green s functions for transversely isotropic piezoelectric functionally graded multilayered half spaces by virtue of two systems of vector functions and the propagator matrix method greens functions for transversely isotropic piezoelectric functionally graded exponentially graded in the vertical direction and multilayered half spaces are derived it is observed that the homogeneous solution and propagator matrices for each functionally graded layer in the transformed domain are independent of the choice of the two systems of vector functions for a point force and point charge density applied at any location of the functionally graded half space greens functions are expressed in terms of one dimensional infinite integrals to carry out the numerical integral involving bessel functions an adaptive gauss quadrature approach is introduced and modified the piezoelectric functionally graded greens functions include those in the corresponding elastic functionally graded media as special results with the latter being also unavailable in the literature two piezoelectric functionally graded half space models are analyzed numerically one is a functionally graded pzt 4 half space and the other a coated functionally graded pzt 4 layer over a homogeneous batio3 half space the effects of different exponential factors on greens function components are clearly demonstrated which could be useful in the design and manufacturing of piezoelectric functionally graded structures 2004 elsevier ltd all rights reserved

state estimation for static neural networks with time varying delays based on an improved reciprocally convex inequality this brief is concerned with the problem of neural state estimation for static neural networks with time varying delays notice that a luenberger estimator can produce an estimation error irrespective of the neuron state trajectory this brief provides a method for designing such an estimator for static neural networks with time varying delays first in depth analysis on a well used reciprocally convex approach is made leading to an improved reciprocally convex inequality second the improved reciprocally convex inequality and some integral inequalities are employed to provide a tight upper bound on the time derivative of some lyapunov krasovskii functional as a result a novel bounded real lemma brl for the resultant error system is derived third the brl is applied to present a method for designing suitable luenberger estimators in terms of solutions of linear matrix inequalities with two tuning parameters finally it is shown through a numerical example that the proposed method can derive less conservative results than some existing ones

finite time synchronization of discontinuous neural networks with delays and mismatched parameters this paper investigates the problem of finite time drive response synchronization for a class of neural networks with discontinuous activations time varying discrete and infinite time distributed delays and mismatched parameters in order to cope with the difficulties induced by discontinuous activations time delays as well as mismatched parameters simultaneously new 1 norm based analytical techniques are developed both state feedback and adaptive controllers with and without the sign function are designed based on differential inclusion theory and lyapunov functional method several sufficient conditions on the finite time synchronization are obtained our results show that the controllers with a sign function can reduce the conservativeness of control gains and the controllers without a sign function can overcome the chattering phenomenon numerical examples are given to show the effectiveness of the theoretical analysis

decomposable measures and nonlinear equations abstract using integrals based on decomposable measures with respect to a pseudo addition related to a semiring a b a b a unified method is given for solving some nonlinear differential ordinary and partial difference and optimization equations for that purpose important tools as pseudo superposition principle and pseudolaplace transform are used

a limit theorem for triangle functions a wide class of triangle functions that can be interpreted as generalized pseudo convolutions of distribution functions has been considered in order to find out whether a nontrivial limit for the sequence of the pseudo convolutions of distribution functions exists or not some pseudo laplace type transformations have been introduced the main result is illustrated with a family of pseudo convolutions based on a family of schweizer sklar t norms and another example is given with a calculation of the analytical form of the limit function

numerical integration of related hankel transforms by quadrature and continued fraction expansion an algorithm is presented for the accurate evaluation of hankel or bessel transforms of algebraically related kernel functions defined here as the non bessel function portion of the integrand that is more widely applicable than the standard digital filter methods without enormous increases in computational burden the algorithm performs the automatic integration of the product of the kernel and bessel functions between the asymptotic zero crossings of the latter and sums the series of partial integrations using a continued fraction expansion equivalent to an analytic continuation of the series the integrands may be saved to allow the rapid computation of related transforms without recalculating the kernel or bessel functions and the integration steps use interlacing quadrature formulas so that no function evaluations are wasted when it is necessary to increase the order of the quadrature rule the continued fraction algorithm allows very slowly divergent or even formally divergent integrals to be computed quite easily the local error is controlled at each step in the algorithm and accuracy is limited largely by machine resolution the algorithm is written in fortran and is listed in an appendix along with a driver program that illustrates its features the driver program and subroutine are available from the seg business offtce

