the set of smooth quasi periodic schrodinger cocycles with positive lyapunov exponent is not open one knows that the set of quasi periodic schrodinger cocycles with positive lyapunov exponent is open and dense in analytic topology in this paper we construct cocycles with positive lyapunov exponent which can be arbitrarily approximated by ones with zero lyapunov exponent in the space of mathcal c l 1 le l le infty smooth quasi periodic cocycles which shows that the set of quasi periodic schrodinger cocycles with positive lyapunov exponent is not open in smooth topology

stability for quasi periodically perturbed hill s equations we consider a perturbed hill s equation of the form open image in new window p0 t p1 t 0 where p0 is real analytic and periodic p1 is real analytic and quasi periodic and is small assuming diophantine conditions on the frequencies of the decoupled system i e the frequencies of the external potentials p0 and p1 and the proper frequency of the unperturbed 0 hill s equation but without making any assumptions on the perturbing potential p1 other than analyticity we prove that quasi periodic solutions of the unperturbed equation can be continued into quasi periodic solutions if lies in a cantor set of relatively large measure in open image in new window where 0 is small enough our method is based on a resummation procedure of a formal lindstedt series obtained as a solution of a generalized riccati equation associated to hill s problem

from ordering based nonmonotonic reasoning to conditional logics as ga rdenfors and makinson have recently shown a nonmonotonic inference relation can be generated from a total pre ordering on the set of formulas or equivalently from an uncertainty valuation we build here on these results we include the pre ordering in the language by introducing a conditional operator and we extend the generation of a nonmonotonic inference relation by allowing the use of incompletely specified pre orderings this allows effective procedures for computing nonmonotonic inferences by translating nonmonotonic reasoning into deduction in a conditional logic authors abstract

positive lyapunov exponents for continuous quasiperiodic schrodinger equations we prove that the continuous one dimensional schrodinger equation with an analytic quasi periodic potential has positive lyapunov exponents in the bottom of the spectrum for large couplings

positive lyapunov exponents for schrodinger operators with quasi periodic potentials we present a new simple way to estimate the rate of exponential growth lyapunov exponent of solutions of the finite difference schrodinger equation h e psi n mathop limits def psi n 1 psi n 1 lambda f alpha n theta psi n heref is a non constant real analytic function of period 1 and is irrational for large we prove that the lyapunov exponent is positive for every energye in the spectrum ofh and a e in particular the absolutely continuous spectrum ofh is empty in the continuum we study the quasi periodic operator onl2 r h frac d 2 dx 2 k 2 cos x cos alpha x theta for largek and show that for wide intervals of low energies the lyapunov exponent is positive the main idea which originated from m herman s subharmonic argument 11 is to deform the phase to the complex plane this enables us to avoid small denominator problems by moving them off the axis making estimates much easier to perform we recover the information for real using an elementary extension of jensen s formula subharmonicity

purely absolutely continuous spectrum for almost mathieu operators using a recent result of sinai we prove that the almost mathieu operators acting onl2 ly n l 1 l cos n n have a purely absolutely continuous spectrum for almost all a provided that is a good irrational and is sufficiently small furthermore the generalized eigen functions are quasiperiodic

a lower bound on the lyapunov exponent for the generalized harper s model we obtain a lower bound for the lyapunov exponent of a family of discrete schrodinger operators hu n u n 1 u n 1 2a 1 cos 2 pi theta n alpha u n 2a 2 cos 4 pi theta n alpha u n that incorporates both a 1 and a 2 thus going beyond the herman s bound

a note on certain generating functions for the generalized bessel polynomials abstract the main object of the present paper is to prove a general theorem on bilinear bilateral or mixed multilateral generating functions for the generalized bessel polynomials it is pointed out that this theorem and some other earlier results on the subject would provide unifications and generalizations of numerous generating functions which were obtained recently by using group theoretic techniques some interesting applications of these general results and their natural connections with the classical laguerre polynomials are also indicated

unifying default reasoning and belief revision in a modal framework abstract we present a logic for reasoning about belief revision in which the process of revising a knowledge base by some sentence is represented with a conditional connective the conditional is not primitive however it is defined in terms of two unary modal operators we show that our notion of revision is equivalent to that determined by the classic agm postulates furthermore unlike current models of revision our approach does not require the limit assumption we also present a model for subjunctive query answering that allows the expression of subjunctive or factual premises integrity constraints and notions of entrenchment and plausibility the modal framework we adopt is sufficiently general to allow the expression of other forms of defeasible reasoning and facilitates the demonstration of some interesting connections between revision default reasoning and autoepistemic logic in particular we show that the normative conditional for default reasoning developed in a companion paper and our subjunctive conditional are identical default reasoning can thus be viewed as the revision of a theory of expectations in manner that naturally relates priorities of default rules to the entrenchment of expectations

