a normalized schur cohn stability test for the delta operator based polynomials the author previously 1997 proposed two delta operator based stability tests or more generally zero location tests those tests establish two families of such tests each spanning from the discrete time to the continuous time with the delta operator providing smooth transitions between the two domains in this paper a third family is proposed specifically the normalized schur cohn test in the discrete time domain is transformed into the delta operator domain resulting in a new delta operator test the limit of this new test as the sampling interval vanishes is shown to be the pham le breton test 1991 in the continuous time domain its relationships with the well known routh test and others are studied a numerical example shows the advantage of the new test for fast sampling

reasonable properties for the ordering of fuzzy quantities ii as a continuation of the first part related to the first and second class of ordering approaches this paper deals with the fulfilment of reasonable properties in the third class of ordering approaches to do so we briefly introduce fuzzy relations on which the third class of approaches is based then we recall some transitivity related concepts and an ordering procedure based on a acyclic fuzzy relation acyclicity is a very weak restriction on a fuzzy relation we prove that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity so we give a widely applicable formulation to derive a total ranking order from a fuzzy relation with our formulation we examine all the ordering indices in the third class with respect to the proposed axioms in part i

a levinson type algorithm for modeling fast sampled data the standard discrete time autoregressive model is poorly suited for modeling series obtained by sampling continuous time processes at fairly rapid rates large computational errors can occur when the levinson algorithm is used to estimate the parameters of this model because the toeplitz covariance matrix is ill suited for inversion an alternative model is developed based on an incremental difference operator rather than the shift operator it is shown that as the sampling period goes to zero unlike the standard autoregressive parameters the coefficients of this model converge to certain parameters that depend directly on the statistics of the continuous time process a levinson type algorithm for efficiently estimating the parameters of this model is derived numerical examples are given to show that when the sampling interval is small this algorithm is considerably less sensitivity to arithmetic roundoff errors than the levinson algorithm

on the influence of sampling and observation times on estimation of the bandwidth parameter of a gauss markov process the statistical problem of estimating the bandwidth parameter of a gauss markov gm process from a realization of fixed and finite duration t at selectable sampling interval spl delta is addressed in this paper as the observation time t is fixed and finite the variance of estimated autocorrelation and continuous time parameter does not vanish as spl delta approaches 0 this necessitates a second order taylor expansion in deriving the parameter estimator bias and variance the second order taylor expansion produces better bias and variance results than a first order one does the distribution of the estimator is also discussed according to the gradient change of the variance a key result is that three sample size regions which are termed finite large and very large corresponding to substantial gradual and very slight decrease in the variance of the parameter estimator respectively are quantified in terms of analysis bw the three regions are 23 35 35 55 and 55 spl infin db the characterization of the tradeoff between the variance decrease and sampling rate results in a practical guideline for choosing sampling rate these results are applied to the prediction problems of a time invariant gm process to show their value

fuzzy flowsort an integration of the flowsort method and fuzzy set theory for decision making on the basis of inaccurate quantitative data nowadays most real life decision problems can be modeled as sorting problems although it is difficult to quantitatively express the evaluation criteria precisely or precise values are inadequate to model the criteria for these situations multicriteria methods can be extended by using fuzzy theory thereby providing mathematical methods able to deal with decision processes in a fuzzy environment in this context we propose a sorting method called fuzzy flowsort f flowsort based on fuzzy set theory and flowsort which is a promethee based sorting method to demonstrate the usefulness and applicability of this new method an illustrative numerical example is presented the result confirms the potential and the applicability of associating fuzzy logic with the flowsort method for processing imprecise data comparisons are made between the results provided by fuzzy flowsort and flowsort and also between fuzzy flowsort and another algorithm based on flowsort that deals with the imprecision of data when they are defined by intervals in addition the association between the results obtained with the f flowsort and flowsort methods and promethee and f promethee methods is investigated

