In this paper, the authors study the Cohen-Fischman-Westreich’s double centralizer theorem for triangular Hopf algebras in the setting of almost-triangular Hopf algebras.

It is a well-known fact that characters of a finite group can give important information about the structure of the group. It was also proved by the third author that a finite simple group can be uniquely determined by its character table. Here the authors attempt to investigate how to characterize a finite almost-simple group by using less information of its character table, and successfully characterize the automorphism groups of Mathieu groups by their orders and at most two irreducible character degrees of their character tables.

For first-order quasilinear hyperbolic systems with zero eigenvalues, the author establishes the local exact controllability in a shorter time-period by means of internal controls acting on suitable domains. In particular, under certain special but reasonable hypotheses, the local exact controllability can be realized only by internal controls, and the control time can be arbitrarily small.

Klapper (1994) showed that there exists a class of geometric sequences with the maximal possible linear complexity when considered as sequences over GF(2), but these sequences have very low linear complexities when considered as sequences over GF(p) (p is an odd prime). This linear complexity of a binary sequence when considered as a sequence over GF(p) is called GF(p) complexity. This indicates that the binary sequences with high GF(2) linear complexities are inadequate for security in the practical application, while, their GF(p) linear complexities are also equally important, even when the only concern is with attacks using the Berlekamp-Massey algorithm [Massey, J. L., Shift-register synthesis and bch decoding, IEEE Transactions on Information Theory, 15(1), 1969, 122–127]. From this perspective, in this paper the authors study the GF(p) linear complexity of Hall’s sextic residue sequences and some known cyclotomic-set-based sequences.

This paper aims to give some examples of diffeomorphic (or homeomorphic) low-dimensional complete intersections, which can be considered as a geometrical realization of classification theorems about complete intersections. A conjecture of Libgober and Wood (1982) will be confirmed by one of the examples.

This paper deals with the relationship between the positivity of the Fock Toeplitz operators and their Berezin transforms. The author considers the special case of the bounded radial function $\varphi \left( z \right) = a + b{e^{ - \alpha {{\left| z \right|}^2}}} + c{e^{ - \beta {{\left| z \right|}^2}}}$, where a, b, c are real numbers and α, β are positive numbers. For this type of φ, one can choose these parameters such that the Berezin transform of φ is a nonnegative function on the complex plane, but the corresponding Toeplitz operator T _φ is not positive on the Fock space.

Isospectral and non-isospectral hierarchies related to a variable coefficient Painlevé integrable Korteweg-de Vries (KdV for short) equation are derived. The hierarchies share a formal recursion operator which is not a rigorous recursion operator and contains t explicitly. By the hereditary strong symmetry property of the formal recursion operator, the authors construct two sets of symmetries and their Lie algebra for the isospectral variable coefficient Korteweg-de Vries (vcKdV for short) hierarchy.

In this paper, the sharp distortion theorems of the Fréchet-derivative type for a subclass of biholomorphic mappings which have a parametric representation on the unit ball of complex Banach spaces are established, and the corresponding results of the above generalized mappings on the unit polydisk in C ⁿ are also given. Meanwhile, the sharp distortion theorems of the Jacobi determinant type for a subclass of biholomorphic mappings which have a parametric representation on the unit ball with an arbitrary norm in C ⁿ are obtained, and the corresponding results of the above generalized mappings on the unit polydisk in C ⁿ are got as well. Thus, some known results in prior literatures are generalized.

Denote by Q _m the generalized quaternion group of order 4m. Let R(Q _m) be its complex representation ring, and Δ(Q _m) its augmentation ideal. In this paper, the author gives an explicit Z-basis for the Δ ⁿ(Q _m) and determines the isomorphism class of the n-th augmentation quotient $\frac{{{\Delta ^n}\left( {{Q_m}} \right)}}{{{\Delta ^{n + 1}}\left( {{Q_m}} \right)}}$ for each positive integer n.

The authors characterize the order boundedness of weighted composition operators acting between Dirichlet type spaces.

Let K be an algebraic number field of finite degree over the rational field Q, and a _K(n) the number of integral ideals in K with norm n. When K is a Galois extension over Q, many authors contribute to the integral power sums of a _K(n), $\sum\limits_{n \leqslant x} {a\kappa {{\left( n \right)}^l}} ,\;l = 1,\;2,\;3, \ldots $. This paper is interested in the distribution of integral ideals concerning different number fields. The author is able to establish asymptotic formulae for the convolution sum ${\sum\limits_{n \leqslant x} {a{\kappa _1}{{\left( {{n^j}} \right)}^l}a{\kappa _2}\left( {{n^j}} \right)} ^l},\;\;j = 1,\;2,\;\;l = \;2,\;3, \ldots $, where K ₁ and K ₂ are two different quadratic fields.

A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically, an invariant finite energy plane converges to a symmetric periodic orbit. In this note, they work out a criterion which guarantees uniruledness for real Liouville domains.

This paper focuses on nonlocal integral boundary value problems for elliptic differential-operator equations. Here given conditions guarantee that maximal regularity and Fredholmness in L _p spaces. These results are applied to the Cauchy problem for abstract parabolic equations, its infinite systems and boundary value problems for anisotropic partial differential equations in mixed L _p norm