on symmetric cauchy riemann manifolds the riemannian symmetric spaces play an important role in different branches of mathematics by definition a connected riemannian manifold m is called symmetric if to every a m there exists an involutory isometric diffeomorphism sa m m having a as isolated fixed point in m or equivalently if the differential dasa is the negative identity on the the tangent space ta tam of m at a in case such a transformation sa exists for a m it is uniquely determined and is the geodesic reflection of m about the point a as a consequence for every riemannian symmetric space m the group g gm generated by all symmetries sa a m is a lie group acting transitively on m in particular m can be identified with the homogeneous space g k for some compact subgroup k g using the elaborate theory of lie groups and lie algebras e cartan classified all riemannian symmetric spaces

solution of systems of boolean equations via the integer domain this paper presents a new method for solving systems of boolean equations the method is based on converting the equations so that we operate in the integer domain in the integer domain better and more efficient methodologies for solving equations are available the conversion leads us to a system of polynomial equations obeying certain characteristics a method is proposed for solving these equations the most computationally demanding step is the repeated multiplication of polynomials we develop a method for this problem that is significantly faster than the standard approach we also introduce another variant of the method the so called hybrid approach that leads to reduced memory requirements theoretical and experimental results indicate the superior performance of the proposed method and its variant compared to the competing methods the proposed method is also validated by applying it to the problem of hardware verification

on the cr structure of compact group orbits associated with bounded symmetric domains let e be a complex vector space of finite dimension and let k gl e be a compact connected subgroup then for fixed a e the orbit k k a is a real analytic submanifold of e that inherits various structures from e for instance choosing a k invariant positive definite inner product x y on e makes k a riemannian manifold on which k acts transitively by isometries on the other hand k inherits from e a cauchy riemann structure cr structure that is given by the distribution of the maximal complex subspaces hx k tx k itx k of the real tangent spaces tx k e x k together with the complex structure on every hx k multiplication by i the subspace hx k is called the holomorphic tangent space to k at x see 9 and 4 as general references for cr manifolds of interest for the geometry of the orbit k k a with respect to its cr structure is the study of the cr functions or more generally cr mappings on k i e of smooth functions f k c that satisfy the tangential cauchy riemann differential equations in the sense that the restriction of the differential df to every holomorphic tangent space is complex linear for instance all holomorphic functions defined in an open neighbourhood of k e give by restriction real analytic cr functions on k actually we deal with the more general continuous cr functions on k which satisfy by definition the tangential cr equations in the distribution sense or equivalently which are locally uniform limits of sequences of smooth cr functions due to the approximation theorem of baouenditreves 6 in this context it is of interest to determine the space of all

holomorphic extension and decomposition from a totally real manifold this paper is to develop an elementary cohomological approach for decomposing a function into boundary values of holomorphic functions and for discussing the corresponding microlocal analysis and hyperfunction theory

algebraicity of holomorphic mappings between real algebraic sets in cn 0 introduction 1 holomorphic nondegenera y of real analytic manifolds 1 1 preliminaries on real submanifolds of c n 1 2 holomorphic nondegeneracy and its propagation 1 3 the levi number and essential finiteness 1 4 holomorphic nondegeneracy of real algebraic sets 2 the segre sets of a real analytic cr submanifold 2 1 complexification of m involution and projections 2 2 definition of the segre sets of m at p0 2 3 homogeneous submanifolds of cr dimension 1 2 4 homogeneous submanifolds of arbitrary cr dimension 2 5 proof of theorem 2 2 1 3 algebraic properties of holomorphic mappings between real algebraic sets 3 1 a generalization of theorems 1 and 4 3 2 propagation of algebralcity 3 3 proof of theorem 3 1 2 3 4 proof of theorem 3 1 8 3 5 an example 3 6 proofs of theorems 1 through 4

universal coalgebra a theory of systems in the semantics of programming finite data types such as finite lists have traditionally been modelled by initial algebras later final coalgebras were used in order to deal with infinite data types coalgebras which are the dual of algebras turned out to be suited moreover as models for certain types of automata and more generally for transition and dynamical systems an important property of initial algebras is that they satisfy the familiar principle of induction such a principle was missing for coalgebras until the work of aczel 1988 on a theory of non wellfounded sets in which he introduced a proof principle nowadays called coinduction it was formulated in terms of bisimulation a notion originally stemming from the world of concurrent programming languages milner 1980 park 1981 using the notion of coalgebra homomorphism the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras aczel and mendler 1989 thus the three basic notions of universal algebra algebra homomorphism of algebras and congruence turn out to correspond to coalgebra homomorphism of coalgebras and bisimulation respectively in this paper the latter are taken as the basic ingredients of a theory called universal coalgebra some standard results from universal algebra are reformulated using the afore mentioned correspondence and proved for a large class of coalgebras leading to a series of results on e g the lattices of subcoalgebras and bisimulations simple coalgebras and coinduction and a covariety theorem for coalgebras similar to birkhoff s variety theorem

