分次zip环与SPlit-null扩张(英文)

本文定义并讨论了分次zip环,讨论了交换环的Split—null扩张的zip性,推广了C.Faith的部分结果。

LIBERAL EXTENSIONS 和反单本原根

设Ｒ≤Ｔ≤Ｓ，其中Ｓ是Ｒ的ＬｉｂｅｒａｌＥｘｔｅｎｓｉｏｎｓａｎｄＴ是Ｒ的ＩｎｔｅｒｍｅｄｉａｔｅＥｘｔｅｎｓｉｏｎ我们证明了下面等式：ｓ（Ｓ）∩Ｒ＝ｓ（Ｒ）＝ｓ（Ｔ）∩Ｒ，且ｓ（Ｔ）ｎ≤ｓ（Ｓ）．其中Ｓ可为反单本原根或反单根。

Mesozoic Large-scale Mineralization and Multiple Lithospheric Extensions in South China

South China is the most important polymetallic （tungsten, tin, bismuth, copper, silver, antimony, mercury, rare metals, heavy rare earth elements, gold and lead-zinc） province in China. This paper describes the basic characteristics of Mesozoic large-scale mineralization in South China. The large-scale mineralization mainly took place in three intervals： 170-150 Ma, 140-126 Ma and 110-80 Ma. Among these the first stage is mainly marked by copper, lead-zinc and tungsten mineralization and the third stage is mainly characterized by tin, gold, silver and uranium mineralization. The stage of 140-126 Ma mainly characterized by tungsten and tin mineralization is a transitional interval from the first to the third stage. In fight of the current research results of the regional tectonic evolution it is proposed that the large-scale mineralization in the three stages is related to post-collision between the South China block and the North China block, transfer of the principal stress-field of tectonic regimes from N-S to E-W direction, and multiple back-arc lithospheric extensions caused by subduction of the Paleo-Pacific plate.

DERIVATIONS AND EXTENSIONS OF LIE COLOR ALGEBRA

In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.

EXTENSIONS OF SOME INEQUALITIES

By using a simple analytic method the following inequalities are proved:(b x+y -a x+y )/(b x-a x)≥[(x+y)/x][(a+b)/2] y, for 0<a<b,x≥1,y>0,x+y≥2; (b x+y -a x+y )/(b x-a x)<[(x+y)/x][(a+b)/2] y, for 0<a<b,0<x<1,y>0,x+y≤2. These inequalities are the extensions of inequalities of Qi Feng, Xu Senlin and Zheng Lin. And a conjection of Qi Feng is proved not true.

A Remark on Double Ore Extensions

The aim of this article is to summarize the relationship between double Ore extensions and iterated Ore extensions, and mainly describe the lifting of properties from an algebra A to a(right) double Ore extension B of A which can not be presented as iterated Ore extensions.

Ore Extensions over Weakly 2-primal Rings

A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorphism and δ an α- derivation of a ring R. We prove that （1） If R is an （α, δ）-compatible and weakly 2-primal ring, then R[x; α, δ] is weakly semicommutative; （2） If R is （α, δ）-compatible, then R is weakly 2-primal if and only if R[x; α, δ] is weakly 2-primal.

The Excellent Extensions of Rings and Copure Dimensions

Let R be a noetherian ring and S an excellent extension of R.cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M.We prove that if M S is a right S-module then cid(M S)=cid(M R) and if S M is a left S-module then cfd(S M)=cfd(R M).Moreover,cid-D(S)=cid-D(R) and cfd-D(S)=cfdD(R).

Extensions of strongly π-regular general rings

The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.

Optimal design of left-lane line extensions considering non-yielding maneuvers at the beginning of the permitted phase

In order to restrict non-yielding maneuvers of left-turning vehicles,an optimal design of left-lane line extensions is proposed to solve the problem.A field observation was conducted to collect a data set of left-turning vehicles at the beginning of a green phase at two similar intersections(one with a permitted phase and the other with a protected phase).The comparative analysis shows no significant difference in the speed distribution using either a permitted phase or a protected phase,but it reveals that a permitted phase can lead to a larger acceleration when the left-turn vehicles pass through the conflict points.Those indicate the existence of non-yielding maneuvers of left-turn vehicles at signalized intersections with a permitted phase.Optimal designed left-lane line extensions contain two types of segments,circular curves and transition curves,and they are only related to four geometry parameters of an intersection.The proposed method is easy to use and it can offer reference for intersection channelization and traffic organization.