extension of a class of decomposable measures using fuzzy pseudometrics in this paper we consider a topological approach to extension of t conorm based decomposable measures by introducing a fuzzy pseudometric structure on an algebra of sets we prove that every non strict continuous archimedean t conorm based decomposable measure can be extended from an algebra to the completion of this algebra under the fuzzy pseudometric and then to the sigma algebra generated by this algebra the existence of such an extension follows very simply from the well known caratheodory result however our topological proof offers an intuitive interpretation of the extension of decomposable measures

pseudo analysis and its applications in railway routing using as a base the pseudo analysis the problem of railway routing is treated first a deterministic approach is applied on three and four stations these problems are treated also with a stochastic approach when one variable is randomized

decision theoretic foundations of qualitative possibility theory abstract this paper presents a justification of two qualitative counterparts of the expected utility criterion for decision under uncertainty which only require bounded linearly ordered valuation sets for expressing uncertainty and preferences this is carried out in the style of savage starting with a set of acts equipped with a complete preordering relation conditions on acts are given that imply a possibilistic representation of the decision maker uncertainty in this framework pessimistic i e uncertainty averse as well as optimistic attitudes can be explicitly captured the approach thus proposes an operationally testable description of possibility theory

holder and minkowski type inequalities for pseudo integral abstract there are proven generalizations of the holder s and minkowski s inequalities for the pseudo integral there are considered two cases of the real semiring with pseudo operations one when pseudo operations are defined by monotone and continuous function g the second semiring a b sup where is generated and the third semiring where both pseudo operations are idempotent i e sup and inf

an open source full 3d electromagnetic modeler for 1d vti media in python empymod abstractthe python code empymod computes the 3d electromagnetic field in a layered earth with vertical transverse isotropy by combining and extending two earlier presented algorithms in this journal the bottleneck in frequency and time domain calculations of electromagnetic responses derived in the wavenumber frequency domain is the transformations from the wavenumber to the space domain and from the frequency to the time domain the so called hankel and fourier transforms three different hankel transform methods quadrature quadrature with extrapolation qwe and filters and four different fourier transform methods fast fourier transform fft fftlog qwe and filters are included in empymod which allows us to compare these different methods in terms of speed and precision the best transform in terms of speed and precision depends on the modeled frequencies published digital filters for the hankel transform are very fast and precise for frequencies in the range of controlled source electromag

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

integrals of set valued functions for decomposable measures abstract in this paper based on weber s 1984 integrals for archimedean t conorms decomposable measures integrals of set valued functions for archimedean t conorms decomposable measures are established some results similar to aumann s set valued integrals are given these include convexity closedness convergence theorems etc all these are the generalization of aumann s results

stability for neural networks with time varying delays via some new approaches this paper considers the problem of delay dependent stability criteria for neural networks with time varying delays first by constructing a newly augmented lyapunov krasovskii functional a less conservative stability criterion is established in terms of linear matrix inequalities second by proposing novel activation function conditions which have not been proposed so far further improved stability criteria are proposed finally three numerical examples used in the literature are given to show the improvements over the existing criteria and the effectiveness of the proposed idea

admissible delay upper bounds for global asymptotic stability of neural networks with time varying delays this paper is concerned with global asymptotic stability of a neural network with a time varying delay where the delay function is differentiable uniformly bounded with delay derivative bounded from above first a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions this inequality provides a tighter bound in the form of a convex combination than some existing ones second by constructing proper lyapunov krasovskii functional global asymptotic stability of the neural network is analyzed for two types of the time varying delays depending on whether or not the lower bound of the delay derivative is known third noticing that sufficient conditions on stability from estimation on the derivative of some lyapunov krasovskii functional are affine both on the delay function and its derivative allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study finally two numerical examples are given to substantiate the effectiveness of the proposed method

decomposable measures and information measures for intuitionistic fuzzy sets the aim of this paper is to construct a decomposable measure on the class of measurable intuitionistic fuzzy sets extending thus the corresponding result for fuzzy sets in a very recent paper the main tool in this construction is a non trivial approximation with restrictions result concerning the intuitionistic fuzzy sets as an application we construct a compositive information measure on the class of intuitionistic fuzzy sets

