numerical analysis of differential operators on raw point clouds 3d acquisition devices acquire object surfaces with growing accuracy by obtaining 3d point samples of the surface this sampling depends on the geometry of the device and of the scanned object and is therefore very irregular many numerical schemes have been proposed for applying pdes to regularly meshed 3d data nevertheless for high precision applications it remains necessary to compute differential operators on raw point clouds prior to any meshing indeed differential operators such as the mean curvature or the principal curvatures provide crucial information for the orientation and meshing process itself this paper reviews a half dozen local schemes which have been proposed to compute discrete curvature like shape indicators on raw point clouds all of them will be analyzed mathematically in a unified framework by computing their asymptotic form when the size of the neighborhood tends to zero they are given in terms of the principal curvatures or of higher order intrinsic differential operators which in return characterize the discrete operators all considered local schemes are of two kinds either they perform a polynomial local regression or they compute directly local moments but the polynomial regression of order 1 is demonstrated to play a special role because its iterations yield a scale space this analysis is completed with numerical experiments comparing the accuracies of these schemes we demonstrate that this accuracy is enhanced for all operators by applying previously the scale space

paracompactness in l topological spaces in this paper a certain fuzzy paracompactness is presented by means of the concept of locally finite family of l fuzzy sets the concept of locally finite family can be used to characterize fuzzy countable compactness this fuzzy paracompactness is a natural generalization of lowen fuzzy compactness a fuzzy countably compact l set is fuzzy paracompact if and only if it is fuzzy compact a topological space x j is paracompact if and only if its induced space x j is fuzzy paracompact when ms l the fuzzy enhanced real line r l is fuzzy paracompact the product of a fuzzy compact set and a fuzzy paracompact set is fuzzy paracompact a fuzzy strongly t2 paracompact space is strongly s regular and strongly ws normal moreover a strongly s regular lindelof space is fuzzy paracompact

induced i l fuzzy topological spaces abstract in this paper we introduce the notion of induced i l fuzzy topological spaces by using the i l valued lower semicontinuous mappings and investigate some of their basic properties in particular we give a necessary and sufficient condition for an i l fuzzy topological space to be induced and prove that this kind of induced space preserves the cartesian product and the n compactness as well

characterizations of input to state stability for infinite dimensional systems we prove characterizations of input to state stability iss for a large class of infinite dimensional control systems including some classes of evolution equations over banach spaces time delay systems ordinary differential equations ode and switched systems these characterizations generalize well known criteria of iss proved by sontag and wang for ode systems for the special case of differential equations in banach spaces we prove even broader criteria for iss and apply these results to show that under some mild restrictions the existence of a noncoercive iss lyapunov functions implies iss we introduce the new notion of strong iss siss that is equivalent to iss in the ode case but is strictly weaker than iss in the infinite dimensional setting and prove several criteria for the siss property at the same time we show by means of counterexamples that many characterizations which are valid in the ode case are not true for general infinite dimensional systems

computation of surface geometry and segmentation using covariance techniques in this correspondence the application of covariance techniques to surface representation of 3 d objects is discussed and such ways of computing surface geometry are compared with traditional methods using differential geometry it is shown how the covariance method provides surface descriptors that are invariant to rigid motions without explicitly using surface parameterizations or derivatives analogous covariance operators for both the gauss and weingarten maps are defined and a range image segmentation technique is presented that labels pixels as jump or crease discontinuities or planar parabolic or curved region types

discrete dynamical systems in l topological spaces in this paper we investigate iteration of zadeh image operators and their discrete dynamical systems in l topological spaces some basic concepts such as limit set invariant set periodic point nonwandering point and recurrent point are discussed in weakly induced topological spaces we also study topological mixing topological transitivity and minimality for such dynamical systems while comparing with those corresponding ones in crisp spaces

compactness in l fuzzy topological spaces abstract a good definition of compactness in an l fuzzy topological space was introduced by warner and mclean 1993 in this paper we give an extension of this notion to arbitrary l fuzzy subsets and study its properties

