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.

Resume Les tumeurs à cellules de Sertoli et Leydig sont des tumeurs sécrétantes rares du mésenchyme et des cordons sexuels. Cependant elles constituent l’une des tumeurs le souvent responsables de syndrome de virilisation. La certitude diagnostique est histologique après la chirurgie et il n’ y'a pas de signe échographie spécifique malgré la forte présomption clinique. Le pronostic comme la plu...

1 Part of this work was accomplished while Denis Bouyssou was visiting the Service de Mathématiques de la Gestion at the Université Libre de Bruxelles (Brus-sels, Belgium). He gratefully acknowledges the warm hospitality of the Service de Mathématique de la Gestion as well as the support of the Belgian Fonds National de la Recherche Scientifique and the Brussels-Capital Region through a " Resea...

A theoretical study of differences in broadband high-index-contrast grating (HCG) reflectors for TM and TE polarizations is presented, covering various grating parameters and properties of HCGs. It is shown that the HCG reflectors for TM polarization (TM HCG reflectors) have much thicker grating thicknesses and smaller grating periods than the TE HCG reflectors. This difference is found to orig...

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...

when power systems are expanded and connected together with weak tie lines, the low-frequency oscillations are increased and the stability margin of the power system decreases. therefore, when designing the transmission system to be used, it is necessary to maintain the dynamic stability of the power system, and to make sure to have the most possible stability margin. sssc is a facts device con...

in this paper we investigate a new notion of bases in hilbert spaces and similarto fusion frame theory we introduce fusion bases theory in hilbert spaces. we also introducea new de nition of fusion dual sequence associated with a fusion basis and show that theoperators of a fusion dual sequence are continuous projections. next we de ne the fusionbiorthogonal sequence, bessel fusion basis, hilbe...