bisimulation for probabilistic transition systems a coalgebraic approach the notion of bisimulation as proposed by larsen and skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of aczel and mendier in terms of a set functor this coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving borel probability measures under reasonable conditions generalized probabilistic bisimilarity can be characterized categorically application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation

reactive generative and stratified models of probabilistic processes abstract we introduce three models of probabilistic processes namely reactive generative and stratified these models are investigated within the context of pccs an extension of milner s sccs in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1 for each model we present a structural operational semantics of pccs and a notion of bisimulation equivalence which we prove to be a congruence we also show that the models form a hierarchy the reactive model is derivable from the generative model by abstraction from the relative probabilities of different actions and the generative model is derivable from the stratified model by abstraction from the purely probabilistic branching structure moreover the classical nonprobabilistic model is derivable from each of these models by abstraction from all probabilities

propagation of holomorphic extendibility and non hypoellipticity of the neumann problem in an exponentially degenerate boundary abstract we prove that cr lines in an exponentially degenerate boundary are propagators of holomorphic extendibility this explains in the context of the cr geometry why in this situation the induced kohn laplacian b is not hypoelliptic christ 2000 2

infinitesimal cr automorphisms of real hypersurfaces let m be an analytic real hypersurface through the origin in c n 1 and let hol m denote the space of vector fields x re z m tangent to m in a neighborhood of the origin where z is a holomorphic vector field defined in a neighborhood of the origin the hypersurface m is holomorphically nondegenerate at the origin if there is no holomorphic vector field tangent to m in a neighborhood of the origin the main result of the paper is that hol m is finite dimensional if and only if m is holomorphically nondegenerate at the origin

extremal discs and the regularity of cr mappings in higher codimension we develop a local theory of extremal analytic discs attached to a strictly pseudoconvex manifold of higher codimension in complex space we then apply the results to prove the regularity of cr homeomorphisms of such manifolds introduction in his celebrated paper lempert li introduced extremal analytic discs as geodesies of the kobayashi metric on a convex domain d c cn let a be the unit disc in the complex plane an analytic disc a d is called extremal if 0 attains its maximum among all analytic discs in d with the same values and directions at 0 g a extremal discs are important holomorphic invariants of d their boundaries lie in the boundary bd of the domain and form an invariant family of curves for the cr structure of bd lempert li l2 applies the extremal discs to the regularity of biholomorphic mappings monge amp re equations and normal forms of convex domains other applications include deformations and embeddibility of cr structures bl bd and polynomial hulls s

cr extension from hypersurfaces of higher type abstract we prove extension of cr functions from a hypersurface m of c n in presence of the so called sector property if m has finite type in the bloom graham sense then our result is already contained in c rea prolongement holomorphe des fonctions cr conditions suffisantes c r acad sci paris 297 1983 163 166 by rea we think however that the argument of our proof carries an expressive geometric meaning and deserves interest on its own right also our method applies in some case to hypersurfaces of infinite type note that for these the classical methods fail cr extension is treated by many authors mainly in two frames extension in directions of iterated of commutators of cr vector fields cf for instance a boggess j pitts cr extension near a point of higher type duke math j 52 1 1985 67 102 a boggess j c polking holomorphic extension of cr functions duke math j 49 1982 757 784 4 m s baouendi l rothschild normal forms for generic manifolds and holomorphic extension of cr functions j differential geom 25 1987 431 467 1 extension through minimality towards unprecised directions a e tumanov extension of cr functions into a wedge mat sb 181 7 1990 951 964 6 a e tumanov analytic discs and the extendibility of cr functions in integral geometry radon transforms and complex analysis venice 1996 in lecture notes in math vol 1684 springer berlin 1998 pp 123 141

coalgebraic modal logic soundness completeness and decidability of local consequence this paper studies finitary modal logics interpreted over coalgebras for an endofunctor and establishes soundness completeness and decidability results the logics are studied within the abstract framework of coalgebraic modal logic which can be instantiated with arbitrary endofunctors on the category of sets this is achieved through the use of predicate liftings which generalise atomic propositions and modal operators from kripke models to arbitrary coalgebras predicate liftings also allow us to use induction along the terminal sequence of the underlying endofunctor as a proof principle this induction principle is systematically exploited to establish soundness completeness and decidability of the logics we believe that this induction principle also opens new ways for reasoning about modal logics our proof of completeness does not rely on a canonical model construction and the proof of the finite model property does not use filtrations

