Centrally clean elements and central Drazin inverses in a ring

Element a in ring R is called centrally clean if it is the sum of central idempotent e and unit u.Moreover,a=e+u is called a centrally clean decomposition of a and R is called a centrally clean ring if every element of R is centrally clean.First,some characterizations of centrally clean elements are given.Furthermore,some properties of centrally clean rings,as well as the necessary and sufficient conditions for R to be a centrally clean ring are investigated.Centrally clean rings are closely related to the central Drazin inverses.Then,in terms of centrally clean decomposition,the necessary and sufficient conditions for the existence of central Drazin inverses are presented.Moreover,the central cleanness of special rings,such as corner rings,the ring of formal power series over ring R,and a direct product ∏ R_(α) of ring R_(α),is analyzed.Furthermore,the central group invertibility of combinations of two central idempotents in the algebra over a field is investigated.Finally,as an application,an example that lists all invertible,central group invertible,group invertible,central Drazin invertible elements,and centrally clean elements of the group ring Z_(2)S_(3) is given.

Calibration of Discrete Element Heat Transfer Parameters by Central Composite Design

The efficiency and precision of parameter calibration in discrete element method （DEM） are not satisfactory, and parameter calibration for granular heat transfer is rarely involved. Accordingly, parameter calibration for granular heat transfer with the DEM is studied. The heat transfer in granular assemblies is simulated with DEM, and the effective thermal conductivity （ETC） of these granular assemblies is measured with the transient method in simulations. The measurement testbed is designed to test the ETC of the granular assemblies under normal pressure and a vacuum based on the steady method. Central composite design （CCD） is used to simulate the impact of the DEM parameters on the ETC of granular assemblies, and the heat transfer parameters are calibrated and compared with experimental data. The results show that, within the scope of the considered parameters, the ETC of the granular assemblies increases with an increasing particle thermal conductivity and decreases with an increasing particle shear modulus and particle diameter. The particle thermal conductivity has the greatest impact on the ETC of granular assemblies followed by the particle shear modulus and then the particle diameter. The calibration results show good agreement with the experimental results. The error is less than 4%, which is within a reasonable range for the scope of the CCD parameters. The proposed research provides high efficiency and high accuracy parameter calibration for granular heat transfer in DEM.

Finite Element Analysis on the Pre-load Structures of the Central Solenoid for the HT-7U Device

The central solenoid is an important part of the HT-7U device. In this paper， the computational analysis of the stress and the displacement on the pre-load structures of the central solenoid have been made by the finite element analysis system COSMOS/M2.0 under room and/or operating temperature. According to the analytical results, the clip aprons and compression plates are all satisfied with safety design criteria.

Geochemical characteristics of REY-rich pelagic sediments from the GC02 in central Indian Ocean Basin

As a potential mineral resource, the clay minerals enriched in rare earth elements including yttrium（REY） in the deep sea have been attracting great attention. However, the enrichment mechanism of REY remains unclear. To understand the geochemical characteristics and factors controlling REY enrichment in zeolite clay in the deep sea, we conducted mineral identification by XRD, major and trace element measurements by XRF and REY analyses by ICP-MS on a 1.4-m-long sediment core（GC02） located in the Central Indian Oceanic Basin（CIOB）. The main findings include：（1） the core sediments in GC02 possess elevated REY contents and exhibited a strong negative Ce anomaly, an apparent MREE bulge and positive Y anomaly. These were comparable with typical REY-rich clays in the Pacific Ocean, indicating the similar REY enrichment mechanism and the presence of REY-rich clays in the CIOB;（2） in comparison with the dataset from the Wharton Basin and DSDP site 213, the higher content of REY and stronger PAAS（Post Archean Australian Shale） normalization patterns in the GC02 sediments were likely caused by the weaker impact of terrigenous materials of GC02. The CIOB was suggested to be a promising place hosting REY rich pelagic sediments.

Annihilator Ideals of Indecomposable Modules of Finite-Dimensional Pointed Hopf Algebras of Rank One

Let H be a finite-dimensional pointed Hopf algebra of rank one over an algebraically closed feld of characteristic zero.We describe all annihilator ideals of indecomposable H-modules by generators.In particular,we give the classification of all ideals of the finite-dimensional pointed rank one Hopf algebra of nilpotent type over the Klein 4-group.

Explicit Generators of the Centre of the Quantum Group

A finite generating set of the centre of any quantum group is obtained,where the generators are given by an explicit formulae.For the slightly generalised version of the quantum group which we work with,we show that this set of generators is algebraically independent,thus the centre is isomorphic to a polynomial algebra.

Universal Enveloping Algebras of Simple Symplectic Anti-Jordan Triple Systems

In this work we axe concerned with the universal associative envelope of a finite-dimensional simple symplectic anti-Jordan triple system （AJTS）. We prove that if T is a triple system as above, then there exists an associative algebra U（T） and an injective homomorphism ε ： T→ U（T）, where U（T） is an AJTS under the triple product defined by （a, b, c） = abc- cba. Moreover, U（T） is a universal object with respect to such homomorphisms. We explicitly determine the PBW-basis of U（T）, the center Z（U（T）） and the Gelfand-Kirillov dimension of U（T）.

Quadratic Algebras of Type AIII(Ⅱ)

This is the last in a series of three articles studying some quadratic algebras related to quantized matrix algebras. Here we determine the full set of so\|called cyclic representations of the quantized matrix algebra M\-q(3). These are irreducible representations in which all generators are invertible and the assumption on q is that it is a primitive m\|th root of 1, with m≥3.