ISSN 1439-8516 CN 11-2039/O1
We study smoothness spaces of Morrey type on Rn and characterise in detail those situations when such spaces of type Ap,qs,τ (Rn) or Au,p,qs(Rn) are not embedded into L∞(Rn). We can show that in the so-called sub-critical, proper Morrey case their growth envelope function is always infinite which is a much stronger assertion. The same applies for the Morrey spaces Mu,p(Rn) with p < u. This is the first result in this direction and essentially contributes to a better understanding of the structure of the above spaces.
A variable coefficient viscoelastic wave equation with acoustic boundary conditions and nonlinear source term is considered. Under suitable conditions on the initial data and the relaxation function g, we show the polynomial decay of the energy solution and the blow up of solutions by energy methods. The estimates for the lifespan of solutions are also given.
In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic Bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator.
We first prove that the subcategory of fixed points of mutation determined by an exceptional object E in a triangulated category coincide with the perpendicular category of E. Based on this characterisation, we prove that the subcategory of fixed points of mutation in the derived category of the coherent sheaves on weighted projective line with genus one is equivalent to the derived category of a hereditary algebra. Meanwhile, we induce two new recollements by left and right mutations from a given recollement.
The use of detecting arrays (DTAs) is motivated by the need to locate and detect interaction faults arising between the factors in a component-based system in software testing. The optimality and construction of DTAs have been investigated in depth for the case in which all the interaction faults are assumed to have the same strength; however, as a practical concern, the strengths of these faults are not always identical. For real world applications, it would be desirable for a DTA to be able to identify and detect faulty interactions of a strength equal to or less than a specified value under the assumption that the faulty interactions are independent from one another. To the best of our knowledge, the optimality and construction of DTAs for independent interaction faults have not been studied systematically before. In this paper, we establish a general lower bound on the size of DTAs for independent interaction faults and explore the combinatorial feature that enable these DTAs to meet the lower bound. Taking advantage of this combinatorial characterization, several classes of optimum DTAs meeting the lower bound are presented.
In this paper, by using the Anick's resolution and Gröbner-Shirshov basis for quantized enveloping algebra of type G2, we compute the minimal projective resolution of the trivial module of Uq+ (G2) and as an application we compute the global dimension of Uq+ (G2).
In this paper, we are concerned with Cauchy problem for the multi-dimensional (N ≥ 3) non-isentropic full compressible magnetohydrodynamic equations. We prove the existence and uniqueness of a global strong solution to the system for the initial data close to a stable equilibrium state in critical Besov spaces. Our method is mainly based on the uniform estimates in Besov spaces for the proper linearized system with convective terms.
Let D be a generalized dihedral group and AutCol(D) its Coleman automorphism group. Denote by OutCol(D) the quotient group of AutCol(D) by Inn(D), where Inn(D) is the inner automorphism group of D. It is proved that either OutCol(D) = 1 or OutCol(D) is an elementary abelian 2-group whose order is completely determined by the cardinality of π(D). Furthermore, a necessary and sufficient condition for OutCol(D) ≠ 1 is obtained. In addition, whenever OutCol(D) = 1, it is proved that AutCol(D) is a split extension of Inn(D) by an elementary abelian 2-group for which an explicit description is given.
In this paper, the structure of Jordan higher derivable maps on triangular algebras by commutative zero products is given. As an application, the form of Jordan higher derivable maps of nest algebras by commutative zero products is obtained.
