In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced.The boundedness of pseudo-differential operators and commutator between two pseudo-dif...In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced.The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on H_(α,2)^(r) are proven with the help of the Weinstein transform technique.展开更多
In this paper, we introduce and study the Sobolev spaces of exponential type associated with the Weinstein operator, via some elements of harmonic analysis related to this operator. In particular, some properties, inc...In this paper, we introduce and study the Sobolev spaces of exponential type associated with the Weinstein operator, via some elements of harmonic analysis related to this operator. In particular, some properties, including completeness and imbedding theorem, are proved. Finally, using the theory of reproducing kernels, some applications are given for these spaces.展开更多
In this paper, using pseudo-holomorphic curve method, one proves the Weinstein conjecture in the product P;×P;of two strongly geometrically bounded symplectic manifolds under some conditions with P;. In particula...In this paper, using pseudo-holomorphic curve method, one proves the Weinstein conjecture in the product P;×P;of two strongly geometrically bounded symplectic manifolds under some conditions with P;. In particular, if N is a closed manifold or a noncompact manifold of finite topological type, our result implies that the Weinstein conjecture in CP;×T*N holds.展开更多
In this note a symplectic capacity of Hofer-Zehnder type that is only invariant under C-1-symplectomorphisms is defined and all computation formulae for Hofer-Zehnder symplectic capacity obtained at present are proved...In this note a symplectic capacity of Hofer-Zehnder type that is only invariant under C-1-symplectomorphisms is defined and all computation formulae for Hofer-Zehnder symplectic capacity obtained at present are proved still holding for it. As a consequence some results on Weinstein conjecture are generalized to C-1-smooth hypersurface of contact type.展开更多
In this paper we consider Weinstein operator. We define and study the continuous Gabor transform associated with this operator. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for ...In this paper we consider Weinstein operator. We define and study the continuous Gabor transform associated with this operator. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. As applications, we obtain analogous of Heisenberg’s inequality for the generalized continuous Gabor transform. At the end we give the practical real inversion formula for the generalized continuous Gabor transform.展开更多
In this paper, we study the Hofer-Zehnder capacity and the Weinstein conjecture in symplectic manifold (M×R^(2n), ω(?)σ). Let us define l_1(M, ω)=inf{<ω, α>|>0, α∈π_2(M)}. Suppose l_1(M, ω)>O...In this paper, we study the Hofer-Zehnder capacity and the Weinstein conjecture in symplectic manifold (M×R^(2n), ω(?)σ). Let us define l_1(M, ω)=inf{<ω, α>|>0, α∈π_2(M)}. Suppose l_1(M, ω)>O, O<πr^2<2/1 l_1(M, ω). Then C_(HZ)(M×B(r))=C_(HZ)(M×Z(r))=πr^2. In the case M is a point {P}, we obtain the well-known result at present. For n>1, consider on Cp^(n-1) the standard symplectic form co such that ω[u]=n for a generator u of H_2(CP^(n-1). Suppose O<πr^2<2/1 n. ThenC_(HZ)(M×B(r))=C_(HZ)(M×Z(r))=πr^2.As an application, we claim that the Weinstein conjecture in M×Z(r) is proved correct.展开更多
一群G叫CLT群,如果它满足Lagrange定理的逆定理:对d_,G,G有d阶子群。 CLT群是一类介于超可解群和可解群之间的一类群。到今为止,CLT群类仍未完全定出。定出CLT群仍是一个值得研究的课题。在M·Weinstein编《Between Nilpotent and S...一群G叫CLT群,如果它满足Lagrange定理的逆定理:对d_,G,G有d阶子群。 CLT群是一类介于超可解群和可解群之间的一类群。到今为止,CLT群类仍未完全定出。定出CLT群仍是一个值得研究的课题。在M·Weinstein编《Between Nilpotent and Solvable》一书中,Henry G·Bray总结了1982年以前几十年有关CLT群的研究工作,展开更多
Muscle-in-vein conduits are used alternatively to nerve grafts for bridging nerve defects. The purpose of this study was to examine short- and long-term regeneration results after digital nerve reconstruction with mus...Muscle-in-vein conduits are used alternatively to nerve grafts for bridging nerve defects. The purpose of this study was to examine short- and long-term regeneration results after digital nerve reconstruction with muscle-in-vein conduits. Static and moving two-point discriminations and Semmes-Weinstein Monofilaments were used to evaluate sensory recovery 6–12 months and 14–35 months after repair of digital nerves with muscle-in-vein in 7 cases. Both follow-ups were performed after clinical signs of progressing regeneration disappeared. In 4 of 7 cases, a further recovery of both two-point discriminations and in another case of only the static two-point discrimination of 1–3 mm could be found between the short-term and long-term follow-up examination. Moreover, a late recovery of both two-point discriminations was demonstrated in another case. Four of 7 cases showed a sensory improvement by one Semmes-Weinstein Monofilaments. This pilot study suggests that sensory recovery still takes place even when clinical signs of progressing regeneration disappear.展开更多
Recently devised new symplectic and differential-algebraic approaches to studying hidden symmetry properties of nonlinear dynamical systems on functional manifolds and their relationships to Lax integrability are revi...Recently devised new symplectic and differential-algebraic approaches to studying hidden symmetry properties of nonlinear dynamical systems on functional manifolds and their relationships to Lax integrability are reviewed. A new symplectic approach to constructing nonlinear Lax integrable dynamical systems by means of Lie-algebraic tools and based upon the Marsden-Weinstein reduction method on canonically symplectic manifolds with group symmetry, is described. Its natural relationship with the well-known Adler-Kostant-Souriau-Berezin-Kirillov method and the associated R-matrix method [1,2] is analyzed in detail. A new modified differential-algebraic approach to analyzing the Lax integrability of generalized Riemann and Ostrovsky-Vakhnenko type hydrodynamic equations is suggested and the corresponding Lax representations are constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of these generalized Riemann type hierarchies are discussed by means of the symplectic, gradientholonomic and geometric methods.展开更多
基金Supported by SERB MATRICS(Grant No.MTR2021/000266)。
文摘In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced.The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on H_(α,2)^(r) are proven with the help of the Weinstein transform technique.
