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.

EXTENSIONS OF SOME THEOREMS ON 1-FACTORS

Let G be a graph and n be a positive integer. A spanning subgraph F of G is called a {1, 3, …, 2n-1} -factor if d_F(x)∈{1, 3, …, 2n-1} for all x∈ V(G). Here we give several results on {1, 3, …, 2n-1} -factors, which are the extensions of some theorems on 1-factors given by Las Vergnas, Sumner and 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. Experimental 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。

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 Modules with ACC on d-annihilators

A unitary right R-module MR satisfies acc on d-annihilators if for every sequence(a_n)_n of elements of R the ascending chain AnnM(a_1)■ AnnM(a_1 a_2)■AnnM(a_1 a_2 a_3)■… 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.

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.

L^(2) EXTENSIONS WITH SINGULAR METRICS ON K?HLER MANIFOLDS

In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.

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.

Transsphenoidal microsurgical operation for pituitary adenomas with suprasellar extensions

Objective: To evaluate the feasibility and therapeutic effectiveness of the transsphenoidal microsurgical removal of pituitary adenomas with suprasellar extensions. MethodS: We reviewed the diagnosticmodes, surgical technique, and outcomes of 152 patients suffering from pituitary adenomas with suprasellarextensions who were treated by transsphenoidal microsurgery in our department. Diagnosis was confirmed byCT or MRI scanning. All tumours with diameter >10 mm were characterized by suprasellar extensions. Op.erations were performed via either sublabio-septo-sphenoidal approach or naso-vestibulo-sphenoidal approachunder microscope. A subarachnoid catheter was preoperatively inserted in the lumbar cistern, through whichsaline was slowly injected during operation to increase the intracranial pressure (ICP) so as to deliver thesuprasellar tumour into the operative field to aid the removal. Result: Of the 152 cases, the gross total removal of adenoma in 106 cases (69. 7% ) and subtotal removal in 37 cases (24. 4% ) were achieved, and partial removal was carried out in the remaining 9 cases (5. 9 % ) of fibrous or dumbbell-shaped adenomas. Therewere no deaths after operation in this group. Follow-up review (median 3. 5 years) in 137 patients revealedgood recovery in 97 patients (70. 8% ), and late recurrence in 40 patients (29. 2% ) who need reoperativemanagement, drug therapy, radiotherapy, or radiosurgery used either alone or combined. Conclusion: Microsurgical technique via transsphenoidal approach is a safe and effective way to remove the pitoitary adenomas with suprasellar extensions but not for fibrous or dumbbell-shaped ones.

Derivations of Skew PBW-Extensions

The paper contains a classification of derivations of skew PBW-extensions of rings.

Gorenstein homological invariant properties under Frobenius extensions

We prove that for a Frobenius extension,a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective.For a separable Frobenius extension between Artin algebras,we obtain that the extension algebra is CM(Cohen-Macaulay)-finite(resp.CM-free)if and only if so is the base algebra.Furthermore,we prove that the representation dimension of Artin algebras is invariant under separable Frobenius extensions.

Invariant properties of representations under cleft extensions

The main aim of this paper is to give the invariant properties of representations of algebras under cleft extensions over a semisimple Hopf algebra. Firstly, we explain the concept of the cleft extension and give a relation between the cleft extension and the crossed product which is the approach we depend upon. Then, by making use of them, we prove that over an algebraically closed field k, for a finite dimensional Hopf algebra H which is semisimple as well as its dual H*, the representation type of an algebra is an invariant property under a finite dimensional H-cleft extension . In the other part, we still show that over an arbitrary field k, the Nakayama property of a k-algebra is also an invariant property under an H -cleft extension when the radical of the algebra is H-stable.

Leakage Is Prohibited:Memory Protection Extensions Protected Address Space Randomization

Code reuse attacks pose a severe threat to modern applications. These attacks reuse existing code segments of vulnerable applications as attack payloads and hijack the control flow of a victim application. With high code entropy and a relatively low performance overhead, Address Space Layout Randomization(ASLR) has become the most widely explored defense against code reuse attacks. However, a single memory disclosure vulnerability is able to compromise this defense. In this paper, we present Memory Protection Extensions(MPX)-assisted Address Space Layout Randomization(M-ASLR), a novel code-space randomization scheme. M-ASLR uses several characteristics of Intel MPX to restrict code pointers in memory. We have developed a fully functioning prototype of M-ALSR, and our evaluation results show that M-ASLR:(1) offers no interference with normal operation;(2) protects against buffer overflow attacks, code reuse attacks, and other sophisticated modern attacks;and(3) adds a very low performance overhead(3.3%) to C/C++ applications.