on stable numerical differentiation based on a regularized volterra equation two different approaches for numeri cal differentiation are considered the first approach consists of solving a regularized volterra equation while the second approach is based on solving a disretized version of the regularized volterra equation numerical experiments show that these methods are efficient and compete fa vorably with the variational regularization method for stable calculating the derivatives of noisy functions

explicit inverse of a generalized vandermonde matrix in this paper the author gives an explicit closed form expression for the nxn inverse matrix v g k n 1 of the generalized nxn vandermonde matrix v g k n by using the elementary symmetric functions symbolic and numerical results are presented

framed bordism and lagrangian embeddings of exotic spheres in dimensions congruent to 1 modulo 4 we prove that the cotangent bundle of an exotic sphere which does not bound a parallelisable manifold is not symplectomorphic to the cotangent bundle of the standard sphere more precisely we prove that such an exotic sphere cannot embed as a lagrangian in the cotangent bundle of the standard sphere the main ingredients of the construction are 1 the fact that the graph of the hopf bration embeds the standard sphere and hence any lagrangian which embeds in its cotangent bundle as a displaceable lagrangian in the product a symplectic vector space of the appropriate dimension with its complex projective space and 2 a moduli space of solutions to a perturbed cauchyriemann equation introduced by gromov

novel class of digital integrators and differentiators a novel class of iir infinite impulse response digital integrators and differentiators is developed a class of digital integrators is first derived from a class of numerical integration rules a class of digital differentiators is subsequently obtained by inverting the transfer functions of the obtained integrators and stabilizing the resulting transfer functions together with magnitude compensation if necessary simulated annealing is applied to optimize some of the obtained integrators and differentiators notice to the reader it is recommended by the editor in chief that the following article not be used for citation after it was determined that it was substantially different from the reviewed and accepted version

on the numerical integration of the schrodinger equation a finite difference method for solving the schrodinger eigenvalue equation is generalised in order to treat a larger number of potentials results are shown for asymmetrical two well oscillators

reconstruction of thermally symmetrized quantum autocorrelation functions from imaginary time data in this paper i propose a technique for recovering quantum dynamical information from imaginary time data via the resolution of a one dimensional hamburger moment problem it is shown that the quantum autocorrelation functions are uniquely determined by and can be reconstructed from their sequence of derivatives at origin a general class of reconstruction algorithms is then identified according to theorem 3 the technique is advocated as especially effective for a certain class of quantum problems in continuum space for which only a few moments are necessary for such problems it is argued that the derivatives at origin can be evaluated by monte carlo simulations via estimators of finite variances in the limit of an infinite number of path variables finally a maximum entropy inversion algorithm for the hamburger moment problem is utilized to compute the quantum rate of reaction for a one dimensional symmetric eckart barrier

a technique for realizing linear phase iir filters a real time iir filter structure is presented that possesses exact phase linearity with 10 approximately 1000 times fewer general multiplies than conventional fir filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay iir filters this structure is based on a technique using local time reversal and single pass sectioned convolution methods to realized a real time recursive implementation of the noncausal transfer function h z sup 1 the time reversed section technique used to realize exactly linear phase iir filters is described the effects of finite section length on the sectional convolution are analyzed a simulation methodology is developed to address the special requirements of simulating a time reversed section filter a design example is presented with computer simulation to illustrate performance in terms of overall magnitude response and phase linearity as a function of finite section length nine example filter specifications are used to compare the performance and complexity of the time reversed section technique to those of a direct fir implementation

closed form expressions for the finite approximations of first and higher derivatives based on taylor series numerical differentiation formulas based on interpolating polynomials operators and lozenge diagrams can be simplified to one of the finite difference approximations based on taylor series in this paper we have presented closed form expressions of these approximations of arbitrary order for first and higher derivatives a comparison of the three types of approximations is given with an ideal digital differentiator by comparing their frequency responses the comparison reveals that the central difference approximations can be used as digital differentiators because they do not introduce any phase distortion and their amplitude response is closer to that of an ideal differentiator it is also observed that central difference approximations are in fact the same as maximally flat digital differentiators in the appendix a computer program written in mathematica is presented which can give the approximation of any order to the derivative of a function at a certain mesh point

numerical differentiation from a viewpoint of regularization theory in this paper we discuss the classical ill posed problem of numerical differentiation assuming that the smoothness of the function to be differentiated is unknown using recent results on adaptive regularization of general ill posed problems we propose new rules for the choice of the stepsize in the finite difference methods and for the regularization parameter choice in numerical differentiation regularized by the iterated tikhonov method these methods are shown to be effective for the differentiation of noisy functions and the order optimal convergence results for them are proved

