On twisted forms and relative algebraic K-theory

This paper introduces a new approach to the study of certain aspects of Galois module theory by combining ideas arising from the study of the Galois structure of torsors of finite group schemes with techniques coming from relative algebraic $K$-theory.Comment: Final version. To appear in the Proceedings of the London Mathematical Societ

Impact of Digital Revolution on the Structure of Nigerian Banks

The study examined the extent to which digital revolution has affected the organizational structure of Nigerian banks. Twenty-five banks were selected for the study in south-western Nigeria. Interview was conducted for middle and top level managers and questionnaire was developed and administered to the other staff using a five-point Likert scale to determine the attitudes and opinions of the staff on the effects of digital revolution on the organizational structure of the banks. The mean was used as an indicator of central tendency for quantitative variables that have frequency distributions in the study. The study found that standard operating procedures, politics, culture, surrounding environment and management decisions were all affected by digital revolution. It affected the organizational balance of rights, privileges, obligations, responsibilities, and feelings that have been established over a long period of time. The revolution brought structural changes in the line and unit of command, the principles of span of control, unity of command, and scalar principle of graded chain of superiors in the studied banks. It encouraged flat organizations as decision making became more decentralized. It also altered the required skill and increased the perceived advantage of workers with computer engineering background. Authority relied on knowledge and competence and not on mere formal position The study concluded that digital revolution has changed the course of history in the banking industry leaving far reaching effects and implications on both the organizational and industrial structure. It is imperative for banks and their staff to effect proper restructuring that will facilitate optimal utilization of the benefits provided by the revolution.Digital Revolution, ICT, e-Commerce, Organizational Structure, Nigerian Banks

Quasi-exact Treatment of the Relativistic Generalized Isotonic Oscillator

We investigate the pseudospin symmetry case of a spin-1/2 particle governed by the generalized isotonic oscillator, by presenting quasi exact polynomial solutions to Dirac equation with pseudospin symmetry vector and scalar potentials. The resulting equation is found to be quasi-exactly solvable owing to the existence of a hidden $sl(2)$ algebraic structure. A systematic and closed form solution to the basic equation is obtained using the Bethe ansatz method. Analytic expression for the energy is obtain and the wavefunction is derived in terms of the roots to a set of Bethe ansatz equations

NeutroVectorSpaces I

Recently, the concept of NeutroAlgebraic and AntiAlgebraic Structures were introduced and analyzed by Florentin Smarandache. His new approach to the study of Neutrosophic Structures presents a more robust tool needed for managing uncertainty, incompleteness, indeterminate and imprecise information. In this paper, we introduce for the first time the concept of NeutroVectorSpaces. Specifically, we study a particular class of the NeutroVectorSpaces called of type 4 S and their elementarily properties are presented. It is shown that the NeutroVectorSpaces of type 4 S may contain NeutroSubspaces of other types and that the intersections of NeutroSubspaces of type 4 S are not NeutroSubspaces. Also, it is shown that if N V is a NeutroVector Space of a particular type and N W is a NeutroSubspace of N V, the NeutroQuotientSpace N V /N W does not necessarily belong to the same type as N V

On the square root of the inverse different

Let N/F be a finite, normal extension of number fields with Galois group G. Suppose that N/F is weakly ramified, and that the square root A(N/F) of the inverse different of N.F is defined. (This latter condition holds if, for example, G is of odd order.) B. Erez has conjectured that the class (A(N/F)) of A(N/F) in the locally free class group Cl(ZG) of ZG is equal to Chinburg's second Omega invariant attached to N/F. We show that this equality holds whenever A(N/F) is defined and N/F is tame. This extends a result of the second-named author and S. Vinatier