关于$\omega$-Smash余积Hopf代数的$(f,\omega)$相容对$(B,,H)$

In this paper we introduce the notion of （f,ω）-compatible pair （B,H）, by which we construct a Hopf algebra in the category HHYD of Yetter-Drinfeld H-modules by twisting the comultiplication of B. We also study the property of ω-smash coproduct Hopf algebras Bω H.     

Programmable criteria for strong $\mathcal {H}$-tensors

Strong \(\mathcal {H}\)-tensors play an important role in identifying positive semidefiniteness of even-order real symmetric tensors. We provide several simple practical criteria for identifying strong \(\mathcal {H}\)-tensors. These criteria only depend on the elements of the tensors; therefore, they are easy to be verified. Meanwhile, a sufficient and necessary condition of strong \(\mathcal {H}\)-tensors is obtained. We also propose an algorithm for identifying the strong \(\mathcal {H}\)-tensors based on these criterions. Some numerical results show the feasibility and effectiveness of the algorithm.     

Additive Maps Preserving the Star Partial Order on $\mathcal{B}(\mathcal{H})$

Let $\mathcal{B}(\mathcal{H})$ be the $C^∗$-algebra of all bounded linear operators on a complex Hilbert space $\mathcal{H}$. It is proved that an additive surjective map $φ$ on $\mathcal{B}(\mathcal{H})$ preserving the star partial order in both directions if and only if one of the following assertions holds. (1) There exist a nonzero complex number $α$ and two unitary operators $\boldsymbol{U}$and$\boldsymbol{V}$ on $\mathcal{H}$ such that $φ(\boldsymbol{X}) = α\boldsymbol{UXV}$or $φ(\boldsymbol{X}) = α\boldsymbol{UX}^∗\boldsymbol{V}$ for all $X ∈ \mathcal{B}(\mathcal{H})$. (2) There exist a nonzero $α$ and two anti-unitary operators$\boldsymbol{U}$and$\boldsymbol{V}$on $\mathcal{H}$ such that $φ(\boldsymbol{X}) = α\boldsymbol{UXV}$ or $φ(\boldsymbol{X}) = α\boldsymbol{UX}^∗\boldsymbol{V}$ for all $X ∈ \mathcal{B}(\mathcal{H})$.     

量子代数${\cal U}_q(f(K,H))$的量子伴随作用

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.     

A remarkable class of second order differential operators on the Heisenberg group ${\mathbb H}_2$

Let L be a differential operator on whose principal part is of the form , where and , are the usual vector fields generating the Lie algebra of the Heisenberg group . We study the problem of local solvability of these doubly characteristic operators. The whole class of operators splits into three subclasses, depending on the sign of a respective determinant. The operators in the first subclass, when the determinant is negative, are generically non-solvable. The operators in the second subclass, when the determinant is positive, are solvable, for arbitrary left-invariant lower order terms, provided that the coefficient matrix is non-degenerate. This fact seems remarkable, since many of these operators have the property that the values taken by their principal symbol are not contained in any proper subcone of the complex plane. Under suitable conditions, solvability even holds in the presence of non-invariant lower order terms. Received: 17 January 2000 / Published online: 4 May 2001     

${\cal H}^1$-estimates of Jacobians by subdeterminants

Let be a mapping in the Sobolev space . We assume that the cofactors of the differential matrix Df(x) belong to . Then, among other things, we prove that the Jacobian determinant detDf lies in the Hardy space . Received: 20 November 2000 / Revised version: 17 December 2001 / Published online: 5 September 2002 Iwaniec was supported by NSF grant DMS-0070807. This research was done while Onninen was visiting Mathematics Department at Syracuse University. He wishes to thank SU for the support and hospitality.     

The Infinite Dimensional Hyperbolic Space H~∞ Does Not Have Property A

The author constructs a sequence of cubes in the infinitely dimensional hyperbolic space H∞ which is equi-coarsely equivalent to Z2n. As a corollary, it is proved that the infinitely dimensional hyperbolic space H∞ does not have property A.     

Analytic criterion for linear convexity of Hartogs domains with smooth boundary in $ {\mathbb{H}^2} $

We establish a criterion for the local linear convexity of sets in the two-dimensional quaternion space \mathbbH² {\mathbb{H}^2} that are analogs of bounded Hartogs domains with smooth boundary in the two-dimensional complex space \mathbbC² {\mathbb{C}^2} .     

$\mathcal{H}$-Matrix approximation for the operator exponential with applications

Summary. We develop a data-sparse and accurate approximation to parabolic solution operators in the case of a rather general elliptic part given by a strongly P-positive operator [4]. In the preceding papers [12]–[17], a class of matrices (-matrices) has been analysed which are data-sparse and allow an approximate matrix arithmetic with almost linear complexity. In particular, the matrix-vector/matrix-matrix product with such matrices as well as the computation of the inverse have linear-logarithmic cost. In the present paper, we apply the -matrix techniques to approximate the exponent of an elliptic operator. Starting with the Dunford-Cauchy representation for the operator exponent, we then discretise the integral by the exponentially convergent quadrature rule involving a short sum of resolvents. The latter are approximated by the -matrices. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different time values. In the case of smooth data (coefficients, boundaries), we prove the linear-logarithmic complexity of the method. Received June 22, 2000 / Revised version received June 6, 2001 / Published online October 17, 2001     

$ P $ -Stability of Some Classes of $ S $ -Acts

Siberian Mathematical Journal - The notion of $ P $ -stability is a particular case of the generalized stability of complete theories. This paper discusses some problems that are related to the $ P...     

On $ p $ -Universal and $ p $ -Minimal Numberings

Siberian Mathematical Journal - We study the $ p $ -reducibility of numberings which was introduced and first studied by Degtev. $ p $ -Reducibility is an effectively bounded version of the $ e $...     

Nonlinear Mixed Jordan Triple $ * $ -Derivations on $ * $ -Algebras

Siberian Mathematical Journal - Let $ {\mathcal{A}} $ be a unital $ \ast $ -algebra containing a nontrivial projection. Under some mild conditions on  $ {\mathcal{A}} $ ,...     

Sensitivity Analysis for a Class of H 0 1 ${{H_{0}^{1}}}$ -Elliptic Variational Inequalities of the Second Kind

Set-Valued and Variational Analysis - We study the stability of solutions to ${H_{0}^{1}}$ -elliptic variational inequalities of the second kind that contain a non-differentiable Nemytskii...     

A Criterion for Binarity of Almost $ \omega $ -Categorical Weakly $ o $ -Minimal Theories

Siberian Mathematical Journal - Continuing the study of weak $ o $ -minimality, we prove a theorem on the behavior of a definable unary function on the set of realizations of a nonalgebraic 1-type...     

Yamabe Invariants and $ Spin^c $ Structures

The Yamabe invariant of a smooth compact manifold is by definition the supremum of the scalar curvatures of unit-volume Yamabe metrics on the manifold. For an explicit infinite class of 4-manifolds, we show that this invariant is positive but strictly less than that of the 4-sphere. This is done by using Dirac operators to control the lowest eigenvalue of a perturbation of the Yamabe Laplacian. These results dovetail perfectly with those derived from the perturbed Seiberg–Witten equations [Le3], but the present method is much more elementary in spirit. Submitted: October 1997     

A New Characterization of Finite $ \sigma $ -Soluble $ P\sigma T $ -Groups

Siberian Mathematical Journal - We prove that  $ G $ is a finite $ \sigma $ -soluble group with transitive $ \sigma $ -permutability if and only if the following hold: (i) $ G $ possesses...