mathematical proof of closed form expressions for finite difference approximations based on taylor series taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms with explicit formulas for their coefficients however those formulas were not derived mathematically and were based on observation of numerical results in this paper we provide a mathematical proof of those formulas by deriving them mathematically from the taylor series

extrapolation methods and derivatives of limits of sequences let s m be an infinite sequence whose limit or antilimit s can be approximated very efficiently by applying a suitable extrapolation method e 0 to s m assume that the s m and hence also s are differentiable functions of some parameter d d s being the limit or antilimit of d d s m and that we need to approximate d d s a direct way of achieving this would be by applying again a suitable extrapolation method e 1 to the sequence d d s m and this approach has often been used efficiently in various problems of practical importance unfortunately as has been observed at least in some important cases when d d s m and s m have essentially different asymptotic behaviors as m the approximations to d d s produced by this approach despite the fact that they are good do not converge as quickly as those obtained for s and this is puzzling in this paper we first give a rigorous mathematical explanation of this phenomenon for the cases in which e 0 is the richardson extrapolation process and e 1 is a generalization of it thus showing that the phenomenon has very little to do with numerics following that we propose a procedure that amounts to first applying the extrapolation method e 0 to s m and then differentiating the resulting approximations to s and we provide a thorough convergence and stability analysis in conjunction with the richardson extrapolation process it follows from this analysis that the new procedure for d d s has practically the same convergence properties as e 0 for s we show that a very efficient way of implementing the new procedure is by actually differentiating the recursion relations satisfied by the extrapolation method used and we derive the necessary algorithm for the richardson extrapolation process we demonstrate the effectiveness of the new approach with numerical examples that also support the theory we discuss the application of this approach to numerical integration in the presence of endpoint singularities we also discuss briefly its application in conjunction with other extrapolation methods

computation of the semantics of autoepistemic belief theories abstract recently one of the authors introduced a simple and yet powerful non monotonic knowledge representation framework called the autoepistemic logic of beliefs aeb theories in aeb are called autoepistemic belief theories every belief theory t has been shown to have the least static expansion t which is computed by iterating a natural monotonic belief closure operator t starting from t this way the least static expansion t of any belieftheory provides its natural non monotonic semantics which is called the static semantics it is easy to see that if a belief theory t is finite then the construction of its least static expansion t stops after countably many iterations however a somewhat surprising result obtained in this paper shows that the least static expansion of any finite belief theory t is in fact obtained by means of a single iteration of the belief closure operator t although this requires t to be of a special form we also show that t can be always put in this form this result eliminates the need for multiple iterations in the computation of static semantics and allows us to replace the fixed point definition of static semantics by the equivalent explicit and straightforward definition given by t t t the second closely related result establishes an intriguing relationship between static semantics t and clark s completions comp t of finite belief theories here we use a slightly generalized version of comp t see definition 3 2 it shows that the static semantics t of t is obtained by augmenting t with the set b comp t b f f comp t thus ensuring that all formulae that belong to clark s completion comp t of t are believed to be true both results open the way for a more efficient implementation of static semantics the first because only one iteration is needed and the second because reasoning in a non standard logic belief theories under static semantics can be reduced to classical theorem proving involving clark s completion

presentation error analysis and numerical experiments on a group of 1 step ahead numerical differentiation formulas in order to achieve higher computational precision in approximating the first order derivative of the target point the 1 step ahead numerical differentiation formulas are presented these formulas greatly remedy some intrinsic weaknesses of the backward numerical differentiation formulas and overcome the limitation of the central numerical differentiation formulas in addition a group of formulas are proposed to obtain the optimal step length moreover the error analysis of the 1 step ahead numerical differentiation formulas and the backward numerical differentiation formulas is further investigated numerical studies show that the proposed optimal step length formulas are effective and the performance of the 1 step ahead numerical differentiation formulas is much better than that of the backward numerical differentiation formulas in the first order derivative approximation

a family of numerov type exponentially fitted predictor corrector methods for the numerical integration of the radial schro dinger equation a family of predictor corrector exponential numerov type methods is developed for the numerical integration of the one dimensional schrodinger equation the formula considered contains certain free parameters which allow it to be fitted automatically to exponential functions the new methods are very simple and integrate more exponential functions than both the well known fourth order numerov type exponentially fitted methods and the sixth algebraic order runge kutta type methods numerical results also indicate that the new methods are much more accurate than the other exponentially fitted methods mentioned above