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

generalization of the jensen inequality for pseudo integral generalizations of the jensen integral inequality for the pseudo integral are proven there are considered two cases of the real semiring with pseudo operations one when pseudo operations are defined by monotone and continuous function g then the pseudo integral reduces on g integral and the second semiring a b max where the pseudo multiplication is generated

extension of a class of decomposable measures via generalized pseudo metrics abstract this study considers the application of generalized pseudo metrics to the extension of decomposable measures we prove that the extension of a non strict archimedean t conorm based decomposable measure can be formulated as the closure of a subset of a certain generalized pseudo metric space we show that the extension via generalized pseudo metrics is equivalent to the completion of t conorm based decomposable measures and the well known caratheodory extension

solving the banach fixed point principle for nonlinear contractions in probabilistic metric spaces abstract the probabilistic version of the classical banach contraction principle was proved in 1972 by sehgal and bharucha reid v m sehgal a t bharucha reid fixed points of contraction mappings on pm spaces math syst theory 6 97 102 their fixed point theorem is further generalized by many authors in the intervening years many others have proved the probabilistic versions of the other known metric fixed point theorems however the problem to prove the probabilistic versions of the very important generalization of the banach contraction principle obtained in 1969 by boyd and wong d w boyd j s w wong on nonlinear contractions proc am math soc 20 1969 458 464 who proved the fixed point theorem for a self mapping of a metric space satisfying the very general nonlinear contractive condition is unsolved in these days similarly as in the metric space case to prove a fixed point theorem for a mapping satisfying the general probabilistic nonlinear contractive condition it was necessary to find a new approach substantially different from the previous technique for cases where a mapping satisfies the probabilistic linear contraction condition introduced by sehgal and bharucha reid and further used by many authors so the problem to obtain a truthful probabilistic version of the banach fixed point principle for general nonlinear contractions existed unsolved for over 35 years we have solved this problem in this paper

stability analysis of distributed delay neural networks based on relaxed lyapunov krasovskii functionals this paper revisits the problem of asymptotic stability analysis for neural networks with distributed delays the distributed delays are assumed to be constant and prescribed since a positive definite quadratic functional does not necessarily require all the involved symmetric matrices to be positive definite it is important for constructing relaxed lyapunov krasovskii functionals which generally lead to less conservative stability criteria based on this fact and using two kinds of integral inequalities a new delay dependent condition is obtained which ensures that the distributed delay neural network under consideration is globally asymptotically stable this stability criterion is then improved by applying the delay partitioning technique two numerical examples are provided to demonstrate the advantage of the presented stability criteria

event triggered generalized dissipativity filtering for neural networks with time varying delays this paper is concerned with event triggered generalized dissipativity filtering for a neural network nn with a time varying delay the signal transmission from the nn to its filter is completed through a communication channel it is assumed that the network measurement of the nn is sampled periodically an event triggered communication scheme is introduced to design a suitable filter such that precious communication resources can be saved significantly while certain filtering performance can be ensured on the one hand the event triggered communication scheme is devised to select only those sampled signals violating a certain threshold to be transmitted which directly leads to saving of precious communication resources on the other hand the filtering error system is modeled as a time delay system closely dependent on the parameters of the event triggered scheme based on this model a suitable filter is designed such that certain filtering performance can be ensured provided that a set of linear matrix inequalities are satisfied furthermore since a generalized dissipativity performance index is introduced several kinds of event triggered filtering issues such as h infty filtering passive filtering mixed h infty and passive filtering q s r dissipative filtering and mathcal l 2 mathcal l infty filtering are solved in a unified framework finally two examples are given to illustrate the effectiveness of the proposed method

robust h_ infty control for t s fuzzy systems with state and input time varying delays via delay product type functional method this paper investigates the problem of robust h infty control for a class of nonlinear systems with state and input time varying delays the nonlinearity is presented by a continuous time takagi sugeno t s fuzzy model with parameter uncertainties a sufficient asymptotic stability condition is first proposed by constructing a delay product type augmented lyapunov krasovskii functional and utilizing an extended reciprocally convex matrix inequality together with a wirtinger based integral inequality then a state feedback controller is derived that guarantees the closed loop fuzzy system being asymptotically stable with an h infty performance index finally four numerical examples are given to reveal the effectiveness and merits of the developed new design techniques

triangular norm based predicate fuzzy logics the paper surveys the present state of knowledge on t norm based predicate fuzzy logics with their double semantics standard the set of truth values being the real interval 0 1 and general with abstract algebras of truth functions

