Two soliton collision for nonlinear Schrödinger equations in dimension 1

We study the collision of two solitons for the nonlinear Schrödinger equation iψt=−ψxx+F(²|ψ|)ψ, F(ξ)=−2ξ+O(ξ²) as ξ→0, in the case where one soliton is small with respect to the other. We show that in general, the two soliton structure is not preserved after the collision: while the large soliton survives, the small one splits into two outgoing waves that for sufficiently long times can be controlled by the cubic NLS: iψt=−ψxx−2²|ψ|ψ.     

Radiochemical Synthesis of 4-[18F]FluorobenzylAzide and Its Conjugation with EGFR-Specific Aptamers

Central nervous system tumors related to gliomas are of neuroectodermal origin and cover about 30% of all primary brain tumors. Glioma is not susceptible to any therapy and surgical attack remains one of the main approaches to its treatment. Preoperative tumor imaging methods, such as positron emission tomography (PET), are currently used to distinguish malignant tissue to increase the accuracy of glioma removal. However, PET is lacking a specific visualization of cells possessing certain molecular markers. Here, we report an application of aptamers to enhancing specificity in imaging tumor cells bearing the epidermal growth factor receptor (EGFR). Glioblastoma is characterized by increased EGFR expression, as well as mutations of this receptor associated with active division, migration, and adhesion of tumor cells. Since 2021, EGFR has been included into the WHO classification of gliomas as a molecular genetic marker. To obtain conjugates of aptamers GR20 and GOL1-specific to EGFR, a 4-[¹⁸F]fluorobenzylazide radiotracer was used as a synthon. For the production of the synthon, a method of automatic synthesis on an Eckert & Ziegler research module was adapted and modified using spirocyclic iodonium ylide as a precursor. Conjugation of 4-[¹⁸F]fluorobenzylazide and alkyne-modified aptamers was carried out using Cu(I)-catalyzed azide-alkyne cycloaddition (CuAAC) with/without the TBTA ligand. As a result, it was possible to obtain ¹⁸F-labelled conjugates with 97% radiochemical purity for [¹⁸F]FB-GR20 and 98% for [¹⁸F]FB-GOL1. The obtained conjugates can be used for further studies in PET analysis on model animals with grafted glioblastoma.     

Behavior of PNIPAM Microgels in Different Organic Solvents

In this research, we studied, in detail, the behavior of common PNIPAM microgels, obtained through surfactant-free precipitation polymerization, in a number of organic solvents. We showed that many of the selected solvents serve as good solvents for the PNIPAM microgels and that the size and architecture of the microgels depend on the solvent chosen. Expanding the range of solvents used for PNIPAM microgel incubation greatly enhances the possible routes for microparticle functionalization and modification, as well as the encapsulation of water-insoluble species. In this demonstration, we successfully encapsulated water-insoluble Sudan III dye in PNIPAM microgels and prepared the aqueous dispersions of such composite-colored microparticles.     

2-Imidazoline Nitroxide Derivatives of Cymantrene

The 2-imidazoline nitroxide derivatives of cymantrene—2-(η⁵-cyclopentadienyl)tricarbonylmanganese(I)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl (NNMn) and 2-(η⁵-cyclopentadienyl)tricarbonylmanganese(I)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-1-oxyl (INMn) were synthesized. It was shown that NNMn and INMn exhibit a sufficiently high kinetic stability both in solids and in solutions under normal conditions. Their structural characteristics, magnetic properties and electrochemical behavior are close to Re(I) analogs. This opens the prospect of using paramagnetic cymantrenes as prototypes in the design of Re(I) half-sandwiched derivatives for theranostics, where therapy is combined with diagnostics by magnetic resonance imaging due to the contrast properties of nitroxide radicals.     

Push-Pull Structures Based on 2-Aryl/thienyl Substituted Quinazolin-4(3H)-ones and 4-Cyanoquinazolines

Design and synthesis of 2-(aryl/thiophen-2-yl)quinazolin-4(3H)-ones and 4-cyano-2-arylquinazolines with Et₂N-, Ph₂N- or carbazol-9-yl- electron donating fragment are described. The key photophysical properties of these compounds have been studied by UV/Vis absorption and fluorescence spectroscopy in solvents of different polarity (toluene and MeCN). 2-(Aryl/thiophen-2-yl)quinazolin-4(3H)-ones show fluorescence in blue-green region in toluene solution with quantum yields up to 89% in the case of 2-(4’-N,N-diphenylamino[1,1’-biphenyl]-4-yl)-quinazolin-4(3H)-one. Moreover, triphenylamino derivative based on quinazolin-4(3H)-one with para-phenylene linker displays the highest quantum yield of 40% in powder. The fluorescence QY of Et₂N and Ph₂N derivatives decrease when going from toluene to MeCN solution, whereas carbazol-9-yl counterparts demonstrate strengthening of intensity that emphasizes the strong influence of donor fragment nature on photophysical properties. 4-Cyanoquinazolines are less emissive in both solvents, as well as, in solid state. The introduction of cyano group into position 4 leads to orange/red colored powder and dual emission bands. Some molecules demonstrate the increase in emission intensity upon addition of water to MeCN solution. According to frontier molecular orbitals (HOMO, LUMO) calculations, the energy gap of 4-cyanoquinazoline decreases by more than 1 eV compared to quinazolin-4-one, that is consistent with experimental data.     