least squares parameter estimation of continuous time arx models from discrete time data when modeling a system from discrete time data a continuous time parameterization is desirable in some situations in a direct estimation approach the derivatives are approximated by appropriate differences for an arx model this lead to a linear regression the well known least squares method would then be very desirable since it can have good numerical properties and low computational burden in particular for fast or nonuniform sampling it is examined under what conditions a least squares fit for this linear regression will give adequate results for an arx model the choice of derivative approximation is crucial for this approach to be useful standard approximations like euler backward or euler forward cannot be used directly the precise conditions on the derivative approximation are derived and analyzed it is shown that if the highest order derivative is selected with care a least squares estimate will be accurate the theoretical analysis is complemented by some numerical examples which provide further insight into the choice of derivative approximation

promethee md 2t method for project selection abstract project selection is a real problem of multicriteria group decision making mcgdm where each decision maker expresses his her preferences depending on the nature of the alternatives and on his her own knowledge over them thus information as much quantitative as qualitative coexists the traditional methods of mcgdm developed for project selection usually discriminates in favour of quantitative information at the expense of qualitative information and this is due to the capability to integrate this first type of information inside their procedure in this article two new multicriteria 2 tuple group decision methods called preference ranking organisation method for enrichment evaluation multi decision maker 2 tuple i and ii promethee md 2t i and ii are presented they are able to integrate inside their procedure both quantitative and qualitative information in an uncertain context this has been performed by integrating a 2 tuple linguistic representation model dealing with non homogeneous and imprecise information data made up by valued intervals numerical and linguistic values into the aggregation operators of promethee methods although they have been developed for project selection problems these proposed methods can be applied to all kinds of decision making problems with heterogeneous and multigranular information therefore the application of these methods to real problems will lead to better results in mcgdm it offers to the decision makers simpler and wider application of the aggregation operators of the promethee multicriteria method without sacrificing any of its advantageous properties and by taking into account the imprecision of data a numerical simulation of the proposed method is carried out to show its possibilities

delta operator formulated discrete time approximations of continuous time systems given a continuous time system a technique to directly obtain an approximate delta operator formulated discrete time system spl delta system is presented for this purpose the analog of the well known boxer thaler integrators q forms applicable to shift operator formulated discrete time systems q systems are derived for spl delta systems next using these spl delta forms a method to obtain an approximate spl delta system of a given continuous time system is derived this algorithm is easily implementable in a computer with little computational burden it is shown that as sampling time decreases the spl delta system thus obtained yields the given continuous time system further verifying the close equivalence between this formulation and continuous time systems two examples illustrating advantages that may be gained by utilizing these spl delta forms in digitizing analog systems are also included

the fundamental group of manifolds of positive isotropic curvature and surface groups in this paper we study the topology of compact manifolds of positive isotropic curvature pic there are many examples of non simply connected compact manifolds with positive isotropic curvature we prove that the fundamental group of a compact riemannian manifold with pic of dimension 5 does not contain a subgroup isomorphic to the fundamental group of a compact riemann surface the proof uses stable minimal surface theory

estimates for the extinction time for the ricci flow on certain 3 manifolds and a question of perelman we show that the ricci flow becomes extinct in finite time on any riemannian 3 manifold without aspherical summands in this note we prove some bounds for the extinction time for the ricci flow on certain 3 manifolds our interest in this comes from a question that grisha perelman asked the first author at a dinner in new york city on april 25th of 2003 his question was what happens to the ricci flow on the 3 sphere when one starts with an arbitrary metric in particular does the flow become extinct in finite time he then went on to say that one of the difficulties in answering this is that he knew of no good way of constructing minimal surfaces for such a metric in general however there is a natural way of constructing such surfaces and that comes from the min max argument where the minimal of all maximal slices of sweep outs is a minimal surface see for instance 2 the idea is then to look at how the area of this min max surface changes under the flow geometrically the area measures a kind of width of the 3 manifold and as we will see for certain 3 manifolds those like the 3 sphere whose prime decomposition contains no aspherical factors the area becomes zero in finite time corresponding to that the solution becomes extinct in finite time moreover we will discuss a possible lower bound for how fast the area becomes zero very recently perelman posted a paper see 9 answering his original question about finite extinction time however even after the appearance of his paper then we still think that our slightly different approach may be of interest in part because it is in some ways geometrically more natural in part because it also indicates that lower bounds should hold and in part because it avoids using the curve shortening flow that he simultaneously with the ricci flow needed to invoke and thus our approach is in some respects technically easier let m 3 be a smooth closed orientable 3 manifold and let g t be a one parameter family of metrics on m evolving by the ricci flow so

