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...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.展开更多
Let X and Y be two normed spaces.Let U be a non-principal ultrafilter on N.Let g:X→Y be a standard ε-phase isometry for someε≥ 0,i.e.,g(0)=0,and for all u.v ∈ X,||‖g(u)+g(v)‖±‖g(u)-g(v)‖|-|‖u+v‖±...Let X and Y be two normed spaces.Let U be a non-principal ultrafilter on N.Let g:X→Y be a standard ε-phase isometry for someε≥ 0,i.e.,g(0)=0,and for all u.v ∈ X,||‖g(u)+g(v)‖±‖g(u)-g(v)‖|-|‖u+v‖±‖u-v‖| |≤ε.The mapping g is said to be a phase isometry provided that ε=0.In this paper,we show the following universal inequality of g:for each u^(*) ∈ w^(*)-exp ‖u^(*)‖B_(x^(*)),there exist a phase function σ_(u^(*)):X→{-1,1} and φ ∈ Y^(*) with ‖φ‖=‖u^(*)‖≡α satisfying that|(u^(*),u)-σ_(u^(*))(u)<φ,g(u)>)|≤5/2εα,for all u ∈ X.In particular,let X be a smooth Banach space.Then we show the following:(1) the universal inequality holds for all u^(*) ∈ X^(*);(2) the constant 5/2 can be reduced to 3/2 provided that Y~*is strictly convex;(3) the existence of such a g implies the existence of a phase isometryΘ:X→Y such that■ provided that Y^(**) has the w^(*)-Kadec-Klee property(for example,Y is both reflexive and locally uniformly convex).展开更多
Let X, Y be two real Banach spaces and ε≥0. A map f : X → Y is said to be a standard ε-isometry if│││f/(x) - f(y)││ - ]ix - Y││x-y││ ε for all x,y C X and with f(O) = O. We say that a pair of Ban...Let X, Y be two real Banach spaces and ε≥0. A map f : X → Y is said to be a standard ε-isometry if│││f/(x) - f(y)││ - ]ix - Y││x-y││ ε for all x,y C X and with f(O) = O. We say that a pair of Banach spaces (X, Y) is stable if there exists γ〉 0 such that, for every such ε and every standard v-isometry f : X → Y, there is a bounded linear operator T : L(f) → f(X) → X so that ││Tf(x) - x││ ≤γε for all x E X. X(Y) is said to be universally left-stable if (X, Y) is always stable for every Y(X). In this paper, we show that if a dual Banach space X is universally left-stable, then it is isometric to a complemented w*-closed subspace of ∞ (1) for some set F, hence, an injective space; and that a Banach space is universally left-stable if and only if it is a cardinality injective space; and universally left-stability spaces are invariant.展开更多
A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with...A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.展开更多
Let M_(t) be an isoparametric foliation on the unit sphere(S^(n−1)(1),g^(st))with d principal curvatures.Using the spherical coordinatesinduced by M_(t),we construct a Minkowski norm with the representation F=r√2f(t)...Let M_(t) be an isoparametric foliation on the unit sphere(S^(n−1)(1),g^(st))with d principal curvatures.Using the spherical coordinatesinduced by M_(t),we construct a Minkowski norm with the representation F=r√2f(t),which generalizes the notions of(α,β)-norm and(α1,α2)-norm.Using the technique of the spherical local frame,we givean exact and explicit answer to the question when F=r√2 f(t)really defines a Minkowski norm.Using the similar technique,we study the Hessian isometry Φ between two Minkowski norms induced by M_(t),which preservesthe orientation and fixes the spherical ξ-coordinates.There aretwo ways to describe this Φ,either by a system of ODEs,or by its restriction toany normal plane for M_(t),which is then reduced to a Hessian isometry between Minkowski norms on R^(2) satisfying certain symmetry and(d)-properties.When d>2,we prove that this Φ can be obtained by gluing positive scalar multiplications and compositions of the Legendre transformation and positive scalar multiplications,so it must satisfy the(d)-property for any orthogonal decomposition R^(n)=V'+V'',i.e.,for any nonzero x=x'+x'' and Φ(x)=x=x'+x''with x',x'∈V'and x'',x''∈V'',we have g_(x)^(F1)(x'',x)=g_(x)^(F2)x(x'',x).As byproducts,we prove the following results.On the indicatrix(S_(F,g)),where F is a Minkowski norm induced by M_(t) and g is the Hessian metric,the foliation N_(t)=S_(F)∩R>_(0)M_(0) is isoparametric.Laugwitz Conjecture is valid for a Minkowski norm F induced by M_(t),i.e.,if its Hessian metric g is flat on R^(n)\{0}with n>2,then F is Euclidean.展开更多
