Nonlinear ODE mathematical analysis of the insulin-glucose model in the presence of a condition in glycemia function H(G).

This work aims to analyze a fifth-order nonlinear ordinary differential equations that describe the glucoregulatory model system based on intravenous injection of glucose via in-vivo experimentation in rats reported previously in the literature. A mathematical analysis shows that existence of an invariant plane condition associated with insulin can determine a type 1 or type 2 diabetes classification. The bounded positive invariant domain (BPID) by applying the Lyapunov direct method establishes a mathematical preamble where maximum cell population is associated to an upper bound set given by a localizing function by applying the LCIS (Localizing Compact Invariant Set) method. Furthermore, an equilibrium point's existing condition is defined if U(t) is an invariant plane and H(G) exists. Also are discussed parameter conditions for renal glucose excretion (k5) and the rate constant of glucose absorption (ka) as a case of study when glycemia function presents existence conditions with or without insulin variable.

Selection of Lattice Invariant Shear in Dilute Zr-Nb Alloy for bcc-hcp Martensitic Transformation

The morphology and substructure of martensite is considered to arise from the lattice invariant shear (LIS) associated with the transformation and this may be slip, twinning or both. Out of the several possible slip shears and twin modes only a few satisfy invariant plane strain criteria of the phenomenological theory of martensite (PTMC). On the basis of crystallographic and energetic criteria, a simple model has been proposed for determining the factors which influence the selection of the preferred LIS mode. In the present work, it is found that for b ® a' martensitic transformation in Zr-2.5 wt%Nb alloy, the preferred slip system is {1101}a'<2113>a' and the preferred twin system is {1101}a'<415 3>a'.

Internal Structure of B19 Martensite in AuTi Shape Memory Alloy

Internal twin of B19 martensite in equiatomic AuTi binary alloy was examined by conventional transmission electron microscopy observation and the phenomenological theory of martensite crystallography (PTMC). The crystal structure of martensite was B19 (orthorhombic) with the lattice parameters of 0.2944nm, 0.4900nm and 0.4633nm. Most of martensite plates were internally twinned by {111}typeI twin. <211>typeII twin was occasionally observed and {011}compound-twin relationship was observed at boundaries between adjacent martensite plates. However, no martensite plate entirely twinned by the <211>typeII twinning or the {011}compound twinning was observed. PTMC analysis showed that the invariant plane is formed only by the introduction of the internal twin of {111}typeI or <211>typeII twin in the present geometry of the transformation. Geometry of a typical martensite plate with internal twin of {111}typeI twin was in good agreement with that required for the formation of habit plane with the invariant plane character. The observed {111}typeI twin is, therefore, considered to be the lattice invariant shear to minimize the elastic strain energy due to the transformation.