pair correlation densities of inhomogeneous quadratic forms under explicit diophantine conditions on 2 w eprove that the local two point correlations of the sequence given by the values m 2 n 2 with m n 2 are those of a poisson process this partly confirms a conjecture of berry and tabor 2 on spectral statistics of quantized integrable systems and also establishes a particular case of the quantitative version of the oppenheim conjecture for inhomogeneous quadratic forms of signature 2 2 the proof uses theta sums and ratner s classification of measures invariant under unipotent flows

uniform stabilization of wave equation with localized damping and acoustic boundary condition abstract in this paper we deal with stability of the nonlinear wave equation with acoustic boundary conditions to non locally reacting boundary

some nonlinear wave equations with acoustic boundary conditions abstract we prove the existence and uniqueness of global solutions to the mixed problem for the carrier equation u tt m u 2 dx u u t u t 0 with acoustic boundary conditions

the role of crisp elements in fuzzy ontologies the case of fuzzy owl 2 el in the last years fuzzy ontologies and fuzzy description logics dls have been applied successfully to several real world domains some recent results on fuzzy dls show an increase in the theoretical complexity even for not expressive languages however it still may be possible to obtain reasoning algorithms performing well in practice this paper studies some cases where reasoning with a fuzzy ontology can be reduced to reasoning with a tractable classical language an owl 2 profile then building on the assumption that not all concepts and roles in fuzzy ontologies are indeed fuzzy we show that reasoning algorithms can be optimized by taking into account the existence of possible crisp concepts and roles we also prove the usefulness on crisp representation reasoning algorithms over an empirical evaluation over fuzzy owl 2 el ontologies and discuss some preliminary techniques to learn which elements should be considered to be crisp or noncrisp

energy decay of a variable coefficient wave equation with memory type acoustic boundary conditions abstract we study the energy decay for a variable coefficient wave equation with memory type acoustic boundary conditions boundary memory is described by an integral term applying the riemannian geometry method we obtain the uniform energy decay under some conditions on the memory function and the coefficient matrix

existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

spacing between phase shifts in a simple scattering problem we prove a scattering theoretical version of the berry tabor conjecture for an almost every surface in a class of cylindrical surfaces of revolution the large energy limit of the pair correlation measure of the quantum phase shifts is poisson that is it is given by the uniform measure

reasoning with the finitely many valued łukasiewicz fuzzy description logic sroiq fuzzy description logics are a formalism for the representation of structured knowledge affected by imprecision or vagueness they have become popular as a language for fuzzy ontology representation to date most of the work in this direction has focused on the so called zadeh family of fuzzy operators or fuzzy logic which has several limitations in this paper we generalize existing proposals and show how to reason with a fuzzy extension of the logic sroiq the logic behind the language owl 2 under finitely many valued lukasiewicz fuzzy logic we show for the first time that it is decidable over a finite set of truth values by presenting a reasoning preserving procedure to obtain a non fuzzy representation for the logic this reduction makes it possible to reuse current representation languages as well as currently available reasoners for ontologies

the pair correlation function of fractional parts of polynomials we investigate the pair correlation function of the sequence of fractional parts of n d n 1 2 n where d 2 is an integer and an irrational we conjecture that for badly approximable the normalized spacings between elements of this sequence have poisson statistics as n

on the accuracy of the semiclassical trace formula the semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit when the dimensionality of the system increases the mean level spacing decreases as while the semiclassical approximation is commonly believed to provide an accuracy of order independently of d if this was true the semiclassical trace formula would be limited to systems in only in this work we set out to define proper measures of the semiclassical spectral accuracy and to propose theoretical and numerical evidence to the effect that the semiclassical accuracy measured in units of the mean level spacing depends only weakly if at all on the dimensionality detailed and thorough numerical tests were performed for the sinai billiard in two and three dimensions substantiating the theoretical arguments

on the failure of the finite model property in some fuzzy description logics fuzzy description logics dls are a family of logics which allow the representation of and the reasoning with structured knowledge affected by vagueness although most of the not very expressive crisp dls such as alc enjoy the finite model property fmp this is not the case once we move into the fuzzy case in this paper we show that if we allow arbitrary knowledge bases then the fuzzy dls alc under lukasiewicz and product fuzzy logics do not verify the fmp even if we restrict to witnessed models in other words finite satisfiability and witnessed satisfiability are different for arbitrary knowledge bases the aim of this paper is to point out the failure of fmp because it affects several algorithms published in the literature for reasoning under fuzzy dls