Dunwoody manifolds are an interesting class of closed connected orientable 3-manifolds, which are defined by means of Heegaard diagrams having a rotational symmetry. They are proved to be cyclic coverings of lens spac...Dunwoody manifolds are an interesting class of closed connected orientable 3-manifolds, which are defined by means of Heegaard diagrams having a rotational symmetry. They are proved to be cyclic coverings of lens spaces (possibly S3) branched over (1, 1)-knots. Here we study the Dunwoody manifolds which are cyclic coverings of the 3-sphere branched over two specified families of Montesinos knots. Then we determine the Dunwoody parameters for such knots and the isometry groups for the considered manifolds in the hyperbolic case. A list of volumes for some hyperbolic Dunwoody manifolds completes the paper.展开更多
This paper solves the isometry problem between two indefinite metrics by using exterior differential systems. We prove that an indefinite metric is either rigid, admits a one parameter group of isometries (rotation...This paper solves the isometry problem between two indefinite metrics by using exterior differential systems. We prove that an indefinite metric is either rigid, admits a one parameter group of isometries (rotation like surfaces), or admits a three parameter group of isometries (K=constant).展开更多
The main result of this paper is to prove Fang and Wang's result by another method: Let E be any normed linear space and Vo : S(E)→ S(l^1) be a surjective isometry. Then V0 can be linearly isometrically extend...The main result of this paper is to prove Fang and Wang's result by another method: Let E be any normed linear space and Vo : S(E)→ S(l^1) be a surjective isometry. Then V0 can be linearly isometrically extended to E.展开更多
Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for a...Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for accurate support recovery of the block K-joint sparse matrix via the BMMV algorithm in the noisy case. Furthermore, we show the optimality of the condition we proposed in the absence of noise when the problem reduces to single measurement vector case.展开更多
If T is an isomorphism of (c0) into C(Ω) (where Ω is a sequentially compact and paracompact space, or a compact metric space in particular), which satisfies the condition ||T||·||T^-1|| ≤ 1 +ε ...If T is an isomorphism of (c0) into C(Ω) (where Ω is a sequentially compact and paracompact space, or a compact metric space in particular), which satisfies the condition ||T||·||T^-1|| ≤ 1 +ε for some ε ∈ (0,1/5), then T/||T|| is close to an isometry with an error less than 9ε. The proof of this article is simple without using the dual space or adjoint operator.展开更多
Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then t...Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then there exists a surjective linear isometry U:X→Y such that∥f(x)−Ux∥=o(∥x∥)as∥x∥→∞.This is a generalization about the result of Lindenstrauss and Szankowski on the same finite dimensional Banach spaces without the assumption of surjectivity.As a consequence,we also obtain a stability result forε-isometries which was established by Dilworth.展开更多
In this paper, some problems for isometric approximation are discussed. It is shown that an almost isometry from the unit ball of C(X) into the unit ball of C(Y) is near to an isometry. We also give a counterexample t...In this paper, some problems for isometric approximation are discussed. It is shown that an almost isometry from the unit ball of C(X) into the unit ball of C(Y) is near to an isometry. We also give a counterexample to this problem on the unit ball of l1.展开更多
In this paper, one of the Aleksandrov problem was resolved, the proof that a mapping f which preserve unit distance between two real p-normed spaces X and Y is an isometry if Y is a p-strictly convex space and f satis...In this paper, one of the Aleksandrov problem was resolved, the proof that a mapping f which preserve unit distance between two real p-normed spaces X and Y is an isometry if Y is a p-strictly convex space and f satisfies locally Lipschitz condition was shown, and a same result in normed spaces was given. In addition, a proof which there doesn't exist any isometry between some spaces was obtained.展开更多