文摘In this paper, we introduce and study the Sobolev spaces of exponential type associated with the Weinstein operator, via some elements of harmonic analysis related to this operator. In particular, some properties, including completeness and imbedding theorem, are proved. Finally, using the theory of reproducing kernels, some applications are given for these spaces.
文摘In this paper, using pseudo-holomorphic curve method, one proves the Weinstein conjecture in the product P;×P;of two strongly geometrically bounded symplectic manifolds under some conditions with P;. In particular, if N is a closed manifold or a noncompact manifold of finite topological type, our result implies that the Weinstein conjecture in CP;×T*N holds.
基金Supported by the NNSF of China(19971045) the MCF of Chinese University
文摘In this note a symplectic capacity of Hofer-Zehnder type that is only invariant under C-1-symplectomorphisms is defined and all computation formulae for Hofer-Zehnder symplectic capacity obtained at present are proved still holding for it. As a consequence some results on Weinstein conjecture are generalized to C-1-smooth hypersurface of contact type.
文摘In this paper we consider Weinstein operator. We define and study the continuous Gabor transform associated with this operator. We prove a Plancherel formula, an inversion formula and a weak uncertainty principle for it. As applications, we obtain analogous of Heisenberg’s inequality for the generalized continuous Gabor transform. At the end we give the practical real inversion formula for the generalized continuous Gabor transform.
基金Project supported by the Science Foundation of Tsinghua University
文摘In this paper, we study the Hofer-Zehnder capacity and the Weinstein conjecture in symplectic manifold (M×R^(2n), ω(?)σ). Let us define l_1(M, ω)=inf{<ω, α>|>0, α∈π_2(M)}. Suppose l_1(M, ω)>O, O<πr^2<2/1 l_1(M, ω). Then C_(HZ)(M×B(r))=C_(HZ)(M×Z(r))=πr^2. In the case M is a point {P}, we obtain the well-known result at present. For n>1, consider on Cp^(n-1) the standard symplectic form co such that ω[u]=n for a generator u of H_2(CP^(n-1). Suppose O<πr^2<2/1 n. ThenC_(HZ)(M×B(r))=C_(HZ)(M×Z(r))=πr^2.As an application, we claim that the Weinstein conjecture in M×Z(r) is proved correct.
文摘Muscle-in-vein conduits are used alternatively to nerve grafts for bridging nerve defects. The purpose of this study was to examine short- and long-term regeneration results after digital nerve reconstruction with muscle-in-vein conduits. Static and moving two-point discriminations and Semmes-Weinstein Monofilaments were used to evaluate sensory recovery 6–12 months and 14–35 months after repair of digital nerves with muscle-in-vein in 7 cases. Both follow-ups were performed after clinical signs of progressing regeneration disappeared. In 4 of 7 cases, a further recovery of both two-point discriminations and in another case of only the static two-point discrimination of 1–3 mm could be found between the short-term and long-term follow-up examination. Moreover, a late recovery of both two-point discriminations was demonstrated in another case. Four of 7 cases showed a sensory improvement by one Semmes-Weinstein Monofilaments. This pilot study suggests that sensory recovery still takes place even when clinical signs of progressing regeneration disappear.
文摘Recently devised new symplectic and differential-algebraic approaches to studying hidden symmetry properties of nonlinear dynamical systems on functional manifolds and their relationships to Lax integrability are reviewed. A new symplectic approach to constructing nonlinear Lax integrable dynamical systems by means of Lie-algebraic tools and based upon the Marsden-Weinstein reduction method on canonically symplectic manifolds with group symmetry, is described. Its natural relationship with the well-known Adler-Kostant-Souriau-Berezin-Kirillov method and the associated R-matrix method [1,2] is analyzed in detail. A new modified differential-algebraic approach to analyzing the Lax integrability of generalized Riemann and Ostrovsky-Vakhnenko type hydrodynamic equations is suggested and the corresponding Lax representations are constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of these generalized Riemann type hierarchies are discussed by means of the symplectic, gradientholonomic and geometric methods.