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

idempotent integral as limit of g integrals we show that sup and inf decomposable measures can be obtained as limits of families of pseudo additive measures with respect to generated pseudo additions the corresponding integrals with respect to sup or inf decomposable measures can be obtained as limits of families of g integrals

further result on guaranteed h_ infty performance state estimation of delayed static neural networks this brief considers the guaranteed h infty performance state estimation problem of delayed static neural networks an arcak type state estimator which is more general than the widely adopted luenberger type one is chosen to tackle this issue a delay dependent criterion is derived under which the estimation error system is globally asymptotically stable with a prescribed h infty performance it is shown that the design of suitable gain matrices and the optimal performance index are accomplished by solving a convex optimization problem subject to two linear matrix inequalities compared with some previous results much better performance is achieved by our approach which is greatly benefited from introducing an additional gain matrix in the domain of activation function an example is finally given to demonstrate the advantage of the developed result

extended dissipative state estimation for markov jump neural networks with unreliable links this paper is concerned with the problem of extended dissipativity based state estimation for discrete time markov jump neural networks nns where the variation of the piecewise time varying transition probabilities of markov chain is subject to a set of switching signals satisfying an average dwell time property the communication links between the nns and the estimator are assumed to be imperfect where the phenomena of signal quantization and data packet dropouts occur simultaneously the aim of this paper is to contribute with a markov switching estimator design method which ensures that the resulting error system is extended stochastically dissipative in the simultaneous presences of packet dropouts and signal quantization stemmed from unreliable communication links sufficient conditions for the solvability of such a problem are established based on the derived conditions an explicit expression of the desired markov switching estimator is presented finally two illustrated examples are given to show the effectiveness of the proposed design method

an automatic technique for presentation of coincident loop impulse response transient electromagnetic data coincident loop tem sounding data are often presented by plotting the half space apparent conductivity as a function of delay time a new algorithm generates an improved presentation that plots the apparent conductivity as a function of depth the resulting data may be further processed to sharpen or spike the smoothly varying apparent conductivity depth curves in an attempt to better represent the rapid changes in conductivity that often exist in the earth the algorithm described involves an approximation but is simple easy to use and computationally efficient a layered conductivity structure is assumed so the algorithm is best for areas where the geology is approximately horizontal however the algorithm can also be used to identify anomalous features that are not infinite horizontal layers the spiked conductivity models derived from synthetic data are consistent with the original layered earth models and show a greater resolution than the apparent conductivity depth curves and sometimes ampl

is the fast hankel transform faster than quadrature the fast hankel transform fht implemented with digital filters has been the algorithm of choice in em geophysics for a few decades however other disciplines have predominantly relied on methods that break up the hankel transform integral into a sum of partial integrals that are each evaluated with quadrature the convergence of the partial sums is then accelerated through a nonlinear sequence transformation while such a method was proposed for geophysics nearly three decades ago it was demonstrated to be much slower than the fht this work revisits this problem by presenting a new algorithm named quadrature with extrapolation qwe the qwe method recasts the quadrature sum into a form conceptually similar to the fhtapproach by using a fixed point quadrature rule the sum of partial integrals is efficiently accelerated using the shanks transformation computed with wynn s algorithm a matlab implementation of the qwe algorithm is compared with the fht method for accuracy and speed on a suite of relevant modeling problems including frequency domain controlledsource em time domain em and a large loop magnetic source problem surprisingly the qwe method is faster than the fht for all three problems however when the integral needs to be evaluated at many offsets and the lagged convolution variant of the fht is applicable the fht is significantly faster than the qwe method for divergent integrals such as those encountered in the large loop problem the qwe method can provide an accurate answer when the fht method fails

