unique decipherability in formal languages abstract we consider several language theoretic aspects of various notions of unique decipherability or unique factorization in formal languages given a language l at some position within the chomsky hierarchy we investigate the language of words ud l in l that have unique factorization over l we also consider similar notions for weaker forms of unique decipherability such as numerically decipherable words nd l multiset decipherable words msd l and set decipherable words sd l although these notions of unique factorization have been considered before it appears that the languages of words having these properties have not been positioned in the chomsky hierarchy up until now we show that ud l nd l msd l and sd l need not be context free if l is context free in fact nd l and msd l need not be context free even if l is finite although ud l and sd l are regular in this case we show that if l is context sensitive then so are ud l nd l msd l and sd l we also prove that the membership problem resp emptiness problem for these classes is pspace complete resp undecidable we finally determine upper and lower bounds on the length of the shortest word of l not having the various forms of unique decipherability into elements of l

canonical complex structures associated to connections and complexifications of lie groups the notion of adapted complex structure is extended from riemannian manifolds to general koszul connections the case of the canonical connection of a lie group and the levi civita connection of a pseudo riemannian manifold is studied

on multiset decipherable codes corresp in certain applications it is necessary to communicate a description of a sequence of events where the information of interest is which one of a set of possible events has occurred including multiplicity but where the order of occurrence is irrelevant typical examples are online compilations of inventories construction of histograms or updating of relative frequencies suitable codes for this purpose need not be uniquely decipherable ud in fact all that is required of such a code is that given a finite message over the code every possible parsing of the message into codewords must yield the same multiset of codewords a code with this property is referred to as a multiset decipherable msd code an msd code is said to be proper if it is not a ud code it is shown that for every n 3 there exist proper msd codes with n words for n 2 every msd code is necessarily a ud code and all evidence points to the same conclusion for n 3 it is further shown that no msd code contains a full prefix code or a full suffix code as a proper subcode and it is conjectured that despite the weaker decipherability condition every msd code satisfies the kraft inequality

compatible complex structures on almost quaternionic manifolds on an almost quaternionic manifold m4 q we study the integrability of almost complex structures which are compatible with the almost quaternionic structure q if n 2 we prove that the existence of two compatible complex structures ii i2 i1 forces m4n q to be quaternionic if n 1 that is m4 q m4 g or is an oriented conformal 4 manifold we prove a maximum principle for the angle function ii i2 of two compatible complex structures and deduce an application to anti self dual manifolds by considering the special class of oproiu connections we prove the existence of a well defined almost complex structure j on the twistor space z of an almost quaternionic manifold m4n q and show that j is a complex structure if and only if q is quaternionic this is a natural generalization of the penrose twistor constructions

hyperkahler metrics and supersymmetry we describe two constructions of hyperkahler manifolds one based on a legendre transform and one on a sympletic quotient these constructions arose in the context of supersymmetric nonlinear models but can be described entirely geometrically in this general setting we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience

on the hyperkahler quaternion kahler correspondence a hyperkahler manifold with a circle action fixing just one complex structure admits a natural hyperholomorphic line bundle this observation forms the basis for the construction of a corresponding quaternionic kahler manifold in the work of a haydys in this paper the corresponding holomorphic line bundle on twistor space is described and many examples computed including monopole and higgs bundle moduli spaces finally a twistor version of the hyperkahler quaternion kahler correspondence is established

the adaptive lagrangian particle method for macroscopic and micro macro computations of time dependent viscoelastic flows we propose a new numerical technique referred to as the adaptive lagrangian particle method alpm for computing time dependent viscoelastic flows using either a differential constitutive equation macroscopic approach or a kinetic theory model micro macro approach in alpm the eulerian finite element solution of the conservation equations is decoupled from the lagrangian computation of the extra stress at a number of discrete particles convected by the how in the macroscopic approach the extra stress carried by the particles is obtained by integrating the constitutive equation along the particle trajectories in the micro macro approach the extra stress is computed by solving along the particle paths the stochastic differential equation associated with the kinetic theory model at each time step alpm automatically enforces that all elements of the mesh have a number of lagrangian particles ranging within a user specified interval results are given for the start up flow between highly eccentric rotating cylinders using the fene and fene p dumbbell models for dilute polymer solutions c 1999 elsevier science s a all rights reserved