some families of generating functions for the extended srivastava polynomials abstract almost four decades ago h m srivastava considered a general family of univariate polynomials the srivastava polynomials and initiated a systematic investigation for this family 10 in 2001 b gonzalez j matera and h m srivastava extended the srivastava polynomials by inserting one more parameter 4 in this study we obtain a family of linear generating functions for these extended polynomials some illustrative results including jacobi laguerre and bessel polynomials are also presented furthermore mixed multilateral and multilinear generating functions are derived for these polynomials

anderson localization for the discrete one dimensional quasi periodic schrodinger operator with potential defined by a gevrey class function in this paper we consider the discrete one dimensional schrodinger operator with quasi periodic potential vn v x n we assume that the frequency satisfies a strong diophantine condition and that the function v belongs to a gevrey class and it satisfies a transversality condition under these assumptions we prove in the perturbative regime that for large disorder and for most frequencies the operator satisfies anderson localization moreover we show that the associated lyapunov exponent is positive for all energies and that the lyapunov exponent and the integrated density of states are continuous functions with a certain modulus of continuity we also prove a partial nonperturbative result assuming that the function v belongs to some particular gevrey classes

new families of generating functions for certain class of three variable polynomials abstract recently srivastava ozarslan and kaanoglu have introduced certain families of three and two variable polynomials which include lagrange and lagrange hermite polynomials and obtained families of two sided linear generating functions between these families h m srivastava m a ozarslan c kaanoglu some families of generating functions for a certain class of three variable polynomials integr transform spec funct ifirst 2010 1 12 the main object of this investigation is to obtain new two sided linear generating functions between these families by applying certain hypergeometric transformations furthermore more general families of bilinear bilateral multilateral finite series relationships and generating functions are presented for them

some families of generating functions for the multiple orthogonal polynomials associated with modified bessel k functions the main object of this paper is to derive several substantially more general families of bilinear bilateral and mixed multilateral finite series relationships and generating functions for the multiple orthogonal polynomials associated with the modified bessel k functions also known as macdonald functions some special cases of the above statements are also given

localization for a class of one dimensional quasi periodic schrodinger operators we prove for small and satisfying a certain diophantine condition the operator h varepsilon 2 delta frac 1 2 pi cos 2 pi j alpha theta j in mathbb z has pure point spectrum for almost all a similar result is established at low energy for h frac d 2 dx 2 k 2 cos 2 pi x cos 2 pi alpha x theta providedk is sufficiently large

a maximum entropy approach to nonmonotonic reasoning an approach to nonmonotonic reasoning that combines the principle of infinitesimal probabilities with that of maximum entropy thus extending the inferential power of the probabilistic interpretation of defaults is proposed a precise formalization of the consequences entailed by a conditional knowledge base is provided the computational machinery necessary for drawing these consequences is developed and the behavior of the maximum entropy approach is compared to related work in default reasoning the resulting formalism offers a compromise between two extremes the cautious approach based on the conditional interpretations of defaults and the bold approach based on minimizing abnormalities

positive lyapunov exponents for a class of ergodic schrodinger operators we present a simple method to estimate the lyapunov exponent e for the system psi j 1 psi j 1 v j omega psi j e psi j where v j is an ergodic family of potentials defined forj we assume that there is a constant 2 and large positive integersl l such that for almost every and everye there is an infinite sequence of disjoint intervalsj n with the following properties under these conditions we prove that meas e e o be l 6 where gb andb are positive constants and ldmeas rd refers to lebesgue measure

conditional entailment bridging two approaches to default reasoning abstract in recent years two conceptually different interpretations of default expressions have been advanced extensional interpretations in which defaults are regarded as prescriptions for extending one s set of beliefs and conditional interpretations in which defaults are regarded as beliefs whose validity is bound to a particular context the two interpretations possess virtues and limitations that are practically orthogonal to each other the conditional interpretations successfully resolve arguments of different specificity e g penguins don t fly in spite of being birds but fail to capture arguments of irrelevance e g concluding red birds fly from birds fly the opposite is true for the extensional interpretations this paper develops a new account of defaults called conditional entailment which combines the benefits of the two interpretations like prioritized circumscriptions conditional entailment resolves arguments by enforcing priorities among defaults however instead of having to be specified by the user these priorities are extracted automatically from the knowledge base similarly conditional entailment possesses a sound and complete proof theory based on interacting arguments and amenable to implementation in conventional atmss