the maslov cocycle smooth structures and real analytic complete integrability this paper proves two main results first it is shown that if is a smooth manifold homeomorphic to the standard n torus t n r n z n and h is a real analytically completely integrable convex hamiltonian on t then is diffeomorphic to tn second it is proven that for some topological 7 manifolds the cotangent bundle of each smooth structure admits a real analytically completely integrable riemannian metric hamiltonian

the unregularized gradient flow of the symplectic action the symplectic action can be defined on the space of smooth paths in a symplectic manifold p which join two lagrangian submanifolds of p to pursue a new approach to the variational theory of this function we define on a subset of the path space the flow whose trajectories are given by the solutions of the cauchy riemann equation with respect to a suitable almost complex structure on p in particular we prove compactness and transversality results for the set of bounded trajectories

a weighted least squares method for the design of stable 1 d and 2 d iir digital filters we present a new approach to the least squares design of stable infinite impulse response iir digital filters the design is accomplished by using an iterative scheme in which the denominator polynomial obtained from the preceding iteration is treated as a part of the weighting function and each iteration is carried out by solving a standard quadratic programming problem that yields a stable rational function when the iteration converges a stable and truly least squares solution is obtained the method is then extended to address the least squares design of stable iir two dimensional 2 d filters examples are included to illustrate the proposed design techniques

a new obstruction to embedding lagrangian tori n let 2n be endowed with the canonical symplectic form a i 1 dxi dy i and consider a lagrangian embedding of a compact manifold j l r 2 a a well known result due to g r o m o v g states that the cohomology class of a in h z e 2 l is non zero we identify l with its image in r2 an equivalent assertion is that the liouville form 2 y 7 1 xldy i pulls back to a closed form j 2 on l whose cohomology class does not vanish g r o m o v s proof uses subtle properties of holomorphic maps into c he shows that there is always a holomorphic disk a in c with boundary in l on such a disk a is positive hence sa a soa 2 0 in this paper we shall only consider the case l t and give an elementary proof of gromov s result elementary should be understood in the sense of number theory that is without using holomorphic functions in fact our result is somewhat more precise and can be stated as follows

new finite difference formulas for numerical differentiation conventional numerical differentiation formulas based on interpolating polynomials operators and lozenge diagrams can be simplified to one of the finite difference approximations based on taylor series and closed form expressions of these finite difference formulas have already been presented in this paper we present new finite difference formulas which are more accurate than the available ones especially for the oscillating functions having frequency components near the nyquist frequency closed form expressions of the new formulas are given for arbitrary order a comparison of the previously available three types of approximations is given with the presented formulas a computer program written in mathematica based on new formulas is given in the appendix for numerical differentiation of a function at a specified mesh point

design of low order linear phase iir filters via orthogonal projection this paper presents an indirect linear phase iir filter design technique based on a reduction of linear phase fir filters the desired filter is obtained by minimizing the l sub 2 norm of the difference between the original fir filter and the lower order iir filter we first establish a relationship between the hankel singular values of the discarded part of the fir filter and the l sub 2 norm of the corresponding filter approximation error based on model truncation this result motivates us to propose a simple finite search method that will achieve better approximation results than commonly used truncation methods such as the balanced truncation bt and the impulse response gramian irg methods we then develop an iterative algorithm for finding an optimal iir filter based on a matrix projection of the original fir filter the convergence of the proposed algorithm is established filters designed using the proposed algorithm are compared with those obtained by other techniques with respect to the amplitude response and group delay characteristics in the passband numerical examples show that the proposed algorithm offers the best performance

evaluating the effect of semi normality on the expressiveness of defaults normal default logic ndl and semi normal default logic sndl are syntactically restricted variants of reiter s default logic dl although semi normal defaults have only a slightly more general form than normal defaults sndl does not share the nice properties of ndl e g semi monotonicity in this note we address the effect of semi normality on the expressive power of defaults using a classification method based on polynomial faithful and modular pfm translation functions the resulting classification indicates that sndl and dl are of equal expressive power which strictly exceeds that of ndl this strengthens an earlier result achieved by marek and truszczynski who establish the equivalence of weak semi normal defaults with general defaults furthermore it is established that prerequisite free fragments of dl and sndl pdl and psndl are of equal expressive power consequently psndl is less expressive than dl and sndl incomparable with ndl and more expressive than preferential entailment a generalized form of circumscription the latter result is in sharp contrast with imielinski s result which states that prerequisite free and semi normal default theories can be modularly translated into preferential entailment