Anterior cruciate ligament(ACL) rupture is one of the commonest knee sport injuries. The annual incidence of the ACL injury is between 100000-200000 in the United States. Worldwide around 400000 ACL reconstructions ar...Anterior cruciate ligament(ACL) rupture is one of the commonest knee sport injuries. The annual incidence of the ACL injury is between 100000-200000 in the United States. Worldwide around 400000 ACL reconstructions are performed in a year. The goal of ACL reconstruction is to restore the normal knee anatomy and kinesiology. The tibial and femoral tunnel placements are of primordial importance in achieving this outcome. Otherfactors that influence successful reconstruction are types of grafts, surgical techniques and rehabilitation programmes. A comprehensive understanding of ACL anatomy has led to the development of newer techniques supplemented by more robust biological and mechanical concepts. In this review we are mainly focussing on the evolution of tunnel placement in ACL reconstruction, focusing on three main categories, i.e., anatomical, biological and clinical outcomes. The importance of tunnel placement in the success of ACL reconstruction is well researched. Definite clinical and functional data is lacking to establish the superiority of the single or double bundle reconstruction technique. While there is a trend towards the use of anteromedial portals for femoral tunnel placement, their clinical superiority over trans-tibial tunnels is yet to be established.展开更多
In this article we bounded symmetric domains study holomorphic isometries of the Poincare disk into Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which a...In this article we bounded symmetric domains study holomorphic isometries of the Poincare disk into Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which are isometrics up to normalizing constants with respect to the Bergman metric, showing in particular that the graph 170 of any germ of holomorphic isometry of the Poincar6 disk A into an irreducible bounded symmetric domain Ω belong to C^N in its Harish-Chandra realization must extend to an affinealgebraic subvariety V belong to C × C^N = C^N+1, and that the irreducible component of V ∩ (△ × Ω) containing V0 is the graph of a proper holomorphic isometric embedding F : A→ Ω. In this article we study holomorphie isometric embeddings which are asymptotically geodesic at a general boundary point b ∈ δ△. Starting with the structural equation for holomorphic isometrics arising from the Gauss equation, we obtain by covariant differentiation an identity relating certain holomorphic bisectional curvatures to the boundary behavior of the second fundamental form σ of the holomorphie isometric embedding. Using the nonpositivity of holomorphic bisectional curvatures on a bounded symmetric domain, we prove that ‖σ‖ must vanish at a general boundary point either to the order 1 or to the order 1/2, called a holomorphie isometry of the first resp. second kind. We deal with special cases of non-standard holomorphic isometric embeddings of such maps, showing that they must be asymptotically totally geodesic at a general boundary point and in fact of the first kind whenever the target domain is a Cartesian product of complex unit balls. We also study the boundary behavior of an example of holomorphic isometric embedding from the Poincare disk into a Siegel upper half-plane by an explicit determination of the boundary behavior of holomorphic sectional curvatures in the directions tangent to the embedded Poincare disk, showing that the map is indeed asymptotically totally geodesic at a general boundary point and of the first kind. For the metric computation we make use of formulas for symplectic geometry on Siegel upper half-planes.展开更多
In this paper, some characterizations of isometric operators and ε-isometric opertors from 2-dim Banach Space E2 into L1[0, 1] are given, where E2 denotes a Banach Spacewhose unit ball is the union of a polygon C and...In this paper, some characterizations of isometric operators and ε-isometric opertors from 2-dim Banach Space E2 into L1[0, 1] are given, where E2 denotes a Banach Spacewhose unit ball is the union of a polygon C and the region enclosd by C in the plane. Also,the answer for IAP(Isometric Approximation Problem) on B(E2,L1 [0, 1]) is obtained.展开更多
