In the paper, we give the almost sure limiting behaviour of the increments of partial sums of a ψ-mixing sequence when the moment generating functions do not exist. The results obtained are close to those for an independent sequence provided that the mixing coefficients tend to zero rapidly enough.
Let A be a finitely generated commutative Z-algebra with Krull dimension d, and let π be an arbitrary finite group. It is proved that the Steinberg group Stn(Aπ) is finitely presented whenever n≥4. If, in addition, n≥d+3, and K1(Aπ) and K2(Aπ) are finitely generated, then En(Aπ) and GLn(Aπ) are finitely presented.
In this paper, we determine the groups (ki are odd), (ki are odd and (ki/2)=0),Jn2,k1,…kf (ki are even and n>kl), (ki are even and n>kl), (ki are even and n>kl, kl≥12), Jn1,2, Jn2,3, Jn1,4. And we obtain the relation Im σnk=Jnl,k.
In the present paper a few coincidence theorems and minimax theorems are given so as to unify and strengthen the corresponding results in [3], [4] and [5].
This paper investigates the enumerative problems of flagged skew plane partitions in which each row (column) has an upper and a lower bounds on the entries. By means of dominance technique, a direct and elementary derivation for their generating functions is presented which may be more accessible to readers.
In the present paper a form of generalization of Gelfond's lemma on dense sequences of polynomials is proposed. For a set of complex numbers θ1, …, θs we define the coefficientsgk(θ1, …, θs) (0≤k≤s) and give the relations between them and the transcendental degrees or the transcendence types of the field O (θ1, …, θs) or its subfields.
The authors prove in this paper the following. Theorem.Let f (Z) be any transcendental meromorphic function in the plane. Then for any given non-constant fractional linear function ψ (Z), the set is at most a countable set.
In this paper we prove that an affine hypersphere with scalar curvature zero in a unimodular affine space of dimension n+1 must be contained either in an elliptic paraboloid or in an affine image of the hypersurface x1x2…xn+1=const. We prove also that an affine complete, affine maximal surface is an elliptic paraboloid if its affine normals omit 4 or more directions in general position.
In this paper,we give a modified proof of Sullivan's eventual theorem for rational dynamics. Our proof is based on some idea of the Sullivan's proof,but does not make use of the Teichmuller theory.
In this paper we get an existence theorem of nontrivial critical points by using the local linking idea. As applications, we study the existence of nontrivial periodic solution of Hamiltonian systems.
