mobile phase consisting of acetonitrile, water and formic acid, and detection at 258 nm. The lowest limit of detection LLOQ was found to be 0.075 μg/mL, showing sufficient sensitivity in relation to therapeutic concentrations of CLB in plasma. The accuracy was from 94.13% to 101.12%, while the intra- and inter-batch precision was ≤9.46%. For quantitation of VPA, a sensitive GC-MS method was developed involving simple pre-column esterification with methanol and extraction with hexane. Chromatography was achieved on an HP-5MSUI column and monitored by MS with an electron impact ionization and selective ion monitoring mode. Using 250 µL of plasma, the LLOQ was found to be 0.075 μg/mL. The accuracy was from 94.96% to 109.12%, while the intra- and inter-batch precision was ≤6.69%. Thus, both methods fulfilled the requirements of FDA guidelines for the determination of drugs in biological materials.     

Hindered rotation around the N(sp2)-C(sp3) single bond in 2,4,6-trimethyl-N-alkylpyridinium cations:H DNMR analysist

Pairwise chemical shift nonequivalence of the 2,6-methyl and 3,5-protons in ¹H NMR spectra, as well as of the 2,6-methyl, 2,6-ring and 3,5-ring carbons in ¹³C NMR spectra, was observed for N-alkyl-2,4,6-trimethylpyridinium salts 2. Dynamic NMR spectroscopy demonstrates appreciably higher activation free energies ΔG^# for rotation around the N(sp²)-C(sp³ bond than ΔG# for the analogously substituted mesityl derivatives, in agreement with the shorter N-C bond distance than for the C-C bond.     

Conformational chirality and chiral crystallization of N-sulfonylpyrimidine derivatives

New N-sulfonylpyrimidine derivatives 1-(p-toluenesulfonyl)uracil (1), 1-(p-toluenesulfonyl)thymine (2), 5-bromo-1-(p-toluenesulfonyl)uracil (3), 1-(methanesulfonyl)uracil (4), 1-(1-naphthylsulfonyl)uracil (5), and 1-(1-naphthylsulfonyl)thymine (6) were prepared by the condensation reaction of silylated pyrimidine derivatives with selected sulfonyl chlorides in acetonitrile. Some members of the series showed unexpected crystal properties as a consequence of their conformational chirality in the solid state. Compounds 1 and 5 exhibited chiral crystallization, which was, in the case of 1, accompanied by the formation of racemically twinned crystals regardless of the solvent used, while 5 gave a conglomerate of enantiomorphous crystals. For 2, 3, and 6, substituents at the C-5 position of the pyrimidine ring prevented chiral crystallization by influencing the crystal packing. Analysis of the crystal structures of 1, 4, and 5, reveals the influence of the arylsulfonyl group on the occurrence or absence of chiral crystallization.     

Interplay of Curie-type and Pauli-type magnetic susceptibilities in HCl-doped polyaniline pellets

The static magnetic susceptibility (χ) of own-made HCl-doped polyaniline pellets is investigated experimentally over the full range of the protonation level Y and in the temperature (T) range 10–300 K.The obtained results suggest that χ and the electrical conductivity σ – which is known from previous work – are interrelated.Namely, there is a weakly Y dependent crossover temperature T ^* where both χ and σ undergo notable changes.In χ, this refers to a simultaneous enhancement (reduction) of the Pauli-type susceptibility χ _P and reduction (enhancement) of the Curie constant C at T = T ^* when T increases (decreases).Below T < T ^*, where thermal effects are weak to moderate, a steep increase of χ _P(Y) around Y = 0.3 occurs together with a drop of C(Y).The above findings are consistent with a picture in which, at T ^*, spins that disappear from C reappear in χ _P, and vice versa.This model is used to address the longitudinal and transversal electron localisation lengths as functions of Y, the former being estimated to take values in the range 7–8 Åand the latter in the range 1–2 Å.     

Composites of multiwall carbon nanotubes and conducting polyaniline: Bulk samples and films produced from a solution in chloroform

Multiwall carbon nanotubes and conducting polyaniline, doped with dodecylbenzenesulfonic acid, are blended by employing the solubility of both materials in chloroform. Pellets are made by pressing the dried powder of the obtained composite, and films by sedimentary deposition onto a plastic substrate. In these composites, the advantageous properties of carbon nanotubes can be utilized in fully conducting bulk and planar structures while the strong decrease of the conductivity of doped polyaniline at low temperatures is simultaneously suppressed. The nanotube content in pellets can be as high as 40% by weight, and this wide range leads to a control over the shape and magnitude of the conductivity versus temperature curves. As the nanotube content grows, the temperature dependence of the conductivity becomes less steep, which is similar to the effect of annealing temperature on the conductivity of certain polycrystalline graphene films. In our case, this change is most likely caused by the increase of the density of highly conducting channels and not by homogeneous delocalization effects.