a new definition of fuzzy compactness in this paper a new definition of fuzzy compactness is presented in l topological spaces when l is a complete demorgan algebra this definition does not rely on the structure of the basis lattice l and no distributivity in l is required the intersection of a fuzzy compact l set and a closed l set is fuzzy compact the continuous image of a fuzzy compact l set is fuzzy compact if the set of all prime elements of l is order generating then the alexander subbase theorem is true when l is a completely distributive demorgan algebra it is equivalent to lowen s fuzzy compactness and in this case its many characterizations are presented by means of open l sets and closed l sets

on stabilizability and sampling for infinite dimensional systems some questions either motivated by or related to time sampling regarding the stabilizability of infinite dimensional or distributed parameter systems are considered in particular these include the characteristics of those systems which are finite rank stabilizable and the preservation of stabilizability under sampling a pathological class of systems which when sampled may be rendered unstabilizable by arbitrarily small perturbations in the sampling rate is identified the approach taken in establishing these results is based upon a spectral decomposition of the infinitesimal generator of the underlying open loop semigroup the results obtained apply to control systems with dynamics described by broad classes of partial and functional differential equations that arise frequently in applications

a note on compactness in a fuzzy setting abstract the concept of filter basis in a fuzzy setting is defined and investigated fuzzy filter bases are then used to introduce the notion of compactness in fuzzy setting the expected basic properties of compactness are explored

l fuzzy topological groups abstract in this paper the theory is applied of the q neighborhood system of a fuzzy point which was introduced in 3 and the fuzzy topological groups and their subgroups normal subgroups and quotients are discussed then some results introduced in 1 and 7 are improved

a new fuzzy compactness defined by fuzzy nets compactness is one of the most important notions in topology and is thoroughly investigated in general topology but it seems that the research about this notion in the area of fuzzy topology is not so effective as in general topology in fact it would seem that there was not even a good definition of compactness in this area until recently indeed soon after the famous article written by zadeh 8 was published chang 1 introduced the notion of fuzzy topological spaces and at the same time a certain fuzzy compactness was given from then on a series of different notions of fuzzy compactness have been discussed 2 3 71 and in 5 they were compared in detail but it seems unsatisfactory that all these fuzzy compactness ideas are defined for the whole fuzzy topological space but not for an arbitrary fuzzy subset therefore they are far from the crisp compactness for example it is impossible to discuss the hereditary property with respect to closed subsets of fuzzy compactness in 1977 pu and liu introduced the notion of fuzzy nets and a new concept of so called q neighborhood was given which could reflect the features of neighborhood structure in fuzzy topological spaces and by this new neighborhood structure the moore smith convergence theory was established spendidly 6 it furnishes us a basic tool to investigate the fuzzy compactness in a more general way to investigate the compactness of arbitrary fuzzy subsets in this paper a new fuzzy compactness defined by fuzzy nets we shall call it n compactness is given but we introduce the notion of r neighborhood see section 2 instead of qneighborhood to establish the moore smith convergence theory for it is perhaps more convennient to use n compactness possesses the following properties 1 n compactness is defined for arbitrary fuzzy subsets 2 for n compactness the hereditary property with respect to closed subsets holds 3 n compactness is a good extension 5 4 the continuous images of ncompact sets are n compact 5 for n compactness the tychonoff product theorem holds 6 if an n compact fuzzy topological space is t2 6 then it will satisfy a stronger separation axiom which will be called t4 in this paper 1 0022 247x 83 3 00

the approximation power of moving least squares a general method for near best approximations to functionals on r d using scattered data information is discussed the method is actually the moving least squares method presented by the backus gilbert approach it is shown that the method works very well for interpolation smoothing and derivatives approximations for the interpolation problem this approach gives mclain s method the method is near best in the sense that the local error is bounded in terms of the error of a local best polynomial approximation the interpolation approximation in r d is shown to be a c function and an approximation order result is proven for quasi uniform sets of data points