on a singular integral equation including a set of multivariate polynomials suggested by laguerre polynomials in this paper we introduce the class of polynomials z n 1 n j a x 1 x j r 1 r j suggested by the multivariate laguerre polynomials we give schlafli s contour integral representation and calculate the fractional order integral of these polynomials furthermore we obtain linear multilinear and mixed multilateral generating functions for them finally we construct a singular integral equation with z n 1 n j a x 1 x j r 1 r j in the kernel and obtain the solution in terms of multivariate analogue of the mittag leffler functions

absence of localisation in the almost mathieu equation the author considers the discrete schrodinger operator on z with the potential lambda cos 2 pi alpha n theta this one dimensional model occurs in the study of an electron in a two dimensional periodic potential with a uniform magnetic field first it is proved that for every alpha and for lambda 2 this operator has no eigenvalue i e localised state furthermore at lambda 2 the eigenvalues if they exist belong to the set where the lyapunov exponent vanishes and the associated eigenvectors at in l2 z but are not summable

dynamics of the quasi periodic schrodinger cocycle at the lowest energy in the spectrum in this paper we consider the quasi periodic schrodinger cocycle over mathbb t d d 1 and in particular its projectivization in the regime of large coupling constants and diophantine frequencies we give an affirmative answer to a question posed by m herman 21 p 482 concerning the geometric structure of certain strange non chaotic attractors which appear in the projective dynamical system we also show that for some phase the lowest energy in the spectrum of the associated schrodinger operator is an eigenvalue with an exponentially decaying eigenfunction this generalizes 39 to the multi frequency case d 1

default reasoning from conditional knowledge bases complexity and tractable cases abstract conditional knowledge bases have been proposed as belief bases that include defeasible rules also called defaults of the form which informally read as generally if then such rules may have exceptions which can be handled in different ways a number of entailment semantics for conditional knowledge bases have been proposed in the literature however while the semantic properties and interrelationships of these formalisms are quite well understood about their computational properties only partial results are known so far in this paper we fill these gaps and first draw a precise picture of the complexity of default reasoning from conditional knowledge bases given a conditional knowledge base kb and a default does kb entail we classify the complexity of this problem for a number of well known approaches including goldszmidt et al s maximum entropy approach and geffner s conditional entailment where we consider the general propositional case as well as natural syntactic restrictions in particular to horn and literal horn conditional knowledge bases as we show the more sophisticated semantics for conditional knowledge bases are plagued with intractability in all these fragments we thus explore cases in which these semantics are tractable and find that most of them enjoy this property on feedback free horn conditional knowledge bases which constitute a new meaningful class of conditional knowledge bases furthermore we generalize previous tractability results from horn to q horn conditional knowledge bases which allow for a limited use of disjunction our results complement and extend previous results and contribute in refining the tractability intractability frontier of default reasoning from conditional knowledge bases they provide useful insight for developing efficient implementations

upper bounds in quantum dynamics of course the case of main interest is where h is given by l2 rd or 2 zd h is a schr dinger operator of the form a v and ip 0 is a localized wavepacket under the time evolution 1 the wavepacket i t will in general spread out with time finding quantitative bounds for this spreading in concrete cases and developing methods for proving such bounds has been the objective of a great number of papers in recent years one is often interested in the growth behavior of the moments of the position operator that is the function 11 x p 2 i 2 these questions are particularly complicated and interesting in situations where singular continuous spectra occur the discovery of the occurrence of such spectra for many models of physical relevance has triggered some activity on the quantum dynamical side for models with absolutely continuous spectra on the other hand quantum dynamical questions have been investigated much earlier in the context of scattering theory and have been answered to a great degree of satisfaction models with point spectrum or more restrictively models exhibiting anderson localization have also been investigated from a quantum dynamical point of view while it is not true in general that spectral localization implies dynamical localization 26 73 it has been shown that the three main approaches to spectral localization the fractional moment method 3 4 5 multi scale analysis 28 27 75 and the bourgain goldstein schlag method 12 37 yield dynamical localization as a by product 2 13 22 31 34 quantum dynamics for schr dinger operators with singular continuous spectra is much less understood the two primary examples motivated by physics are the harper model also known as the almost mathieu operator at critical cou pling which describes a bloch electron in a constant magnetic field with irrational flux through a unit cell and the fibonacci model which describes a standard one dimensional quasicrystal both models have been studied heavily in both the physics and mathematics communities

