the structure of pan addition operator with pre determined pan multiplication based on the structure of general pan multiplication operators and the theory of first order linear partial differential equations we study the structure of pan addition operators with pre determined pan multiplication operators at first we describe the structure of pan addition operators under the ordinary multiplication then with this structure in place we derive the general representation for the structure of pan addition operators

fundamental limitations in passive time delay estimation part i narrow band systems time delay estimation of a noise like random signal observed at two or more spatially separated receivers is a problem of considerable practical interest in passive radar sonar applications a new method is presented to analyze the mean square error performance of delay estimation schemes based on a modified improved version of the ziv zakai lower bound zzlb this technique is shown to yield the tightest results on the attainable system performance for a wide range of signal to noise ratio snr conditions for delay estimation using narrow band ambiguity prone signals the fundamental result of this study is illustrated in fig 3 the entire domain of snr is divided into several disjoint segments indicating several distinct modes of operation if the available snr does not exceed snr 1 signal observations from the receiver outputs are completely dominated by noise thus essentially useless for the delay estimation as a result the attainable mean square error bar epsilon 2 is bounded only by the a priori parameter domain if snr 1 2 the modified zzlb coincides with the barankin bound in this regime differential delay observations are subject to ambiguities if snr snr 3 the modified zzlb coincides with the cramer rao lower bound indicating that the ambiguity in the differential delay estimation can essentially be resolved the transition from the ambiguity dominated mode of operation to the ambiguity free mode of operation starts at snr 2 and ends at snr 3 this is the threshold phenomenon in time delay estimation the various deflection points snr i and the various segments of the bound fig 3 are given as functions of such important system parameters as time bandwidth product wt signal bandwidth to center frequency ratio w 0 and the number of half wavelengths of the signal center frequency contained in the spacing between receivers with this information the composite bound illustrated in fig 3 provides the most complete characterization of the attainable system performance under any prespecified snr conditions

an accurate algebraic solution for moving source location using tdoa and fdoa measurements this paper proposes an algebraic solution for the position and velocity of a moving source using the time differences of arrival tdoas and frequency differences of arrival fdoas of a signal received at a number of receivers the method employs several weighted least squares minimizations only and does not require initial solution guesses to obtain a location estimate it does not have the initialization and local convergence problem as in the conventional linear iterative method the estimated accuracy of the source position and velocity is shown to achieve the crame spl acute r rao lower bound for gaussian tdoa and fdoa noise at moderate noise level before the thresholding effect occurs simulations are included to examine the algorithm s performance and compare it with the taylor series iterative method

several inequalities for the pan integral several inequalities for the pan integral are investigated it is shown that the chebyshev inequality holds for an arbitrary subadditive measure if and only if the integrands f g are comonotone thus we provide a new characterization for nonnegative comonotone functions it is also shown that the holder and minkowski inequalities for the pan integral hold if the monotone measure is subadditive since the pan integral coincides with the concave integral when is subadditive our results can also be applied to the concave integral

pan operations structure with non idempotent pan addition abstract the structure of pan operations involving a pan addition and a pan multiplication which form a commutative isotonic semiring as defined by wang and klir are discussed based on semi group theory special properties of identity element and the idempotent of pan addition and pan multiplication the case of a non idempotent pan addition are studied our results correct a theorem of mesiar and rybarik moreover a sufficient and necessary condition for the continuity of a pan operator defined on 0 is presented our conclusions are expected to result in the introduction of the concept of general fuzzy integral

explicitly stable fundamental measure theory models for classical density functional theory the derivation of the state of the art tensorial versions of fundamental measure theory a form of classical density functional theory for hard spheres is reexamined in the light of the recently introduced concept of global stability of the density functional based on its boundedness lutsko and lam phys rev e 98 012604 2018 2470 004510 1103 physreve 98 012604 it is shown that within the present paradigm explicit stability of the functional can be achieved only at the cost of giving up accuracy at low densities it is argued that this is an acceptable trade off since the main value of dft lies in the study of dense systems explicit calculations for a wide variety of systems show that a proposed explicitly stable functional is competitive in all ways with the popular white bear models while sharing some of their weaknesses when applied to non close packed solids

