Into the study of quasi-relaxation, in the pastresearches it is have concluded that the conditionof meta-stability in the metallic specimen is givenby the plasticity explained by the plastic energy inthe process of the quasi-relaxation , and . Itis calculate through of quasi-relaxation functionalof this energy to obtain a spectra in the space D(s- e, t), that induced the existence of functions j(t),and Y(t), related with the fundamental curves ofquasi-relaxation given by s(t), with their poles in t= -1/k(s0 - s1), the which it is get in the maximumof stress given by s0 = s1. Also the tensor ofplastic deformation that represents the plastic loadduring the application of specimen machine ,not can be obtained without poles in the spaceD(s, t), corresponding to the curves calculated in, into the space D(s - e, t), by curves that inthe kinetic of the process of quasi-relaxation arerepresented by experimental curves in coordinateslgs - t . This situation not can be eluded,since in this phenomena exist dislocations that goconform fatigue in the nano-crystalline structureof metals . From this point of view, is necessaryto obtain a spectral study related with the energyusing functions that permits the modeling andcompute the states of quasi-relaxation included inthe poles in the deformation problem to completethe solutions in the space D(s - e, t), and try a newmethod of solution of the differential equationsof the quasi-relaxation analysis. In a nearly futuredevelopment, the information obtained by thisspectral study (by our integral transforms) will canto gives place to the programming through of thespectral encoding of the materials in the metastabilitystate, that which is propitious to a nanotechnologicaltransformation of materials, concretecase, some metals.
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