Synthesis and In vitro Study of Cytotoxic Activity of New Tetrazole-Containing 2,4-Diamino-1,3,5-triazine Derivatives

Russian Journal of General Chemistry - New tetrazole-containing derivatives of 2,4-diamino-1,3,5-triazine were synthesized. The cytotoxic activity of the obtained compounds against Huh-7 and HeLa...     

On continuation of inviscid vortex patches

This investigation concerns solutions of the steady-state Euler equations in two dimensions featuring finite area regions with constant vorticity embedded in a potential flow. Using elementary methods of the functional analysis we derive precise conditions under which such solutions can be uniquely continued with respect to their parameters, valid also in the presence of the Kutta condition concerning a fixed separation point. Our approach is based on the Implicit Function Theorem and perturbation equations derived using shape-differentiation methods. These theoretical results are illustrated with careful numerical computations carried out using the Steklov–Poincaré method which show the existence of a global manifold of solutions connecting the point vortex and the Prandtl–Batchelor solution, each of which satisfies the Kutta condition.     

On an attempt to simplify the Quartapelle–Napolitano approach to computation of hydrodynamic forces in open flows

In this paper we are interested in the Quartapelle–Napolitano approach to calculation of forces in viscous incompressible flows in exterior domains. We study the possibility of deriving a simpler formulation of this approach which might lead to a more convenient expression for the hydrodynamic force, but conclude that such a simplification is, within the family of approaches considered, impossible. This shows that the original Quartapelle–Napolitano formula is in fact “optimal” within this class of approaches.     

Adjoint-based optimization of PDEs in moving domains

In this investigation we address the problem of adjoint-based optimization of PDE systems in moving domains. As an example we consider the one-dimensional heat equation with prescribed boundary temperatures and heat fluxes. We discuss two methods of deriving an adjoint system necessary to obtain a gradient of a cost functional. In the first approach we derive the adjoint system after mapping the problem to a fixed domain, whereas in the second approach we derive the adjoint directly in the moving domain by employing methods of the noncylindrical calculus. We show that the operations of transforming the system from a variable to a fixed domain and deriving the adjoint do not commute and that, while the gradient information contained in both systems is the same, the second approach results in an adjoint problem with a simpler structure which is therefore easier to implement numerically. This approach is then used to solve a moving boundary optimization problem for our model system.     

Enantioselectivity of the reaction of α-amino acids with sodium azide and triethyl orthoformate in the synthesis of tetrazoles

Russian Journal of Organic Chemistry -     

Synthesis,Structure, and Antiproliferative Activity of <Emphasis Type="Italic">trans</Emphasis>-Palladium(II) Complexes with Tetrazol-2-ylacetic Acid Derivatives

A series of trans-palladium(II) complexes (trans-[PdCl₂L₂], L = ethyl 5-R-2H-tetrazol-2-ylacetate, 5-R-2H-tetrazol-2-ylacetamides, R = Me, Ph) has been synthesized, and their structure has been proved by ¹H and ¹³C–{¹H} NMR and high-resolution mass spectra and X-ray analysis. Antiproliferative activity of the synthesized complexes has been determined, and the mechanism of their interaction with DNA has been studied by UV and CD spectroscopy.