on the numerical integration of the schrodinger equation in the finite difference schemes abstract formulae for the integration of the schrodinger equation for bound states based on the scheme of central differences are generated from the taylor expansion with the help of formal pade approximants these methods are studied in matrix form and a limiting formula the best for a given discretization is obtained

semantical considerations on nonmonotonic logic abstract commonsense reasoning is nonmonotonic in the sense that we often draw on the basis of partial information conclusions that we later retract when we are given more complete information some of the most interesting products of recent attempts to formalize nonmonotonic reasoning are the nonmonotonic logics of mcdermott and doyle 1 2 these logics however all have peculiarities that suggest they do not quite succeed in capturing the intuitions that prompted their development in this paper we reconstruct nonmonotonic logic as a model of an ideally rational agent s reasoning about his own beliefs for the resulting system called autoepistemic logic we define an intuitively based semantics for which we can show autoepistemic logic to be both sound and complete we then compare autoepistemic logic with the approach of mcdermott and doyle showing how it avoids the peculiarities of their nonmonotonic logic

general explicit difference formulas for numerical differentiation through introducing the generalized vandermonde determinant the linear algebraic system of a kind of vandermonde equations is solved analytically by use of the basic properties of this determinant and then we present general explicit finite difference formulas with arbitrary order accuracy for approximating first and higher derivatives which are applicable to unequally or equally spaced data comparing with other finite difference formulas the new explicit difference formulas have some important advantages basic computer algorithms for the new formulas are given and numerical results show that the new explicit difference formulas are quite effective for estimating first and higher derivatives of equally and unequally spaced data

design of iir digital differentiators using constrained optimization a new optimization method for the design of fullband and lowpass iir digital differentiators is proposed in the new method the passband phase response error is minimized under the constraint that the maximum passband amplitude response relative error is below a prescribed level for lowpass iir differentiators an additional constraint is introduced to limit the average squared amplitude response in the stopband so as to minimize any high frequency noise that may be present extensive experimental results are included which show that the differentiators designed using the proposed method have much smaller maximum phase response error for the same passband amplitude response error and stopband constraints when compared with several differentiators designed using state of the art competing methods

from answer set logic programming to circumscription via logic of gk we first embed pearce s equilibrium logic and ferraris s propositional general logic programs in lin and shoham s logic of gk a nonmonotonic modal logic that has been shown to include as special cases both reiter s default logic in the propositional case and moore s autoepistemic logic from this embedding we obtain a mapping from ferraris s propositional general logic programs to circumscription and show that this mapping can be used to check the strong equivalence between two propositional logic programs in classical logic we also show that ferraris s propositional general logic programs can be extended to the first order case and our mapping from ferraris s propositional general logic programs to circumscription can be extended to the first order case as well to provide a semantics for these first order general logic programs

a remainder formula of numerical differentiation for the generalized lagrange interpolation through exploiting the generalized lagrange interpolation for continuous piecewise smooth functions a remainder term of numerical differentiation is given also the error estimates for the numerical differentiation formula are presented

simplified analytical expressions for numerical differentiation via cycle index based on the lagrange interpolation to the function f x 0 for arbitrarily chosen x 0 and logarithmic differentiation we give a simple approach to analytical expressions for numerical differentiation using cycle index a detailed analysis for the remainder is also included

a finite difference domain decomposition algorithm for numerical solution of the heat equation a domain decomposition algorithm for numerically solving the heat equation in one and two space dimensions is presented in this procedure interface values between subdomains are found by an explicit finite difference formula once these values are calculated interior values are determined by backward differencing in time a natural extension of this method allows for the use of different time steps in different subdomains maximum norm error estimates for these procedures are derived which demonstrate that the error incurred at the interfaces is higher order in the discretization parameters

nonmonotonic logic ii nonmonotonic modal theories tradmonal logics suffer from the monotomclty problem new axioms never mvahdate old theorems one way to get nd of this problem ts to extend traditional modal logic in the following way the operator m usually read possible is extended so that mp is true whenever p is consistent with the theory then any theorem of this form may be mvahdated if p s added as an axiom this extension results m nonmonotomc versions of the systems t 4 and 5 these systems are complete in that a theorem is provable in a theory based on one of them just if it is true m all noncommittal models of that theory where a noncommittal model ts one m which as many thmgs are possible as possible nonmonotomc 4 is probably the most interesting of the three since it is stronger than ordinary 4 but has all the usual inferential machinery of 4 there is a straightforward proof procedure for the sententlal subset of nonmonotomc 4 this approach to nonmonotonlc logic may be applied to several problems in knowledge representation for aruficml mtelhgence its main advantages over competmg approaches are that tt factors out problems of resource hmltattons and allows the symbol m to appear m any context since m is a meaningful part of the language