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

approximate frechet derivatives in inductive electromagnetic soundings frechet derivatives play dual roles in electromagnetic em methods as averaging functions relating conductivity to em fields and as sensitivity functions relating conductivity perturbations to changes in these fields for one dimensional em inductive sounding the frechet derivatives are not strongly model dependent even for quite diverse earth models in fact using a scaled version of the frechet derivative for a uniform half space to approximate the exact jacobian in a layered earth inversion program can actually improve the convergence to an acceptable model this lack of a strong model dependence makes it possible to consider the capabilities and limitations of em imaging methods from the perspective of frechet derivatives of particular interest is that noninductive frechet derivatives are strongly model dependent and hence the em fields generated by this mode are less amenable to imaging techniques

pseudo optimal measures based on a pseudo addition on 0 pseudo optimal measures related to non negative set functions vanishing at the empty set non negative games are introduced for a fixed pseudo addition an equivalence on non negative set functions is studied a special stress is given to pure pseudo optimal measures admitting no other equivalent set function

on nonlinear functional spaces based on triangular conorms abstract in this paper we discuss the nonlinear functional spaces based on triangular conorms particularly we discuss the properties of the upper closures of the regular subspaces of the nonlinear functional space based on a continuous triangular conorm furthermore we prove that with respect to a strict triangular conorm a subset of the nonlinear functional space is an upper complete normal subspace if and only if the family of all sets whose characteristic functionals are contained in the given subset of the nonlinear functional space is a sigma algebra

transforming a time domain electromagnetic signal to a frequency domain electromagnetic response using regularization inversion abstractwide applications of time domain electromagnetic tem data require 3d inversion a possible strategy is to use the developed 3d inversion algorithms in frequency domain fd electromagnetic em methods thus the key of the strategy is how to transform the time domain t d em signal into the fd an inversion algorithm has been developed to transform the t d signal into a corresponding fd response in this method a step off current is presumed under this assumption the fourier transform relating the em fd response to the t d signal becomes a sine or cosine transformation using the polynomial approximation method the transformation turns into a linear equation from a set of t d signals fd responses could be obtained by solving these linear equations in the least squares sense to reduce the nonuniqueness of the solution and enhance the solution stability an additional smoothness constraint on the fd response is imposed thus converting the minimization problem into a regularization inver

3d finite difference frequency domain modeling of controlled source electromagnetic data direct solution and optimization for high accuracy three dimensional modeling of marine controlled source electromagnetic csem data is vital to improve the understanding of electromagnetic em responses collected in increasingly complex geologic settings a modeling tool for simulating 3d marine csem surveys based on a finite difference discretization of the helmholtz equation for the electric fields has been developed optimizations for csem simulations include the use of a frequency domain technique a staggering scheme that reduces inaccuracies especially for horizontal electric dipole sources located near the seafloor and a new interpolation technique that provides highly accurate em field values for receivers located in the immediate vicinity of the seafloor source singularities are eliminated through a secondary field approach in which the primary fields are computed analytically for a homogeneous or a 1d layered background the secondary fields are computed using the finite difference technique exploiting recent advances in computer technology and algorithmic developments the system of finite difference equations is solved using the mumps direct matrix solver in combination with the other optimizations this allows accurate em field computations for moderately sized models on small computer clusters the explicit availability of matrix factorizations is advantageous for multisource modeling and makes the algorithm well suited for future use within an inversion scheme comparisons of simulated data for 1 1d models to data generated using a 1d reflectivity technique and 2 3d models to published 3d data demonstrate the accuracy and benefits of the approach

integrals based on monotone set functions an overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set called here monotone measures our survey includes not only the choquet integral 1954 10 the shilkret integral 1971 66 and the sugeno integral 1974 71 and some of their properties but also some more general and more recent concepts as universal integrals klement et al 2010 27 and decomposition integrals even 2014 13 together with some of their properties such as integral inequalities and convergence theorems

pseudo lp space and convergence in the framework of the pseudo analysis the classical l p space is generalized and there are proved important properties of introduced space three types of convergence of sequences of measurable functions are considered in this space the inequalities for integrals based on pseudo integral have been recently proposed as the holder minkowski and markov inequalities which are applied in observing relationship among introduced convergences

distributivity and conditional distributivity of a uninorm and a continuous t conorm the open problem recalled by klement in the linz2000 closing session related to distributivity and conditional distributivity of a uninorm and a continuous t conorm is solved for the most usual known classes of uninorms from the obtained results it is deduced that distributivity and conditional distributivity are equivalent for these cases it is remarkable that solutions appear involving not only strict t conorms but also ordinal sums of the maximum with a strict t conorm conversely the distributivity of a t conorm over a uninorm is also studied leading only to already known solutions moreover the dual case of distributivity and conditional distributivity involving uninorms and continuous t norms is also solved proving again the equivalence of both kinds of distributivities

