on groups of finite morley rank with a split bn pair of rank 1 abstract we study groups of finite morley rank with a split bn pair of tits rank 1 in the case where the normal complement to b n in b is infinite and abelian for such groups we give conditions ensuring that the standard action of g on the cosets of b is isomorphic to the natural action of psl 2 f on p 1 f for f an algebraically closed field in particular we show that sl 2 f and psl 2 f are the only infinite quasisimple l groups of finite morley rank possessing a split bn pair of tits rank 1 where the normal complement to b n in b is infinite abelian our approach is through the theory of moufang sets and is tied to work attempting to classify the abelian moufang sets of finite morley rank

asymmetric perfectly matched layer for the absorption of waves the perfectly matched layer pml has become a standard for comparison in the techniques that have been developed to close the system of maxwell equations more generally wave equations when simulating an open system the original berenger pml formulation relies on a split version of maxwell equations with numerical electric and magnetic conductivities we present here an extension of this formulation which introduces counterparts of the electric and magnetic conductivities affecting the term which is spatially differentiated in the equations the phase velocity along each direction is also multiplied by an additional coefficient we show that under certain constraints on the additional numerical coefficients this medium does not generate any reflection at any angle or any frequency and is thus a perfectly matched layer technically it is a superset of berenger s pml to which it reduces for a specific set of parameters and like it it is anisotropic however unlike the pml it introduces some asymmetry in the absorption rate and is therefore labeled an apml for asymmetric perfectly matched layer we present here the numerical considerations that have led us to introduce such a medium as well as its theory several finite difference numerical implementations are derived in one two and three dimensions and the performance of the apml is contrasted with that of the pml in one and two dimensions using plane wave analysis we show that our apml implementations lead to higher absorption rates than the considered pml implementations although we have considered in this paper the finite difference discretization of maxwell like equations only the apml system of equations may be used with other discretization schemes such as finite elements and may be applied to other equations for applications beyond electromagnetics

set approximations in fuzzy formal concept analysis formal concept analysis and rough set theory are two important tools in knowledge representation and knowledge discovery in relational information systems the purpose of this paper is to study rough set approximations within formal concept analysis in fuzzy environment properties of existent fuzzy concept lattices derived from an adjoint pair of operations are first reviewed and examined based on both lattice theoretic and fuzzy set theoretic operators two new pairs of rough fuzzy set approximations within fuzzy formal contexts are then defined finally properties of the rough fuzzy set approximation operators are presented in detail

an extended fdtd scheme for the wave equation application to multiscale electromagnetic simulation abstract an algorithm for the application of the mesh refinement technique to finite difference calculation of the wave equation is presented via the introduction of a new extended fdtd scheme this scheme can be viewed as an extension of the yee scheme using a new set of variables relating to the direction of propagation of the waves along an axis because of this additional information this scheme allows a more natural implementation of the mesh refinement technique the extended scheme is presented for both a one dimensional and a multidimensional system the mesh refinement algorithm is given in one dimension and the performances are compared to other proposed schemes

weakly split spherical tits systems in quasi reductive groups we will prove that any weakly split spherical tits system b n in g bf g k bf g a quasi reductive k group such as a connected reductive k group satisfying some natural conditions is standard in particular if bf g is anisotropic over k then such a tits system is trivial i e b g n

proper moufang sets with abelian root groups are special moufang sets are split bn pairs of rank one or the moufang buildings of rank one as such they have been studied extensively being the basic building blocks of all split bn pairs a moufang set is proper if it is not sharply 2 transitive we prove that a proper moufang set whose root groups are abelian is special this resolves an important conjecture in the area of moufang sets it enables us to apply the theory of quadratic jordan division algebras to such moufang sets

formal concept analysis via multi adjoint concept lattices several fuzzifications of formal concept analysis have been proposed to deal with uncertain information in this paper we focus on concept lattices under a multi adjoint paradigm which enriches the language providing greater flexibility to the user in that he she can choose from a number of different connectives multi adjoint concept lattices are shown to embed different fuzzy extensions of concept lattices found in the literature the main results of the paper being the representation theorem of this paradigm and the embedding of other well known approaches

