In this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $M$-hyponormal operator‎. ‎We show that every analytic extension of a $n$th roots of $M$-hyponormal operator is subscalar of order $2k+2n$‎. ‎As a consequence‎, ‎we get that if the spectrum of such operator $T$ has a nonempty interior in $mathbb{C}$‎, ‎then $T$ has a nontrivial invariant subspace‎. ‎Finally‎, ‎w...

The “main conjecture” of equivariant Iwasawa theory concerns the situation where • l is a fixed odd prime number and K/k is a Galois extension of totally real number fields with k/Q and K/k∞ finite, where k∞/k is the cyclotomic Zl-extension (we set G = G(K/k) and Γk = G(k∞/k)), • S is a fixed finite set (which will normally be suppressed in the notation) of primes of k containing all primes whi...

The “main conjecture” of equivariant Iwasawa theory concerns the situation where • l is a fixed odd prime number and K/k is a Galois extension of totally real number fields with k/Q and K/k∞ finite, where k∞/k is the cyclotomic Zl-extension (we set G = G(K/k) and Γk = G(k∞/k)), • S is a fixed finite set (which will normally be suppressed in the notation) of primes of k containing all primes whi...

It is investigated when a cyclic p-class field of an imaginary quadratic number field can be embedded in an infinite pro-cyclic p-extension. Résumé. On donne des conditions pour qu’un p-corps de classes cyclique d’un corps de nombres quadratique imaginaire soit plongeable dans une p-extension pro-cyclique infinie. Consider an imaginary quadratic number field K. Let p be an odd prime number, and...

In this present paper, the main aim of the authors are to present extended k-gamma, k-beta functions and extended k-beta distribution where k > 0. These newly defined functions are the generalized forms of the extended gamma, beta functions and extended beta distribution. Also, we further generalize the said functions and some of their properties.

We study the computational complexity of problems that arise in abstract argumentation in the context of dynamic argumentation, minimal change, and aggregation. In particular, we consider the following problems where always an argumentation framework F and a small positive integer k are given. • The Repair problem asks whether a given set of arguments can be modified into an extension by at mos...

We present some results concerning extensions of models of ZFC in which cofinalities of cardinals are changed and/or cardinals are collapsed, in particular on minimal such extensions. Our main tools are perfect tree forcing PF(S) and Namba forcing Nm(S). We prove that if N 2 M is an extension such that (i) M k K = I+ > H,, (ii) 1 fl N E M and (iii) N = Mlf] for some cofinal f : oo+ K, then N 2 ...

Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...