the nonuniform hard rod fluid revisited the statistical mechanics of the one dimensional nonuniform pure hard core fluid is formulated in the spirit of the reiss frisch lebowitz rfl scaled particle theory by emphasizing the importance of the core dependence a more intuitive and simpler derivation can be given the wiener hopf type construction of the pair direct correlation function is formulated via the dyson variational method of inverse scattering theory which is compared with the particle hole theory the new approach allows us to lift the global free energy functional into a larger space where all the symmetries become apparent

the inverse problem in classical statistical mechanics we address the problem of whether there exists an external potential corresponding to a given equilibrium single particle density of a classical system results are established for both the canonical and grand canonical distributions it is shown that for essentially all systems without hard core interactions there is a unique external potential which produces any given density the external potential is shown to be a continuous function of the density and in certain cases it is shown to be differentiable as a consequence of the differentiability of the inverse map which is established without reference to the hard core structure in the grand canonical ensemble we prove the existence of the ornstein zernike direct correlation function a set of necessary but not sufficient conditions for the solution of the inverse problem in systems with hard core interactions is derived

lower bounds on worst case probability of large error for two channel time delay estimation a lower bound on the worst case probability of large error for two channel time delay estimation using random signals is developed the bound is based on the minimum probability of error m ary hypothesis test using a maximum likelihood estimator mle the bound can only be evaluated approximately however it can be determined arbitrarily well via simulation if the mle can be instrumented the bound is evaluated in detail for uniform lowpass signal and noise spectra and large bandwidth time product it is then compared with another lower bound based on a binary hypothesis test with computer simulation results for an approximate mle instrumentation and with an upper bound established via computer simulation for a correlator for a uniform lowpass spectrum the m ary bound is shown to be very nearly a greatest lower bound over the full range of input signal to noise ratio further the correlator is shown to be very nearly an optimal instrumentation in the sense of reaching the minimum probability of large error

capon algorithm mean squared error threshold snr prediction and probability of resolution below a specific threshold signal to noise ratio snr the mean squared error mse performance of signal parameter estimates derived from the capon algorithm degrades swiftly prediction of this threshold snr point is of practical significance for robust system design and analysis the exact pairwise error probabilities for the capon and bartlett algorithm derived herein are given by simple finite sums involving no numerical integration include finite sample effects and hold for an arbitrary colored data covariance via an adaptation of an interval error based method these error probabilities along with the local error mse predictions of vaidyanathan and buckley facilitate accurate prediction of the capon threshold region mse performance for an arbitrary number of well separated sources circumventing the need for numerous monte carlo simulations a large sample closed form approximation for the capon threshold snr is provided for uniform linear arrays a new exact two point measure of the probability of resolution for the capon algorithm that includes the deleterious effects of signal model mismatch is a serendipitous byproduct of this analysis that predicts the snrs required for closely spaced sources to be mutually resolvable by the capon algorithm last a general strategy is provided for obtaining accurate mse predictions that account for signal model mismatch

fundamental measure density functional theory for nonadditive hard core mixtures the one dimensional case we treat a one dimensional binary mixture of hard core particles that possess nonadditive diameters for this model a density functional theory is constructed following similar principles as an earlier extension of rosenfeld s fundamental measure theory to three dimensional nonadditive hard sphere mixtures the theory applies to arbitrary positive and moderate negative nonadditivity and reduces to percus exact functional in the additive case bulk direct correlation functions are obtained as functional derivatives of the excess free energy functional results for the partial pair correlation functions in bulk as calculated via the ornstein zernike route and using the direct correlation functions as input show very good agreement with results from our monte carlo computer simulations of the mixture