lyapunov exponents of the schrodinger equation with quasi periodic potential on a strip we prove that all the non negative lyapunov exponents of difference schrodinger equation y n 1 q n y n y n 1 0 infty n infty are strictly positive herey n er m andq n is a symmetricm m matrix whose offdiagonal elements do not depend onn and the diagonal elements are quasiperiodic functions q nj theta lambda f j e 2 pi i theta n alpha e with allf i non constant analytic functions sufficiently large and any irrational number

floquet solutions for the 1 dimensional quasi periodic schrodinger equation we show that the 1 dimensional schrodinger equation with a quasiperiodic potential which is analytic on its hull admits a floquet representation for almost every energye in the upper part of the spectrum we prove that the upper part of the spectrum is purely absolutely continuous and that for a generic potential it is a cantor set we also show that for a small potential these results extend to the whole spectrum

spectral behavior of quasi periodic potentials spectral properties of schrodinger operators of the typeh v where is the laplacian v a quasiperiodic potential and a coupling constant are developed v is taken to be finite sum of exponentials with generic frequencies for small a strong stability is shown on the other hand examples in the finite diffeence case are given for which a transition in the type of spectrum occurs as is increased

the schrodinger equation with a quasi periodic potential we consider the schrodinger equation dx2 v e cosx cos cix 0 v eqi where e is small and a satisfies the diophantine inequality lp qcl c q2 forp qez q 0 we look for solutions of the form ikx ikx in x im ax 0 m x e q x e 2m ne inxne e if we try to solve for v v mn we are led to the schrodinger equation on the lattice z2 h k q ba v k q en where a is the discrete laplacian without diagonal terms and v k is some 2 potential on z we have two main results 4 for e sufficiently small h k has pure point spectrum for almost every k 2 for e sufficiently small the operator d dx 2 e cosx cos ax has no point spectrum to prove our results we must get decay estimates on the green s function e h 1 the decay of the eigenfunction follows from this in general we must keep track of small divisors which can make the green s function large this is accomplished by a kam kolmogorov arnold moser type of multiscale perturbation analysis

an approach to default reasoning based on a first order conditional logic revised report abstract an approach to default reasoning based on an extension to classical first order logic is presented in this approach first order logic is augmented with a variable conditional operator for representing default statements the statement is read as if then normally truth in the resulting logic is based on a possible worlds semantics is true just when is true in the least exceptional worlds in which is true this system provides a basis for representing and reasoning about default statements inferences of default properties of individuals rely on two assumptions first that the world being modelled is as unexceptional as consistently possible and second that sentences that may consistently be assumed to be irrelevant to a default inference are in fact irrelevant to the inference two formulations of default inferencing are developed the first involves extending the set of default statements to include all combinations of irrelevant properties the second involves assuming that the world being modelled is among the simplest worlds consistent with the defaults and with what is contingently known in the end the two approaches prove to be equivalent with respect to their respective set of default inferences finally it is shown how the approach treats two current problems in default reasoning the first problem concerns the ordering of default statements the second concerns a problem of hanks and mcdermott for dealing with multiple extensions of a set of defaults

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

conditional logics of normality a modal approach abstract several conditional theories of default reasoning have recently been proposed for the representation of statements about normal states of affairs or prototypical properties the natural semantics of these systems and their ability to reason about default rules make these approaches quite appealing we present a family of modal logics in which we define a conditional connective for statements of normality and examine its properties we also demonstrate that two of the most important conditional approaches are equivalent to fragments of our conditional logics of normality and to standard modal logics the approach we take is general enough to allow the expression of a number of different forms of defeasible reasoning and can be used to illustrate the relationship between these types of reasoning e g belief revision subjunctive and autoepistemic reasoning and our default logics this relationship is explored in a companion paper

anderson localization for the 1 d discrete schrodinger operator with two frequency potential we prove the complete exponential localization of eigenfunctions for the 1 d discrete schrodinger operators with quasi periodic potentials having two basic frequencies it is shown also that for such operators there is no forbidden zones in the spectrum unlike the operators with one basic frequency

