Groups in which every non-abelian subgroup is permutable

A subgroupH of a groupG is said to bepermutable ifHX=XH for every subgroupX ofG. In this paper the structure of groups in which every subgroup either is abelian or permutable is investigated. This work was done while the last author was visiting the University of Napoli Federico II. He thanks the “Dipartimento di Matematica e Applicazioni” for its financial support.     

Pre—Separation Axioms in Fuzzifying Topology

1　 IntroductionYing[5,6 ] introduced and elementally developed so called fuzzifying topology with the semanticmethod of continuous valued L ogic.Shen[7] introduced and studied T0 -,T1-,T2 (Hausdorff) -,T3(regularity) -,T4 (normality) -separation axioms in fuzzifying topology.In [3 ]the concepts of thefamily of fuzzifying pre-open sets,fuzzifying pre-neighbourhood structure of a point and fuzzifyingpre-closure are introduced and studied.It is worth to mention that pre-separation axioms are …     

A Two-Dimensional Operator-Difference Scheme for Fluid Dynamics in Lagrangean Coordinates on an Irregular Triangular Grid with the Property of Local Approximation near the Symmetry Axis

The projection approach is applied to construct and investigate an operator-difference scheme for fluid dynamics in Lagrangean variables which has first-order local approximation in the axisymmetric case near the symmetry axis. The scheme also has operator properties that make it suitable for rederiving and substantiating previous results, methods, and algorithms.     

Weak density of smooth maps for the Dirichlet energy between manifolds

We prove that given a simply connected compact manifold M and a closed manifold N, any map in the Sobolev space W ^1,2(M,N) can be approximated weakly by smooth maps between M and N. Submitted: September 2002, Final version: November 2002.     

Martensite Transformation in Nanoparticles and Nanomaterials

Journal of Nanoparticle Research - It was shown that the thermoelastic martensite transformation B2 ? B19 inside nanoparticles surrounded by amorphous matrix in Ni–Ti–Cu alloys as...     

A technique to construct symmetric variable-stepsize linear multistep methods for second-order systems

Some previous works show that symmetric fixed- and variable-stepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts, in such a way that the former have the same order as the latter. The order and symmetry of the integrators obtained is proved independently of the order of the underlying fixed-stepsize integrators. As this technique looks for efficiency, we concentrate on explicit linear multistep methods, which just make one function evaluation per step, and we offer some numerical comparisons with other one-step adaptive methods which also show a good long-term behaviour.

     

Optimal Control of Distributions

The article develops the principles of optimal control theory for probability distributions on the configuration space of a controlled dynamical system. Necessary conditions of optimality are derived in the form of the Pontryagin principle for various classes of problems. Analytical representations in the space of distributions and observables are considered. Special modes are examined. The relationship between distribution control theory and nonlocal optimization problems is demonstrated.