delay estimation using narrow band processes array processing of narrow band gaussian signals is studied with emphasis on delay estimation the barankin bound is used to examine the effect of ambiguity on mean square measurement error when the bound is plotted as a function of signal to noise ratio one observes a distinct threshold above the critical signal to noise ratio the lower bound on mean square error is given by the cramer rao inequality which is approached by the barankin inequality under these conditions below the threshold the barankin bound can exceed the cramer rao bound by large factors the relative magnitude of the bounds in that region depends critically on the ratio of signal center frequency to signal bandwidth

composite bound on the attainable mean square error in passive time delay estimation from ambiguity prone signals corresp the location of a radiating source can be determined by measuring the relative time delay of its signal wavefront to several spatially separated receivers a new technique is presented to investigate the performance of time delay measurement schemes based on a modified version of the ziv zakai lower bound this technique is shown to yield a tight bound on the attainable mean square measurement error for any prespecified signal to noise ratio conditions

connective generators for archimedian triangular operators abstract triangular norms form the kernel of fuzzy logic and fuzzy systems here in this paper my main motivation is to provide three new connective generators that can generate different classes of fuzzy connectives in this study i have tried to show that there are many possible fuzzy connective generators that can be associative and yet monotonic the study contemplates mainly on three different connective generators these generators use simple monotonic and continuous functions that are both bounded in the domain 0 1 and the range 0 1

deriving the rosenfeld functional from the virial expansion in this article we replace the semiheuristic derivation of the rosenfeld functional of hard convex particles with the systematic calculation of mayer clusters it is shown that each cluster integral further decomposes into diagrams of intersection patterns that we classify by their loop number this extends the virial expansion of the free energy by an expansion in the loop order with the rosenfeld functional as its leading contribution rosenfeld s weight functions then follow from the derivation of the intersection probability by generalizing the equation of blaschke santalo and chern it is found that the 0 loop order can be derived exactly and reproduces the rosenfeld functional we further discuss the influence of particle dimensions topologies and geometries on the mathematical structure of the calculation

extended ziv zakai lower bound for vector parameter estimation the bayesian ziv zakai bound on the mean square error mse in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than mse the extended bound is evaluated for some representative problems in time delay and bearing estimation the resulting bounds have simple closed form expressions and closely predict the simulated performance of the maximum likelihood estimator in all regions of operation

density functional theory for nearest neighbor exclusion lattice gases in two and three dimensions to speak about fundamental measure theory obliges us to mention dimensional crossover this feature inherent to the systems themselves was incorporated in the theory almost from the beginning although at first it was thought to be a consistency check for the theory it rapidly became its fundamental pillar thus becoming the only density functional theory which possesses such a property it is straightforward that dimensional crossover connects for instance the parallel hard cube system three dimensional with that of squares two dimensional and rods one dimensional we show here that there are many more connections which can be established in this way through them we deduce from the functional for parallel hard hyper cubes in the simple hyper cubic lattice the corresponding functionals for the nearest neighbor exclusion lattice gases in the square triangular simple cubic face centered cubic and body centered cubic lattices as an application the bulk phase diagram for all these systems is obtained

dimensional crossover of the fundamental measure functional for parallel hard cubes we present a regularization of the recently proposed fundamental measure functional for a mixture of parallel hard cubes the regularized functional is shown to have correct dimensional crossovers to any smaller dimension thus allowing its use to study highly inhomogeneous phases such as the solid phase furthermore it is shown how the functional of the slightly more general model of parallel hard parallelepipeds can be obtained using the zero dimensional functional as a generating functional extensions to the multicomponent system a restricted orientation model and mixtures or prallel hard cylinders are also given s0031 9007 97 03105 0

density functional theory for fluids in porous media as models for substances adsorbed within amorphous solid matrices we consider mixtures of spheres with either hard or ideal interactions where several matrix components are quenched and the remaining adsorbate components are equilibrated we propose a density functional theory based on the exact zero dimensional limit which treats both matrix and adsorbate components on the level of the respective one body density profiles as a test we calculate pair correlation functions for hard spheres adsorbed in either a hard sphere or an ideal sphere matrix and find good agreement with our computer simulation results

