On optimal design of rigid plastic beams with additional supports in the case of impulsive loading

A rigid plastic beam under implusive loading is considered. In order to increase the stiffness of the beam, some additional supports are applied. The locations of these supports must be selected so as to minimize the maximal permanent deflection of the beam. This problem is solved with the aid of the optimal control theory of distributed parameter systems. Optimality conditions are deduced. The case where the problem is self-conjugate is examined. An example is given.     

Propagation of two-dimensional plastic waves in a thick plate

A study is made of the propagation and interaction of two-dimensional waves of high amplitude in a thick plate. A monotonically decreasing pressure is applied to the surface of the plate. Deformations are assumed to be large; the problem is formulated and solved in Lagrangian variables. An approximate method for constructing the fronts of the shock waves is proposed. The pressure and particle velocity at an arbitrary point and at an arbitrary instant of time are determined by the method of characteristics. A numerical example is given.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 100–106, January–Febraury, 1971.     

Semigroups strongly Morita equivalent to monoids

Periodica Mathematica Hungarica - We consider semigroups strongly Morita equivalent to a fixed monoid. We prove that such semigroups are precisely the enlargements of that monoid. We also show that...     

Optimal design of impulsively loaded plastic beams for asymmetric mode motions

Optimal design of a rigid-plastic stepped beam is discussed assuming the mode form of motion. Such beam dimensions are sought for which a minimum of local or mean deflection is attained within designs of constant volume. It is assumed that the prescribed kinetic energy is imparted to the structure at the initial instant with free motion occurring afterwards. It is shown that besides three symmetric modes of motion, also the asymmetric modes may exist. An optimal design for asymmetric modes is determined and compared with a respective design for symmetric modes, obtained previously in [1].     

Layer-by-Layer-Assembled Capsule Size Affects the Efficiency of Packaging and Delivery of Different Genetic Cargo

The lack of an efficient and versatile intracellular nucleic acids delivery platform impedes the clinical implementation of gene therapy. Advances in layer-by-layer (LbL) technology have led to the production of LbL polymer capsules, a promising universal delivery tool. The biocompatibility, sufficient packaging capacity, safety, low cost, and high variability of structure and composition of the LbL capsules make it possible to meet the requirements for clinical-grade nonviral gene transfer. Here, the possibility of polymeric LbL capsules of different sizes (micrometer and sub-micrometer-sized) to serve as universal nonviral carriers for messenger RNA (mRNA) and small interfering RNA (siRNA) is considered. In particular, the internalization of capsules into human mesenchymal stem cells (hMSCs, as an example of adult primary stem cells), capsule uptake, and intracellular delivery of mRNA and siRNA is studied. Importantly, the use of micrometer- or sub-micrometer-sized polymer capsules (MicCaps and SubCaps) allows the mRNA or siRNA to be packaged and transferred into hMSCs with high efficiency. While the uptake efficiency is comparable between MicCaps and SubCaps, the latter are significantly more efficient than MicCap when transferring siRNAs. These results demonstrate the potential of the LbL capsules as a universal gene delivery platform, which can be tuned according to the properties of genetic cargo.