Callus Culture of Scorzonera radiata as a New,Highly Productive and Stable Source of Caffeoylquinic Acids

During our ongoing efforts to investigate biotechnological sources of caffeoylquinic acid (CQA) metabolites, we discovered the plant Scorzonera radiata Fisch. (Asteraceae), which is able to produce callus cultures with high yield and extremely high stability. An actively growing callus line, designated as Sr-L1, retained the ability to produce 11 CQAs during long-term cultivation (more than 20 years). A total of 29 polyphenolic compounds were identified in the leaves and Sr-L1 callus culture of S. radiata, including CQAs, lignol derivatives, flavonoids, and dihydrostilbenes. The composition of CQAs in the Sr-L1 culture was identical to that in the S. radiata leaves. Sr-L1 calli did not produce flavonoids and dihydrostilbenes, but produced lignol derivatives, which were absent in leaves. The HPLC-UV-HRMS determination showed the presence of monoacyl derivatives of CQAs such as 5-CQA, 4-CQA, cis-5-CQA, and 5-O-p-coumaroylquinic acid in the Sr-L1 culture. Among diacyl derivatives, 3,4-diCQA, 3,5-diCQA, cis-3,5-diCQA, 4,5-diCQA, 3-O-p-coumaroyl-5-O-CQA, and 3-O-caffeoyl-5-O-p-coumaroylquinic acid were found. The content of 5-CQA reached 7.54 mg/g dry weight and the content of 3,5-diCQA was as high as 18.52 mg/g dry weight. 3,5-diCQA has been reported to be of high nutritional and pharmacological value, as it alleviates inflammatory pain, reverses memory impairment by preventing neuronal apoptosis, and counteracts excessive adipose tissue expansion, serving as an attractive treatment option for obesity. The high content of 3,5-diCQA and the exceptional stability of biosynthesis make callus cultures of S. radiata a promising source for the development of drugs and nutraceuticals.     

Modelling of electrolyte mixtures with application to chemical equilibria in mixtures—prototypes of blood''s plasma and calcification of soft tissues

Modelling of the biologic solutions has a great importance for basic physicochemical backgrounds of the living processes, mechanism of the diseases and drugs action, etc. The modelling of the chemical equilibria in solution that served as a prototype of the blood plasma with application to calcification of the tissues is performed. The concentrations of molecular–ionic forms containing calcium and hydrogen cations and phosphate anions in the range of ionized-calcium and total phosphorus concentrations from 0.5 to 3.0 mM and at the solution pH of 7.1–7.8 were calculated. The activities of the ionized species were described in approach to Debye–Hückel's theory. The full set of the equilibria taking into consideration dissociation of the water, phosphoric acid, formation of both inert and ionic calcium phosphates was considered. The states of calcium hydrophosphate dihydrate CaHPO₄·2H₂O (CHPD), calcium phosphate Ca₃(PO₄)₂ (CP), calcium hydrophosphate-phosphate dihydrate Ca₄H(PO₄)₃·2H₂O (CHPPD) and hydroxyapatite Ca₃OH(PO₄)₃ (HA) with respect to the boundary of the region in which they crystallise were determined. A criterion has been introduced to characterize the degree of salt supersaturation with respect to crystallisation, which is based on the concentration distance between the states of a salt in solution and at the boundary of its crystallisation. This criterion is used to provide a quantitative characteristic of the supersaturation of the phosphates and their tendency to crystallise in blood's plasma. It was established that the most soluble of the phosphates, CaHPO₄·2H₂O, is undersaturated and the other phosphates are supersaturated with respect to crystallisation. Thus, this phosphate does not take part in the calcification, and this is the source for ionized calcium in a blood plasma from the soft tissues. The role of the other phosphates in calcification of the soft tissues is decreased in the series HA>CP>CHPPD. The dependencies of the supersaturation of the solution on the pH and on the concentrations of calcium and phosphorus in a mixture are discussed.     

Solutions of some singular integral equation

A singular integral equation with a Holderian second member function on [a,b] is considered and solved for four different type of kernels in the class of functions that are unbounded at the end points of the interval.