closed loop least mean square time delay estimator an lms closed loop time delay estimator is presented it uses the error between two samples of the incoming signal the difference between the delayed signal and the reference signal passed through a known delay as a performance index for the estimator the lms algorithm adaptively controls the delay so as to minimize the mean square of this error the controlled delay is implemented using surface acoustic wave devices certain design conditions are applied resulting in a unique minimum for the performance surface it is shown that the proposed estimator is unbiased and has a small variance if the input signal occupies most of the system bandwidth in fact the variance depends on the input noise power and the generalized noise to signal power ratio r n 0 r s 0 as well as on the loop gain the analysis performed also gives a bound on the loop gain required for convergence of the estimator and predicts its rate of convergence computer simulation results show good agreement with the theory

deriving fundamental measure theory from the virial series consistency with the zero dimensional limit fundamental measure theory fmt for hard particles has great potential for predicting the phase behavior of colloidal and nanometric shapes the modern versions of fmt are usually derived from the zero dimensional limit a system of at most one particle confined in a collection of cavities in the limit that all cavities shrink to the size of the particle in phys rev e 85 041150 2012 a derivation from an approximated and resummed virial expansion was presented whose result was not fully consistent with the fmt from the zero dimensional limit here we improve on this derivation and obtain exactly the same fmt functional as was obtained earlier from the zero dimensional limit as a result further improvements of fmt based on the virial expansion can now be formulated some of which we suggest in the outlook

a note on the idempotent functions with respect to pseudo convolution a general notion of pseudo convolution based on pseudo arithmetical operations is recalled the idempotents with respect to pseudo convolutions are investigated complete characterization of idempotents with respect to pseudo convolutions based on the generalized sugeno integral is given several other cases based on the idempotent pseudo additions are studied

exact density functionals in one dimension we propose a new and general method for deriving exact density functionals in one dimension for lattice gases with finite range pairwise interactions corresponding continuum functionals are derived by applying a proper limiting procedure the method is based on a generalized markov property which allows us to set up a rather transparent scheme that covers all previously known exact functionals for one dimensional lattice gas or fluid systems implications for a systematic construction of approximate density functionals in higher dimensions are pointed out

cluster density functional theory for lattice models based on the theory of mobius functions rosenfeld s fundamental measure theory for lattice models is given a rigorous formulation in terms of the theory of mobius functions of partially ordered sets the free energy density functional is expressed as an expansion in a finite set of lattice clusters this set is endowed with a partial order so that the coefficients of the cluster expansion are connected to its mobius function because of this it is rigorously proven that a unique such expansion exists for any lattice model the low density analysis of the free energy functional motivates a redefinition of the basic clusters zero dimensional cavities which guarantees a correct zero density limit of the pair and triplet direct correlation functions this new definition extends rosenfeld s theory to lattice models with any kind of short range interaction repulsive or attractive hard or soft one or multicomponent finally a proof is given that these functionals have a consistent dimensional reduction i e the functional for dimension d can be obtained from that for dimension d d d if the latter is evaluated at a density profile confined to a d dimensional subset

a unified approach to closed loop time delay estimation systems two generalized configurations for a closed loop delay estimation system cldes are discussed the indirect correlation ic configuration is compared to the conventional cldes the direct correlation dc configuration it is shown that the baseband equivalents of the two configurations differ only by the input noise however the noise power in the ic configuration is far less than that of the dc configuration using the known procedure for calculation of the variance of the time delay estimator it is shown that the two configurations result in the same variance however this procedure is known to be incorrect since for the direct correlation configuration which is known to have an intrinsic noise that persists even when the input signals are ideal the variance is nonzero for zero input signal to noise ratio snr thus another procedure is suggested for variance calculation that overcomes this problem it is shown using this expression that the variance of the time delay estimator is smaller for the ic configuration provided the input snr is not less than 0 db