a note on scale transformations in the promethee v method abstract as already noted by mavrotas et al 2006 the promethee v method for multi attribute analysis of portfolio problems will fail to include an item in a portfolio if it has a negative net flow with respect to other items although adding such an item might actually improve the entire portfolio however the model formulated by mavrotas et al introduces a bias in favor of large portfolios because the promethee v method is sensitive to scale transformations the present paper analyzes this effect and proposes a method to correct it

an efficient order recursive algorithm with a lattice structure for estimating continuous time ar process parameters abstract an order recursive algorithm is proposed to solve the normal equation in estimating continuous time ar process parameters the new algorithm requires o m 2 computations where m is the order of the ar process and therefore is computationally efficient this is similar to the levinson type algorithm of pham and le breton however the proposed algorithm has a new associated lattice structure and as a consequence a new stability test for continuous time systems not just ar processes by checking the reflection coefficients of the lattice this can be viewed as a continuous time analogy that is recursive in order of the well known discrete time version its discrete time approximation when sampled data are given and connections with other algorithms are also discussed

improved finite word length characteristics in digital control using delta operators this paper examines some of the consequences of finite word lengths in digital control it is shown that in many cases of practical importance the usual shift operator formulation is inferior to an alternative formulation which we designate the delta operator approach this latter approach is shown to give better coefficient representation and less roundoff noise in many cases we thus argue that the shift operator and its associated z transform can be replaced by delta operators and their associated transform which we designate a transform an added advantage of this approach is that discrete designs and transforms converge to their continuous time counterparts as the sampling rate is increased

delta levinson and schur type rls algorithms for adaptive signal processing in this paper we develop delta operator based levinson and schur type on line rls algorithms such algorithms have the potential of improved numerical behavior for ill conditioned input data these new algorithms are obtained by a unified transformation on the existing q operator based ones we first show that the conventional lattice structure can be naturally derived when the backward delta operator is used with this operator levinson and schur algorithms for the stationary stochastic model in q domain can easily be transformed into the delta domain then same transformation will be applied to the q domain on line levinson and schur type rls algorithms to obtain the delta domain counterparts their normalized versions as well as a systolic array architecture implementing the new delta schur rls algorithm are proposed extension to the equal length multichannel case is also given computer simulations show the expected numerical advantages of the delta based algorithms for fast sampled data in real time over the q domain ones under finite precision implementation

note a preference ranking organisation method the promethee method for multiple criteria decision making principles for a new family of outranking methods are given the main aim of the proposed promethee approach is to be as easily understood as possible by the decision maker it is based on extensions of the notion of criterion six possible extensions are considered these extensions can easily be identified by the decision maker because the parameters to be defined at most 2 have an economic significance a valued outranking graph is constructed by using a preference index two possibilities are considered to solve the ranking problem by using this valued graph promethee i provides a partial preorder and promethee ii a total preorder on the set of the possible actions

a delta least squares lattice algorithm for fast sampling most shift operator based adaptive algorithms exhibit poor numerical behavior when the input discrete time process is obtained from a continuous time process by fast sampling this includes the shift operator based least squares lattice algorithm we develop a delta least squares lattice algorithm this algorithm has a low computational complexity compared with the delta levinson rls algorithm and shows better numerical properties compared with the shift least squares lattice algorithm under fast sampling computer simulations show that the new algorithm also outperforms an existing delta least squares lattice algorithm

a delta mywe algorithm for parameter estimation of noisy ar processes we develop a delta operator based modified yule walker equation algorithm mywe for parameter estimation of a noisy autoregressive ar process the methodology in developing this new algorithm is similar to the previous works on pure ar processes computer simulation results are given to show the improvement of performance in estimating ar parameters in white noise over the q operator mywe algorithm

