Criteria for the injectivity of analytic sheaves

It is shown that a moduleL over the sheafO of germs of holomorphic functions on a domain G of Cⁿ is injective if and only if the following conditions are satisfied; a)L is flabby; b) for every closed set S ?G and every point z λ G, the stalk se _z of the sheafS ^L;U1→Γ S ^(U:L) is an injectiveO _z -module. It follows in particular that the sheaf of germs of hyperfunctions is injective over the sheaf of germs of analytic functions.     

A new type of magnetoplastic effects in linear amorphous polymers

A new type of magnetoplastic effects in polymers is revealed. This effect cannot be explained by the reorientation of macromolecular units that possess a magnetic susceptibility anisotropy. It is shown that the joint action of magnetic and electric fields and the rotational mobility of side groups in macromolecules are factors of crucial importance in changing the plasticity of polymers in pulsed magnetic fields.     

Motion of a pair of bubbles in a liquid of low viscosity

Lagrange's equations are used to examine the long-range interaction of bubbles. The Lagrange function equals the kinetic energy of an ideal liquid flowing around a bubble. The generalized external forces include the upthrust and the viscous resistance to flow around each buble. The azimuthal angle is increased by the long-range interaction. The locus for the relative motion is calculated for: 1) the case in ~hieh the relative speed is fairly high, which allows one to neglect the effects of viscosity on the collision time. 2) low relative speed, where the viscous forces determine the motion. Estimates are given for the differential effective cross-section for elastic scattering and the coalescence cross-section.We are indebted to V. G. LevichandV. V. Tolmachev for discussions.     

Transfer of energy from an evaporating drop in a vapor medium

The article considers the temperature distribution around an evaporating drop in a vapor medium. The transfer of energy is effected by molecular thermal conductivity, convection, and radiation. The mean length of the free flight path of the radiation considerably exceeds the characteristic distance at which the temperature changes. The times required for relaxation of the temperature to a steady-state value are determined, as well as the characteristic distances at which the temperature distribution changes.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 74–78, January–February, 1972.The authors thank V. G. Levich for his evaluation of the results obtained.     

Drift of a reacting droplet due to the chemoconcentration capillary effect

The motion of a droplet with a first-order chemical reaction taking place at its surface with the participation of a surfactant dissolved in the external medium is considered. Approximate expressions are obtained for the velocity and other characteristics of the autonomous motion of the droplet caused by the surface capillary forces due to the nonuniform distribution of the surfactant over the surface of the moving droplet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 51–61, May–June, 1990.     

Chemoconcentration capillary effect associated with the motion of a drop in a liquid

The effect of a surface chemical reaction involving a weak soluble surface active substance on the motion of a drop in a liquid is investigated. It is shown that as a result of the Marangoni effect the non-uniformity in the distribution of the substance along the surface associated with the proper motion of the drop and the chemical reaction has an important influence on the nature of the motion of the drop and on the force exerted by the surrounding Liquid. Under certain conditions this Leads to the development of a thrust proportional to the velocity of the drop (chemoconcentration capillary effect). The condition of occurrence of the thrust is obtained, together with its dependence on various physical parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 147–154, January–February, 1988.     

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.     

Effect of the conditions of dynamic nanoindentation on the strain-rate sensitivity of hardness for solids with different structures

A technique for the determination of the strain-rate sensitivity of hardness during dynamic nanoindentation is proposed. The strain-rate sensitivities of the dynamic hardnesses of a wide class of materials (fcc metals, carbon steels, bulk amorphous metallic alloys, ionic and covalent crystals, polymers, and ceramics) are determined. The variation of these strain-rate sensitivities with the relative-strain rate (in the [(e)\dot]\dot \varepsilon range from 3 × 10⁻³ to 5 × 10³ s⁻¹) and the indentation depth (in the range from 30 nm to 2μm) is studied.