taylor series based finite difference approximations of higher degree derivatives a new type of taylor series based finite difference approximations of higher degree derivatives of a function are presented in closed forms with their coefficients given by explicit formulas for arbitrary orders characteristics and accuracies of presented approximations and already presented central difference higher degree approximations are investigated by performing example numerical differentiations it is shown that the presented approximations are more accurate than the central difference approximations especially for odd degrees however for even degrees central difference approximations become attractive as the coefficients of the presented approximations of even degrees do not correspond to equispaced input samples

grounded fixpoints and their applications in knowledge representation in various domains of logic researchers have made use of a similar intuition that facts or models can be derived from the ground up they typically phrase this intuition by saying e g that the facts should be grounded or that they should not be unfounded or that they should be supported by cycle free arguments et cetera in this paper we formalise this intuition in the context of algebraical fixpoint theory we define when a lattice element x l is grounded for lattice operator o l l on the algebraical level we investigate the relationship between grounded fixpoints and the various classes of fixpoints of approximation fixpoint theory including supported minimal kripke kleene stable and well founded fixpoints on the logical level we investigate groundedness in the context of logic programming autoepistemic logic default logic and argumentation frameworks we explain what grounded points and fixpoints mean in these logics and show that this concept indeed formalises intuitions that existed in these fields we investigate which existing semantics are grounded we study the novel semantics for these logics that is induced by grounded fixpoints which has some very appealing properties not in the least its mathematical simplicity and generality our results unveil a remarkable uniformity in intuitions and mathematics in these fields

all i know a study in autoepistemic logic abstract current approaches to formalizing nonmonotonic reasoning using logics of belief require the definition of new metalogical properties over sets of sentences this research attempts to show how some of these patterns of reasoning can be captured using only the classical notions of logic satisfiability validity implication this is done by extending a logic of belief so that it is possible to say that only a certain proposition or finite set of them is believed this research also extends previous approaches to handle quantifiers and equality provides a semantic account of certain types of nonmonotonicity and through a simple proof theory allows formal derivations to be generated

comparison of taylor finite difference and window finite difference and their application in fdtd the finite difference time domain fdtd method is an important tool in numerical electromagnetic simulation there are many ways to construct a finite difference approximation such as the taylor series expansion theorem the filtering theory etc this paper aims to provide the comparison between the taylor finite difference tfd scheme based on the taylor series expansion theorem and the window finite difference wfd scheme based on the filtering theory their properties have been examined in detail separately in addition the formula of the generalized finite difference gfd scheme is presented which can include both the tfd scheme and the wfd scheme furthermore their application in the numerical solution of maxwell s equations is presented the formulas for the stability criterion and the numerical dispersion relation are derived and analyzed in order to evaluate their performance more accurately a new definition of error is presented upon it the effect of several factors including the grid resolution the courant number and the aspect ratio of the cell on the performance of the numerical dispersion is examined

derivative kernels numerics and applications a generalized framework for numerical differentiation nd is proposed for constructing a finite impulse response fir filter in closed form the framework regulates the frequency response of nd filters for arbitrary derivative order and cutoff frequency selected parameters relying on interpolating power polynomials and maximally flat design techniques compared with the state of the art solutions such as gaussian kernels the proposed nd filter is sharply localized in the fourier domain with ripple free artifacts here we construct 2d maxflat kernels for image directional differentiation to calculate image differentials for arbitrary derivative order cutoff level and steering angle the resulted kernel library renders a new solution capable of delivering discrete approximation of gradients hessian and higher order tensors in numerous applications we tested the utility of this library on three different imaging applications with main focus on the unsharp masking the reported results highlight the high efficiency of the 2d maxflat kernel and its versatility with respect to robustness and parameter control accuracy

a finite difference method for the numerical solution of the schro dinger equation a new approach which is based on a new property of phase lag for computing eigenvalues of schrodinger equations with potentials is developed in this paper we investigate two cases i the specific case in which the potential v x is an even function with respect to x it is assumed also that the wave functions tend to zero for x ii the general case of the morse potential and of the woods saxon or optical potential numerical and theoretical results show that this new approach is more efficient compared to previously derived methods