Extensions of Modules with ACC on d-annihilators

A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.

Expanders, Group Extensions, Hadamard Manifolds and Certain Banach Spaces

In this note,we prove that expanders cannot be coarsely embedded into group extensions of sequences of groups which are coarsely embeddable into Hardamad manifolds and certain Banach spaces due to the similar concentration theorems.

SUPERSYMMETRIC INVARIANCE AND UNIVERSAL CENTRAL EXTENSIONS OF LIE SUPERTRIPLE SYSTEMS

In this article, we discuss some properties of a supersymmetric invariant bilinear form on Lie supertriple systems. In particular, a supersymmetric invariant bilinear form on Lie supertriple systems can be extended to its standard imbedding Lie superalgebras. Furthermore, we generalize Garland＇s theory of universal central extensions for Lie supertriple systems following the classical one for Lie superalgebras. We solve the problems of lifting automorphisms and lifting derivations.

A Note on Abelian Extensions

Let K/Q be any abelian extension where Q is the field of rational numbers. By Galois theory and the Frobenius formula for induced characters, we prove that there exists a metabelian group G and an irreducible character X of G such that K=Q（X）.

The Almost Split Sequences for Trivial Extensions of Hereditary Algebras

Let A be a basic hereditary artin algebra and R = A Q be the trivial extension of A by its minimal injective cogenerator Q. We construct some right （left） almost split morphisms and irreducible morphisms in modR through the corresponding morphisms in modA. Furthermore, we can determine its almost split sequences in modR.

WHITEHEAD GROUPS OF MODULE EXTENSIONS

When R satisfies (strong unit) 1-stable range and M is a R-R-bimodule, the authors calculate that K_1(R(?) M)≌U(R(?) M)/L(R(?) M). As applications, the authors also calculate some Whitehead groups for exchange rings with artinian primitive factors.

Two-Dimensional Lithium-Ion Battery Modeling with Electrolyte and Cathode Extensions

A two-dimensional model for transport and the coupled electric field is applied to simulate a charging lithium-ion cell and investigate the effects of lithium concentration gradients within electrodes on cell performance. The lithium concentration gradients within electrodes are affected by the cell geometry. Two different geometries are investigated: extending the length of the electrolyte past the edges of the electrodes and extending the length of the cathode past the edge of the anode. It is found that the electrolyte extension has little impact on the behavior of the electrodes, although it does increase the effective conductivity of the electrolyte in the edge region. However, the extension of the cathode past the edge of the anode, and the possibility for electrochemical reactions on the flooded electrode edges, are both found to impact the concentration gradients of lithium in electrodes and the current distribution within the electrolyte during charging. It is found that concentration gradients of lithium within electrodes may have stronger impacts on electrolytic current distributions, depending on the level of completeness of cell charge. This is because very different gradients of electric potential are expected from similar electrode gradients of lithium concentrations at different levels of cell charge, especially for the LixC6 cathode investigated in this study. This leads to the prediction of significant electric potential gradients along the electrolyte length during early cell charging, and a reduced risk of lithium deposition on the cathode edge during later cell charging, as seen experimentally by others.

An Introduction to High Efficiency Video Coding Range Extensions

High Efficiency Video Coding (HEVC) is the latest international video coding standard, which can provide the similar quality with about half bandwidth compared with its predecessor, H.264/MPEG?4 AVC. To meet the requirement of higher bit depth coding and more chroma sampling formats, range extensions of HEVC were developed. This paper introduces the coding tools in HEVC range extensions and provides experimental results to compare HEVC range extensions with previous video coding standards. Ex?perimental results show that HEVC range extensions improve coding efficiency much over H.264/MPEG?4 AVC High Predictive profile, especially for 4K sequences.

H-separable Hopf Galois Extensions and Azumaya Algebra

Let H be a finite dimensional semisimple Hopf algebra over a field and A an H-module algebra. In this paper, we characterize any H-separable Galois extension of an Azumaya algebra. Assuming that A/AH is an H-separable extension, we prove that A/AH is H-Galois and AH is Azumaya if and only if A#H is an Azumaya Z-algebra, where Z is the center of A#H(not necessarily C(A)H).

Splitting Extensions of Abelian by Hyper-(cyclic or finite) Groups (Ⅱ)

Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained： if G∈F, f（ ∞ ） include f（p）, f（p） ≠φ for each p∈π, and A has no nonzero F central ZG- images, then any extension E of A by G splits conjugately over A, and A has no nonzero F central ZG-factors.