ON LINEAR EXTENSION OF 1-LIPSCHITZ MAPPING FROM HILBERT SPACE INTO A NORMED SPACE

In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry on the whole space.

One Roper-Suffridge Extension Operator in Complex Banach Spaces

In this paper, by the definition of almost spirallike mappings of type β and order α and the geometric property of the spirallike mapping of type β, we prove that the generalized Roper-Suffridge extension operator preserves almost spirallikeness of type β and order α in complex Banach spaces. Key words：

Loewner Chains Associated with the Generalized Roper-Suffridge Extension Operator on the Unit Ball in Hilbert Spaces

In this paper, we prove that the generalized Roper-Suffridge extension operator can be embeded in Loewner chains on the unit ball in Hibert spaces, and obtain the fact that the operator keeps the properties of almost spirallike mapping of typeβ and order α, almost starlikeness of order α, spirallikeness of type ofβ and starlikeness.

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.

A Note on Linear Extension of Isometries Between the Unit Spheres in β-normed Spaces

In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.

HARNACK EXTENSION FOR THE HENSTOCK INTEGRAL IN THE EUCLIDEAN SPACE

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SIR phasing by combination of SOLVE/RESOLVE and dual-space fragment extension involving OASIS

A new phasing procedure has been proposed for dealing with single isomorphous replacement （SIR） x-ray diffraction data. The procedure combines SOLVE/RESOLVE with the dual-space fragment extension involving OASIS. Two sets of SIR data at 0.28 nm resolution taken from the protein （R）-phycoerythrin （PDB code： 1LIA） were used in the test. For one of the two SIR data sets, a default run of SOLVE/RESOLVE based on the heavy-atom substructure found by SHLEXD led automatically to an interpretable electron density map. OASIS could not effectively improve the result. For the other set of SIR data, SOLVE/RESOLVE resulted in a fragmented model consisting of 454 of the total 668 residues, in which only 29 residues were docked into the sequence. Based on this model, 7 iteration cycles of OASIS-DM- RESOLVE （build only） yielded automatically a model of 547 residues with 133 residues docked into the sequence. The overall-averaged phase error decreased considerably and the quality of electron density map was improved significantly. Two more cycles of iterative OASIS-DM-RESOLVE were carried out, in which the output phases and figures of merit from DM were merged with that from the original run of SOLVE/RESOLVE before they were passed onto RESOLVE （build only）. This led automatically to a model containing 452 residues with 173 docked into the sequence. The resultant electron density map is manually traceable. It is concluded that when results of SOLVE/RESOLVE are not sufficiently satisfactory, the combination of SOLVE/RESOLVE and OASIS-DM-RESOLVE （build only） may significantly improve them.

ON CONDITIONS FOR THE NON LOCALLY CONVEX LINEAR TOPOLOGICAL SPACE TO HAVE THE H．－B． EXTENSION PROPERTY

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A Theorem for Generalized Extension of Operators and Some Applications

In this note it is shown that every bounded linear operator T∈B(Y, Z) defined on a closed subspace Y of a Banach space X admits a generalized extension T∈B(X, V). Some examples of the applications are given; especially, a character-ization of H.I. spaces is obtained.

Harmonic extension of Q-type space related to logarithmic functions

This paper studies a class of Q-type spaces Q^(m)_(log,λ)(R^(n))related to logarithmic functions.We first investigate some basic properties ofQ^(m)_(log,λ)(R^(n)).Further,by the aid of Poisson integral and harmonic function spaces H^(m)_(log,λ)(R_(+)^(n+1)),the harmonic extension of Q^(m)_(log,λ)(R^(n))and the boundary value problem of H^(m)_(log,λ)(R_(+)^(n+1))are obtained.

ISOMETRY AND PHASE-ISOMETRY OF NON-ARCHIMEDEAN NORMED SPACES

In this paper,we study isometries and phase-isometries of non-Archimedean normed spaces.We show that every isometry f:Sr(X)→Sr(X),where X is a finite-dimensional non-Archimedean normed space and Sr(X)is a sphere with radius r∈||X||,is surjective if and only if is spherically complete and k is finite.Moreover,we prove that if X and Y are non-Archimedean normed spaces over non-trivially non-Archimedean valued fields with|2|=1,any phase-isometry f:X→Y is phase equivalent to an isometric operator.

