It is proved that the modules in any component of the AR-quiver of a wild hereditary Artin algebra are uniquely determined by their composition factors.
Resonances of Schrödinger operators are closely related to the poles of certain meromorphic extension of the resolvent. In this paper, we study the resonances in Stark effect, generated by negative eigenvalues. We give precise location for the resonances and prove in particular that the widths of resonances are exponentially small and can be measured by some Agmon's distance.
For any polynomial p(z)=a0zn+a|zn-1+…+an, a 0≠0, n≥2,F is the Julia set and μ* is the equilibrium distribution on F. Hans Brolin [1] proved that γ (F)>0, and Sμ* =F. Up to now, we know nothing about rational functions. The aim of this paper is to discuss the case of rational functions.
Paracommutator was first introduced and studied by Janson and Peetre in 1985. They mainly discussed its boundedness and Schatten-von Neumann properties on L2-space. In this paper we study the boundedness of paracommutator on Lp-spaces and obtain some useful criteria.
It is shown that the number of square-full numbers in the interval is asymptotically equal to for every θ in the range 1/6>θ≥0.14254, which extends P.Shiu's range 1/6>θ≥0.1526.
In this paper,utilizing equivariant Mose theory for isolated critical orbits developed in [16] we study the versions of Morse identities under group actions,i.e.the global property of equivariant Morse theory. Combining the concept of critical multiplicity we give a lower bound of the critical multiplicities for a class of invariant functionals.As applications we study the bifuractions of a class of equivariant potential operators and generalize some results due to Benci and Pacella, Chang Rabinowitz, etc.
Suppose that Xl,…, Xn are samples drawn from a population with density function f andfn(x)=fn (x;Xl,…, Xn is an estimate off(x), Denote by mnr=∫|fn(x)-f(n)|rdx and Mnr=E(mnr) the Integrated r-th Order Error and Mean Integrated r-th Order Error of fn for some r-1 (when r=2,they are the familiar and widely studied ISE and MISE), In this paper the same necessary and sufficient condition for and a.s. is obtained when fn(x) is the ordinary histogram estimator.
In this paper we develop a sequence Z0,…,Zn,…(n∈ω) of axiom systems for set theory, such that (1) the consistency of any system within the sequence is provable in its succeeding systems, (2) the first system in the sequence is Zermelo's system Z and the union of all systems in the sequence is just ZF.