solving boolean equations using rosop forms boolean equations are important tools in digital logic previous algorithms for solving boolean equations are based on the boolean algebra of disjoint sop forms in this paper we develop a new boolean algebra with more efficient boolean operation algorithms called the reduced ordered sop rosop forms which are canonical representations rosops are closely related to the well known obdd data structure the results here also show the algebraic structure of obdds

extension of cr functions into weighted wedges through families of nonsmooth analytic discs the goal of this paper is to develop a theory of nonsmooth analytic discs attached to domains with lipschitz boundary in real submanifolds of c n we then apply this technique to establish a propagation principle for wedge extendibility of cr functions on these domains along cr curves and along boundaries of attached analytic discs the technique from this paper has been also extensively used by the authors recently to obtain sharp results on wedge extension of cr functions on wedges in prescribed directions extending results of boggess polking and eastwood graham

on cr mappings between algebraic cauchy riemann manifolds and separate algebraicity for holomorphic functions we prove the algebraicity of smooth cr mappings between algebraic cauchy riemann manifolds a generalization of separate algebraicity principle is established

some additions to solution of switching equations based on a tabular algebra a method was presented by a l ruiz p p trabado and j o lopera see ibid vol 42 no 5 p 591 6 1993 for efficiently generating the solutions of boolean equations by using tables i e rectangular arrays or matrices of 0 s 1 s and dashes to represent boolean expressions some enhancements of their method are presented first it is shown how the uniting theorem can be applied directly to simplify tables then it is shown how to complement a table which would make their method henceforth referred to as rtl directly applicable to expressions containing complemented subexpressions the latter result allows the method to be extended from the solution of equations of the form f x 1 to equations of the form f x 0 and more generally to equations of the form f x g x or to simultaneous equations of the same types

modalities in the stone age a comparison of coalgebraic logics coalgebra develops a general theory of transition systems parametric in a functor t the functor t specifies the possible one step behaviours of the system a fundamental question in this area is how to obtain for an arbitrary functor t a logic for t coalgebras we compare two existing proposals moss s coalgebraic logic and the logic of all predicate liftings by providing one step translations between them extending the results in raul andres leal 2008 34 by making systematic use of stone duality our main contribution then is a novel coalgebraic logic which can be seen as an equational axiomatisation of moss s logic the three logics are equivalent for a natural but restricted class of functors we give examples showing that the logics differ in general finally we argue that the quest for a generic logic for t coalgebras is still open in the general case

on certain partial differential operators of finite odd type let p be a linear partial differential operator of order m 1 with real analytic coefficients defined in q an open set of rn and let y be in the cotangent space of q minus the zero section if p is of odd finite type k and if the hormander numbers are 1 ki k2 k2 odd then p is analytic hypoelliptic at y these operators are not semirigid introduction in this paper we present a microlocal analytic hypoellipticity result for a class of linear partial differential operators of finite type with real analytic coefficients the assumption is that the type of the operator is an odd positive integer k and that there are two hormander numbers k1 k2 with 1 k k2 and k2 is odd the main difference between this result and previous results obtained by the author is that the operators here may not be semirigid therefore we view it as a partial result of the more general problem of giving necessary and sufficient conditions for microlocal analytic hypoellipticity of operators of finite type for cr structures a version of this problem has been recently solved by tumanov 10 sufficient conditions and baouendi rothschild 1 necessary conditions in the analytic case the necessity was proved in 2 the condition used in 10 is a condition at a point in the base space called the minimality condition an analytic cr structure is minimal at a point if it is of finite type at this point for c cr structures finite type implies minimality but not vice versa the finite type condition used in this paper is microlocal the new difficulty that arises in the proof of this result is that the phase function may contain terms of degree less than k which is the degree of the terms that result from the type of the operator to make these lower degree terms negligible we choose a special good contour and we use a more general sufficient condition than the one used in 6 received by the editors december 18 1989 1980 mathematics subject classification 1985 revision primary 35h05 secondary 58g15 the author was partially supported by nsf 1991 american mathematical society 0002 9947 91 1 00 25 per page

