Abstract We study direct-sum decompositions of torsion-free, finitely generated modules over a (commutative) Bass ring R through the factorization theory corresponding monoid T ( ). Results Levy–Wiegand and Levy–Odenthal together with local case yield an explicit description The is typically neither factorial nor cancellative. Nevertheless, we construct transfer homomorphism to graph agglomerat...

Precursory fracture induced electromagnetic (EM) emissions, rooted in opening cracks and ranging from MHz to kHz, with the MHz appearing earlier, are produced and detected both at laboratory and geophysical scale. Recently, we have proposed the following two epochs/stages model of EQ generation: (i) The final kHz part is triggered by the fracture of high strength and large asperities that are d...

In the early 60’s J. B. Keller and D. Levy discovered a fundamental property: instability tongues in Mathieu-type equations lose sharpness with addition of higher-frequency harmonics Mathieu potentials. Twenty years later, V. Arnold similar phenomenon on circle maps (and rediscovered result Levy). this paper we find third class object where type behavior takes place: area-preserving cylinder. l...

We prove theorems of Landau and Hardy-Littlewood type for Goldbach, Chen, Lemoime-Levy and other binary partitions of positive integers. We also pose some new conjectures.

the levy-type analytical solution is employed for the problem of bending of cross-ply and antisymmetric angle-ply piezoelectric hybrid laminated plates with at least two simply supported opposite edges. the governing equations of equilibrium are derived in the framework of the first-order shear deformation plate theory. the equations are classified according to the crystallography type of piezo...