An Adaptive Measurement Scheme (AMS) is investigated with Compressed Sensing (CS) theory in Cognitive Wireless Sensor Network (C-WSN). Local sensing information is collected via energy detection with Analog-to-Informa...An Adaptive Measurement Scheme (AMS) is investigated with Compressed Sensing (CS) theory in Cognitive Wireless Sensor Network (C-WSN). Local sensing information is collected via energy detection with Analog-to-Information Converter (AIC) at massive cognitive sensors, and sparse representation is considered with the exploration of spatial temporal correlation structure of detected signals. Adaptive measurement matrix is designed in AMS, which is based on maximum energy subset selection. Energy subset is calculated with sparse transformation of sensing information, and maximum energy subset is selected as the row vector of adaptive measurement matrix. In addition, the measurement matrix is constructed by orthogonalization of those selected row vectors, which also satisfies the Restricted Isometry Property (RIP) in CS theory. Orthogonal Matching Pursuit (OMP) reconstruction algorithm is implemented at sink node to recover original information. Simulation results are performed with the comparison of Random Measurement Scheme (RMS). It is revealed that, signal reconstruction effect based on AMS is superior to conventional RMS Gaussian measurement. Moreover, AMS has better detection performance than RMS at lower compression rate region, and it is suitable for large-scale C-WSN wideband spectrum sensing.展开更多
Broadband wireless channels are often time dispersive and become strongly frequency selective in delay spread domain. Commonly, these channels are composed of a few dominant coefficients and a large part of coefficien...Broadband wireless channels are often time dispersive and become strongly frequency selective in delay spread domain. Commonly, these channels are composed of a few dominant coefficients and a large part of coefficients are approximately zero or under noise floor. To exploit sparsity of multi-path channels (MPCs), there are various methods have been proposed. They are, namely, greedy algorithms, iterative algorithms, and convex program. The former two algorithms are easy to be implemented but not stable;on the other hand, the last method is stable but difficult to be implemented as practical channel estimation problems be-cause of computational complexity. In this paper, we introduce a novel channel estimation strategy using smooth L0 (SL0) algorithm which combines stable and low complexity. Computer simulations confirm the effectiveness of the introduced algorithm. We also give various simulations to verify the sensing training signal method.展开更多
Non-rigid shape deformation without tearing or stretching is called isometry. There are many difficulties to research non-rigid shape in Euclidean space. Therefore, non-rigid shapes are firstly embedded into a none-Eu...Non-rigid shape deformation without tearing or stretching is called isometry. There are many difficulties to research non-rigid shape in Euclidean space. Therefore, non-rigid shapes are firstly embedded into a none-Euclidean space. Spectral space is chosen in this paper. Then three descriptors are proposed based on three spectral distances. The existence of zero-eigenvalue has negative effects on computation of spectral distance, Therefore the spectral distance should be computed from the first non-zcro-eigenvalue. Experiments show that spectral distance distributions are very effective to describe the non-rigid shapes.展开更多
基金supported by the Natural Science Foundation of China (12271402)the Natural Science Foundation of Tianjin City (22JCYBJC00420)。
文摘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.
基金supported by the NSFC(12126329,12171266,12126346)the NSF of Fujian Province of China(2023J01805)+5 种基金the Research Start-Up Fund of Jimei University(ZQ2021017)supported by the NSFC(12101234)the NSF of Hebei Province(A2022502010)the Fundamental Research Funds for the Central Universities(2023MS164)the China Scholarship Councilsupported by the Simons Foundation(585081)。
文摘Let X and Y be two normed spaces.Let U be a non-principal ultrafilter on N.Let g:X→Y be a standard ε-phase isometry for someε≥ 0,i.e.,g(0)=0,and for all u.v ∈ X,||‖g(u)+g(v)‖±‖g(u)-g(v)‖|-|‖u+v‖±‖u-v‖| |≤ε.The mapping g is said to be a phase isometry provided that ε=0.In this paper,we show the following universal inequality of g:for each u^(*) ∈ w^(*)-exp ‖u^(*)‖B_(x^(*)),there exist a phase function σ_(u^(*)):X→{-1,1} and φ ∈ Y^(*) with ‖φ‖=‖u^(*)‖≡α satisfying that|(u^(*),u)-σ_(u^(*))(u)<φ,g(u)>)|≤5/2εα,for all u ∈ X.In particular,let X be a smooth Banach space.Then we show the following:(1) the universal inequality holds for all u^(*) ∈ X^(*);(2) the constant 5/2 can be reduced to 3/2 provided that Y~*is strictly convex;(3) the existence of such a g implies the existence of a phase isometryΘ:X→Y such that■ provided that Y^(**) has the w^(*)-Kadec-Klee property(for example,Y is both reflexive and locally uniformly convex).