a hierarchy of probabilistic system types we arrange various classes of probabilistic systems studied in the literature in an expressiveness hierarchy our expressiveness criterion is the existence of a system translation from the less expressive type into the more expressive type that preserves and reflects probabilistic bisimilarity we model the different system types as coalgebras of suitable behaviour functors and argue that the corresponding coalgebraic bisimilarity coincides with probabilistic bisimilarity for the classes for which the latter notion has been proposed in the literature the theory of coalgebras provides a unified framework for the presentation of the different classes and the system translations we needed to establish the hierarchy all these translations arise in a standard way from natural transformations between the two behaviour functors involved such a translation generally preserves coalgebraic bisimilarity we exploit a new result that under mild assumptions on the behaviour functors a system translation induced by a natural transformation with injective components also reflects bisimilarity

wedge removability of metrically thin sets and application to the cr meromorphic extension we give a wedge removability theorem for metrically thin sets of two codimensional hausdorff null measure following 22 this removability theorem combined with the wedge removability theorem of 21 for closed subsets of two codimensional manifolds gives a cr meromorphic extension theorem in the greater codimensional case

parametric argument principle and its applications to cr functions and manifolds it follows from the classical argument principle that if a holomor phic mapping f from the unit discto c or more generally to c n smooth in the closed disc is homologicaly trivial on the unit circle i e h1 0 f s 1 which is equivalent to either being a point or having endpoints i e 6 then f const in other words the image of the unit disc degenerates to a point we establish a parametric version of this fact for a variety of holomorphic map pings fromto c n in place of a single mapping we find conditions for a holomorphic mapping of the unit disc depending on additional real parameters under which homological triviality of the boundary image implies collapse of the dimension of the image of the interior as an application we obtain estimates of dimensions of complex tan gent bundles of real submanifolds in c n in terms of zero moment conditions on families of closed curves covering the manifold apply ing this result to the graphs of functions we obtain solution of several known problems about characterization of holomorphic cr functions in terms of moment conditions on families of curves

the hull of holomorphy of a nonisotropic ball in a real hypersurface of finite type we show that the hull of holomorphy of a nonisotropic ball in a real hypersurface of finite type in cn contains an open set in cn which emanates from the hypersurface a distance which is proportional to the length of the minor axis of the nonisotropic ball in addition we prove a maximal function estimate for plurisubharmonic functions which is important in the study of boundary values of holomorphic functions

the hartogs phenomenon on weakly pseudoconcave hypersurfaces in 2002 henkin and michel proved a local hartogs phenomenon for real analytic cr functions on real analytic weakly pseudoconcave cr manifolds the aim of the present article is to remove the assumptions on real analyticity in the case of weakly pseudoconcave hypersurfaces m subset mathbb c n if m is a graph of class mathcal c 2 and n 3 a global theorem is proved for the extension of holomorphic germs along m if the appearing domains have nicely shaped boundary a hartogs theorem even holds for continuous cr functions where the difference to the case of holomorphic germs relies on the possible presence of lower dimensional cr orbits levi flat hypersurfaces in mathbb c 2 require a separate treatment here an affirmative answer is given to the question of tomassini whether 2 spheres bound 3 balls in m

extension of cr functions on wedges we generalize the extension theorem of ajrapetyan henkin ah81 and boggess polking bp82 to wedge like domains v in a generic manifold m for each complex tangent vector to m we introduce its complex angle with respect to v and show that cr functions on v have natural extension in the direction of the levi form of any tangent vector whose angle is greater than 2 this gives an explanation of the extension phenomenon recently discovered by eastwood graham eg99 eg01 we further demonstrate by an example that the angle 2 is optimal and cannot be replaced by any smaller angle we conclude by giving applications to holomorphic extension to a full neighborhood of the reference point

a property of the functions and distributions annihilated by a locally integrable system of complex vector fields page introduction 387 1 basic notation and ingredients 389 2 approximation and constancy on the fibers of the classical solutions of the homogeneous equations 393 3 first consequences and interpretation of the fundamental theorem 398 4 distribution solutions of the homogeneous equations 402 5 regularity of the solutions of the homogeneous equations 409 6 example of a system that is analytic hypo elliptic but not co hypo elliptic 413 references 420

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

differential equations with singular coefficients differential equations with singular coefficients such as bessel s equation legendre s equation chebychev s equation and laguerre s equation are solved by the decomposition method

boolean sets and most general solutions of boolean equations the aim of this paper is twofold first we determine the most general form of the subsumptive general solution of a boolean equation theorems 1 and 2 then we discuss several characterizations of boolean sets meaning sets of zeros of boolean functions and prove that every boolean transformation email protected t is the parametric general solution of a certain boolean equation