Let Ω be an algebraic closure of Qp and let F be a finite extension of Qp contained in Ω. Given positive integers f and e, the number of extensions K/F contained in Ω with residue degree f and ramification index e was computed by Krasner. This paper is concerned with the number I(F, f, e) of F -isomorphism classes of such extensions. We determine I(F, f, e) completely when p2 ∤ e and get partia...

We consider three notions of factorization arising in different frameworks: factorizing languages, factorization of the natural numbers, factorizing codes. A language X ⊆ A∗ is called factorizing if there exists a language Y ⊆ A∗ such that XY = A∗ and the product is unambiguous. This is a decidable property for recognizable languages X . If we consider the particular case of unary alphabets, we...

In this paper, we introduce new expansion classes, namely weakly $ (k,n) $-absorbing hyperideals and primary of a Krasner (m,n) $-hyperring, including hyperideal hyperideal. Therefore, give generalizations Also, examine the relations between classical explore some ways to connect them. Additionally, main results examples are given explain structures these concepts. Finally, study version Nakaya...

Objective(s): Fibromyalgia (FM) is a central nervous system disorder characterized by widespread mechanical hyperalgesia due to unknown mechanisms. Several inflammatory mediators, such as interleukin-1 (IL-1), IL-6, IL-8, and tumor necrosis factor, are increased in the serum of FM patients. Although medications including pregabalin, duloxetine, and milnacipran are used...

This paper enables connectivity on everyday objects by transforming them into FM radio stations. To do this, we show for the first time that ambient FM radio signals can be used as a signal source for backscatter communication. Our design creates backscatter transmissions that can be decoded on any FM receiver including those in cars and smartphones. This enables us to achieve a previously infe...