基金Supported by National Natural Science Foundation of China(Grant Nos.11071201 and 11001231)
文摘Let X, Y be two real Banach spaces and ε≥0. A map f : X → Y is said to be a standard ε-isometry if│││f/(x) - f(y)││ - ]ix - Y││x-y││ ε for all x,y C X and with f(O) = O. We say that a pair of Banach spaces (X, Y) is stable if there exists γ〉 0 such that, for every such ε and every standard v-isometry f : X → Y, there is a bounded linear operator T : L(f) → f(X) → X so that ││Tf(x) - x││ ≤γε for all x E X. X(Y) is said to be universally left-stable if (X, Y) is always stable for every Y(X). In this paper, we show that if a dual Banach space X is universally left-stable, then it is isometric to a complemented w*-closed subspace of ∞ (1) for some set F, hence, an injective space; and that a Banach space is universally left-stable if and only if it is a cardinality injective space; and universally left-stability spaces are invariant.
文摘A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.
基金supported by Beijing Natural Science Foundation(Grant No.Z180004)National Natural Science Foundation of China(Grant Nos.11771331 and 11821101)Capacity Building for SciTech Innovation—Fundamental Scientific Research Funds(Grant No.KM201910028021)。
文摘Let M_(t) be an isoparametric foliation on the unit sphere(S^(n−1)(1),g^(st))with d principal curvatures.Using the spherical coordinatesinduced by M_(t),we construct a Minkowski norm with the representation F=r√2f(t),which generalizes the notions of(α,β)-norm and(α1,α2)-norm.Using the technique of the spherical local frame,we givean exact and explicit answer to the question when F=r√2 f(t)really defines a Minkowski norm.Using the similar technique,we study the Hessian isometry Φ between two Minkowski norms induced by M_(t),which preservesthe orientation and fixes the spherical ξ-coordinates.There aretwo ways to describe this Φ,either by a system of ODEs,or by its restriction toany normal plane for M_(t),which is then reduced to a Hessian isometry between Minkowski norms on R^(2) satisfying certain symmetry and(d)-properties.When d>2,we prove that this Φ can be obtained by gluing positive scalar multiplications and compositions of the Legendre transformation and positive scalar multiplications,so it must satisfy the(d)-property for any orthogonal decomposition R^(n)=V'+V'',i.e.,for any nonzero x=x'+x'' and Φ(x)=x=x'+x''with x',x'∈V'and x'',x''∈V'',we have g_(x)^(F1)(x'',x)=g_(x)^(F2)x(x'',x).As byproducts,we prove the following results.On the indicatrix(S_(F,g)),where F is a Minkowski norm induced by M_(t) and g is the Hessian metric,the foliation N_(t)=S_(F)∩R>_(0)M_(0) is isoparametric.Laugwitz Conjecture is valid for a Minkowski norm F induced by M_(t),i.e.,if its Hessian metric g is flat on R^(n)\{0}with n>2,then F is Euclidean.
文摘Dunwoody manifolds are an interesting class of closed connected orientable 3-manifolds, which are defined by means of Heegaard diagrams having a rotational symmetry. They are proved to be cyclic coverings of lens spaces (possibly S3) branched over (1, 1)-knots. Here we study the Dunwoody manifolds which are cyclic coverings of the 3-sphere branched over two specified families of Montesinos knots. Then we determine the Dunwoody parameters for such knots and the isometry groups for the considered manifolds in the hyperbolic case. A list of volumes for some hyperbolic Dunwoody manifolds completes the paper.
基金the National Natural Science Foundationof China (No.1970 10 17)
文摘This paper solves the isometry problem between two indefinite metrics by using exterior differential systems. We prove that an indefinite metric is either rigid, admits a one parameter group of isometries (rotation like surfaces), or admits a three parameter group of isometries (K=constant).