the maslov class of the lagrange surfaces and gromov s pseudo holomorphic curves for an immersed lagrange submanifold w c t x one can define a nonnegative integer topologic invariant m w such that the image of h1 w z under the maslov class is equal to m w z in this paper the value of m w is calculated for the case of a two dimensional oriented manifold x with the universal cover homeomorphic to r2 and an embedded lagrange torus w it is proved that if x t2 and w is homologic to the zero section then m w 0 in all the other cases m w 2 the last result is true also for a wide class of oriented properly embedded lagrange surfaces in t r the proof is based on the gromov s theory of pseudo holomorphic curves some applications to the hamiltonian mechanics are mentioned

linear phase low pass iir digital differentiators a novel approach to designing approximately linear phase infinite impulse response iir digital filters in the passband region is introduced the proposed approach yields digital iir filters whose numerators represent linear phase finite impulse response fir filters as an example low pass iir differentiators are introduced the range and high frequency suppression of the proposed low pass differentiators are comparable to those obtained by higher order fir low pass differentiators in addition the differentiators exhibit almost linear phases in the passband regions

design of linear phase iir filters via impulse response gramians a new method for the design of a linear phase infinite impulse response iir filter is presented it involves designing a finite impulse response fir filter satisfying the given frequency response specifications and subsequently obtaining a significantly lower order iir filter using model reduction based on impulse response gramians the general outline of the method and a brief overview of the existing linear phase fir filter design and model reduction techniques are presented the impulse response gramian and the model reduction algorithm used are presented the method is illustrated by design examples and is compared with other methods for the design of linear phase iir filters using equalizers

addendum to floer cohomology of lagrangian intersections and pseudo holomorphic discs i this is an addendum to the author s earlier paper floer cohomology of lagrangian intersection and pseudo holomorphic discs i comm pure appl math 46 1993 pp 949 993 the main result of this addendum extends the definition of the floer cohomology of lagrangian intersection to the case where the minimal maslov number is equal to 2 1996 john wiley sons inc

symplectic fixed points and holomorphic spheres letp be a symplectic manifold whose symplectic form integrated over the spheres inp is proportional to its first chern class on the loop space ofp we consider the variational theory of the symplectic action function perturbed by a hamiltonian term in particular we associate to each isolated invariant set of its gradient flow an abelian group with a cyclic grading it is shown to have properties similar to the homology of the conley index in locally compact spaces as an application we show that if the fixed point set of an exact diffeomorphism onp is nondegenerate then it satisfies the morse inequalities onp we also discuss fixed point estimates for general exact diffeomorphisms

three valued nonmonotonic formalisms and semantics of logic programs abstract we introduce three valued extensions of major nonmonotonic formalisms and we prove that the recently proposed well founded semantics of logic programs is equivalent for arbitrary logic programs to three valued forms of mccarthy s circumscription reiter s closed world assumption moore s autoepistemic logic and reiter s default theory this result not only provides a further justification of the well founded semantics as a natural extension of the perfect model semantics from the class of stratified programs to the class of all logic programs but it also establishes the class of all logic programs as a large class of theories for which natural forms of all four nonmonotonic formalisms coincide it also paves the way for using efficient computation methods developed for logic programming as inference mechanisms for nonmonotonic reasoning

autoepistemic logic autoepistemic logic is one of the principal modes of nonmonotonic reasoning it unifies several other modes of nonmonotonic reasoning and has important application in logic programming in the paper a theory of autoepistemic logic is developed this paper starts with a brief survey of some of the previously known results then the nature of nonmonotonicity is studied by investigating how membership of autoepistemic statements in autoepistemic theories depends on the underlying objective theory a notion similar to set theoretic forcing is introduced expansions of autoepistemic theories are also investigated expansions serve as sets of consequences of an autoepistemic theory and they can also be used to define semantics for logic programs with negation theories that have expansions are characterized and a normal form that allows the description of all expansions of a theory is introduced our results imply algorithms to determine whether a theory has a unique expansion sufficient conditions stratification that imply existence of a unique expansion are discussed the definition of stratified theories is extended and under some additional assumptions efficient algorithms for testing whether a theory is stratified are proposed the theorem characterizing expansions is applied to two classes of theories k1 theories and ae programs in each case simple hypergraph characterization of expansions of theories from each of these classes is given finally connections with stable model semantics for logic programs with negation is discussed in particular it is proven that the problem of existence of stable models is np complete authors abstract