distribution of energy levels of quantum free particle on the liouville surface and trace formulae we consider the weyl asymptotic formula left e n leqq r 2 right frac area q 4 pi r 2 n r for eigenvalues of the laplace beltrami operator on a two dimensional torusq with a liouville metric which is in a sense the most general case of an integrable metric we prove that if the surfaceq is non degenerate then the remainder termn r has the formn r r1 2 r where r is an almost periodic function of the besicovitch classb1 and the fourier amplitudes and the fourier frequencies of r can be expressed via lengths of closed geodesics onq and other simple geometric characteristics of these geodesics we prove then that if the surfaceq is generic then the limit distribution of r has a densityp t which is an entire function oft possessing an asymptotics on a real line logp t c t4 ast an explicit expression for the fourier transform ofp t via fourier amplitudes of r is also given we obtain the analogue of the guillemin duistermaat trace formula for the liouville surfaces and discuss its accuracy

stabilization of hyperbolic and parabolic systems with nonlinearly perturbed boundary conditions abstract sufficient conditions for the local exponential stabilizability of abstract systems described by an arbitrary co semigroup with nonlinear unbounded perturbations are formulated applications to parabolic and in particular hyperbolic problems with nonlinearity appearing in the boundary conditions are given

regularity theory of hyperbolic equations with non homogeneous neumann boundary conditions ii general boundary data abstract this paper studies the regularity of solutions of general mixed second order time dependent hyperbolic problems of neumann type in a previous paper i lasiecka and r triggiani ann mat pura appl iv clvii 1990 285 367 using pseudo differential calculus we have provided sharp regularity results of the solutions and their traces when the non homogeneous data are in l 2 now we complement this study by providing a regularity when the non homogeneous data are more regular than as well as less regular than l 2 in contrast with our previous paper a functional analytic approach based on the l 2 results of our previous paper is used throughout

on the wave equation with semilinear porous acoustic boundary conditions the goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary interior sources and a nonlinear boundary interior damping first applying the nonlinear semigroup theory we show the existence and uniqueness of local in time solutions the main difficulty in proving the local existence result is that the neumann boundary conditions experience loss of regularity due to boundary sources using an approximation method involving truncated sources and adapting the ideas in lasiecka and tataru 1993 28 we show that the existence of solutions can still be obtained second we prove that under some restrictions on the source terms then the local solution can be extended to be global in time in addition it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ode and depends on the behavior of the damping terms in several situations the obtained ode can be easily solved and the decay rates can be given explicitly third we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping then the solution ceases to exists and blows up in finite time moreover in either the absence of the interior source or the boundary source then we prove that the solution is unbounded and grows as an exponential function

fuzzy description logics with general t norms and datatypes fuzzy description logics dls are a family of logics which allow the representation of and the reasoning within structured knowledge affected by vagueness although a relatively important amount of work has been carried out in the last years current fuzzy dls still present several limitations in this work we face two problems the common restriction to zadeh and lukasiewicz fuzzy logics and the inability to deal with datatypes different from fuzzy sets in particular we propose a semantics based on the use of a general left continuous t norm and an involutive negation specially focused on product logic and furthermore we show how to handle functional concrete roles relating individuals of the domain and strings real or integer numbers

geometric characterization of nodal domains the area to perimeter ratio in an attempt to characterize the distribution of forms and shapes of nodal domains in wavefunctions we define a geometric parameter the ratio between the area of a domain and its perimeter measured in units of the wavelength we show that the distribution function can distinguish between domains in which the classical dynamics is regular or chaotic for separable surfaces we compute the limiting distribution and show that it is supported on a compact interval which is independent of the properties of the surface in systems which are chaotic or in random waves the area to perimeter distribution has substantially different features which we study numerically we compare the features of the distribution for chaotic wavefunctions with the predictions of the percolation model to find agreement but only for nodal domains which are big with respect to the wavelength scale this work is also closely related to and provides a new point of view on isoperimetric inequalities

optimising fuzzy description logic reasoners with general concept inclusion absorption general concept inclusion gci absorption algorithms have shown to play an important role in classical description logic dl reasoners they allow to transform gcis into simpler forms to which we may apply specialised inference rules returning important performance gains in this work we develop the first absorption algorithm for fuzzy dls implement it in the fuzzydl reasoner and evaluate it extensively over both classical and fuzzy ontologies the results show that our algorithm improves the performance of the reasoner significantly