nonmonotonic reasoning preferential models and cumulative logics abstract many systems that exhibit nonmonotonic behavior have been described and studied already in the literature the general notion of nonmonotonic reasoning though has almost always been described only negatively by the property it does not enjoy i e monotonicity we study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties we concentrate on a number of families of nonmonotonic consequence relations defined in the style of gentzen 13 both proof theoretic and semantic points of view are developed in parallel the former point of view was pioneered by gabbay 10 while the latter has been advocated by shoham 38 five such families are defined and characterized by representation theorems relating the two points of view one of the families of interest that of preferential relations turns out to have been studied by adams 2 the preferential models proposed here are a much stronger tool than adams probabilistic semantics the basic language used in this paper is that of propositional logic the extension of our results to first order predicate calculi and the study of the computational complexity of the decision problems described in this paper will be treated in another paper

certain classes of finite series relationships and generating functions involving the generalized bessel polynomials recently by making use of the familiar group theoretic lie algebraic method a certain mixed trilateral finite series relationship was proven for the generalized bessel polynomials the main object of this paper is to derive several substantially more general families of bilinear bilateral and mixed multilateral finite series relationships and generating functions for these and other related classes of hypergeometric polynomials a duly corrected and modified analogue of the aforementioned trilateral finite series relationship is shown to follow by suitably specializing one of the general results presented here several closely related presumably new finite series relationships and generating functions some of which also involve for example the stirling numbers of the second kind are onsidered rather briefly

some properties of multiple orthogonal polynomials associated with macdonald functions abstract multiple orthogonal polynomials corresponding to two weights on 0 associated with modified bessel functions macdonald functions k and k 1 were introduced in van assche yakubovich integral transforms special funct 9 2000 229 244 and recently also studied by ben cheikh douak meth appl anal to appear we obtain explicit formulas for type i vector polynomials a n n b n n and a n 1 n b n 1 n and for type ii polynomials p n n and p n 1 n we also obtain generating functions for types i and ii polynomials

generalized transition fronts for one dimensional almost periodic fisher kpp equations this paper investigates the existence of generalized transition fronts for fisher kpp equations in one dimensional almost periodic media assuming that the linearized elliptic operator near the unstable steady state admits an almost periodic eigenfunction we show that such fronts exist if and only if their average speed is above an explicit threshold this hypothesis is satisfied in particular when the reaction term does not depend on x or in some cases is small enough moreover except for the threshold case the fronts we construct and their speeds are almost periodic in a sense when our hypothesis is no longer satisfied such generalized transition fronts still exist for an interval of average speeds with explicit bounds our proof relies on the construction of sub and super solutions based on an accurate analysis of the properties of the generalized principal eigenvalues

weak nonmonotonic probabilistic logics we present an approach where probabilistic logic is combined with default reasoning from conditional knowledge bases in kraus et al s system p pearl s system z and lehmann s lexicographic entailment the resulting probabilistic generalizations of default reasoning from conditional knowledge bases allow for handling in a uniform framework strict logical knowledge default logical knowledge as well as purely probabilistic knowledge interestingly probabilistic entailment in system p coincides with probabilistic entailment under g coherence from imprecise probability assessments we then analyze the semantic and nonmonotonic properties of the new formalisms it turns out that they all are proper generalizations of their classical counterparts and have similar properties as them in particular they all satisfy the rationality postulates of system p and some conditioning property moreover probabilistic entailment in system z and probabilistic lexicographic entailment both satisfy the property of rational monotonicity and some irrelevance property while probabilistic entailment in system p does not we also analyze the relationships between the new formalisms here probabilistic entailment in system p is weaker than probabilistic entailment in system z which in turn is weaker than probabilistic lexicographic entailment moreover they all are weaker than entailment in probabilistic logic where default sentences are interpreted as strict sentences under natural conditions probabilistic entailment in system z and lexicographic entailment even coincide with such entailment in probabilistic logic while probabilistic entailment in system p does not finally we also present algorithms for reasoning under probabilistic entailment in system z and probabilistic lexicographic entailment and we give a precise picture of its complexity

