Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

the generalization of p-frame in banach spaces is considered in this paper. the concepts of an $tilde{x}$-frame and a system conjugate to $tilde{x}$-frame were introduced. analogues of the results on the existence of conjugate system were obtained. the stability of $tilde{x}$-frame having a conjugate system is studied.

Stress shadowing affects the simultaneous propagation of fractures from multiple perforation clusters. Employing uniform parameters for all clusters cause unbalanced growth fractures, which arouses demand optimizing non-uniform parameters. An optimization workflow combining a fracture model and particle swarm method (PSO) is proposed multi-cluster fracturing in this study. The considers couplin...

The results of the study radiation produced by electrical explosion Al foil with a thickness 4 μm an artificial periodic structure holes 50–400 steps created laser engraving are presented. experiments were carried out on KING pulse high-current generator (220 kA, 40 kV, 300 ns). Images exploded foils recorded using pinhole cameras 20 aperture four-frame microchannel plate camera 5 ns temporal r...

In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...