Dynamical systems on a Riemannian manifold that admit normal shift

Newtonian dynamical systems that admit normal shift on an arbitrary Riemannian manifold are considered. The determining equations for these systems, which constitute the condition of weak normality, are derived. The extension of the algebra of tensor fields to manifolds is considered.Bashkir State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 2, pp. 256–266, May, 1995.     

Multidimensional dynamical systems that admit normal shift

Dynamical systems in R _n of the formR ⁿ of the form that admit normal shift of submanifolds of codimension 1 are considered. The concept of weak normality for such systems is defined, and defining partial differential equations for the force function of dynamical systems with the properties of weak and complete normality are derived.Bashkir State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 2, pp. 264–269, August, 1994.     

The problem of metrizability of dynamical systems that admit normal shift

The problem of metrizability of dynamical systems that admit normal shift is formulated and solved. The explicit form of the force field for a Newtonian dynamical system _tt r=F(r, _t r) along which normal shift coincides with the metric normal shift for some conformally Euclidean metric is found.State University, Bashkir. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 101, No. 1, pp. 85–93, October, 1994.     

Operators that admit a moment sequence

We consider the question of which operators on Hilbert space admit a moment sequence, and show, in particular, that ifT is any operator inL(itH) that can be written asT=N+K, whereN is normal andK is compact, andM⊂itH is any invariant subspace forT, then the restrictionT/itM admits such a sequence.     

Banach spaces that admit support sets

It is shown that the existence of a closed convex set all of whose points are properly supported in a Banach space is equivalent to the existence of a certain type of uncountable ordered one-sided biorthogonal system. Under the continuum hypothesis, we deduce that this notion is weaker than the existence of an uncountable biorthogonal system.

     

Graphs that admit right angle crossing drawings

We consider right angle crossing (RAC) drawings of graphs in which the edges are represented by polygonal arcs and any two edges can cross only at a right angle. We show that if a graph with n vertices admits a RAC drawing with at most 1 bend or 2 bends per edge, then the number of edges is at most 6.5n and 74.2n, respectively. This is a strengthening of a recent result of Didimo et al.     

Construction of finite p-groups that admit partitions

Dedicated to the memory of A. I. Mal'tsev.     

3-manifolds that admit knotted solenoids as attractors

Motivated by the study in Morse theory and Smale's work in dynamics, the following questions are studied and answered: (1) When does a 3-manifold admit an automorphism having a knotted Smale solenoid as an attractor? (2) When does a 3-manifold admit an automorphism whose non-wandering set consists of Smale solenoids? The result presents some intrinsic symmetries for a class of 3-manifolds.

     

Automorphisms that admit an approximation by periodic transformations

Summary We are concerned with a class of automorphisms which can be approximated by periodic transformations. We show that such an automorphism T is ergodic and that a relationship exists between the spectrum of T, the measure of the sets which are invariant under T, and the ergodicity of the powers of T. Finally, we exhibit conditions under which T is weakly mixing and not strongly mixing.This research was supported by NSF Grant No. GP-7490.     

Operators that admit a moment sequence, II

As the title indicates, this note is a continuation of a paper by Foias, Jung, Ko and Pearcy, in which it was shown that certain classes of operators on a Hilbert space admit moment sequences. Herein we extend these results.

     

Spaces that admit hypercyclic operators with hypercyclic adjoints

A continuous linear operator is hypercyclic if there is an such that the orbit is dense. A result of H. Salas shows that any infinite-dimensional separable Hilbert space admits a hypercyclic operator whose adjoint is also hypercyclic. It is a natural question to ask for what other spaces does contain such an operator. We prove that for any infinite-dimensional Banach space with a shrinking symmetric basis, such as and any , there is an operator , where both and are hypercyclic.

     

Field-theory models that admit alternative Lagrangian formulations. II

A large class of field-theory models that admit alternative Lagrangian formulations is described. It includes, in particular, all bi-Lagrangian field theories with hyperregular first-order Lagrangians.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 1, pp. 55–64, January, 1992.     

Field-theory models that admit alternative Lagrangian formulations. I

Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 89, No. 1, pp. 121–131, October, 1991.     

On matrices that admit unitary reduction to band form

It is proved in the paper that any low rank perturbation of a Hermitian matrix is unitarily reducible to band form. Moreover, if a normal matrix is unitarily reducible to band form, then any of its rank one perturbations is unitarily reducible as well.Translated fromMatematicheskie Zametki, Vol. 64, No. 6, pp. 871–880, December, 1998.     

Some classes of electromagnetic waves that admit parabolic helices

We describe classes of electromagnetic waves that admit the subgroups of the Poincaré group such that the subgroups contain parabolic helices. Representatives of some classes are constructed. __________ Translated from Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 12, No. 7, pp. 79–92, 2006.     

On biquadratic fields that admit unit power integral basis

We consider biquadratic number fields whose maximal orders have power integral bases consisting of units. We prove an effective and efficient criteria to decide whether the maximal order of a biquadratic field has a unit power integral basis or not. In particular we can determine all trivial biquadratic fields whose maximal orders have a unit power integral basis.     

A note on finite semifield planes that admit affine homologies

Let be a translation plane of order n that admits an abelian group of order n in its translation complement. If admits an affine homology then it is a semifield plane.