unified type non stationary lyapunov matrix equation simultaneous eigenvalue bounds abstract simultaneous eigenvalue bounds for the solution of the unified non stationary lyapunov matrix equation are presented when the solution becomes stationary the results reduce to bounds of the unified type algebraic lyapunov equation in the limiting cases the results reduce to bounds for the solution of the differential and difference lyapunov equations the bounds given in this paper are a generalization of some existing bounds obtained separately for the continuous and discrete type stationary and non stationary lyapunov equations

stability of classical solutions of two dimensional grassmannian models we show that the only finite action solutions of the two dimensional grassmannian model that are stable under small fluctuations are the anti instanton solutions

a qr type algorithm for fitting the delta ar model to autocorrelation windowed data a qr algorithm is developed to fit the delta autoregressive dar model of vijayan et al see ieee trans automat cont vol 36 p 314 1991 to autocorrelation windowed sampled data to obtain the dar model parameters one must solve a linear system in the matrix called q sub n unfortunately there is presently no way to obtain good estimates of q sub n the proposed qr type algorithm overcomes this problem by computing the dar model parameters without the need for estimating q sub n directly the qr algorithm proposed is a simple modification of the classical qr algorithm for the conventional ar model due to c p rialan and l l scharf 1986

on properties of information matrices of delta operator based adaptive signal processing algorithms in this paper we study the properties of information matrices of the difference operator or the so called delta spl delta operator based algorithms for adaptive signal processing we show that the conditioning of a transformed information matrix in the spl delta domain is always better than that of the original information matrix in the conventional q domain for ill conditioned problems the results obtained in this paper give an explanation of the advantages of using delta operator algorithms for adaptive signal processing that have been developed the analysis in this paper also helps to clarify the problem about the effect of spl delta in the delta operator algorithms and justify the use of sampling interval as spl delta in most cases when the ill conditioning is caused by fast sampling of continuous time systems

a structural view of asymptotic convergence speed of adaptive iir filtering algorithms i infinite precision implementation for pt i see ibid vol 41 no 4 p 1493 1517 1993 finite precision fp implementation is the ultimately inevitable reality of all adaptive filters including adaptive infinite impulse response iir filters this paper continues to examine the asymptotic convergence speed of adaptive iir filters of various structures and algorithms including the simple constant gain type and the newton type but under fp implementation a stochastic differential equation sde approach is used in the analysis such an approach not only greatly simplifies the fp analysis which is traditionally very involved algebraically but it also provides valuable information about the first order as well as the second order moments that the latter are not available using the ordinary differential equation ode approach the asymptotic convergence speed as well as the convergent values of the pertinent moments of fp errors are examined in terms of unknown system pole zero locations the adverse effects of lightly damped low frequency ldlf poles resulting from fast sampling on the local transient and convergent behavior of various structures and algorithms are analyzed and compared the new results agree with the existing ones when reduced to the finite impulse response fir case in particular the explosive behavior of pertinent error variances of newton type iir algorithms when the forgetting factor spl lambda 1 is also concluded computer simulation verifies the predicted theoretical results

existence of min max free boundary disks realizing the width of a manifold abstract we perform a replacement procedure in order to produce a free boundary minimal surface whose area achieves the min max value over all disk sweepouts of a manifold whose boundary lies in a submanifold our result is based on a proof of the convexity of the energy for free boundary harmonic maps and a generalization of colding minicozzi replacement procedure

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

fundamental groups of manifolds with positive isotropic curvature a central theme in riemannian geometry is understanding the relationships between the curvature and the topology of a riemannian manifold positive isotropic curvature pic is a natural and much studied curvature condition which includes manifolds with pointwise quarter pinched sectional curvatures and manifolds with positive curvature operator by the results of micallef and moore there is only one topological type of compact simply connected manifold with pic namely any such manifold must be homeomorphic to the sphere on the other hand there is a large class of nonsimply connected manifolds with pic an important open problem has been to understand the fundamental groups of manifolds with pic in this paper we prove a new result in this direction we show that the fundamental group of a compact manifold m n with pic n 5 does not contain a subgroup isomorphic to the techniques used involve minimal surfaces