infinite dimensional lur e systems input to state stability and convergence properties we consider forced lur e systems in which the linear dynamic component is an infinite dimensional well posed system numerous physically motivated delay and partial differential equations are know

a new approach to fuzzy topological spaces and various fuzzy topological notions defined by nets n fuzzy spaces introduced by the authors are further investigated various fuzzy topological motions such as fuzzy local compactness functions with closed fuzzy graph fuzzy subcontinuity inverse fuzzy subcontinuity etc are studied in the light of n i these notions are found to be more coherent in n i than in the chang s category

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

stability of higher order discrete time lur e systems abstract we consider discrete time lur e systems obtained by applying nonlinear feedback to a system of higher order difference equations arma models the arma model relates the inputs and outputs of the linear system and does not involve any internal or state variables a stability theory subsuming results of circle criterion type is developed including criteria for input to output stability a concept which is very much reminiscent of input to state stability

robust estimation of adaptive tensors of curvature by tensor voting although curvature estimation from a given mesh or regularly sampled point set is a well studied problem it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise such input is ubiquitous in computer vision in this paper we propose a three pass tensor voting algorithm to robustly estimate curvature tensors from which accurate principal curvatures and directions can be calculated our quantitative estimation is an improvement over the previous two pass algorithm where only qualitative curvature estimation sign of gaussian curvature is performed to overcome misalignment errors our improved method automatically corrects input point locations at subvoxel precision which also rejects outliers that are uncorrectable to adapt to different scales locally we define the radiushit of a curvature tensor to quantify estimation accuracy and applicability our curvature estimation algorithm has been proven with detailed quantitative experiments performing better in a variety of standard error metrics percentage error in curvature magnitudes absolute angle difference in curvature direction in the presence of a large amount of misalignment noise

integral control of linear systems with actuator nonlinearities lower bounds for the maximal regulating gain closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller is known to ensure asymptotic tracking of constant reference signals provided that 1 the steady state gain of the linear part of the plant is positive 2 the positive integrator gain is sufficiently small and 3 the reference value is feasible in a very natural sense here lower bounds are derived for the maximal regulating gain for various special cases including systems with nonovershooting step response and second order systems with a time delay in the input or output the lower bounds are given in terms of open loop frequency step response data and the lipschitz constant of the nonlinearity and are hence readily obtainable

monotonicity methods for input to state stability of nonlinear parabolic pdes with boundary disturbances we introduce a monotonicity based method for studying input to state stability iss of nonlinear parabolic equations with boundary inputs we first show that a monotone control system is iss if an

some properties of fuzzy topological groups abstract it is well known that if s is a subgroup of a topological group g so is s if s is a normal subgroup of g so is s and if u is the system of all neighborhoods of the identity e in a topological group x then b bu ub for any subset b of x we extend these to the corresponding theorems in fuzzy topological groups that is based on the q neighborhood system of fuzzy points and the structure of a fuzzy topological group defined by ma and yu fuzzy sets and systems 12 1984 289 we characterize some basic properties of fuzzy topological groups show that if h is a fuzzy subgroup of a fuzzy topological group x and h h h h so is h and if h is a fuzzy normal subgroup of x and h h h h so is h and show that for any fuzzy subset a of a fuzzy topological group if x p aw wa and 0 5 then x p a and if x p a and p q then aw x wa x 0 where w is the system of all q neighborhoods of the identity e q

stability of nonnegative lur e systems a stability instability trichotomy for a class of nonnegative continuous time lur e systems is derived asymptotic exponential and input to state stability concepts are considered the presented trichotomy rests on perron frobenius theory absolute stability theory and recent input to state stability results for lur e systems applications of the results derived arise in various fields including density dependent population dynamics and two examples are discussed in detail