formal concept analysis and lattice valued chu systems this paper links formal concept analysis fca both to order theoretic developments in the theory of galois connections and to chu spaces or systems viewed as a common rubric for both topological systems and systems arising from predicate transformers in programming semantics 13 these links are constructed for each of traditional fca and l fca where l is a commutative residuated semiquantale surprising and important consequences include relationships between formal l contexts and l topological systems within the category of l chu systems relationships justifying the categorical study of formal l contexts and linking such study to l chu systems applications and potential applications are primary motivations including several example classes of formal l contexts induced from data mining notions throughout categorical frameworks are given for fca and lattice valued fca in which morphisms preserve the birkhoff operators on which all the structures of fca and lattice valued fca rest and further the results of this paper show that under very general conditions these categorical frameworks are both sufficient and necessary for the interchange or preservation of l concepts and l protoconcepts structures central to fca and lattice valued fca

a new absorbing layer boundary condition for the wave equation a new absorbing boundary condition using an absorbing layer is presented for application to finite difference time domain fdtd calculation of the wave equation this algorithm is by construction a hybrid between the berenger perfectly matched layer pml algorithm and the one way sommerfeld algorithm the new prescription contains both of these earlier ones as particular cases and retains benefits from both numerical results indicate that the new algorithm provides absorbing rates superior to those of the pml algorithm

concept lattices and conceptual knowledge systems abstract concept lattice is the central notion of formal concept analysis a new area of research which is based on a set theoretical model for concepts and conceptual hierarchies this model yields not only a new approach to data analysis but also methods for formal representation of conceptual knowledge these methods are outlined on three levels first basics on concept lattices are explained starting from simple data contexts which consist of a binary relation between objects and attributes indicating which object has which attribute on the second level conceptual relationships are discussed for data matrices which assign attribute values to each of the given objects finally a mathematical model for conceptual knowledge systems is described this model allows us to study mathematically the representation inference acquisition and communication of conceptual knowledge

constructing l fuzzy concept lattices without fuzzy galois closure operation abstract improving construction efficiency of fuzzy concept lattices remains one of the important issues in the field of fuzzy formal concept analysis building l fuzzy concept lattice is usually based on the closure operation of the fuzzy galois connection and each closure operation needs to scan the fuzzy concept context twice this becomes a significant computing overhead especially when the fuzzy formal context is large we propose a batch mode algorithm for directly constructing fuzzy concept lattices based on union and intersection operations of the fuzzy set that scans the fuzzy formal context once only experimental results show that it improves the construction efficiency of the complete fuzzy concept lattice especially for large fuzzy formal contexts with small truth sets

moufang polygons and irreducible spherical bn pairs of rank 2 i let g be a group with an irreducible spherical bn pair of rank 2 satisfying the additional condition there exists a normal nilpotent subgroup u of b with b tu where t b n and jw ja16 forthe weyl gr oup w n b n we show that g corresponds to a moufang polygon and hence is essentially known r 2003 elsevier science usa all rights reserved

continued fraction absorbing boundary conditions for convex polygonal domains continued fraction absorbing boundary conditions cfabcs are highly effective boundary conditions for modelling wave absorption into unbounded domains they are based on rational approximation of the exact dispersion relationship and were originally developed for straight computational boundaries in this paper cfabcs are extended to the more general case of polygonal computational domains the key to the current development is the surprising link found between the cfabcs and the complex co ordinate stretching of perfectly matched layers pmls this link facilitates the extension of cfabcs to oblique corners and thus to polygonal domains it is shown that the proposed cfabcs are easy to implement expected to perform better than pmls and are effective for general polygonal computational domains in addition to the derivation of cfabcs a novel explicit time stepping scheme is developed for efficient numerical implementation numerical examples presented in the paper illustrate that effective absorption is attained with a negligible increase in the computational cost for the interior domain although this paper focuses on wave propagation its theoretical development can be easily extended to the more general class of problems where the governing differential equation is second order in space with constant coefficients copyright 2005 john wiley sons ltd

the use of linguistic variables and fuzzy propositions in the l fuzzy concept theory the use of linguistic variables and fuzzy propositions in the interval valued l fuzzy contexts can be an interesting tool to extract a more complete information from them in this paper we analyze three different situations first we obtain significant relations in order to study all the objects and attributes of the interval valued l fuzzy context by means of the interval valued l fuzzy concepts after that we show how to replace the erroneous values to be able to study in a suitable way the context finally we use the linguistic labels to obtain a subcontext that represents our interest of study we also show an experimental evaluation in the paper

special moufang sets their root groups and their μ maps we prove timmesfeld s conjecture that special abstract rank one groups are quasisimple we give two characterizations of the root groups in special moufang sets a normal subgroup of the point stabilizer is a root group if it is either regular or nilpotent and transitive we prove that if a root group of a special moufang set contains an involution then it is of exponent 2 we also show that the root groups are abelian if and only if the so called maps are involutions