minimal two spheres and the topology of manifolds with positive curvature on totally isotropic two planes there has been much interest among differential geometers in finding relationships between curvature and topology of riemannian manifolds for the most part efforts have been directed towards understanding the implications of positive or negative sectional curvature ricci curvature or scalar curvature but there are other hypotheses on the curvature which also deserve investigation in this article we will consider the topological implications of a new curvature assumption positive curvature on totally isotropic two planes and we will prove via the sacks uhlenbeck theory of minimal two spheres that a compact simply connected riemannian manifold of dimension at least four with positive curvature on totally isotropic two planes is homeomorphic to a sphere as corollaries we will obtain a proof via minimal two spheres for riemannian manifolds of dimension at least four of the berger klingenberg rauch toponogov sphere theorem strengthened to pointwise quarter pinching as well as a proof that every simply connected compact riemannian manifold with positive curvature operators is homeomorphic to a sphere let m be an n dimensional riemannian manifold with tangent space tpm at the point p e m recall that the curvature operator at p is the self adjoint

fuzzy group decision making for facility location selection the selection of a facility location among alternative locations is a multicriteria decision making problem including both quantitative and qualitative criteria the conventional approaches to facility location problem tend to be less effective in dealing with the imprecise or vagueness nature of the linguistic assessment under many situations the values of the qualitative criteria are often imprecisely defined for the decision makers the aim of the paper is to solve facility location problems using different solution approaches of fuzzy multi attribute group decision making the paper includes four different fuzzy multi attribute group decision making approaches the first one is a fuzzy model of group decision proposed by blin the second is the fuzzy synthetic evaluation the third is yager s weighted goals method and the last one is fuzzy analytic hierarchy process although four approaches have the same objective of selecting the best facility location alternative they come from different theoretic backgrounds and relate differently to the discipline of multi attribute group decision making these approaches are extended to select the best facility location alternative by taking into account quantitative and qualitative criteria a short comparative analysis among the approaches and a numeric example to each approach are given

the heat flow in nonlinear hodge theory we study the nonlinear hodge systemd 0 and 2 0 for an exterior form on a compact oriented riemannian manifold m where q is a given positive function the solutions are called harmonic forms they are the stationary points on cohomology classes of the functional e me 2 dm with e q q 2 the codifferential of a form is defined as 1 with 2 we evolve a given closed form 0 by the nonlinear heat flow system d for a time dependent exterior form x t on m this system is the differential of the normalized gradient flow u for e with 0 du under a technical assumption on the function 2 q q q we show that the nonlinear heat flow system d with initial condition 0 0 has a unique solution for all times which converges to a harmonic form in the cohomology class of 0 this yields a nonlinear hodge theorem that every cohomology class of m has a unique harmonic representative

on delta operator schur cohn zero location tests for fast sampling a stability test or more generally a zero location test algorithm similar to the well known schur cohn test is proposed when a complex polynomial formulated in the delta operator is given the real polynomial case falls out naturally as a special case the method used is a simple linear transformation based on the schur cohn test and the proposed algorithm is computationally efficient furthermore it is shown that as the sampling interval vanishes the new algorithm converges to a new continuous time test therefore providing a smooth transition from the shift operator based discrete time algorithm to the continuous time one furthermore a sensitivity analysis shows that the sensitivity of the new test in the delta operator remains finite with respect to parameter perturbation and converges to that of the continuous time one whereas that of the shift operator grows without bound as the sampling interval vanishes examples are given to show the clear numerical advantages over the traditional shift operator based schur cohn test in the case of fast sampling

compact manifolds with a little negative curvature on etend le theoreme de bochner et le theoreme de myers pour des p formes en donnant des obstructions topologiques pour des varietes admettant des metriques avec une petite courbure negative

painleve formulas of the limiting distributions for nonnull complex sample covariance matrices in a recent study of large non null sample covariance matrices a new sequence of functions gener alizing the gue tracy widom distribution of random matrix theory was obtained this paper derives painleve formulas of these functions and use them to prove that they are indeed distribution functions applications of these new distribution functions to last passage percolation queues in tandem and to tally asymmetric simple exclusion process are also discussed as a part of the proof a representation of orthogonal polynomials on the unit circle in terms of an operator on a discrete set is presented

