We give realizations of irreducible non-weight modules of three classes of not-finitely graded algebras arisen from the completed Witt algebra, we also obtain some interesting combinatorial identities.
We mainly discuss the property of the modified Roper-Suffridge operators. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve almost spirallikeness of order α and type β, spirallikeness of order α and type β, strong spiral-likeness of type β on Bn, respectively. Sequentially, we get that the modified Roper-Suffridge operators preserve almost starlikeness of order α, starlikeness of order α and strong starlikeness on Bn. The conclusions provide a new approach to construct these biholomorphic mappings in several complex variables.
Under linearly degenerate condition, the stability of leftmost and right-most families of traveling wave solutions to Cauchy problem for quasilinear hyperbolic system had been established in our recent work, while for the intermediate families, their possible instability is illustrated. This paper is concerned with the stability of traveling wave solutions with appropriate small W1,1∩L∞ norm to Cauchy problem for quasilinear hyperbolic system under weakly linearly degenerate condition, and the stability results can be applied to the diagonalizable quasilinear hyperbolic systems and Chaplygin gas.
We mainly focus our attention on the ramification of primes in cyclic num-ber fields. By the Kronecker-Weber theorem and Hilbert ramification theory for global fields, we present explicitly in this note the formula for conductor of cyclic number fields, which the number of ramified primes is fixed in advance, with prime degree over rational number fields.
The sufficient and necessary conditions are studied on the strong convergence of the modified Ishikawa iterative sequence with errors and the modified Mann iterative sequence with errors for uniformly L-Lipschitz mappings in Banach spaces. The results of this paper improve and extend some corresponding results in the recent literature.
Poisson algebras are algebras with an algebra structure and a Lie algebra structure, both of which satisfy the Leibniz law. The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra W(0) of differential operators of order at most one, which is connected with certain moduli spaces of curves. This paper mainly determines the Poisson structure of the Lie algebra W(0) as well as the twisted Heisenberg-Virasoro algebra.
Under the assumption that the missing data mechanism is ignorable, we derive the maximum likelihood and unbiased estimators of the Cholesky decomposition of covariance and precision matrices in a conditional independent normal model with monotone missing data. By introducing a special group, we obtain the best equivariant estimators under more generalized losses, which implies that the maximum likelihood and unbiased estimators are all inadmissible. Finally, some simulations are given to examine the performance of the relevant results.
Let G be a finite group with subgroups A and B such that G=AB. If A is subnormal in G and for any p∈π(G) and any p'-element x of A∪B with prime power order,|xG| is not divisible by p2, then G is supersolvable. This result gives a positive answer to a problem posed in 2013 by Shi Xiangdong, Wei Huaquan and Ma Xuanlong and a unify generalization of three theorems obtained in 2011 by Liu Xiaolei.
This paper considers a k/n(G) repairable system with replaceable repair facility where the repair facility may fail during the repair period. Assume that the lifetime of each component and the work time of the repair facility are exponentially distributed random variables, while the repair time of broken component and the replacement time of the repair facility follow general distributions. By using the Markov renewal process theory and the Laplace (Laplace-Stieltjes) transform, the mean time to first failure, the availability and the rate of occurrence of failures of the system, the probability that the repair facility is being replaced and the rate of occurrence of failures of the repair facility are discussed. Further more, the recursive expressions of these reliability measures are obtained. Finally, two special cases 1/2(G) repairable system and (n-1)/n(G) repairable system are derived.
We prove that for a transcendental meromorphic function f of finite order which has two Borel exceptional values a(∈C) and b(∈C∪{∞}), if f(z+η)-f(z) and f(z) share values a, b CM, where η(∈C) satisfies f(z+η)?f(z), then b=∞, a=0且f(z)=cec1z, where c, c1 are two nonzero constants.
We study the problem of finite-dimensional approximation of the Moore-Penrose inverse of a closed densely defined operator with closed range. Because the admissible conditions are quite strong, so we put forward the weaker condition PG(Tn).jpg){kind=small}
PG(T) to study finite-dimensional approximation of the Moore-Penrose inverse of a closed densely defined operator, which has the same conclusion. Especially, if T is a bounded linear operator and Tn=QnTPn, then the condition PG(Tn).jpg){kind=small}
PG(T) will hold naturally and many results of the Moore-Penrose inverse of a bounded linear operator be corollaries of Theorem 3.3.
On the basis of the characterizations of the boundedness and compactness of the Riemann-Stieltjes operator Ig,φ and Jg,φ from Hardy spaces Hp to Zygmund-type spaces, the authors provide an estimate for the essential norm of Ig,φ and Jg,φ by means of constructing some test functions in Hp, the definition of the essential norm of an operator and the properties of the analytic function.
We study the dilations of row contractive representations of multivariable C*-dynamical systems on Hilbert C*-modules. We show that if (A,α) is a multivari-able C*-dynamical system, then every covariant representation (π，T，E) of (A,α) on a Hilbert C*-module E admits an isometric dilation (ρ,V,F) on some Hilbert module F containing E as a complemented submodule.
