Constructions of quaternion and octonion algebras, suggested to have new level and sublevel values, are proposed and justified. In particular, octonion algebras of level and sublevel 6 and 7 are constructed. In addition, Hoffmann’s proof of the existence of infinitely many new values for the level of a quaternion algebra is generalised and adapted.

In this paper we begin a classification of simple and semisimple totally antiflexible algebras (finite-dimensional) over splitting fields of char. ^2, 3.. For such an algebra A , let P be the largest associative ideal in A and let /V+ be the radical of P. We determine all simple and semisimple totally antiflexible algebras in which N ■ N =0. Defining A to be of type (m, n) if N is nilpotent of ...

Let V be a vertex operator algebra. We construct a sequence of associative algebras A n (V) (n = 0; 1; 2; :::) such that A n (V) is a quotient of A n+1 (V) and a pair of functors between the category of A n (V)-modules which are not A n?1 (V)-modules and the category of admissible V-modules. These functors exhibit a bijection between the simple modules in each category. We also show that V is r...

In this paper we investigate the validity of a cancellation law for some classes of monounary algebras.

In this paper, we determine the isomorphism classes of the central simple Poisson algebras introduced earlier by the second author. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.

We describe a general framework to define dendriform algebras and a general construction to obtain new dendriform algebra structures from known structures and from linear operators. The construction includes recent constructions of the quadri-algebra, the ennea-algebras, the dendriformNijenhuis algebras and the octo-algebras.

Background: Radiotherapy with large mantle field is an effective technique in increasing the risk of secondary cancers among HL (Hodgkin Lymphoma) patients; therefore, it is essential to choose an effective treatment field including the least medical conditions in radiotherapy.Objective: The present study aimed to plan separate fields for neck and mediastinum using various energies, to compare ...

This paper analyzes local convergence rates of primal-dual interior point methods for general nonlinearly constrained optimization problems. For this purpose, we first discuss modified Newton methods and modified quasi-Newton methods for solving a nonlinear system of equations, and show local and Qquadratic/Q-superlinear convergence of these methods. These methods are characterized by a perturb...

[1] New slope measurements from the Mars Orbiter Laser Altimeter (MOLA), in conjunction with the Rock Mass Rating system (RMR), permit inversions of slope height and angle from wallrock and interior deposits within Valles Marineris troughs for strength and lithology. Wallrock (50 < RMR < 65) is stronger than interior deposits (30 < RMR < 55). These values are consistent with layered igneous roc...