rigidity of einstein manifolds with positive scalar curvature we prove that if m n n ge 4 is a compact einstein manifold whose normalized scalar curvature and sectional curvature satisfy pinching condition r 0 sigma n k max where sigma n in frac 1 4 1 is an explicit positive constant depending only on n then m must be isometric to a spherical space form moreover we prove that if an n ge 4 dimensional compact einstein manifold satisfies k min ge eta n r 0 where eta n in frac 1 4 1 is an explicit positive constant then m is locally symmetric it should be emphasized that the pinching constant eta n is optimal when n is even we then obtain some rigidity theorems for einstein manifolds under n 2 th ricci curvature and normalized scalar curvature pinching conditions finally we extend the theorems above to einstein submanifolds in a riemannian manifold and prove that if m is an n ge 4 dimensional compact einstein submanifold in the simply connected space form f n c with constant curvature c ge 0 and the normalized scalar curvature r 0 of m satisfies r 0 frac a n a n 4n 8 c h 2 where a n n 3 5n 2 8n and h is the mean curvature of m then m is isometric to a standard n sphere

singular root distribution problem for delta operator based real polynomials efficient zero location tests for the delta operator based polynomials have been a recent topic of interest these tests not only provide the needed efficient tests for the delta operator formulated systems control and signal processing problems which are numerically better behaved than the traditional shift operator based tests for fast sampling they also provide missing links between classical tests in the z domain and the s domain such as the schur cohn test sct and the routh test rt these will also be accomplished in this paper but for the singular cases specifically the recently developed singular case i schur cohn test by pal and kailath 1994 is modified and transformed into the delta domain as the sampling interval vanishes this new algorithm converges to an s domain singular case i test associated with the recently developed s domain sct singular case ii is also considered and the difference between the traditional approaches in the z domain and the s domain reconciled numerical examples are given to illustrate better numerical properties of the new test over pal kailath recursion for fast sampling

min max minimal hypersurfaces in non compact manifolds in this work we prove the existence of embedded closed minimal hypersurfaces in non compact manifolds containing a bounded open subset with smooth and strictly mean concave boundary and a natural behavior on the geometry at infinity for doing this we develop a modified min max theory for the area functional following almgren and pitts setting to produce minimal hypersurfaces with intersecting properties in particular we prove that any strictly mean concave region of a compact riemannian manifold without boundary intersects a closed minimal hypersurface

sigma model solitons and their moduli space metrics we discuss the supersymmetric model and its soliton solutions in 2 1 dimensions we classify supersymmetric maps and derive bogomolny bounds we also give the modified superalgebra and describe the metric on the parameter space of solitons

bumpy metrics and closed parametrized minimal surfaces in riemannian manifolds the purpose of this article is to study conformal harmonic maps f m where is a closed riemann surface and m is a compact riemannian manifold of dimension at least four such maps define parametrized minimal surfaces possibly with branch points we show that when the ambient manifold m is given a generic metric all prime closed parametrized minimal surfaces are free of branch points and are as morse nondegenerate as allowed by the group of automorphisms of e they are morse nondegenerate in the usual sense if has genus at least two lie on two dimensional nondegenerate critical submanifolds if s has genus one and on six dimensional nondegenerate critical submanifolds if has genus zero

delay replacement in direct form structures a class of high order low sensitivity digital filter structures is generated by means of a direct transformation of a high order direct form df structure the proposed structures have low coefficient dynamic range and exhibit low coefficient frequency response sensitivity and roundoff noise characteristics yet require only 3n multiplications per output sample as compared to 2n in the direct form case

an extension of the promethee method for decision making in fuzzy environment ranking of alternative energy exploitation projects abstract in the decision making process for the development of local resources a number of factors sometimes conflicting have to be considered multicriteria decision making procedures are widely applied today to ensure a rigorous analysis in this presentation a multicriteria method of ranking alternative projects promethee is extended to deal with fuzzy input data the method is applied for the evaluation and ranking of alternative energy exploitation schemes of a low temperature geothermal field it is demonstrated that this approach is more realistic and produces a more reliable ranking for problems such as the evaluation of alternative energy exploitation scenarios where the input data are not well defined

