Logical Analysis of Data in Structure‐Activity Investigation of Polymeric Gene Delivery

To date semi‐empirical or surrogate modeling has demonstrated great success in the prediction of the biologically relevant properties of polymeric materials. For the first time, a correlation between the chemical structures of poly(β‐amino esters) and their efficiency in transfecting DNA was established using the novel technique of logical analysis of data (LAD). Linear combination and explicit representation models were introduced and compared in the framework of the present study. The most successful regression model yielded satisfactory agreement between the predicted and experimentally measured values of transfection efficiency (Pearson correlation coefficient, 0.77; mean absolute error, 3.83). It was shown that detailed analysis of the rules provided by the LAD algorithm offered practical utility to a polymer chemist in the design of new biomaterials.

     

The fundamental matrix of solutions of the Cauchy problem for a class of parabolic systems of the Shilov type with variable coefficients

We constructed a fundamental matrix of solutions of the Cauchy problem and studied its basic properties for a new class of linear parabolic systems with smooth bounded variable coefficients that includes a class of the Shilov-type parabolic systems of partial differential equations with nonnegative genus.     

Synthesis of azabicyclo[n.1.0]alkane-derived bifunctional building blocks via the Corey–Chaykovsky cyclopropanation

An efficient approach towards the synthesis of monoprotected azabicyclo[5.1.0]octane-derived conformationally restricted γ-amino acids and diamines is reported. Optimization of the conditions for the key Corey–Chaykovsky reaction allowed the construction of two isomeric methanoazepane frameworks on a multigram scale in 55–65% yield. Additionally, the developed approach was used in the three-step synthesis of 3,4-methano-β-proline and its diamine derivatives.     

Modified Shephard’s problem on projections of convex bodies

We disprove a conjecture of A. Koldobsky asking whether it is enough to compare (n − 2)-derivatives of the projection functions of two symmetric convex bodies in the Shephard problem in order to get a positive answer in all dimensions. The author was supported in part by the European Network PHD, FP6 Marie Curie Actions, RTN, Contract MCRN-511953     

Cyclooctatetraenide-based single-ion magnets featuring bulky cyclopentadienyl ligand

We report a family of organometallic rare-earth complexes with the general formula (COT)M(Cp^ttt) (where (COT)²⁻ = cyclooctatetraenide, (Cp^ttt)⁻ = 1,2,4-tri(tert-butyl)cyclopentadienide, M = Y(iii), Nd(iii), Dy(iii) and Er(iii)). Similarly to the prototypical Er(iii) analog featuring pentamethylcyclopentadienyl ligand (Cp*)⁻, (COT)Er(Cp^ttt) behaves as a single-ion magnet. However, the introduction of the sterically demanding (Cp^ttt)⁻ imposes geometric constraints that lead to a simplified magnetic relaxation behavior compared to the (Cp*)⁻ containing complexes. Consequently, (COT)Er(Cp^ttt) can be viewed as a model representative of this organometallic single-ion magnet architecture. In addition, we demonstrate that the increased steric profile associated with the (Cp^ttt)⁻ ligand permits preparation, structural characterization and interrogation of magnetic properties of the early-lanthanide complex, (COT)Nd(Cp^ttt). Such a mononuclear derivative could not be obtained when a (Cp*)⁻ ligand was employed, a testament to larger ionic radius of this early lanthanide ion.

Application of steric control principles allows for simplification of the magnetic behavior of an iconic single-ion magnet architecture as well as the preparation of its previously inaccessible representative.     

Simple estimation on effective transport properties of a random composite material with cylindrical fibres

Improved bounds for effective transport properties of a random non-percolated composite with cylindrical fibres are developed by means of the security-spheres approach. The key point of the method is to obtain a solution for a regular composite that can be valid for all values of the volume fractions and properties of the components. For this aim we use the asymptotic homogenization method; a cell problem is solved by a modified version of the boundary shape perturbation technique.      

Study of wave dispersion in periodic composites by higher-order asymptotic homogenization method

We present [1] an application of the higher-order asymptotic homogenization method (AHM) to the study of wave dispersion in periodic composite materials. When the wavelength of a travelling signal becomes comparable to the size of heterogeneities, successive reflections and refractions of the waves at the components interfaces lead to the formation of a complicated sequence of pass and stop frequency bands. The AHM provides a long-wave approximation valid in the low frequency range. Solution for the high frequencies is obtained on the basis of the Floquet–Bloch theorem by the plane-wave (PW) expansions method. Anti-plane shear waves in a fibre-reinforced composite with a square lattice of cylindrical fibres are considered. The dispersion curves are obtained, the pass and stop bands are identified. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical study of the load transfer in fibre-reinforced 2D composite materials

The phenomenon of the load diffusion from a fibre to a surrounding matrix is analysed for the 2D case. We use an approximate analytical approach based on the asymptotic reduction of the governing biharmonic problem into two harmonic problems. The comparison of the obtained solutions with known results of other authors shows an acceptable accuracy of the proposed asymptotic simplifications. All solutions are obtained in closed analytical form.The case of perfect bonding between fibre and matrix for a single fibre and for a periodic system of fibres is firstly considered. Then we study the influence of the interface stiffness. In the case when only a single fibre is loaded, the influence of all other fibres is predicted by means of a three-phase model. The proposed approach gives a possibility to solve the problems for a broken fibre and for a broken matrix, as well as for partly debonded fibres. The important problem of infinite matrix cracks is also solved in the present paper.The obtained results can be used for the calculation of pull-out and push-out tests, as well as for the investigation of the fracture of composite materials.