a note on multiset decipherable codes in a recent paper a lempel ibid vol it 32 p 714 16 1986 introduced the notion of a multiset decipherable msd code to handle some special problems of information transmission he showed that no msd code contains a full prefix code as a proper subcode he further conjectured that no msd code contains a full uniquely decipherable code as a proper subcode and that every msd code satisfies the kraft inequality a proof of the first conjecture and a disproof of the second are given

hyperkahler and quaternionic kahler geometry a quaternion hermitian manifold of dimension at least 12 with closed fundamental 4 form is shown to be quaternionic kahler a similar result is proved for 8 manifolds hyperkahler metrics are constructed on the fundamental quaternionic line bundle with the zero section removed of a quaternionic kahler manifold indefinite if the scalar curvature is negative this construction is compatible with the quaternionic kahler and hyperkahier quotient constructions and allows quaternionic kahler geometry to be subsumed into the theory of hyperkahler manifolds it is shown that the hyperkahler metrics that arise admit a certain type of su 2 action possess functions which are kahler potentials for each of the complex structures simultaneously and determine quaternionic kahler structures via a variant of the moment map construction quaternionic kahler metrics are also constructed on the fundamental quaternionic line bundle and a twistor space analogy leads to a construction of hyperkahler metrics with circle actions on complex line bundles over kahler einstein complex contact manifolds nilpotent orbits in a complex semi simple lie algebra with the hyperkahler metrics defined by kronheimer are shown to give rise to quaternionic kahler metrics and various examples of these metrics are identified it is shown that any quaternionic kahler manifold with positive scalar curvature and sufficiently large isometry group may be embedded in one of these manifolds the twistor space structure of the projectivised nilpotent orbits is studied

on unique multiset and set decipherability of three word codes the concepts of unique decipherability ud multiset decipherability msd and set decipherability sd of codes were developed to handle some special problems in the transmission of information in unique decipherability different sequences of codewords carry different information in multiset decipherability the information of interest is the multiset of codewords used in the encoding process so that order in which transmitted words are received is immaterial in set decipherability it is the set of codewords that is relevant information so the order and the multiplicity of words are immaterial lempel 1986 showed that the ud and msd properties coincide for two word codes and conjectured that every three word msd code is a ud code guzman 1995 showed that the ud msd and sd properties coincide for two word codes and conjectured that these properties coincide for three word codes in this paper we answer both conjectures positively for all three word codes c sub 1 c sub 2 c sub 3 satisfying c sub 1 c sub 2 spl les c sub 3 our procedures are based on techniques related to dominoes

deciding multiset decipherability an o n sup 2 l time and o n k l space algorithm is provided for deciding whether or not a finite set c consisting of n words having total length l where all words are taken over a k element alphabet is a multiset decipherable code the algorithm is based on a technique related to dominoes at an easily stage it decides in o nl time and o n k l space whether or not the set c is uniquely decipherable

mathscr h space with a cosmological constant it is demonstrated that a real analytic 3 manifold with riemannian conformal metric is naturally the conformal infinity of a germ unique real analytic 4 manifold with real analytic riemannian metric satisfying the self dual einstein equations with cosmological constant 1 moreover this result holds if riemannian is replaced in the first case by lorentzian i e signature and in the second case by pseudo riemannian with signature or if real analytic is replaced by complex analytic and 9riemannian is replaced by holomorphic this provides a cosmological constant analogue of newman s space construction newman 1976 1977

twist geometry of the c map we discuss the geometry of the c map from projective special kahler to quaternionic kahler manifolds using the twist construction to provide a global approach to hitchin s description as found by alexandrov et al and alekseevsky et al this is related to the quaternionic flip of haydys we prove uniqueness statements for several steps of the construction in particular we show that given a hyperkahler manifold with a rotating symmetry there is essentially only a one parameter degree of freedom in constructing a quaternionic kahler manifold of the same dimension we demonstrate how examples on group manifolds arise from this picture