A remark on a comparison theorem

A recent comparison result ([3]) allows to get pointwise estimates for the solution of the Dirichlet problem for linear second–order elliptic equations in terms of the solution of a suitable "symmetrized" problem. In this paper we prove that equality is achieved only in the spherically symmetric situation.     

On a Kleinecke-Shirokov theorem

Czechoslovak Mathematical Journal - We prove that for normal operators N1, $${N_2} \in {\cal L}({\cal H})$$ , the generalized commutator [N1, N2; X] approaches zero when [N1, N2; [N1, N2; X]] tends...     

On a density theorem

Translated from Matematichskie Zametki, Vol. 51, No. 6, pp. 32–40, June, 1992.     

On a minimax theorem

The aim of this note is to prove the following statement. It gives an extension of the theorem proved by O. Y. Borenshtein and V. S. Shul'man in [1].     

ON A MIN-MAX THEOREM

In this paper we prove a nonvariational form of a rain-max problem in [l] and give its application to a periodical problem.     

On a fixed-point theorem

Institute of Mathematics, Hanoi. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 30, No. 3, pp. 93–94, July–September, 1996.     

A comparison theorem

The existence of an explosive singularity in the unsteady boundary layer on a rotating disc in a counter-rotating fluid has now been shown incontrovertibly following the work of K. Stewartson, C. J. Simpson, and R. J. Bodonyi (J. Fluid. Mech.121 (1982), 507–515). Here, we develop some asymptotic results for the governing differential equations to help gain an understanding of the mechanism behind this phenomenon. No definite conclusions are possible, but the presence of inertial oscillations at the edge of the boundary layer could well play a definite role.     

On a theorem of Halin

This note presents a new, elementary proof of a generalization of a theorem of Halin to graphs with unbounded degrees, which is then applied to show that every connected, countably infinite graph G, with \(\aleph _0 \le |{\text {Aut}}(G)| < 2^{\aleph _0}\) and subdegree-finite automorphism group, has a finite set F of vertices that is setwise stabilized only by the identity automorphism. A bound on the size of such sets, which are called distinguishing, is also provided. To put this theorem of Halin and its generalization into perspective, we also discuss several related non-elementary, independent results and their methods of proof.     

On a theorem of kemer

Kemer has shown that the standard identitys _n implies some Capelli identityd _m. We prove thatm is bounded above by a subexponential function ofn.     

On a theorem of Schauffler

Translated from Matematicheskie Zametki, Vol. 53, No. 2, pp. 84–93, February, 1993.