what does a conditional knowledge base entail abstract this paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation a conditional knowledge base consisting of a set of conditional assertions of the type if then represents the explicit defeasible knowledge an agent has about the way the world generally behaves we look for a plausible definition of the set of all conditional assertions entailed by a conditional knowledge base in a previous paper kraus and the authors defined and studied preferential consequence relations they noticed that not all preferential relations could be considered as reasonable inference procedures this paper studies a more restricted class of consequence relations rational relations it is argued that any reasonable nonmonotonic inference procedure should define a rational relation it is shown that the rational relations are exactly those that may be represented by a ranked preferential model or by a nonstandard probabilistic model the rational closure of a conditional knowledge base is defined and shown to provide an attractive answer to the question of the title global properties of this closure operation are proved it is a cumulative operation it is also computationally tractable this paper assumes the underlying language is propositional

holder continuity of the integrated density of states for quasi periodic schrodinger equations and averages of shifts of subharmonic functions in this paper we consider various regularity results for discrete quasiperiodic schr6dinger equations n l pn 1 v 9 nw on eon with analytic potential v we prove that on intervals of positivity for the lyapunov exponent the integrated density of states is holder continuous in the energy provided w has a typical continued fraction expansion the proof is based on certain sharp large deviation theorems for the norms of the monodromy matrices and the avalanche principle the latter refers to a mechanism that allows us to write the norm of a monodromy matrix as the product of the norms of many short blocks in the multi frequency case the integrated density of states is shown to have a modulus of continuity of the form exp log tl for some 0 a 1 but currently we do not obtain holder continuity in the case of more than one frequency we also present a mechanism for proving the positivity of the lyapunov exponent for large disorders for a general class of equations the only requirement for this approach is some weak form of a large deviation theorem for the lyapunov exponents in particular we obtain an independent proof of the herman sorets spencer theorem in the multi frequency case the approach in this paper is related to the recent nonperturbative proof of anderson localization in the quasi periodic case by j bourgain and m goldstein

global theory of one frequency schrodinger operators we study schrodinger operators with a one frequency analytic potential focusing on the transition between the two distinct local regimes characteristic respectively of large and small potentials from the dynamical point of view the transition signals the emergence of non uniform hyperbolicity so the dependence of the lyapunov exponent with respect to parameters plays a central role in the analysis though often ill behaved by conventional measures we show that the lyapunov exponent is in fact remarkably regular in a stratified sense which we define the irregularity comes from the matching of nice analytic or smooth functions along sets with complicated geometry this result allows us to establish that the critical set for the transition lies within countably many codimension one subvarieties of the infinite dimensional parameter space a more refined renormalization based analysis shows that the critical set is rather thin within those subvarieties and allows us to conclude that a typical potential has no critical energies such acritical potentials also form an open set and have several interesting properties only finitely many phase transitions may happen but never at any specific point in the spectrum and the lyapunov exponent is minorated in the region of the spectrum where it is positive on the other hand we do show that the number of phase transitions can be arbitrarily large

operators with singular continuous spectrum iii almost periodic schrodinger operators we prove that one dimensional schrodinger operators with even almost periodic potential have no point spectrum for a dense g in the hull this implies purely singular continuous spectrum for the almost mathieu equation for coupling larger than 2 and a dense g in even if the frequency is an irrational with good diophantine properties

phase transition and semi global reducibility for 1d continuous schodinger operators with large analytic quasi periodic potentials of two frequencies one knows that the spectral measure is singular at the bottom of the spectrum and purely absolutely continuous in the upper part of the spectrum so there is a phase transition when energy increases in this paper we obtain the exact power law for the phase transition in energy by the semi global reducibility theory of analytic quasi periodic linear systems

reducibility or nonuniform hyperbolicity for quasiperiodic schrodinger cocycles we show that for almost every frequency r q for every c o potential v r z r and for almost every energy e the corresponding quasiperiodic schr nodinger cocycle is either reducible or nonuniformly hyperbolic this result gives very good control on the absolutely continuous part of the spectrum of the corresponding quasiperiodic schr nodinger operator and allows us to complete the proof of the aubry andr le conjecture on the measure of the spectrum of the almost mathieu operator

anderson transitions for a family of almost periodic schrodinger equations in the adiabatic case this work is devoted to the study of a family of almost periodic one dimensional schrodinger equations using results on the asymptotic behavior of a corresponding monodromy matrix in the adiabatic limit we prove the existence of an asymptotically sharp anderson transition in the low energy region more explicitly we prove the existence of energy intervals containing only singular spectrum and of other energy intervals containing absolutely continuous spectrum the zones containing singular spectrum and those containing absolutely continuous are separated by asymptotically sharp transitions the analysis may be viewed as utilizing a complex wkb method for adiabatic perturbations of periodic schrodinger equations the transition energies are interpreted in terms of phase space tunneling