基金Foundation item: the National Natural Science Foundation of China (No. 10571090) the Research Fund for the Doctoral Program of Higher Education (No. 20060055010) and the Fund of Tianjin Educational Comittee (No. 20060402).
文摘The main result of this paper is to prove Fang and Wang's result by another method: Let E be any normed linear space and Vo : S(E)→ S(l^1) be a surjective isometry. Then V0 can be linearly isometrically extended to E.
文摘Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for accurate support recovery of the block K-joint sparse matrix via the BMMV algorithm in the noisy case. Furthermore, we show the optimality of the condition we proposed in the absence of noise when the problem reduces to single measurement vector case.
基金National Natural Science Foundation of China(10571090)the Research Fund for the Doctoral Program of Higher Education(20060055010)
文摘If T is an isomorphism of (c0) into C(Ω) (where Ω is a sequentially compact and paracompact space, or a compact metric space in particular), which satisfies the condition ||T||·||T^-1|| ≤ 1 +ε for some ε ∈ (0,1/5), then T/||T|| is close to an isometry with an error less than 9ε. The proof of this article is simple without using the dual space or adjoint operator.
基金Supported by National Natural Science Foundation of China(11731010 and 12071388)。
文摘Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then there exists a surjective linear isometry U:X→Y such that∥f(x)−Ux∥=o(∥x∥)as∥x∥→∞.This is a generalization about the result of Lindenstrauss and Szankowski on the same finite dimensional Banach spaces without the assumption of surjectivity.As a consequence,we also obtain a stability result forε-isometries which was established by Dilworth.
文摘In this paper, some problems for isometric approximation are discussed. It is shown that an almost isometry from the unit ball of C(X) into the unit ball of C(Y) is near to an isometry. We also give a counterexample to this problem on the unit ball of l1.
文摘In this paper, one of the Aleksandrov problem was resolved, the proof that a mapping f which preserve unit distance between two real p-normed spaces X and Y is an isometry if Y is a p-strictly convex space and f satisfies locally Lipschitz condition was shown, and a same result in normed spaces was given. In addition, a proof which there doesn't exist any isometry between some spaces was obtained.
文摘Anterior cruciate ligament(ACL) rupture is one of the commonest knee sport injuries. The annual incidence of the ACL injury is between 100000-200000 in the United States. Worldwide around 400000 ACL reconstructions are performed in a year. The goal of ACL reconstruction is to restore the normal knee anatomy and kinesiology. The tibial and femoral tunnel placements are of primordial importance in achieving this outcome. Otherfactors that influence successful reconstruction are types of grafts, surgical techniques and rehabilitation programmes. A comprehensive understanding of ACL anatomy has led to the development of newer techniques supplemented by more robust biological and mechanical concepts. In this review we are mainly focussing on the evolution of tunnel placement in ACL reconstruction, focusing on three main categories, i.e., anatomical, biological and clinical outcomes. The importance of tunnel placement in the success of ACL reconstruction is well researched. Definite clinical and functional data is lacking to establish the superiority of the single or double bundle reconstruction technique. While there is a trend towards the use of anteromedial portals for femoral tunnel placement, their clinical superiority over trans-tibial tunnels is yet to be established.
