Generalized steiner problem in outerplanar networks

The generalized Steiner problem (GSP) is concerned with the determination of a minimum cost subnetwork of a given network where some (not necessarily all) vertices satisfy certain pairwise (vertex or edge) connectivity requirements.The GSP has applications to the design of water and electricity supply networks, communication networks and other large-scale systems where connectivity requirements ensure the communication between the selected vertices when some vertices and/or edges can become inoperational due to scheduled maintenance, error, or overload.The GSP is known to beNP-complete. In this paper we show that if the subnetwork is required to be biconnected or respectively edge-biconnected, and the underlying network is outerplanar, the GSP can be solved in linear time.     

Probability measures on operator algebras

The problem of linearity of probability measures on hyperfinite factors is studied in Part I. Part II contains the extension of Vital-Hahn-Saks, Egoroff and Lusic theorems for probability measures on von Neumann algebras. These problems have immediate connections with properties of physical states on observable algebras in the sense of Mackey.     

Reduced sub-powers and the decision problem for finite algebras in arithmetical varieties

The aim of this paper is to prove that every finitely generated, arithmetical variety of finite type, in which every subdirectly irreducible algebra has linearly ordered congruences has a decidable first order theory of its finite members. The proof is based on a representation of finite algebras from such varieties by some quotients of special subdirect products in which sets of indices are partially ordered into dual trees. Then the result of M. O. Rabin about decidability of the monadic second order theory of two successors is applied.Presented by Stanley Burris.     

The magnetic field,force and inductance of the system consisting of a thin ellipsoidal coil and a ferromagnetic ellipsoid

The method of separation of variables has been applied to determine the magnetic field of the system consisting of a thin ellipsoidal coil and a ferromagnetic ellipsoid of revolution. The inductance and the force acting between the coil and the ellipsoid are also examined.     

Graph Approach to the Computation of the Homology of Continuous Maps

We introduce an efficient algorithm to compute the homomorphism induced in (relative) homology by a continous map. The algorithm is based on a cubical approximation of the map and the theory of multivalued maps. A software implementation of the algorithms introduced in this paper is available at [27].     

Non-trivial negative links have positive signature

A negative link is an oriented link that can be represented by a diagram with all the crossings negative. In this paper we prove the following theorem.     

EPR studies of Gd3+-doped Ce2(SO4)3.8H2O and La2(SO4)3.9H2O single crystals

EPR spectra of Gd³⁺-doped Ce₂(SO₄)₃.8H₂O and La₂(SO₄)₃.9H₂O single crystals have been measured with an X-band spectrometer at room and low temperatures. The absolute signs of spin Hamiltonian parameters have been determined for the La₂(SO₄)₃.9H₂O host from intensities of lines at liquid helium temperature; for the Ce₂(SO₄).8H₂O host the lines broaden considerably below 60 K, not permitting the determination of absolute signs of spin Hamiltonian parameters. The data are analysed using a rigourous least-squares procedure, fitting simultaneously all lines obtained for several orientations of the external magnetic field. The zero-field splittings have been computed for both the hosts. The characteristics of EPR spectra of Gd³⁺ in these hosts are compared with those obtained in other rare-earth trisulphate octahydrate hosts.     

The dichlorovinylation of enolates

The condensation of certain ketone and ester enolates with trichloroethylene proceeds with surprising ease to yield dichlorovinylation products. The $\text{trans}$ stereochemistry for one such product is established by X-ray, and subsequent transformations of these initial products to ethinyl or ω-chloroethinyl derivatives is described.