semi global incremental input to state stability of discrete time lur e systems abstract we present sufficient conditions for semi global incremental input to state stability of a class of forced discrete time lur e systems the results derived are reminiscent of well known absolute stability criteria such as the small gain theorem and the circle criterion we derive a natural sufficient condition which guarantees that asymptotically almost periodic inputs generate asymptotically almost periodic state trajectories as a corollary we obtain sufficient conditions for the converging input converging state property to hold

minimal hausdorff l fuzzy topological spaces abstract in this paper the author introduced the concept of minimal hausdorff l fuzzy topological spaces investigated basic properties of it by means of fuzzy ideals and fuzzy nets and compared it with the concepts of compactness and h closedness

relations between the good definitions of compactness in l fuzzy topological spaces abstract in this paper we state the different definitions of compactness in l fuzzy topological spaces where l is a completely distributive lattice we obtain other characterizations of some of these notions and study them with respect to their goodness finally we establish the inter relations between the compactnesses which are good extensions we also obtain an improvement of our theorem 7 6 in 3

preserving fuzzy subgroups and indistinguishability operators abstract in this paper we study the class of all fuzzy subgroups defined with respect to a given t norm on a fixed group we find necessary and sufficient conditions over two t norms to guarantee that the class of all fuzzy subgroups induced by the first t norm is contained in the class of all fuzzy subgroups with respect to by the second one we characterize the functions that transform fuzzy subgroups into fuzzy subgroups the close relationship between indistinguishability operators and fuzzy subgroups allows us to obtain similar results for some classes of indistinguishability operators

paracompactness in fuzzy topological spaces abstract in this paper we introduce two kinds of fuzzy paracompactnesses which are defined on general fuzzy subsets each of them is a good extension of crisp paracompactness they are all hereditary with respect to closed subsets and take n compactness and some other compactnesses in fuzzy topological spaces as special cases of them furthermore in a class of spaces so called weakly induced spaces which connects crisp spaces with fuzzy spaces both a fuzzy regular lindeloff property and a fuzzy pseudo metric property imply these two kinds of paracompactnesses

input to state stability of discrete time lur e systems an input to state stability theory which subsumes results of circle criterion type is developed in the context of discrete time lur e systems the approach developed is inspired by the complexified aizerman conjecture

fuzzy semiprime ideals in semigroups abstract in this paper we shall introduce the notion of fuzzy semiprimality in a semigroup which is an extension of semiprimality in it and characterize a semigroup that is a semilattice of simple semigroups in terms of fuzzy semiprimality

o convergence of fuzzy nets and its applications abstract in this paper an o convergence theory of fuzzy nets is built in l topological spaces by means of neighborhoods of fuzzy points it has many nice properties it can be used to characterize the closed set open set t 2 separation axiom and fuzzy compactness

fuzzy subcontinuity inverse fuzzy subcontinuity and a new category of fuzzy topological spaces the notions of subcontinuity and inverse subcontinuity are extended to the fuzzy setting adopting fuzzy net theoretic approach various properties of fuzzy subcontinuous and inversely fuzzy subcontinuous mappings are studied a category of fuzzy topological spaces is constructed canonical example is constructed by using fuzzy translation of fuzzy numbers introduced by rodabaugh to show that fuzzy subcontinuity does not imply kfuzzy continuity in the process n compactness is characterized and fuzzy unit interval is shown to be n compact also a direct proof is provided showing that fuzzy addition of fuzzy numbers is fuzzy continuous

input to state stability of differential inclusions with applications to hysteretic and quantized feedback systems input to state stability iss of a class of differential inclusions is proved every system in the class is of lur e type a feedback interconnection of a linear system and a set valued nonlinearity applications of the iss results in the context of feedback interconnections with a hysteresis operator or a quantization operator in the feedback path are developed

on fuzzy right topological semigroups on etend des resultats de foster sur les images homomorphes et les images inverses aux semigroupes topologiques a droite flous

on the direct product of fuzzy topological groups we discuss the following problems the direct product group of a finite family of fuzzy topological groups and the decomposition of the direct product of a fuzzy topological group our results are generalizations of the corresponding results in crisp topological groups

