Volume 31, Issue 1

We discuss some examples and counterexamples that are used in first-year calculus courses to illustrate the interconnections between various function classes. Particular emphasis is put on the two-parameter family of functions (1.1) which provides an unexhaustable source of counterexamples.

Let v : [0,∞) → ]0,∞) be a function such that the inequality v ( ts ) ≥ ct - μ v ( s ) holds for 0 < t,s ≤ 1 and some real number μ . In the generalized Triebel–Lizorkin spaces F p,q v (R n ), we will study the boundedness of the pseudo-differential operators whose symbols belong to Hörmander´s class S 1, δ m ,0 ≤ δ < 1.

In this paper, we show the joint universality of the set of the Steuding class L -functions { L ( s + i δ l τ )} l =1 m for almost all ( δ 1 ,…, δ m )∈R m . From this property, we obtain the result that { L ( s + i δ l τ )} l = j,k , where δ j and δ k are two of the above, has a kind of generalized strong recurrence. Roughly speaking, this means that L ( s + i δ j τ ) can be uniformly approximated by L ( s + i δ k τ ) in the sense of universality. Moreover, we consider the relation between the generalized strong recurrence and zeros of the Selberg and Steuding class L -functions L ( s ). Finally, we obtain the upper bound for the density of universality for the Steuding class L -functions.

In this paper a geometric property, namely the corkscrew condition, has been obtained for minimal sets.

In this paper we study the uniqueness of entire functions concerning shared values of entire functions and their two or more derivatives. The results in this paper improve the corresponding ones given by H. L. Zhong and L. Z. Yang, and others.

We solve two problems of analysis and special function theory recently posed by Furdui. The series in question are special cases in our solution.

Let P be a differential polynomial with constant coefficients and F a family of meromorphic functions in the unit disk. We study the situation that P [ f ] and P ´[ f ] share a finite nonzero value CM for all f ∈ F and give conditions on P for F to be normal. Furthermore, a corresponding Picard type theorem for entire functions is given. Connections to Picard type theorems for exceptional values of differential polynomials are shown. The general results are applied to several specific differential polynomials such as P [ u ]:= u n + au ( k ) or P [ u ]:= u n u ( k ) .

Yosida´s version of the mean ergodic theorem is extended to positive Toeplitz matrices and locally convex spaces. This is used to provide extensions of the results of Albanese, Bonet and Ricker on the structure of Fréchet spaces and also Köthe echelon spaces.

In this short note we show that in codimension one all homogeneous algebraic selfsimilar solutions of the mean curvature flow are either algebraic minimal hypersurfaces or belong to the class of well known self-shrinking quadrics.