local hadamard well posedness for nonlinear wave equations with supercritical sources and damping abstract we consider the wave equation with supercritical interior and boundary sources and damping terms the main result of the paper is local hadamard well posedness of finite energy weak solutions the results obtained 1 extend the existence results previously obtained in the literature by allowing more singular sources 2 show that the corresponding solutions satisfy hadamard well posedness conditions during the time of existence this result provides a positive answer to an open question in the area and it allows for the construction of a strongly continuous semigroup representing the dynamics governed by the wave equation with supercritical sources and damping

the limits of decidability in fuzzy description logics with general concept inclusions fuzzy description logics dls can be used to represent and reason with vague knowledge this family of logical formalisms is very diverse each member being characterized by a specific choice of constructors axioms and triangular norms which are used to specify the semantics unfortunately it has recently been shown that the consistency problem in many fuzzy dls with general concept inclusion axioms is undecidable in this paper we present a proof framework that allows us to extend these results to cover large classes of fuzzy dls on the other hand we also provide matching decidability results for most of the remaining logics as a result we obtain a near universal classification of fuzzy dls according to the decidability of their consistency problem

riemannian manifolds with maximal eigenfunction growth on any compact riemannian manifold m g of dimension n the l sp 2 normalized eigenfunctions phi sb lambda satisfy lvert rvert phi sb lambda lvert rvert sb infty leq c lambda sp n 1 2 where delta phi sb lambda lambda sp 2 phi sb lambda the bound is sharp in the class of all m g since it is obtained by zonal spherical harmonics on the standard n sphere s sp n but of course it is not sharp for many riemannian manifolds for example for flat tori mathbb r sp n gamma we say that s sp n but not mathbb r sp n gamma is a riemannian manifold with maximal eigenfunction growth the problem that motivates this paper is to determine the m g with maximal eigenfunction growth our main result is that such an m g must have a point x where the set mathscr l sb x of geodesic loops at x has positive measure in s sp ast sb xm we show that if m g is real analytic this puts topological restrictions on m for example only m s sp 2 or m mathbb r p sp 2 topologically in dimension 2 can possess a real analytic metric of maximal eigenfunction growth we further show that generic metrics on any m fail to have maximal eigenfunction growth in addition we construct an example of m g for which mathscr l sb x has positive measure for an open set of x but which does not have maximal eigenfunction growth thus it disproves a naive converse to the main result

decay estimates for some semilinear damped hyperbolic problems let be a bounded open domain in rn g r r a non decreasing continuous function such that g 0 0 and h e lloc1 r l2 under suitable assumptions on g and h the rate of decay of the difference of two solutions is studied for some abstract evolution equations of the general form u lu g u h t x as t the results obtained by use of differential inequalities can be applied to the case of the semilinear wave equation u u delta u g text u t text h text in r times omega text u text 0 on r times partial omega in r u 0 onr for instance if g s c left s right p 1 s d left s right q 1 s with c d 0 and 1 p q n 2 q n 2 then if h in l infty r l 2 omega all solutions are bounded in the energy space for t 0 and if u v are two such solutions the energy norm of u t v t decays like t 1 p 1 as t

existence and decay of solutions for a viscoelastic wave equation with acoustic boundary conditions abstract in this paper we consider a multi dimensional damped semilinear viscoelastic wave equation with variable coefficient and acoustic boundary conditions first we prove a local existence theorem by using the faedo galerkin approximations combined with a contraction mapping theorem second we show that under suitable conditions on the initial data and the relaxation function the solution exists globally in time and we prove the uniform decay rate of the energy

reasoning within fuzzy owl 2 el revisited abstract description logics dls are logics with interesting representational and computational features and are at the core of the web ontology language owl 2 and its profiles among which there is owl 2 el the main feature of owl 2 el is that instance subsumption checking can be decided in polynomial time on the other hand fuzzy dls have been proposed as an extension to classical dls with the aim of dealing with fuzzy concepts and we focus here on fuzzy owl 2 el under standard and godel semantics we provide some reasoning algorithms showing that instance subsumption checking decision problems remain polynomial time for fuzzy owl 2 el we also identify some issues in previous related work essentially incompleteness problems

decay rate estimates for wave equations of memory type with acoustic boundary conditions abstract a wave equation of memory type u u 0 t g t s u s d s 0 with acoustic boundary conditions is considered this work is devoted to investigating the influence of the kernel function g and proving general rates of decay of solutions when g does not necessarily decay exponentially

