The authors prove the local unramified correspondence for a new type of construction of CAP representations of even orthogonal groups by a generalized automorphic descent method. This method is expected to work for all classical groups.
In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity $x'' + V'(x) + g(x) = e(t,x,x'),$ where the assumptions on V, g and e are regular, described precisely in the introduction. Using a variant of Moser’s twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where e depends on the velocity.
By considering the one-dimensional model for describing long, small amplitude waves in shallow water, a generalized fifth-order evolution equation named the Olver water wave (OWW) equation is investigated by virtue of some new pseudo-potential systems. By introducing the corresponding pseudo-potential systems, the authors systematically construct some generalized symmetries that consider some new smooth functions {X iβ} β=1,2,··· ,N i=1,2,··· ,n depending on a finite number of partial derivatives of the nonlocal variables v β and a restriction i.e., $\sum\limits_{i,\alpha ,\beta } {\left( {\tfrac{{\partial \xi ^i }}{{\partial v^\beta }}} \right) + \left( {\tfrac{{\partial \eta ^\alpha }}{{\partial v^\beta }}} \right)} \ne 0$ ≠ 0, i.e., $\sum\limits_{i,\alpha ,\beta } {\left( {\tfrac{{\partial G^\alpha }}{{\partial v^\beta }}} \right)} \ne 0$. Furthermore, the authors investigate some structures associated with the Olver water wave (AOWW) equations including Lie algebra and Darboux transformation. The results are also extended to AOWW equations such as Lax, Sawada-Kotera, Kaup-Kupershmidt, Itˆo and Caudrey-Dodd-Gibbon-Sawada-Kotera equations, et al. Finally, the symmetries are applied to investigate the initial value problems and Darboux transformations.
The authors consider the partially linear model relating a response Y to predictors (x, T) with a mean function x T β 0+g(T) when the x′s are measured with an additive error. The estimators of parameter β 0 are derived by using the nearest neighbor-generalized randomly weighted least absolute deviation (LAD for short) method. The resulting estimator of the unknown vector β 0 is shown to be consistent and asymptotically normal. In addition, the results facilitate the construction of confidence regions and the hypothesis testing for the unknown parameters. Extensive simulations are reported, showing that the proposed method works well in practical settings. The proposed methods are also applied to a data set from the study of an AIDS clinical trial group.
Let (M n, g) and (N n+1, G) be Riemannian manifolds. Let TM n and TN n+1 be the associated tangent bundles. Let f: (M n, g) → (N n+1,G) be an isometrical immersion with $g = f*G,F = (f,df):(TM^n ,\bar g) \to (TN^{n + 1} ,G_s )$ be the isometrical immersion with $\bar g = F*G_s$ where (df) x: T x M → T f(x) N for any x ∈ M is the differential map, and G s be the Sasaki metric on TN induced from G. This paper deals with the geometry of TM n as a submanifold of TN n+1 by the moving frame method. The authors firstly study the extrinsic geometry of TM n in TN n+1. Then the integrability of the induced almost complex structure of TM is discussed.
In this paper, the authors use the analytic methods and the properties of character sums mod p to study the computational problem of one kind of mean value involving the classical Dedekind sums and two-term exponential sums, and give an exact computational formula for it.
The authors first construct an explicit minimal projective bimodule resolution (ℙ, δ) of the Temperley-Lieb algebra A, and then apply it to calculate the Hochschild cohomology groups and the cup product of the Hochschild cohomology ring of A based on a comultiplicative map Δ: ℙ → ℙ ⊗ A ℙ. As a consequence, the authors determine the multiplicative structure of Hochschild cohomology rings of both Temperley-Lieb algebras and representation-finite q-Schur algebras under the cup product by giving an explicit presentation by generators and relations.
This paper deals with backward stochastic differential equations with jumps, whose data (the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.