on a multivariable extension of jacobi matrix polynomials the classical jacobi matrix polynomials only for commutative matrices were first studied by defez et al e defez l jodar a law jacobi matrix differential equation polynomial solutions and their properties comput math appl 48 2004 789 803 the main aim of this paper is to construct a multivariable extension with the help of the classical jacobi matrix polynomials jmps generating matrix functions and recurrence relations satisfied by these multivariable matrix polynomials are derived furthermore general families of multilinear and multilateral generating matrix functions are obtained and their applications are presented

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

qualitative probabilities for default reasoning belief revision and causal modeling abstract this paper presents a formalism that combines useful properties of both logic and probabilities like logic the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and like probability it permits us to express if then rules with different levels of firmness and to retract beliefs in response to changing observations rules are interpreted as order of magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds inferences are supported by a unique priority ordering on rules which is syntactically derived from the knowledge base this ordering accounts for rule interactions respects specificity considerations and facilitates the construction of coherent states of beliefs practical algorithms are developed and analyzed for testing consistency computing rule ordering and answering queries imprecise observations are incorporated using qualitative versions of jeffrey s rule and bayesian updating with the result that coherent belief revision is embodied naturally and tractably finally causal rules are interpreted as imposing markovian conditions that further constrain world rankings to reflect the modularity of causal organizations these constraints are shown to facilitate reasoning about causal projections explanations actions and change

upper quantum lyapunov exponent and parametric oscillators we introduce a definition of upper lyapunov exponent for quantum systems in the heisenberg representation and apply it to parametric quantum oscillators we provide a simple proof that the upper quantum lyapunov exponent ranges from zero to a positive value as the parameters range from the classical system s region of stability to the instability region it is also proved that in the instability region the parametric quantum oscillator satisfies the discrete quantum anosov relations defined by emch narnhofer sewell and thirring

on the consistency of defeasible databases abstract we propose a norm of consistency for a mixed set of defeasible and strict sentences which guided by a probabilistic interpretation of these sentences establishes a clear distinction between exceptions ambiguities and outright contradictions a notion of entailment is then defined which represents a minimal core of beliefs that must follow from the database if one is committed to avoid inconsistencies the paper establishes necessary and sufficient conditions for consistency and provides a simple decision procedure for testing the consistency of a database or whether a given sentence is entailed by the database it is also shown that if all sentences are of horn type consistency and entailment can be tested in polynomial time finally we discuss procedures for reasoning with inconsistent databases and identifying sentences directly responsible for the inconsistency

uniform positivity and continuity of lyapunov exponents for a class of c 2 quasiperiodic schrodinger cocycles abstract we show that for a class of c 2 quasiperiodic potentials and for any fixed diophantine frequency the lyapunov exponent of the corresponding schrodinger cocycles as a function of energies are uniformly positive and weakly holder continuous as a corollary we obtain that the corresponding integrated density of states is weakly holder continuous as well our approach is of purely dynamical systems which depends on a detailed analysis of asymptotic stable and unstable directions we also apply it to more general sl 2 r cocycles which in turn can be applied to get uniform positivity and continuity of lyapunov exponents around unique nondegenerate extremal points of any smooth potential and to a certain class of c 2 szeg cocycles

some families of generating functions for the bessel polynomials abstract the main object of this paper is to show how readily some general results on bilinear bilateral or mixed multilateral generating functions for the bessel polynomials would provide unifications and generalizations of numerous generating functions which were proven recently by using group theoretic techniques

on the spectrum of odd order self adjoint ordinary differential operators on the real line with quasi periodic coefficients in this paper we prove that an odd order self adjoint differential operator on the real line with quasi periodic coefficients has only absolute continuous simple spectrum for large enough energies ordinary differential operators with quasi periodic coefficients have been studied a lot during the last 20 years these operators arise naturally from physical considerations people have mainly been interested in the one dimensional schro dinger operator with a quasi periodic potential see be te din sin eli ji si mo mo po su and so sp such hamiltonians come up naturally in solid state physics see pa fi in this paper we study ordinary differential operators of higher order with quasi periodic coefficients such operators also come up in physics for example in the study of boussinesq s equation article no de963225