基金supported by the CERG grant HKU701803 of the Research Grants Council, Hong Kong
文摘In this article we bounded symmetric domains study holomorphic isometries of the Poincare disk into Earlier we solved the problem of analytic continuation of germs of holomorphic maps between bounded domains which are isometrics up to normalizing constants with respect to the Bergman metric, showing in particular that the graph 170 of any germ of holomorphic isometry of the Poincar6 disk A into an irreducible bounded symmetric domain Ω belong to C^N in its Harish-Chandra realization must extend to an affinealgebraic subvariety V belong to C × C^N = C^N+1, and that the irreducible component of V ∩ (△ × Ω) containing V0 is the graph of a proper holomorphic isometric embedding F : A→ Ω. In this article we study holomorphie isometric embeddings which are asymptotically geodesic at a general boundary point b ∈ δ△. Starting with the structural equation for holomorphic isometrics arising from the Gauss equation, we obtain by covariant differentiation an identity relating certain holomorphic bisectional curvatures to the boundary behavior of the second fundamental form σ of the holomorphie isometric embedding. Using the nonpositivity of holomorphic bisectional curvatures on a bounded symmetric domain, we prove that ‖σ‖ must vanish at a general boundary point either to the order 1 or to the order 1/2, called a holomorphie isometry of the first resp. second kind. We deal with special cases of non-standard holomorphic isometric embeddings of such maps, showing that they must be asymptotically totally geodesic at a general boundary point and in fact of the first kind whenever the target domain is a Cartesian product of complex unit balls. We also study the boundary behavior of an example of holomorphic isometric embedding from the Poincare disk into a Siegel upper half-plane by an explicit determination of the boundary behavior of holomorphic sectional curvatures in the directions tangent to the embedded Poincare disk, showing that the map is indeed asymptotically totally geodesic at a general boundary point and of the first kind. For the metric computation we make use of formulas for symplectic geometry on Siegel upper half-planes.
文摘In this paper, some characterizations of isometric operators and ε-isometric opertors from 2-dim Banach Space E2 into L1[0, 1] are given, where E2 denotes a Banach Spacewhose unit ball is the union of a polygon C and the region enclosd by C in the plane. Also,the answer for IAP(Isometric Approximation Problem) on B(E2,L1 [0, 1]) is obtained.
基金Supported by the National Natural Science Foundation of China (No. 61102066, 60972058)the China Postdoctoral Science Foundation (No. 2012M511365)the Scientific Research Project of Zhejiang Provincial Education Department (No. Y201119890)
文摘An Adaptive Measurement Scheme (AMS) is investigated with Compressed Sensing (CS) theory in Cognitive Wireless Sensor Network (C-WSN). Local sensing information is collected via energy detection with Analog-to-Information Converter (AIC) at massive cognitive sensors, and sparse representation is considered with the exploration of spatial temporal correlation structure of detected signals. Adaptive measurement matrix is designed in AMS, which is based on maximum energy subset selection. Energy subset is calculated with sparse transformation of sensing information, and maximum energy subset is selected as the row vector of adaptive measurement matrix. In addition, the measurement matrix is constructed by orthogonalization of those selected row vectors, which also satisfies the Restricted Isometry Property (RIP) in CS theory. Orthogonal Matching Pursuit (OMP) reconstruction algorithm is implemented at sink node to recover original information. Simulation results are performed with the comparison of Random Measurement Scheme (RMS). It is revealed that, signal reconstruction effect based on AMS is superior to conventional RMS Gaussian measurement. Moreover, AMS has better detection performance than RMS at lower compression rate region, and it is suitable for large-scale C-WSN wideband spectrum sensing.
文摘Broadband wireless channels are often time dispersive and become strongly frequency selective in delay spread domain. Commonly, these channels are composed of a few dominant coefficients and a large part of coefficients are approximately zero or under noise floor. To exploit sparsity of multi-path channels (MPCs), there are various methods have been proposed. They are, namely, greedy algorithms, iterative algorithms, and convex program. The former two algorithms are easy to be implemented but not stable;on the other hand, the last method is stable but difficult to be implemented as practical channel estimation problems be-cause of computational complexity. In this paper, we introduce a novel channel estimation strategy using smooth L0 (SL0) algorithm which combines stable and low complexity. Computer simulations confirm the effectiveness of the introduced algorithm. We also give various simulations to verify the sensing training signal method.
基金Partly Supported by NKBRPC(2004CB318006)NNSFC(60873164 and 60533090)
文摘Non-rigid shape deformation without tearing or stretching is called isometry. There are many difficulties to research non-rigid shape in Euclidean space. Therefore, non-rigid shapes are firstly embedded into a none-Euclidean space. Spectral space is chosen in this paper. Then three descriptors are proposed based on three spectral distances. The existence of zero-eigenvalue has negative effects on computation of spectral distance, Therefore the spectral distance should be computed from the first non-zcro-eigenvalue. Experiments show that spectral distance distributions are very effective to describe the non-rigid shapes.