attribute reduction in generalized one sided formal contexts in this paper we present a new pair of adjoint mappings between a power set and the direct product of complete lattices the proposed pair of adjoint mappings form a galois connection and the corresponding concept lattice is constructed from a generalized one sided formal context we also propose a lattice keep based attribute reduction approach for generalized one sided formal contexts specifically we present concrete judgment theorems and an algorithm to calculate the attribute reducts in generalized one sided formal contexts furthermore according to the importance of attributes we discuss attributive characteristics for the proposed generalized one sided concept lattice

far field filtering operators for suppression of reflections from artificial boundaries the concern of this paper is the treatment of far field artificial boundaries for first order hyperbolic systems where the aim is to suppress nonphysical reflections of outgoing waves we construct far field filtering operators of two types 1 slowing down operators and 2 damping operators the operators are activated in anarrow sponge layer near the far field boundary and have the following properties a the operators act only on the outgoing part of the solution leaving the incoming part unharmed b the passage of waves across the modified layer is reflection free and c the implementation of the operators amounts to a small modification of the governing equations in the far field in either case the treatment of the boundary itself is greatly simplified since the outgoing waves either do not reach the boundary or have practically zero strength when they do well posedness of the modified equations and stability of the discretization scheme are established we also show that such reflection

optimizing the perfectly matched layer the berenger perfectly matched layer or pml 4 3 is used in computational electromagnetism as a sponge layer to terminate finite element approximations of scattering problems an infinite perfectly matched layer creates no reflection for incident waves of any frequency or any incident direction and the waves decay exponentially in magnitude into the layer this property is lost when the layer is truncated since the truncation boundary generates a reflected wave discretization of the differential equations further changes the reflection coefficient of the layer in this talk we shall describe the pml in the simple case of a two dimensional electromagnetic problem the first part of this abstract is expository we shall show how to derive the layer using a change of variable approach 5 9 6 after this derivation we describe some new analysis to show the effects of truncating and discretizing the pml 9 we end by showing how to compute an optimal layer and make some remarks about pml for the full maxwell system

moufang sets and jordan division algebras we give a simple criterion which determines when a permutation group u and one additional permutation give rise to a moufang set we apply this criterion to show that every jordan division algebra gives rise in a very natural way to a moufang set to provide sufficient conditions for a moufang set to arise from a jordan division algebra and to give a characterization of the projective moufang sets over a commutative field of characteristic different from 2

evolution in time of l fuzzy context sequences in this work we consider a complete lattice l and we study l fuzzy context sequences which represent the evolution in time of an l fuzzy context to carry out this study in the first part of the paper we consider n ary owa operators in complete lattices which enable us to make a general analysis and a temporal analysis at any moment in time of l fuzzy context sequences after that evolution in time of the relationship between the objects and the attributes is considered in particular we analyze the concepts of trend and persistent formal contexts finally we illustrate our results with an example where we consider the particular lattice l j 0 1

moufang sets of finite morley rank of odd type abstract we show that for a wide class of groups of finite morley rank the presence of a split bn pair of tits rank 1 forces the group to be of the form psl 2 and the bn pair to be standard our approach is via the theory of moufang sets specifically we investigate infinite and so called hereditarily proper moufang sets of finite morley rank in the case where the little projective group has no infinite elementary abelian 2 subgroups and show that all such moufang sets are standard and thus associated to psl 2 f for f an algebraically closed field of characteristic not 2 provided the hua subgroups are nilpotent further we prove that the same conclusion can be reached whenever the hua subgroups are l groups and the root groups are not simple

on possible generalization of fuzzy concept lattices using dually isomorphic retracts we provide a generalization of fuzzy concept lattices based on so called weak galois connections generalization is that instead of dually isomorphic closure systems we consider dually isomorphic retracts of complete lattices we also give a generalization of the concept lattices with hedges proposed by belohlavek and vychodil based on composition of interior operators with galois connections

concept lattices defined from implication operators abstract we introduce the work with two extensions of the concept definition of wille to the fuzzy theory showing the relationship between them we continue with the study of fuzzy material implications and their associated operators of kohout and bandler that lump together the definitions given until this moment to conclude we show an example where we compare the results obtained from the l fuzzy concepts using the fuzzy implications of lukasiewicz kleene dienes and godel brower