A 15.2-to-18.2GHz Balanced Dual-Core Inverse-Class-F VCO with Q-Enhanced 2nd-Harmonic Resonance Achieving 187-to-188.1dBc/Hz FoM in 28nm CMOS

AbstractIn this paper, double commutativity and the reverse order law for the core inverse are considered. Then new characterizations of the Moore–Penrose inverse of a regular element are given by one-sided invertibilities in a ring. Furthermore, the characterizations and representations of the core and dual core inverses of a regular element are considered.

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The (b,c)-inverse for products and lower triangular matrices

Journal of Algebra and Its Applications ◽

10.1142/s021949881750222x ◽

2017 ◽

Vol 16 (12) ◽

pp. 1750222 ◽

Cited By ~ 4

Author(s):

Yuanyuan Ke ◽

Zhou Wang ◽

Jianlong Chen

Keyword(s):

Sufficient Conditions ◽

Triangular Matrix ◽

Drazin Inverse ◽

Triangular Matrices ◽

Core Inverse ◽

Special Cases ◽

Lower Triangular ◽

Necessary And Sufficient ◽

Lower Triangular Matrices ◽

Dual Core

Let [Formula: see text] be a semigroup and [Formula: see text]. The concept of [Formula: see text]-inverses was introduced by Drazin in 2012. It is well known that the Moore–Penrose inverse, the Drazin inverse, the Bott–Duffin inverse, the inverse along an element, the core inverse and dual core inverse are all special cases of the [Formula: see text]-inverse. In this paper, a new relationship between the [Formula: see text]-inverse and the Bott–Duffin [Formula: see text]-inverse is established. The relations between the [Formula: see text]-inverse of [Formula: see text] and certain classes of generalized inverses of [Formula: see text] and [Formula: see text], and the [Formula: see text]-inverse of [Formula: see text] are characterized for some [Formula: see text], where [Formula: see text]. Necessary and sufficient conditions for the existence of the [Formula: see text]-inverse of a lower triangular matrix over an associative ring [Formula: see text] are also given, and its expression is derived, where [Formula: see text] are regular triangular matrices.

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Three limit representations of the core-EP inverse

Filomat ◽

10.2298/fil1817887z ◽

2018 ◽

Vol 32 (17) ◽

pp. 5887-5894 ◽

Cited By ~ 14

Author(s):

Mengmeng Zhou ◽

Jianlong Chen ◽

Tingting Li ◽

Dingguo Wang

Keyword(s):

Explicit Expression ◽

Full Rank ◽

The Core ◽

Core Inverse ◽

Rank Decomposition ◽

Dual Core

In this paper, we present three limit representations of the core-EP inverse. The first approach is based on the full-rank decomposition of a given matrix. The second and third approaches, which depend on the explicit expression of the core-EP inverse, are established. The corresponding limit representations of the dual core-EP inverse are also given. In particular, limit representations of the core and dual core inverse are derived.

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On the continuity and differentiability of the (dual) core inverse in C*-algebras

Linear and Multilinear Algebra ◽

10.1080/03081087.2018.1516187 ◽

2018 ◽

Vol 68 (4) ◽

pp. 686-709 ◽

Cited By ~ 4

Author(s):

Julio Benítez ◽

Enrico Boasso ◽

Sanzhang Xu

Keyword(s):

C Algebras ◽

Core Inverse ◽

Dual Core

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The core and dual core inverse of a morphism with factorization

Journal of Algebra and Its Applications ◽

10.1142/s0219498819500981 ◽

2019 ◽

Vol 18 (05) ◽

pp. 1950098 ◽

Cited By ~ 1

Author(s):

Tingting Li ◽

Jianlong Chen

Keyword(s):

The Core ◽

Core Inverse ◽

Dual Core

Let [Formula: see text] be a category with an involution ∗. Suppose that [Formula: see text] is a morphism and [Formula: see text] is an (epic, monic) factorization of [Formula: see text] through [Formula: see text], then [Formula: see text] is core invertible if and only if [Formula: see text] and [Formula: see text] are both left invertible if and only if [Formula: see text], [Formula: see text] and [Formula: see text] are all essentially unique (epic, monic) factorizations of [Formula: see text] through [Formula: see text]. We also give the corresponding result about dual core inverse. In addition, we give some characterizations about the coexistence of core inverse and dual core inverse of an [Formula: see text]-morphism in the category of [Formula: see text]-modules of a given ring [Formula: see text].

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Core and dual core inverses of a sum of morphisms

Filomat ◽

10.2298/fil1910931l ◽

2019 ◽

Vol 33 (10) ◽

pp. 2931-2941 ◽

Cited By ~ 1

Author(s):

Tingting Li ◽

Jianlong Chen ◽

Dingguo Wang ◽

Sanzhang Xu

Keyword(s):

Jacobson Radical ◽

The Core ◽

Unital Ring ◽

Additive Category ◽

Core Inverse ◽

Dual Core

Let C be an additive category with an involution *. Suppose that ? : X ? X is a morphism of C with core inverse ?# : X ? X and ? : X ? X is a morphism of C such that 1X + ?#? is invertible. Let ? = (1X+?#?)-1, ? = (1X+??#)-1, ? = (1X-??#)??(1X-?#?), ? = ?(1X-?#?)?-1??#?,? = ??#??-1(1X-??#)?,? = ?*(?#(*?*(1X-??#)?. Then f = ? + ? ? ? has a core inverse if and only if 1X-?, 1X-? and 1X-? are invertible. Moreover, the expression of the core inverse of f is presented. Let R be a unital *-ring and J(R) its Jacobson radical, if a ? R# with core inverse a # and j ? J(R), then a + j ? R# if and only if (1-aa#)j(1+a#j)-1(1-a#a) = 0. We also give the similar results for the dual core inverse.

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