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AbstractLet A be an m × n complex matrix and let B, C be n × m complex matrices. The main purpose of this article is to derive several new properties of the (B, C)-core inverse. Also, we introduce and investigate the dual (B, C)-core inverse in the context of rectangular matrices. The connection between (dual) (B, C)-core inverses and other generalized inverses is given. Finally, the minimum norm solution and least square solution to the equation are expressed by using the (B, C)-core inverse. [ABSTRACT FROM AUTHOR]

Let S be a * -semigroup and let a , w , v ∈ S . The initial goal of this work is to introduce two new classes of generalized inverses, called the w-core inverse and the dual v-core inverse in S. An element a ∈ S is w-core invertible if there exists some x ∈ S such that a w x 2 = x , xawa = a and (awx) * = awx . Such an x is called a w-core inverse of a. It is shown that the core inverse and the pseudo core inverse can be characterized in terms of the w-core inverse. Several characterizations of the w-core inverse of a are derived, and the expression is given by the inverse of w along a and {1, 3}-inverses of a in S. Also, the connections between the w-core inverse and other generalized inverses are given. In particular, when S is a * -ring, the criterion for the w-core inverse is given by units. The dual v-core inverse of a is defined by the existence of y ∈ S satisfying y 2 v a = y , avay = a and (yva) * = yva . Dual results for the dual v-core inverse also hold. Communicated by Pace Nielsen [ABSTRACT FROM AUTHOR]

This paper contributes to define one-sided versions of 'w-core inverse' introduced by the writer. Given any ∗ -ring R and a , w ∈ R , a is called right w-core invertible if there exists some x ∈ R satisfying awxa = a, a w x 2 = x and a w x = (a w x) ∗ . Several characterizations for this type of generalized inverses are given, and it is shown that a is right w-core invertible if and only if a is right w (a w) n − 1 -core invertible if and only if there exists a Hermitian element p such that pa = 0 and p + (a w) n is right invertible for any integer n ≥ 1 , in which case, the expression of right w-core inverses is given. Finally, it is proved that right w-core inverses are instances of right inverses along an element, right (b , c) -inverses and right annihilator (b , c) -inverses. As an application, the characterization for the Moore–Penrose inverse is given. [ABSTRACT FROM AUTHOR]

Let R be a * -ring. In this article, we introduce good * -clean elements and left * -suitable elements in R, respectively. An element a ∈ R is good * -clean if it can be written as the sum of a projection and a unitary element. An element a ∈ R is left * -suitable if there exists a projection p ∈ R a such that 1 − p ∈ R (1 − a). Several properties of them are given and their characterizations are derived by the solvability of the Sylvester equation X A − B X = C in a ring. Finally, we use generalized inverses to give the existence criterion of left * -suitable elements. [ABSTRACT FROM AUTHOR]

TBK1 (TANK-binding kinase 1) is an essential receptor protein required for the innate immune response, but the mechanisms underlying TBK1 stability, especially those regulated via autophagy, remain poorly understood. Here, we demonstrate that USP19 (ubiquitin specific peptidase 19) interacts with and promotes TBK1 lysosomal degradation via chaperone-mediated autophagy (CMA). We observed that TBK1 had a canonical CMA motif, knocking down key proteins involved in CMA (HSPA8/HSC70 or LAMP2A) or inhibiting CMA-prevented USP19-mediated TBK1 degradation. Furthermore, USP19 deficiency in macrophages caused an elevation of TBK1 and the activation of the type-I interferon signaling pathway after vesicular stomatitis virus (VSV) infection. Consistently, macrophage-specific usp19 knockout in mice resulted in attenuated VSV replication and resistance to VSV infection in vivo. Altogether, our results suggest that USP19 is a key regulator of TBK1 and uncovers a previously uncharacterized role for USP19 in CMA-mediated TBK1 degradation and infectious diseases. [ABSTRACT FROM AUTHOR]

Ethylene residue pitch (ETP) is the by-product in the process of producing ethylene from the pyrolysis of crude oil. ETP is a kind of complex organic matrix with a lower aromaticity, a larger number of aliphatic chain hydrocarbons, and a higher content of carbon. To study the effects of thermal polycondensation on the quality of derived needle coke, 5 types of thermally modified ETPs have been used as the feedstock for needle coke production. Thermal modification is a favorable method to adjust the molecular structure parameters of ETP (especially on Iar and CH3/CH2). Iar is also a key parameter to determine the quality of ETP-based needle coke. Thermal modification treatment of ETP followed by liquid-phase carbonization is a feasible strategy to obtain high-quality ETP-based needle coke with the content of tended regular carbon microcrystals higher than 74%, the specific area (SBET) lower than 6 m2·g−1, the microstrength higher than 61%, and the resistance lower than 5.747 Ω. Therefore, moderate thermal modification of ETP significantly enhances the properties of the derived needle coke. [ABSTRACT FROM AUTHOR]