two hard spheres in a spherical pore exact analytic results in two and three dimensions the partition function and the one and two body distribution functions are evaluated for two hard spheres with different sizes constrained into a spherical pore the equivalent problem for hard disks is addressed too we establish a relation valid for any dimension between these partition functions second virial coefficient for inhomogeneous systems in a spherical pore and third virial coefficients for polydisperse hard spheres mixtures using the established relation we were able to evaluate the cluster integral b2 v related with the second virial coefficient for the hard disc system into a circular pore finally we analyse the behaviour of the obtained expressions near the maximum density

a new generalized cross correlator a new generalized cross correlator gcc for the passive time delay estimation problem is presented the interpretation of this gcc is that of estimating the cross correlation function by cross correlating the least mean square estimates of the signal component in each of the observed waveforms the implementation is simply a gcc with the weighting filter equal to the magnitude coherency squared numerical evaluation of the performance of this processor and a robust version indicate that they compare favorably to some of the well known gcc procedures

density functional for the widom rowlinson model we present a density functional theory for the m component widom rowlinson model for a mixture of spherical particles where the unlike species interact with a hard core potential and the interactions between like species vanish the functional is exact for small densities and in the zero dimensional limit it predicts the fluid structure in good agreement with simulations and yields a continuous demixing phase transition for m 2 in the limit of large m the widom rowlinson model reduces to effective hard spheres in the mixed phase and the asakura oosawa colloid ideal polymer model in the demixed phase within the present theory both cases are captured correctly for intermediate m we find a first order demixing phase transition with a rapidly broadening density discontinuity upon increasing m

on the validity of the inverse conjecture in classical density functional theory it is shown that the basic assumptions of the classical density functional approach are rigorously correct forh stable systems in the grand canonical ensemble moreover it is established that the set of all single particle densities is convex these results are derived by providing necessary and sufficient conditions for the solution of the classical inverse problem for single particle densities analogous results are obtained for the solution of the higher order correlation inverse problem and the ramifications of these results for the validity of two body decomposition of forces are discussed

time domain adaptive delay estimation in this correspondence a new adaptive delay estimator using only two lms filters is presented compared with other algorithms a significant reduction in computational complexity is obtained because only time domain processing is required in addition a new frequency domain adaptive delay estimator has been introduced and the link between both methods is clarified comparison with algorithms described in literature turns out favorably

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

the classical fluid of associating hard rods in an external field two models of one dimensional fluids of associating hard rods in an arbitrary external field are investigated in the first model particles can only form dimers while in the second model which has been solved previously by percus aggregates of any size coexist in both cases the grand canonical potential and the external potential are found exactly as functionals of the density it is shown that wertheim s thermodynamic perturbation theory of polymerization provides a straightforward route to the exact solution by expanding the functional space to include more density parameters this suggests that wertheim s theory should be used also for studying the structure and not only the thermo dynamics of real associating fluids

density functional theory for soft interactions by dimensional crossover a density functional theory for spherical particles interacting via an arbitrary soft pair potential is presented the derivation is solely based on limits where the behavior is exactly known namely a zero dimensional cavity and the low density virial expansion the approach generalizes the fundamental measure theory for hard bodies and yields the structure and thermodynamics of the homogeneous fluid as an output we apply the theory to an ultrasoft logarithmic potential that mimics star polymers in a good solvent the theory when supplemented by a rescaling procedure reproduces the peculiar features of the pair correlations in this system that we also find in computer simulations

fundamental measure theory and dimensional interpolation for the hard spheres fluid abstract this paper presents a short review of the recent advances in the development of density functional for hard spheres the fundamental measure theory as developed originally by y rosenfeld and in its more recent versions is compared with other density functional approximations the results for dimensional crossover from the hard spheres fluid in three dimensions to hard rods in one dimension and to zero dimensional cavities are discussed new results on the fluid crystal coexistence and on the crossover to the hard disc fluid in two dimensions are presented