autoepistemic logic of knowledge and beliefs abstract in recent years various formalizations of nonmonotonic reasoning and different semantics for normal and disjunctive logic programs have been proposed including autoepistemic logic circumscription cwa gcwa ecwa epistemic specifications stable well founded stationary and static semantics of normal and disjunctive logic programs in this paper we introduce a simple nonmonotonic knowledge representation framework which isomorphically contains all of the above mentioned nonmonotonic formalisms and semantics as special cases and yet is significantly more expressive than each one of these formalisms considered individually the new formalism called the autoepistemic logic of knowledge and beliefs aelb is obtained by augmenting moore s autoepistemic logic ael already employing the knowledge operator l with an additional belief operator b as a result we are able to reason not only about formulae f which are known to be true i e those for which l f holds but also about those which are only believed to be true i e those for which b f holds the proposed logic constitutes a powerful new formalism which can serve as a unifying frame work for several major nonmonotonic formalisms it allows us to better understand mutual relationships existing between different formalisms and semantics and enables us to provide them with simpler and more natural definitions it also naturally leads to new even more expressive flexible and modular formalizations and semantics

a recursive algorithm for optimizing differentiation in this paper a recursive algorithm will be introduced to improve the differentiation method proposed by hasan et al 2012 their algorithm is based on the undetermined coefficient method and uses the taylor series expansion and vandermonde matrix inverse to calculate weighting coefficients with a complexity of o n 4 our method reduces time complexity from o n 4 to o n 3 moreover we obtain a substantial optimality when the required degree and the order of accuracy increase finally the implementation of the proposed method follows and experimentations prove the validity of the algorithm and compare previous and new methods in terms of execution time besides the combination of our optimization and parallel processing provides valuable results in real world applications particularly qrs detection in ecg signal processing has been considered and we have shown that how features of our method could be used in order to increase accuracy and speed for this application

fractional bilinear transform for analog to digital conversion in this correspondence we propose a fractional bilinear transform used in analog to digital a d conversion this transfer function is derived by means of fractional delay filters according to this transformation first order differentiator can be easily designed next some design examples are illustrated to show the linear frequency mapping property when doing a d conversion finally the designed low order digital differentiator is compared with the existing differentiators

on the design of fir digital differentiators which are maximally linear at the frequency pi p p in positive integers digital differentiators dds which are maximally linear at the spot frequency omega pi p p in positive integers are proposed for operation over a narrow band of frequencies the suggested dds besides giving zero phase error over the entire band of frequencies pi

examples of symplectic structures in this paper we construct symplectic forms tilde omega k k geqq 0 on a compact manifold tilde y which have the same homotopy theoretic invariants but which are not diffeomorphic

a technique to truncate iir filter impulse response and its application to real time implementation of linear phase iir filters a technique for realizing linear phase infinite impulse response iir filters has been proposed by powell and chau 1991 and gives a real time implementation of h z sup 1 spl middot h z where h z is a causal iir filter function in their system the input signal is divided into l sample sections time reversed section convolved with h z and time reversed again the signal is then filtered by h z to give the system output with a processing delay of 3l 1 samples however the group delay response of the system exhibits a minor sinusoidal variation superimposed on some constant value this variation will degrade image quality in image processing and signal quality in signal transmission applications furthermore the output of the system contains harmonic distortion for a sinusoidal input the main drawbacks of powell and chau s technique are the large processing delay of 3l 1 samples and the accompanying phase and harmonic distortions a smaller processing delay increases the phase and harmonic distortions yet the amplitude response remains acceptable previously the present authors presented a method of reducing the processing delay by shortening the section length by an integer factor n using a structure with increased number of paths for the time reversed signal the authors consider how to reduce the phase and harmonic distortions we examined the operation of the sectioned convolution and analyzed it based on a state space representation then we found that the cause of the distortions is a periodic variation of the impulse response length in the sectioned convolution to overcome this problem a technique is devised to realize a recursive circuit having a truncated impulse response with a fixed length l a system applying this technique to the powell chau system is demonstrated to exhibit perfect linear phase characteristic and produce virtually no harmonic distortion therefore the section length l can be reduced without limitation due to phase and harmonic distortions two methods for reducing the increased computational complexity of this technique assuming fixed l are developed and simulations are performed for the proposed system to confirm the expected improvements

semantic forgetting in answer set programming the notion of forgetting also known as variable elimination has been investigated extensively in the context of classical logic but less so in nonmonotonic logic programming and nonmonotonic reasoning the few approaches that exist are based on syntactic modifications of a program at hand in this paper we establish a declarative theory of forgetting for disjunctive logic programs under answer set semantics that is fully based on semantic grounds the suitability of this theory is justified by a number of desirable properties in particular one of our results shows that our notion of forgetting can be entirely captured by classical forgetting we present several algorithms for computing a representation of the result of forgetting and provide a characterization of the computational complexity of reasoning from a logic program under forgetting as applications of our approach we present a fairly general framework for resolving conflicts in inconsistent knowledge bases that are represented by disjunctive logic programs and we show how the semantics of inheritance logic programs and update logic programs from the literature can be characterized through forgetting the basic idea of the conflict resolution framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency in particular we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming

atomft solving odes and daes using taylor series abstract taylor series methods compute a solution to an initial value problem in ordinary differential equations by expanding each component of the solution in a long taylor series the series terms are generated recursively using the techniques of automatic differentiation the atomft system includes a translator to transform statements of the system of odes into a fortran 77 object program that is compiled linked with the atomft runtime library and run to solve the problem we review the use of the atomft system for nonstiff and stiff odes the propagation of global errors and applications to differential algebraic equations arising from certain control problems to boundary value problems to numerical quadrature and to delay problems

an algorithm for the finite difference approximation of derivatives with arbitrary degree and order of accuracy in this paper we introduce an algorithm and a computer code for numerical differentiation of discrete functions the algorithm presented is suitable for calculating derivatives of any degree with any arbitrary order of accuracy over all the known function sampling points the algorithm introduced avoids the labour of preliminary differencing and is in fact more convenient than using the tabulated finite difference formulas in particular when the derivatives are required with high approximation accuracy moreover the given matlab computer code can be implemented to solve boundary value ordinary and partial differential equations with high numerical accuracy the numerical technique is based on the undetermined coefficient method in conjunction with taylor s expansion to avoid the difficulty of solving a system of linear equations an explicit closed form equation for the weighting coefficients is derived in terms of the elementary symmetric functions this is done by using an explicit closed formula for the vandermonde matrix inverse moreover the code is designed to give a unified approximation order throughout the given domain a numerical differentiation example is used to investigate the validity and feasibility of the algorithm and the code it is found that the method and the code work properly for any degree of derivative and any order of accuracy

representation for the lagrangian numerical differentiation formula involving elementary symmetric functions by using elementary symmetric functions this paper presents an explicit representation for the lagrangian numerical differentiation formula as well as the error estimate for local approximation and we also point out that the numerical differentiation formula constructed by li j p li general explicit difference formulas for numerical differentiation j comput appl math 183 2005 29 52 is actually a special case of the lagrangian numerical differentiation formula to approximate the values of the derivatives at the nodes

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

generalized possibilistic logic foundations and applications to qualitative reasoning about uncertainty this paper introduces generalized possibilistic logic gpl a logic for epistemic reasoning based on possibility theory formulas in gpl correspond to propositional combinations of assertions such as it is certain to degree that the propositional formula is true as its name suggests the logic generalizes possibilistic logic pl which at the syntactic level only allows conjunctions of the aforementioned type of assertions at the semantic level pl can only encode sets of epistemic states encompassed by a single least informed one whereas gpl can encode any set of epistemic states this feature makes gpl particularly suitable for reasoning about what an agent knows about the beliefs of another agent e g allowing the former to draw conclusions about what the other agent does not know we introduce an axiomatization for gpl and show its soundness and completeness w r t possibilistic semantics subsequently we highlight the usefulness of gpl as a powerful unifying framework for various knowledge representation formalisms among others we show how comparative uncertainty and ignorance can be modelled in gpl we also exhibit a close connection between gpl and various existing formalisms including possibilistic logic with partially ordered formulas a logic of conditional assertions in the style of kraus lehmann and magidor answer set programming and a fragment of the logic of minimal belief and negation as failure finally we analyse the computational complexity of reasoning in gpl identifying decision problems at the first second third and fourth level of the polynomial hierarchy

peak constrained least squares optimization we presented the basic concepts for peak constrained least squares pcls optimization in previous papers we present advanced pcls optimization concepts in this paper this paper discusses only a few of the many ways that pcls design problems can be formulated we believe that the pcls optimality criterion can be customized to fit virtually any practical application for example pcls optimization can readily be used to design equalizers in the prefilter equalizer or interpolated fir implementations of filters

on the relationship between circumscription and negation as failure abstract the aim of this paper is to investigate two powerful methods of handling negative information in logic based knowledge representation systems the logical minimization in the form of circumscription and the negation as failure rule formalized by various closures or completions of original theories we suggest a new more powerful form of the negation as failure rule and describe an important class of theories for which this form of negation as failure is equivalent to particular forms of circumscription these results establish a close relationship between the two important formalizations of nonmonotonic reasoning and provide a syntactic characterization of the corresponding circumscriptive theories this allows us to apply existing methods of deduction using various negation as failure rules to answering queries in a broad class of circumscriptive theories