Metal halide perovskite semiconductors could potentially be used to create field-effect transistors (FETs) with high carrier mobilities. This review summarizes progress achieved recently in three-dimensional (3D) lead-based and two-dimensional (2D) tin-based perovskite FETs, and identifies the evolution of electrical characteristics and stability, then discusses outstanding challenges and provides an outlook on the possibilities offered by this electronic material family for use in backplane drivers for active matrix displays. [ABSTRACT FROM AUTHOR]

Let R be an associative ring. In this paper, we give a positive answer to the question of M.P. Drazin, "whether a ∈ R has a unique core-quasi-nilpotent decomposition implies that it must be quasi-invertible". [ABSTRACT FROM AUTHOR]

Let R be a unital ∗ -ring and let a , e , f ∈ R with e,f invertible Hermitian elements. In this paper, we define two types of outer generalized inverses, called pseudo e-core inverses and pseudo f-dual core inverses. An element a ∈ R is pseudo e-core invertible if there exist an element x ∈ R and some positive integer n such that x a x = x , x R = a n R and R x = R (a n) ∗ e. Dually, a is pseudo f-dual core invertible if there exist an element x ∈ R and some positive integer m such that xax=x, R x = R a m and f x R = (a m) ∗ R. Moreover, we investigate both of them for their characterizations and properties. Also, the relations between the pseudo e-core inverse (resp. the pseudo f-dual core inverse) and the inverse along an element are given. [ABSTRACT FROM AUTHOR]

A three-stage failure process divides a product's life into three stages: normal, minor defective and severe defective stages. Under the condition-based renewable warranty policy, inspections are carried out to check which stage the product is in. Condition-based activities, such as shorting inspection intervals, preventive replacement and failure replacement, are carried out properly. From a manufacturer's perspective, the inspection interval is optimized by minimizing the expected cost rate per unit time over the whole warranty coverage. For comparison, the expected cost rate per unit time for warranty models without inspections and with fixed interval inspections are also derived. Numerical examples show that condition-based renewable warranty policy replacement policy can reduce the manufacturer's warranty cost significantly. [ABSTRACT FROM AUTHOR]

Let R be a unital -ring. In this paper, we give several characterizations for the pseudo core and dual pseudo core inverses of an element by units in R. Moreover, their relations with -DMP are obtained. As a special case, the existence criteria for EP elements (-DMP with index 1) are given. Then, the double commutant property of hybrid (b, c)-inverses is considered. Finally, the relations of the inverse along an element and the hybrid (b, c)-inverse, the (dual) pseudo core inverses and the hybrid (b, c)-inverse are investigated. [ABSTRACT FROM AUTHOR]

Let R be a unital -ring. In this paper, we introduce pseudo DMP inverses and generalized m-EP elements in R, which can been seen as extensions of DMP inverses and m-EP matrices, respectively. Also, we investigate both pseudo DMP inverses and generalized m-EP elements for their characterizations and properties. [ABSTRACT FROM AUTHOR]

Let R be an associative ring with unity 1 and let a,b,c∈R. In this paper, several characterizations for hybrid (b,c)-inverses of a are given. Also, the hybrid (b,c)-inverse of a is characterized by the group inverse of ab, under certain hypothesis. In particular, existence criteria for the the inverse along an element are obtained. Finally, we get the double commutant property and the reverse order law of annihilator (b,c)-inverses. [ABSTRACT FROM AUTHOR]

Let R be a unital -ring and a, p, q elements of R. When a is regular, and and , we derive the existence criterion and formula of the Moore-Penrose inverses of paq in a ring. Also, we give necessary and sufficient conditions for the existence of the core and dual core inverses of paq. As applications, the existence criterion and the expression of the core and dual core inverses of 2 by 2 matrices over a ring are given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept called left (right) g-MP inverse in a-monoid. The relations of this type of generalized inverse with left inverse along an element are investigated. Also, the reverse order law for the inverse along an element is studied. Then, the existence criteria and formulae of the inverse of the product of triple elements along an element are investigated in a monoid. Finally, we further study left and right g-MP inverses, the inverse along an element in the context of rings. [ABSTRACT FROM AUTHOR]

In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring. As applications, we present the equivalent conditions for the existence and expressions of the inverse along a matrix. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a new notion in a semigroupas an extension of Mary’s inverse. Let. An elementis called left (resp. right) invertible alongif there existssuch that(resp.) and(resp.). An existence criterion of this type inverse is derived. Moreover, several characterizations of left (right) regularity, left (right)-regularity and left (right)-regularity are given in a semigroup. Further, another existence criterion of this type inverse is given by means of a left (right) invertibility of certain elements in a ring. Finally, we study the (left, right) inverse along a product in a ring, and, as an application, Mary’s inverse along a matrix is expressed. [ABSTRACT FROM PUBLISHER]