mutual tracking in phase and delay of randomly modulated signals a two parameter tracking loop that mutually locks the phases and delays of two noise contaminated replicas of a randomly phase modulated signal received via different channels is analyzed it is shown that at high snr i e small tracking errors the twoparameter loop can be considered as two uncoupled single parameter loops provided the signals are beaten down to zero center frequency special emphasis is put on the delay error variance it is found that in general the broadening of the phase loop bandwidth provided for more rapid acquisition induces larger delay tracking errors also such broadening decreases the expected time to loss of delay lock the influence of the location of the absorbing boundaries for this problem is investigated quantitative results for a typical configuration are presented in figs 1 9

on the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids it is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density we derive the explicit form that the functional takes for a system of hard rods and propose an approximate one for hard spheres attractive interactions are also considered in mean field approximation in all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated

from zero dimension cavities to free energy functionals for hard disks and hard spheres we present a systematic approach to derive fundamental measure theory free energy functionals for hard disks and hard spheres entirely from the exact free energy in the zero dimensional limit of a narrow cavity which cannot hold more than one molecule the functionals are within the generic class that includes the previous successful versions but have the remarkable property to yield the exact functional for quasi one dimensional density distributions

inhomogeneous ising model on the bethe lattice abstract a new approach to the spin 1 2 ising model with nonconstant interactions and a site dependent external field is presented it represents a straightforward way for solving the inverse problems the external field required to produce a given magnetization profile is given explicitly for spin 1 2 systems on the bethe lattice with an arbitrary coordination number q

finite size analysis of the hard square lattice gas we investigate the hard square lattice gas model by means of transfer matrix calculations and a finite size scaling analysis using a minimal set of assumptions we find that the spectrum of correction to scaling exponents is consistent with that of the exactly solved ising model and that the critical exponents and correlation length amplitudes closely follow the relation predicted by conformal invariance assuming that these spectra are exactly identical and conformal invariance we determine the critical point the conformal anomaly and the temperature and magnetic exponents with numerical margins of 10 11 or less these results are in a perfect agreement with the exactly known ising universal parameters in two dimensions in order to obtain this degree of precision we included system sizes as large as feasible and used extended precision floating point arithmetic the latter resource provided a substantial improvement of the analysis despite the fact that it restricted the transfer matrix calculations to finite sizes of at most 34 lattice units

distribution functions for fluids in random media a random medium is considered composed of identifiable interactive sites or obstacles equilibrated at a high temperature and then quenched rapidly to form a rigid structure statistically homogeneous on all but molecular length scales the equilibrium statistical mechanics of a fluid contained inside this quenched medium is discussed various particle particle and particle obstacle correlation functions which differ from the corresponding functions for a fully equilibrated binary mixture are defined through an averaging process over the static ensemble of obstacle configurations and application of topological reduction techniques the ornstein zernike equations also differ from their equilibrium counterparts

new collective modes of interaction nature in inhomogeneous ising networks we propose a vertex formulation of the ising model with inhomogeneous external field on multiconnected networks possessing a superbond structure the related technique based on gauge degrees of freedom enables us to recognize new collective modes of interaction nature which provide an exact solution of the inverse profile problem and an explicit form of a local free energy functional on an extended magnetization mode space application is made to a square strip

peel or coat spheres by convolution repeatedly a convolution transformation is presented that maps the four fundamental measures minkowski functionals of a three dimensional sphere to those of a sphere with a different radius it is shown that the set of all these transformations parametrized by the induced change in radius forms an abelian commutative group and hence constitutes a flexible framework for the manipulation of spheres the corresponding one dimensional case is laid out and the relationship to fundamental measure density functional theory is discussed briefly

the simple cubic lattice gas with nearest neighbour exclusion ising universality abstract the lattice gas with nearest neighbour exclusion on the simple cubic lattice is studied by means of statistically accurate monte carlo simulations with an efficient cluster algorithm our results for critical exponents are y h 2 47 1 and y t 1 60 2 these results agree well with the three dimensional ising universality class we explain the discrepancy with an earlier study the critical activity is z c 1 0559 1 the size distribution of the clusters indicates that the percolation threshold of the cluster formation process of the monte carlo algorithm coincides with the critical point