fuzzy outranking for environmental assessment case study iron and steel making industry recent years have seen a world wide change in the environmental policy towards integrated pollution prevention taking into account all environmental media consequently the environmental assessment of production techniques has to consider multiple criteria which cannot be aggregated to one single index the concepts of multi criteria decision making mcdm seem a suitable means in order to implement life cycle assessment lca into integrated decision processes the outranking methods as a special subgroup of mcdm methods are particularly suitable for integral decision making through the notion of weak preference and incomparability which better represent the real decision situation as demonstrated in this paper especially the outranking method promethee brings together flexibility and simplicity for the user and is therefore chosen for the enhancement towards the evaluation of fuzzy data on preferences scores and weights

estimation of continuous time ar process parameters from discrete time data the problem of estimating continuous time autoregressive process parameters from discrete time data is considered the basic approach used here is based on replacing the derivatives in the model by discrete time differences forming a linear regression and using the least squares method such a procedure is simple to apply computationally flexible and efficient and may have good numerical properties it is known however that all standard approximations of the highest order derivative such as repeated use of the delta operator gives a biased least squares estimate even as the sampling interval tends to zero some of our previous approaches to overcome this problem are reviewed then two new methods which avoid the shift in our previous results are presented one of them which is termed bias compensation is computationally very efficient finally the relationship of the above least squares approaches with an instrumental variable method is investigated comparative simulation results are also presented

efficient zero location tests for delta operator based polynomials two different kinds of stability tests or more generally zero location tests are proposed when a real polynomial formulated in the delta operator is given the method used is a simple linear transformation based on some known discrete time tests including the schur cohn test sct and the proposed algorithms are computationally efficient furthermore it is shown that as the sampling interval vanishes all new algorithms converge to their continuous time limits therefore providing smooth transitions from the shift operator based discrete time tests to the continuous time ones one of these limits is the classic routh test rt and the other is a new test closely related to the rt examples are given to demonstrate the tests which show clear numerical advantages over the traditional shift operator based ones such as the sct in case of fast sampling the significance of these new tests lies beyond the fact that they have provided efficient and reliable zero location tests directly in the delta domain these tests provide the missing links between the discrete time shift operator based tests and the continuous time ones as a consequence two separate and yet related families of zero location tests are established which include the well known rt and the sct

integrated framework for preference modeling and robustness analysis for outranking based multiple criteria sorting with electre and promethee a novel framework for preference modeling and robustness analysis is proposed we apply a sorting rule deriving from the semantic meaning of an outranking relation we ensure input output correspondence with respect to three sorting perspectives the generality of our framework is illustrated with its two specific implementations preference modeling can be simplified when using model instances providing precise assignments we introduce an integrated framework for preference modeling and robustness analysis in outranking based multiple criteria sorting the preference information supplied by the decision maker dm is composed of parts of desired recommendation and imprecise requirements that the delivered outcomes should satisfy its allowed forms are imprecise assignment examples desired class cardinalities and assignment based pairwise comparisons the exploitation of all instances of the outranking model compatible with these preferences results in three types of outcomes these raise robustness concerns in terms of the stability of a suggested assignment for each alternative an observed size of each class and a comparison between recommendation delivered for pairs of alternatives the correspondence between different types of inputs and outputs facilitates the dialogue with the dm and enhances her his confidence in the suggested recommendation while referring only to a semantic meaning of an outranking relation we present the procedures for translating the preference information into parameters of compatible outranking model instances and for deriving various kinds of sorting results then we implement this general framework in the context of outranking models specific for electre and promethee finally we show how preference modeling and robustness analysis can be performed and greatly simplified with a set of preference model instances providing precise assignments for the alternatives the framework proposed for this case is based on mixed integer linear programming milp being independent of the underlying model and method application of the approaches is demonstrated on the case of classifying polish research units into four quality classes