a new approach is proposed to model a crack in orthotropic composite media using the extended finite element method (xfem). the xfem uses the concept of partition of unity in addition to meshless basic idea of approximating a field variable by its values at a set of surrounding nodes. as a result, higher order approximations can be designed with the same total number of degrees of freedom. in t...

We show that in a spontaneously broken effective gauge field theory, quantized general background \(R_\xi \)-gauge, also the fields undergo non-linear (albeit background-gauge invariant) redefinition induced by radiative corrections. This proves to be crucial order renormalize coupling constants of gauge-invariant operators gauge-independent way. The classical background-quantum splitting is no...

this study was performed to evaluate the results of 14 years of application of ilizarov method in treatment of infected non-:union:s of tibia and femur in patients with severe trauma and battlefield wounds. seventeen patients with long bone non:union: (14 were with infected non:union: of tibia out of whom two were associated with tibial bone defects and 3 with infected non-:union: of femur) wer...

The essential fact behind the so-called field-descent method is that certain cyclotomic integers necessarily are contained in relatively small fields and thus must have relatively small complex modulus. In this paper, we develop a method which reveals a complementary phenomenon: certain cyclotomic integers cannot be contained in relatively small fields and thus must have relatively large comple...