optimal g closure bounds via stability under lamination optimal bounds for a two dimensional g closure problem are proved they are obtained by combining together bounds derived using fine properties of quasiconformal mappings and a stability property of the g closure which is known as stability under lamination

exponential sums and lattice points iii the gauss circle problem and the dirichlet divisor problem are special cases of the problem of counting the points of the integer lattice in a planar domain bounded by a piecewise smooth curve in the bombieri iwaniec mozzochi exponential sums method we must count the number of pairs of arcs of the boundary curve which can be brought into coincidence by an automorphism of the integer lattice these coincidences are parametrised by integer points close to certain plane curves the resonance curves this paper sets up an iteration step from a strong hypothesis about integer points close to curves to a bound for the discrepancy the number of integer points minus the area as in the latest work on single exponential sums the bombieri iwaniec mozzochi method itself gives bounds for the number of integer points close to a curve in part of the required range and it can in principle be used iteratively we use a bound obtained by swinnerton dyer s approximation determinant method in the discrepancy estimate o r k log r lambda in terms of the maximum radius of curvature r we reduce k from 2 3 classical and 46 73 paper ii in this series to 131 208 the corresponding exponent in the dirichlet divisor problem becomes k 2 131 416

wave equation with porous nonlinear acoustic boundary conditions generates a well posed dynamical system we consider a structural acoustic wave equation with nonlinear acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with boundary conditions on the interface we prove wellposedness in the hadamard sense for strong and weak solutions the main tool used in the proof is the theory of nonlinear semigroups we present the system of partial differential equations as a suitable cauchy problem dw dt aw though the operator a is not maximally dissipative we are able to show that it is a translate of a maximally dissipative operator the obtained semigroup solution is shown to satisfy a suitable variational equality thus giving weak solutions to the system of pdes the results obtained i dispel the notion that the model does not generate semigroup solutions ii provide treatment of nonlinear models and iii provide existence of a correct state space which is invariant under the flow thus showing that physical model under consideration is a dynamical system the latter is obtained by eliminating compatibility conditions which have been assumed in previous work on the linear case

spectral statistics on zoll surfaces the subject of this article is a family of partly conjectural spectral invariants of a laplace operator with a discrete spectrum j known as its k level correlation functions k and level spacings distribution the 2 level or pair correlation function 2 for instance measures the asymptotic number of spacings i j between normalized eigenvalues i as the eigenvalues tend to infinity the normalization is so that the mean level spacing i 1 i is one these invariants have been studied by many physicists including wigner dyson and berry and are conjectured to have certain universal forms depending on the qualitative behaviour of the corresponding classical geodesic flow

number variance for arithmetic hyperbolic surfaces we prove that the number variance for the spectrum of an arithmetic surface is highly nonrigid in part of the universal range in fact it is close to having a poisson behavior this fact was discovered numerically by schmit bogomolny georgeot and giannoni it has its origin in the high degeneracy of the length spectrum first observed by selberg

on the un decidability of fuzzy description logics under łukasiewicz t norm recently there have been some unexpected results concerning fuzzy description logics fdls with general concept inclusions gcis they show that unlike the classical case the dl alc with gcis does not have the finite model property under lukasiewicz logic or product logic the proposed reasoning algorithms are neither correct nor complete and specifically knowledge base satisfiability is an undecidable problem for product logic in this work we show that knowledge base satisfiability is also an undecidable problem for lukasiewicz logic we additionally provide a decision algorithm for acyclic alc knowledge bases under lukasiewicz logic via a mixed integer linear programming milp based procedure note however that the decidability of this problem is already known while similar milp based algorithms have been proposed in the literature for acyclic alc knowledge bases under lukasiewicz logic none of them exhibit formal proofs of their correctness and completeness which is the additional contribution here

mniblos a smt based solver for continuous t norm based logics and some of their modal expansions in the literature little attention has been paid to the development of solvers for systems of mathematical fuzzy logic and in particular there are few works concerned with infinitely valued logics in this paper it is presented mniblos a modal nice bl logics solver a modular smt based solver complete with respect to a wide family of continuous t norm based fuzzy modal logics both with finite and infinite universes restricting the modal structures to the finite ones at the propositional level the solver works with some of the best known infinitely valued fuzzy logics including bl ukasiewicz godel and product logics and with all the continuous t norm based logics that can be finitely expressed in terms of the previous ones concerning the modal expansion mniblos imposes no boundary on the cardinality of the modal structures considered the solver allows to test 1 satisfiability of equations tautologicity and logical consequence problems the logical language supported extends the usual one of fuzzy modal logics with rational constants and the monteiro baaz operator the code of mniblos is of free distribution and can be found in the web page of the author

uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions abstract a variable coefficient wave equation with nonlinear damped acoustic boundary conditions is considered the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients the uniform decay of the energy is achieved without any geometrical conditions on the shape of the dissipative portion of the boundary

distribution of the error term for the number of lattice points inside a shifted circle define begin array 20 c n x r left n in z d x n leqslant r right x in 0 1 d end array 1 1 and f x r r frac d 1 2 n x r r d text vol d b 1 1 2 where b 1 is the unit ball in r d thus n x r is the number of lattice points in z d in the r ball centered at x and f x r is the normalized difference with the volume of the ball we are interested in the problem of the distribution of f x r as a function of r for given x

well posedness and optimal decay rates for the wave equation with nonlinear boundary damping source interaction we establish subject to some natural additional assumptions imposed on the relation between the source and the damping both well posedness and effective optimal decay rates for the solutions of a semilinear model of the wave equation the theory presented allows to consider both superlinear and sublinear behaviours of the dissipation in the presence of unstructured sources

global existence for the wave equation with nonlinear boundary damping and source terms abstract the paper deals with local and global existence for the solutions of the wave equation in bounded domains with nonlinear boundary damping and source terms the typical problem studied is u tt u 0 in 0 u 0 on 0 0 u u t m 2 u t u p 2 u on 0 1 u 0 x u 0 x u t 0 x u 1 x on where r n n 1 is a regular and bounded domain 0 1 m 1 2 p r where r 2 n 1 n 2 when n 3 r when n 1 2 and the initial data are in the energy space we prove local existence of the solutions in the energy space when m r r 1 p or n 1 2 and global existence when p m or the initial data are inside the potential well associated to the stationary problem

well posedness for a variable coefficient wave equation with nonlinear damped acoustic boundary conditions abstract we consider a variable coefficient wave equation with nonlinear damped acoustic boundary conditions well posedness in the hadamard sense for strong and weak solutions is proved by using the theory of nonlinear semigroups

global existence and global nonexistence of solutions of the cauchy problem for a nonlinearly damped wave equation abstract in this paper we consider the long time behavior of solutions of the initial value problem for semilinear wave equations of the form formula

a small scale density of states formula let m g be a c compact riemann manifold with classical hamiltonian h c t m assume that the corresponding quantization p1 op h is quantum completely integrable we establish an microlocal weyl law on short spectral intervals of size 2 e e 0 for various families of operators p1u u i containing p1 both in the mean and pointwise a e for u i the microlocalization refers to a small tubular neighbourhood of a non degenerate stable periodic bicharacteristic t m 0

polynomial decay of a variable coefficient wave equation with an acoustic undamped boundary condition abstract we consider a variable coefficient wave equation with an acoustic undamped condition this is a coupled system of second and first order in time partial differential equations with an acoustic boundary condition on the interface the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients we obtain the polynomial energy decay

energy level statistics of model quantum systems universality and scaling in a lattice point problem we investigate the statistics of the numbern r s of lattice pointsn z 2 in an annular domain r w r w a ra wherer w 0 herea is a fixed convex set with smooth boundary andw is chosen so that the area of r w iss the statistics comes fromr being taken as random with a smooth density in some interval c 1 t c 2 t c 2 c 1 0 we find that in the limitt the variance and distribution of n n r s s depend strongly on hows grows witht there is a saturation regimes t ast in which the fluctuations in n coming from the two boundaries of are independent then there is a scaling regime s t z 0 z in which the distribution depends onz in an almost periodic way going to a gaussian asz 0 the variance in this limit approachesz for generic a but can be larger for degenerate cases the former behavior is what one would expect from the poisson limit of a distribution for annuli of finite area

energy decay rate for a von karman system with a boundary nonlinear delay term abstract in this paper we show the energy decay rate for a von karman system with a boundary nonlinear delay term this work is devoted to investigate the influence of kernel function g and the effect of the boundary nonlinear term 1 u t t m 1 u t t a boundary nonlinear time delay term 2 u t t m 1 u t t and prove energy decay rates of solutions when g do not necessarily decay exponentially and the boundary condition has a time delay

strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions we consider a wave equation with semilinear porous acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with possibly semilinear boundary conditions on the interface the results obtained are i strong stability for the linear model ii exponential decay rates for the energy of the linear model and iii local exponential decay rates for the energy of the semilinear model this work builds on a previous result showing generation of a well posed dynamical system the main tools used in the proofs are i the stability theorem of arendt batty ii energy methods used in the study of a wave equation with boundary damping and iii an abstract result of i lasiecka applicable to hyperbolic like systems with nonlinearly perturbed boundary conditions

energy decay for a nonlinear wave equation of variable coefficients with acoustic boundary conditions and a time varying delay in the boundary feedback abstract a variable coefficient wave equation with acoustic boundary conditions and a time varying delay in the boundary feedback is considered applying the riemannian geometry method we show that the decay rates of the nonlinear system with a time varying delay are described by solutions to a first order ode

spectral form factors of rectangle billiards the berry tabor conjecture asserts that local statistical measures of the eigenvalues j of a generic integrable quantum system coincide with those of a poisson process we prove that in the case of a rectangle billiard with random ratio of sides the sum behaves for random and n large like a random walk in the complex plane with a non gaussian limit distribution the expectation value of the distribution is zero its variance which is essentially the average pair correlation function is one in accordance with the berry tabor conjecture but all higher moments 4 diverge the proof of the existence of the limit distribution uses the mixing property of a dynamical system defined on a product of hyperbolic surfaces the berry tabor conjecture and the existence of the limit distribution for a fixed generic rectangle are related to an equidistribution conjecture for long horocycles on this product space

global nonexistence theorems for a class of evolution equations with dissipation we study abstract evolution equations with nonlinear damping terms and source terms including as a particular case a nonlinear wave equation of the type ba cl u tt delta u b u t m 2 u t c u p 2 u t x in 0 t times omega 6pt u t x 0 t x in 0 t times partial omega 6pt u 0 cdot u 0 in h 0 1 omega quad u t 0 cdot v 0 in l 2 omega es ea where 0 p 2 m 1 we prove a global nonexistence theorem for positive initial value of the energy when 1 1

reasoning in fuzzy description logics using automata automata based methods have been successfully employed to prove tight complexity bounds for reasoning in many classical logics and in particular in description logics dls very recently the ideas behind these automata based approaches were adapted for reasoning also in fuzzy extensions of dls with semantics based either on finitely many truth degrees or the godel t norm over the interval 0 1 clearly due to the different semantics in these logics the construction of the automata for fuzzy dls is more involved than for the classical case in this paper we provide an overview of the existing automata based methods for reasoning in fuzzy dls with a special emphasis on explaining the ideas and the requirements behind them the methods vary from deciding emptiness of automata on infinite trees to inclusions between automata on finite words overall we provide a comprehensive perspective on the automata based methods currently in use and the many complexity results obtained through them

making fuzzy description logic more general a version of fuzzy description logic based on the basic continuous t norm based fuzzy predicate logic bl is presented problems of satisfiability validity and subsumption of concepts are discussed and reduced to problems of fuzzy propositional logic known to be decidable for any continuous t norm for lukasiewicz t norm some stronger results are obtained

level spacings for integrable quantum maps in genus zero we study the pair correlation function for a variety of completely integrable quantum maps in one degree of freedom for simplicity we assume that the classical phase space m is the riemann sphere p 1 and that the classical map is a fixed time map of a hamilton flow the quantization is then a unitary n n matrix u t n and its pair correlation measure gives the distribution of spacings between eigenvalues in an interval of length comparable to the mean level spacing 1 n the physicists conjecture berry tabor conjecture is that as should converge to the pair correlation function of a poisson process for any 2 parameter family of hamiltonians of the form with we prove that this conjecture is correct for almost all along the subsequence of planck constants in the addendum to this paper z addendum we further show that for polynomial phases the a e convergence to poisson holds along the full sequence of planck constants for the cesaro means of

global nonexistence of solutions for a nonlinear wave equation with time delay and acoustic boundary conditions abstract we consider a quasilinear wave equation u t t u t d i v u 2 u d i v u t 2 u t a u t m 2 u t 1 u t x t 2 u t x t b u p 2 u a b 0 associated with initial and dirichlet boundary conditions at one part and acoustic boundary conditions at another part respectively we prove under suitable conditions on m p and for negative initial energy a global nonexistence of solutions