infinite dimensional input to state stability and orlicz spaces in this work the relation between input to state stability and integral input to state stability is studied for linear infinite dimensional systems with an unbounded control operator although a special focus is laid on the case l infty general function spaces are considered for the inputs we show that integral input to state stability can be characterized in terms of input to state stability with respect to orlicz spaces since we consider linear systems the results can also be formulated in terms of admissibility for parabolic diagonal systems with scalar inputs both stability notions with respect to l infty are equivalent

on the compactness of l fuzzy topological groups this paper discusses the compactness of l fuzzy topological groups and the results relative to the compactness of fuzzy topological groups which appeared in fuzzy sets and systems 23 1987 281 288 are improved and generalized also the induced l fuzzy topological groups as an important kind of example of l fuzzy topological groups are studied

a set of new separation axioms in l fuzzy topological spaces in this paper a set of new separation axioms in l fuzzy topological spaces are defined and studied we give several characterizations of these separation axioms and discuss certain relationships among them moreover some of their basic properties are also examined

stability and convergence properties of forced infinite dimensional discrete time lur e systems incremental stability and convergence properties for forced infinite dimensional discrete time lur e systems are addressed lur e systems have a linear and nonlinear component and arise as the fe

stability of infinite dimensional sampled data systems suppose that a static state feedback stabilizes a continuous time linear infinite dimensional control system we consider the following question if we construct a sampled data controller by applying an idealized sample and hold process to a continuous time stabilizing feedback will this sampled data controller stabilize the system for all sufficiently small sampling times here the state space x and the control space u are hilbert spaces the system is of the form x t ax t bu t where a is the generator of a strongly continuous semigroup on x and the continuous time feedback is u t fx t the answer to the above question is known to be yes if x and u are finite dimensional spaces in the infinite dimensional case if f is not compact then it is easy to find counterexamples therefore we restrict attention to compact feedback we show that the answer to the above question is yes if b is a bounded operator from u into x moreover if b is unbounded we show that the answer yes remains correct provided that the semigroup generated by a is analytic we use the theory developed for static state feedback to obtain analogous results for dynamic output feedback control

generalized sampled data stabilization of well posed linear infinite dimensional systems we consider well posed linear infinite dimensional systems the outputs of which are sampled in a generalized sense using a suitable weighting function under certain natural assump tions on the system the weighting function and the sampling period we show that there exists a generalized hold function such that unity sampled data feedback renders the closed loop system exponentially stable in the state space sense as well as l 2 stable in the input output sense to illustrate our main result we describe an application to a structurally damped euler bernoulli beam

stabilization of well posed infinite dimensional systems by dynamic sampled data feedback it is shown that a set of six natural conditions is necessary and sufficient for the existence of a finite dimensional stabilizing sampled data controller for a well posed infinite dimensional system the underlying stability concept for the sampled data system is reminiscent of the notion of input to state stability from nonlinear control theory

on some gross misunderstandings about the theory of topological molecular lattices abstract some gross misunderstandings have arisen since the theory of topological molecular lattices briefly tmls was presented wang 1989 1992 certain scholars think that there is a correspondence between tmls and classical spaces and they could obtain the results in the theory of tmls hence fuzzy topology by simply translating the corresponding results in classical topology the aim of this paper is to clear out such misunderstandings

brief input to state stability for a class of lurie systems we analyze input to state stability iss for the feedback interconnection of a linear block and a nonlinear element this study is of importance for establishing robustness against actuator nonlinearities and disturbances in the absolute stability framework we prove iss from a positive real property of the linear block by restricting the sector nonlinearity to grow unbounded as its argument tends to infinity when this growth condition is violated examples show that the iss property is lost the result is used to give a simple proof of boundedness for negative resistance oscillators such as the van der pol oscillator in a separate application we relax the minimum phase assumption of an earlier boundedness result for systems with nonlinearities that grow faster than linear