COMPARISON OF HOMOLOGIES AND AUTOMATIC EXTENSIONS OF INVARIANT DISTRIBUTIONS

Let G be a reductive Nash group,acting on a Nash manifold X.Let Z be a G-stable closed Nash submanifold of X and denote by U the complement of Z in X.Letχbe a character of G and denote by g the complexified Lie algebra of G.We give a sufficient condition for the natural linear map H_(k)(g,S(U)×χ)→H_k(g,S(X)×χ)between the Lie algebra homologies of Schwartz functions to be an isomorphism.For k=0,by considering the dual,we obtain the automatic extensions of g-invariant(twisted by-χ)Schwartz distributions.

IMPROVED REGULARITY OF HARMONIC DIFFEOMORPHIC EXTENSIONS ON QUASIHYPERBOLIC DOMAINS

Let X be a Jordan domain satisfying certain hyperbolic growth conditions.Assume that φ is a homeomorphism from the boundary ?X of X onto the unit circle.Denote by h the harmonic diffeomorphic extension of φ from X onto the unit disk.We establish the optimal Orlicz-Sobolev regularity and weighted Sobolev estimate of h.These generalize the Sobolev regularity of h in [A.Koski,J.Onninen,Sobolev homeomorphic extensions,J.Eur.Math.Soc.23(2021) 4065-4089,Theorem 3.1].

Impact of trading hours extensions on foreign exchange volatility:intraday evidence from the Moscow exchange

Using transaction-level tick-by-tick data of same-and next-day settlement of the Russian Ruble versus the US Dollar exchange rate(RUB/USD)traded on the Moscow Exchange Market during the period 2005–2013,we analyze the impact of trading hours extensions on volatility.During the sample period,the Moscow Exchange extended trading hours three times for the same-day settlement and two times for the next-day settlement of the RUB/USD rate.To analyze the effect of the implementations,various measures of historical and realized volatility are calculated for 5-and 15-min intraday intervals spanning a period of three months both prior to and following trading hours extensions.Besides historical volatility measures,we also examine volume and spread.We apply an autoregressive moving average-autoregressive conditional heteroscedasticity(ARMA-GARCH)model utilizing realized volatility and a trade classification rule to estimate the probability of informed trading.The extensions of trading hours cause a significant increase in both volatility and volume for further analyzing the reasons behind volatility changes.Volatility changes mostly occur after the opening of the market.The length of the extension has a significant positive effect on realized volatility.The results indicate that informed trading increased substantially after the opening for the rate of same-day settlement,whereas this is not observed for next-day settlement.Although trading hours extensions raise opportunities for more transactions and liquidity in foreign exchange markets,they may also lead to higher volatility in the market.Furthermore,this distortion is more significant at opening and midday.A potential explanation for the increased volatility mostly at the opening is that the trading hours extension attracts informed traders rather than liquidity providers.

An Introduction to the Theory of Field Extensions

This paper unfolds and reviews the theory of abstract algebra, field extensions and discusses various kinds of field extensions. Field extensions are said to be algebraic or transcendental. We pay much attention to algebraic extensions. Finally, we construct finite extensions of Q and finite extensions of the function field over finite field Fp using the notion of field completion, analogous to field extensions. With the study of field extensions, considering any polynomial with coefficients in the field, we can find the roots of the polynomial, and with the notion of algebraically closed fields, we have one field, F, where we can find the roots of any polynomial with coefficients in F.

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.

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）.

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.

Landforms Evolution of Wadi Qudaid Area, West Central Arabian Shield, Saudi Arabia: An Example of the Role of the Geological Factors in the Urban Extensions

Wadi Qudaid is located in the west central part of Saudi Arabia. It about 135 km to the northeast of Jeddah city along Al Haramein highway and it represents the upstream of the very large alluvial plain along the Red Sea coast. It runs in NE direction parallel to many wadis of the west central part of Saudi Arabia i.e. Wadi Fatima, wadi Sitarah. The wadi floor is filled by Quaternary deposits which represent good groundwater aquifer. Geologically, the present-day residual landforms of Wadi Qudaid are composed mainly of Precambrian Arabia shield rocks overlained by Tertiary sedimentary rocks and finally harrat (Tertiary volcanic). The Precambrian rocks are represented by 1) a lower layered basic and intermediate volcanic and the intercalated volcaniclastics. This unit is correlatable with Samran Group, 2) an upper layered acidic volcanic and the intercalated acidic volcaniclastics. The Arabian shield rocks are intensively folded and dragged along the major NE faults. They are directly overlain by Tertiary basic volcanic (harrat) and the related volcanoclastic red beds). The main geomorphologic elements of the study area include plateau, scarps, and the wadi floor. The plateau is represented by the black basaltic sheet that contains some semi-rounded depressions filled with Quaternary eolian sands. The scarps of the main wadi and its tributaries are nearly steep and contain many asphaltic roads with some isolated cone hills detached from the scarps. Geomorphological, Wadi Qudaid represents the incomplete erosion cycle that begins with the formation of deep galleries and very steep and narrow wadies formed along the major NE faults and related fractures and folds. The progress of the erosion processes led to the formation of narrow interfluves as a result of pedimentation and sculpturing of the wadies sides by scarp retreat. The peniplanation stages of the erosion cycles are reached in the southwestern and the central part of the wadi where fast peniplained areas were formed. The results of this study revealed the role of the different geological processes (lithology, structural elements and climatic conditions) in the distribution of present-day human populations in urban extensions. Qudaid, Dhubaya-Jumah, Dabyah, Al Khamrah, Almansa and Al Massamah are the main villages of Wadi Qudaid area.

随需而变，Quest软件的桌面组策略扩展——Group Policy Extensions for Desktops

工欲善其事。必先利其器。面对着越来越多的移动用户。桌面管理员们常常会通过各种组策略设置来满足他们的工作需求。但遗憾的是。仅通过微软内置的组策略还不能满足他们更细化的应用需求。他们更需要一种能够自动适应用户环境变化的弹性策略。在本文中，将介绍一个小巧实用的工具——Ouest Group Policy Extensions for Desktops。通过它来扩展一些组策略的设置。

SQL Server Powershell Extensions使用免费工具自动完成管理任务

PowerShell是一种非常强大的脚本语言，利用它几乎可以自动执行所有管理任务。本月的免费工具是一套非常方便的PowerShell脚本，SQL Server PowerShell Extensions（SQLPSX）。SQLPSX是由Chad Miller编写的，他生活在佛罗里达州Tampa市，是一位SOL ServerDBA，SQLPSX可以自动完成SQLServer中许多常见的管理任务。

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 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.

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.

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.

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.

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).

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.

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.

Ideal cotorsion pairs over one point extensions

Let R[P] be the one point extension of a k-algebra R by a projective R-module P.We prove that the extension of a complete ideal cotorsion pair in R-Mod is still a complete ideal cotorsion pair in R[P]-Mod.As an application,it is obtainable that the operation(-)_(m)[P]satisfies the so-called distributive law relating the operations of products and extensions of ideals under appropriate conditions.