We show that, on a -manifold endowed with a -structure induced by an almost-complex structure, a self-dual (positive) spinor field is the same as a bundle morphism acting on the fiber by self-dual conformal transformations, such that the Clifford multiplication is just the evaluation of on tangent vectors, and that the squaring map acts by pulling-back the fundamental form of the almost-complex structure. We use this to detect Kähler and symplectic structures.
The aim of this paper is to study the adjoint action for the quantum algebra Uq(f(K, H)), which is a natural generalization of quantum algebra Uq(sl2) and is regarded as a class of generalized Weyl algebra..The structure theorem of its locally finite subalgebra F(Uq(f(K, H))) is given. 相似文献
In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system. 相似文献
Let be a complete Riemannian manifold with no conjugate points and a principal -bundle, where is a Lie group acting by isometries and the smooth quotient with the Riemannian submersion metric.
We obtain a characterization of conjugate point-free quotients in terms of symplectic reduction and a canonical pseudo-Riemannian metric on the tangent bundle , from which we then derive necessary conditions, involving and , for the quotient metric to be conjugate point-free, particularly for a reducible Riemannian manifold.
Let , with the Lie Algebra of , be the moment map of the tangential -action on and let be the canonical pseudo-Riemannian metric on defined by the symplectic form and the map , . First we prove a theorem, stating that if is not positive definite on the action vector fields for the tangential action along then acquires conjugate points. (We proved the converse result in 2005.) Then, we characterize self-parallel vector fields on in terms of the positivity of the -length of their tangential lifts along certain canonical subsets of . We use this to derive some necessary conditions, on and , for actions to be tangentially positive on relevant subsets of , which we then apply to isometric actions on complete conjugate point-free reducible Riemannian manifolds when one of the irreducible factors satisfies certain curvature conditions.
The problem of determining the pair w:={F(x, t);f(t)} of sourceterms in the hyperbolic equation utt = (k(x)ux)x + F(x, t) andin the Neumann boundary condition k(0)ux(0, t) = f(t) from themeasured data µ(x):=u(x, T) and/or (x):=ut(x, t) at thefinal time t = T is formulated. It is proved that both componentsof the Fréchet gradient of the cost functionals J1(w)= ||u(x, t;w) – µ(x)||02 and J2(w) = ||ut(x, T;w)– (x)||02 can be found via the solutions of correspondingadjoint hyperbolic problems. Lipschitz continuity of the gradientis derived. Unicity of the solution and ill-conditionednessof the inverse problem are analysed. The obtained results permitone to construct a monotone iteration process, as well as toprove the existence of a quasi-solution. 相似文献
In this paper, we construct a space of boundary values for minimal symmetric 1D Hamiltonian operator with defect index (1,1) (in limit‐point case at a(b) and limit‐circle case at b(a)) acting in the Hilbert space In terms of boundary conditions at a and b, all maximal dissipative, accumulative, and self‐adjoint extensions of the symmetric operator are given. Two classes of dissipative operators are studied. They are called “dissipative at a” and “dissipative at b.” For 2 cases, a self‐adjoint dilation of dissipative operator and its incoming and outgoing spectral representations are constructed. These constructions allow us to establish the scattering matrix of dilation and a functional model of the dissipative operator. Further, we define the characteristic function of the dissipative operators in terms of the Weyl‐Titchmarsh function of the corresponding self‐adjoint operator. Finally, we prove theorems on completeness of the system of root vectors of the dissipative operators. 相似文献
The Euler‐Bernoulli beam model with fully nonconservative boundary conditions of feedback control type is investigated. The output vector (the shear and the moment at the right end) is connected to the observation vector (the velocity and its spatial derivative on the right end) by a 2 × 2 matrix (the boundary control matrix), all entries of which are nonzero real numbers. For any combination of the boundary parameters, the dynamics generator, , of the model is a non–self‐adjoint matrix differential operator in the state Hilbert space. A set of 4 self‐adjoint operators, defined by the same differential expression as on different domains, is introduced. It is proven that each of these operators, as well as , is a finite‐rank perturbation of the same self‐adjoint dynamics generator of a cantilever beam model. It is also shown that the non–self‐adjoint operator, , shares a number of spectral properties specific to its self‐adjoint counterparts, such as (1) boundary inequalities for the eigenfunctions, (2) the geometric multiplicities of the eigenvalues, and (3) the existence of real eigenvalues. These results are important for our next paper on the spectral asymptotics and stability for the multiparameter beam model. 相似文献