entropy of a one dimensional mixed lattice gas this paper deals with the grand canonical entropy of a lattice gas mixture the entropy is a function of the multisite densities corresponding to the interaction pattern of the system in question it is first evaluated for a nearest neighborinteraction one dimensional simple lattice gas to show how the structure of bulk fluid is locally maintained generalization requires one set of interrelations among multisite densities presented in closed form for an arbitrary lattice and one set between boltzmann factors and multisite densities which is written down for simply connected lattices application is made to two row lattices which turn out to have local behavior from this viewpoint as do all single row or bethe lattices with complete range p interactions nonlocal examples are also given and suggestions made for approximation sequences in general lattices

a note on the application of the hilbert transform to time delay estimation it is shown that the hilbert transform may be employed to convert the maximum finding task of a delay estimator to one of finding a zero crossing the basic theory of the technique is shown and a few applications are described its primary application is in servo tracking and servo velocity measurement systems which employ correlation techniques a review of prior work in this field is given

pan operations structure abstract the structure of pan addition and pan multiplication of a commutative isotonic semiring r is analyzed we show that if v supremum then r is a g semiring i e a b g 1 g a g b and d a b g 1 g a g b conclusions for pan integrals with respect to a measure are shown

the structure and performance of estimators for real time estimation of randomly varying time delay structures for time delay estimation are described which are deduced using the maximum likelihood technique the performance of estimators designed for time invariant delays is discussed for the case of signals with a time variable delay a two step algorithm for the estimation of a randomly varying time delay between two stochastic signals is developed in the first step the maximum likelihood estimate is computed over an observation interval small enough to consider the delay to be approximately constant due to the short averaging interval the probability of ambiguous peaks in the estimation function and the variance of the estimate are greatly increased therefore in the second step a decision directed adaptive postfiltering algorithm is presented that effectively suppresses outliers and reduces the variance

on a certain class of aggregative operators abstract here our starting point is a study of connection with dombi aggregative operators uninorms strict t norms and t conorms we present a new representation theorem of strong negations that explicitly contains the neutral value then the relationships for aggregative operators and strong negations are verified as well as those for the t norm and t conorm using the pan operator concept we introduce the multiplicative pliant concept and give the necessary and sufficient conditions for it we study a certain class of weighted aggregative operators representable uninorms which build a self demorgan class with infinitely many negations we provide the necessary and sufficient conditions for these operators

density functional theory for hard particles in n dimensions recently it has been shown that the heuristic rosenfeld functional can be derived from the virial expansion for particles overlapping in one center here we generalize this approach to any number of intersections starting from the virial expansion in ree hoover diagrams it is shown in the first part that each intersection pattern corresponds to exactly one infinite class of diagrams determining their automorphism groups we sum over all its elements and derive a generic functional the second part shows that this functional factorizes into a convolute of integral kernels for each intersection center we derive this kernel for n dimensional particles in the n dimensional flat euclidean space the third part focuses on three dimensions and determines the functionals for up to four intersection centers comparing the leading order to rosenfeld s result we close by proving a generalized form of the blaschke santalo chern equation of integral geometry

generating function density functional theory free energy functionals and direct correlation functions for hard spheres abstract a recent density functional theory for the inhomogeneous hard sphere fluid expresses the free energy in terms of a set of derivatives with respect to the particle radius of a simple generating function in the present paper this generating function approach gfa is reformulated in terms of general conditions on the coefficients of the differential operator involved in the theory this gives more flexibility to the theory and allows for ready derivation of new functionals that are tested in the calculation of density profiles of hard spheres near a hard wall comparison with the results of the previous formulation of the gfa shows a better performance of the new functionals and also gives a much deeper understanding of the structure of the theory and its connections with the fundamental measures theory of rosenfeld a simple modification of the gfa pair direct correlation functions yields explicit analytic expressions with very good agreement with simulation results