We present category-theoretic framework for universal homogeneous structures, with selected applications. Most of the material had been presented as a series of lectures for graduate students at Department of Mathematics, University of Silesia in Katowice, Poland (21 – 23 November 2012).

The development of bio-based epoxy resins from aliphatic biomass and lignin has rapidly increased over the past few decades. While thermal curing such monomers with polyfunctional amines anhydrides been intensively discussed in literature, surprisingly, their polymerization behavior using alcohols as co-curing agents resulting mechanical properties have not investigated detail up to now. Herein...

Thermal buckling behavior of functionally graded Euler-Bernoulli beams in thermal conditions is investigated analytically. The beam with material and thermal properties dependent on the temperature and position is considered. Based on the transformed-section method, the functionally graded beam is considered as an equivalent homogeneous Euler-Bernoulli beam with an effective bending rigidity un...

A new model for homogeneous nucleation of structural phase transformations, which can span the range of nucleation from classical to nonclassical, is presented. This model is extended from the classical nucleation theory by introducing driving-force dependencies into the interfacial free energy, themisfit strain energy, and the nucleus chemical free-energy change in order to capture the nonclas...

We model the 10 µm absorption spectra of nonspherical particles composed of amorphous silicate. We consider two classes of particles, compact ones and fractal aggregates composed of homogeneous spheres. For the compact particles we consider Gaussian random spheres with various degrees of non-sphericity. For the fractal aggregates we compute the absorption spectra for various fractal dimensions....

Living chick embryo spinal ganglion neurons grown from 1 to 4 weeks in vitro were studied under the phase contrast microscope. In the peripheral cytoplasm of the earliest stages studied, a homogeneous, phase-dense material is seen which corresponds in location to the cytoplasmic basophil material of the same stages. As maturation proceeds, this material increases in extent, and becomes separate...

(Received 26 February 1984; accepted for publication 20 November 1984) A theoretical nalysis ofsound propagation in cylindrical ducts lined with porous material {bulk absorbers) is presented. Three configurations are discussed. (1) The porous material is homogeneous; thenthe sound field is built up of modes. (2) The properties of the liner vary slowly in an axial direction. A pure modal solutio...