Multiple twinning in cubic crystals is represented geometrically by a three-dimensional fractal and algebraically by a groupoid. In this groupoid, the variant crystals are the objects, the misorientations between the variants are the operations, and the Sigma3(n) operators are the different types of operations (expressed by sets of equivalent operations). A general formula gives the number of v...

in the current research, polyvinylchloride based mixed matrix heterogeneous anion exchange membranes were prepared by a solution casting technique. titanium dioxide nanoparticles were also utilized as inorganic filler additive in the membrane fabrication. the effect of tio2 nanoparticles concentration in the casting solution on the membrane physico-chemical properties was studied. membrane wate...

We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. This model turns out to be strong enough to capture the current best algorithms for a variety of problems, e.g., O(n ) time matrix multiplication, O(n logn) time discrete Fourier transform, O(n ) time 3t-clique counting and O∗(2n) time for computing the permanent of a matrix. For counting homomorphism...

The structures of the configuration space of the six-vertex models with various boundaries and boundary conditions are investigated, and it is derived that the free energies depend on the boundary conditions, and that they are classified by the fractal structures. The ”n-equivalences” of the boundary conditions are defined with a property that the models with nequivalent boundary conditions res...

The high dislocation density (ρd) in Fe-C and/or Fe-N martensite is known to be one of the main causes its overall yield strength. Experiments indicate that and, therefore, strength low and medium C steels, follows a well defined behavior with respect background concentration (co). In present work, we introduce model based on finding after γ→α′ sufficiently accommodate/trap most available inter...

The tension-tension fatigue behavior of unidirectional C/SiC ceramic-matrix composite at room temperature and 800 °C under air has been investigated. The fatigue hysteresis modulus and fatigue hysteresis loss energy corresponding to different number of applied cycles have been analyzed. The fatigue hysteresis loops models for different interface slip cases have been derived based on the fatigue...

Self-assembly is ubiquitous in nature, particularly in biology, where it underlies the formation of protein quaternary structure and protein aggregation. Quaternary structure assembles deterministically and performs a wide range of important functions in the cell, whereas protein aggregation is the hallmark of a number of diseases and represents a nondeterministic self-assembly process. Here we...

The Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C T; A G], where C, T, A, G are the letters of the genetic alphabet. The matrix [C T; A G] in the second Kronecker power is the (4*4)-matrix of 16 duplets. The matrix [C T; A G] in the third Kronecker power is the (8*8)-matrix of 64 triplets. It is significant that peculiarities of the degeneracy...