“In Space” or “As Space”?: Spatial Autocorrelation Properties of the Earth’s Interior

In this analysis, natural systems are posed to subsystemize in a manner facilitating both structured information/energy sharing and an entropy maximization process projecting a three-dimensional, spatial outcome. Numerical simulations were first carried out to determine whether n × n input-output matrices could, once entropy-maximized, project a three-dimensional Euclidean metric. Only 4 × 4 matrices could;a small proportion passed the test. Larger proportions passed when grouped random patterns on and within two- and three-dimensional forms were tested. The pattern of structural zonation within the earth was then tested in analogous fashion using spatial autocorrelation measures, and for three time periods: current, 95 million years b.p. and 200 million years b.p. All expected results were obtained;not only do the geometries of zonation project a three-dimensional structure as anticipated, but also do secondary statistical measures reveal levels of equilibrium among the zones in all three cases that are nearly total, distinguishing them from simulations that do not incorporate a varying-surface zone-width element.

A Simple Proof for a Property of the Vector Space Ⅴ Over the Field F

In this paper we’ll prove a fundameutal property of the vector space by means of the ex-tension field,i.e.the numbers of the elements of a basis of the vector space V over the field Fequal to the d imensions(V:F).

Think ＂ Big＂ and become ＂ Big＂ ： On the architectureand space of an urban museum

Nowadays many urban museums are situated in ever-changing cities face with problems regardingspace and architecture. The main question this paper wants to discuss is how the museum could achieve accessibilityand inclusiveness to a greater extent via rethinking and reshaping its space, both physically and vir -tually,Based on practices conducted by the Museum of London since its establishment in the 20th century, Iendeavour to understand how the museum architecture was established during the negotiation and compro -mise among different individuals and parties and to extend the conception by exploring the possibilities of expanding out of the traditional realm of the museum architecture.

Extension of isometries on the unit sphere of l^p (Γ) space

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 【 p 【 ∞,p≠2) onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto E,so,we give an affirmative answer to the corresponding Tingley’s problem.

Polynomials,Higher Order Sobolev Extension Theorems and Interpolation Inequalities on Weighted Folland-Stein Spaces on Stratified Groups

This paper consists of three main parts.One of them is to develop local and global Sobolev interpolation inequalities of any higher order for the nonisotropic Sobolev spaces on stratified nilpotent Lie groups.Despite the extensive research after Jerison’s work[3]on Poincaré-type inequalities for Hrmander’s vector fields over the years,our results given here even in the nonweighted case appear to be new.Such interpolation inequalities have crucial applications to subelliptic or parabolic PDE’s involving vector fields.The main tools to prove such inequalities are approximating the Sobolev func- tions by polynomials associated with the left invariant vector fields on G.Some very useful properties for polynomials associated with the functions are given here and they appear to have independent interests in their own rights.Finding the existence of such polynomials is the second main part of this paper.Main results of these two parts have been announced in the author’s paper in Mathematical Research Letters[38]. The third main part of this paper contains extension theorems on anisotropic Sobolev spaces on stratified groups and their applications to proving Sobolev interpolation inequalities on(εδ)domains. Some results of weighted Sobolev spaces are also given here.We construct a linear extension operator which is bounded on different Sobolev spaces simultaneously.In particular,we are able to construct a bounded linear extension operator such that the derivatives of the extended function can be controlled by the same order of derivatives of the given Sobolev functions.Theorems are stated and proved for weighted anisotropic Sobolev spaces on stratified groups.

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.

射孔间距-倾角对深煤层水力裂缝扩展影响的离散元分析

研究煤岩储层裂缝扩展的影响因素,对提高煤层气采收率十分重要。为探究不同射孔间距-倾角对深层煤岩裂缝扩展规律的影响,利用离散元分析方法,考虑井周煤岩应力变化特征、最大周向应力准则、原始储层等条件,研究射孔间距-倾角对压裂缝网扩展形态及延伸范围的影响规律。模拟结果表明:随射孔间距从40 mm变化至100 mm,当间距为60 mm时裂缝条数数量最多;当射孔倾角从15°到60°变化时,当射孔角度为45°时,缝网形态最为复杂;即射孔间距为60 mm且射孔倾角为θ=45°时,水力裂缝的缝网形态复杂度显著增大,缝网扩展范围最大。通过神府北木瓜区Y-1井验证,预测结果与实测数据具有一致性,证明所建煤岩数值模型的正确性。

The isometrical extensions of 1-Lipschitz mappings on Gteaux differentiability spaces

Let X and Y be real Banach spaces.Suppose that the subset sm[S1(X)] of the smooth points of the unit sphere [S1(X)] is dense in S1(X).If T0 is a surjective 1-Lipschitz mapping between two unit spheres,then,under some condition,T0 can be extended to a linear isometry on the whole space.

The isometric extension of “into” mappings on unit spheres of AL-spaces

In this paper, we show that if V0 is an isometric mapping from the unit sphere of an AL-space onto the unit sphere of a Banach space E, then V0 can be extended to a linear isometry defined on the whole space.