stability of time delay systems via wirtinger based double integral inequality based on the wirtinger based integral inequality a double integral form of the wirtinger based integral inequality hereafter called as wirtinger based double integral inequality is introduced in this paper to show the effectiveness of the proposed inequality two stability criteria for systems with discrete and distributed delays are derived within the framework of linear matrix inequalities lmis the advantage of employing the proposed inequalities is illustrated via two numerical examples

fuzzy integrals based on pseudo additions and multiplications on definit un semi groupe ou un groupe qui est isomorphe au semi groupe ou du groupe ou la mesure de lebesque est definie on definit une integrale par pseudo addition et pseudo multiplication qui sont des operations de semi anneaux distributives et associatives

a hybrid fast hankel transform algorithm for electromagnetic modeling a hybrid fast hankel transform algorithm has been developed that uses several complementary features of two existing algorithms anderson s digital filtering or fast hankel transform fht algorithm and chave s quadrature and continued fraction algorithm a hybrid fht subprogram called hybfht written in standard fortran 77 provides a simple user interface to call either subalgorithm the hybrid approach is an attempt to combine the best features of the two subalgorithms in order to minimize the user s coding requirements and to provide fast execution and good accuracy for a large class of electromagnetic problems involving various related hankel transform sets with multiple arguments special cases of hankel transforms of double order and double argument are discussed where use of hybfht is shown to be advantageous for oscillatory kernel functions

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

on pseudo metric spaces induced by σ decomposable measures in this paper we study the relationship between the pseudo metric and decomposable measures with respect to a triangular conorm decomposable measures for short we first construct a pseudo metric on the measurable sets of a given decomposable measure and then discuss several properties such as completeness and continuity of the constructed pseudo metric space finally we show that the separability and nonatom of the decomposable measure can be characterized in the constructed pseudo metric space our results suggest that the standard approach for obtaining a metric from a given probability measure can be generalized to the setting of decomposable measure

on the generated hsb type equation and plsp abstract the aim of this paper is to study sustainability of the pseudo linear superposition principle that is of the nonlinear superposition principle nlsp observed in the pseudo analysis framework the focus of this paper is on the so called generated partial differential equation that is for the purpose of this study based on the stochastic burger s equation

choquet like integrals abstract integrals based on a pseudo addition and a pseudo multiplication with properties similar to those of the choquet and the sugeno integral respectively are introduced the structure of convenient pseudo arithmetical operations leading to a choquet like integral is studied

extrapolation methods for sommerfeld integral tails a review is presented of the extrapolation methods for accelerating the convergence of sommerfeld type integrals i e semi infinite range integrals with bessel function kernels which arise in problems involving antennas or scatterers embedded in planar multilayered media attention is limited to partition extrapolation procedures in which the sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real axis tail segment spl alpha spl infin of the integration path where spl alpha 0 is selected to ensure that the integrand is well behaved an analytical form of the asymptotic truncation error or the remainder which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods is derived several extrapolation algorithms deemed to be the most suitable for the sommerfeld integrals are described and their performance is compared it is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points spl rho and by the choice of the subinterval break points furthermore it is found that some well known extrapolation techniques may fail for a number of values of spl rho and ways to remedy this are suggested finally the most effective extrapolation methods for accelerating sommerfeld integral tails are recommended

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

generalized pseudo convolution in the theory of probabilistic metric spaces information fuzzy numbers optimization system theory a notion of the generalized pseudo convolution of functions based on pseudo operations is introduced it is proved that such general pseudo convolution is commutative associative operation that in some cases has a unit element we present that the generalized pseudo convolution occurs as a basic notion in many different theories as probabilistic metric spaces information theory fuzzy numbers optimization system theory

on the probabilistic hausdorff distance and a class of probabilistic decomposable measures in this paper some useful properties associated with the probabilistic hausdorff distance are further derived especially we provide a direct proof for an existing important result afterwards the t norm based probabilistic decomposable measure is presented in which the value of measure is characterized by a probability distribution function meantime several examples are constructed to illustrate different notions and then further properties are examined moreover for a given menger pm space a probabilistic decomposable measure can be induced by means of the resulting probabilistic hausdorff distance we prove that this type of measure is s email protected probabilistic subdecomposable measure for the strongest t norm furthermore we also prove that the class of all measurable sets forms an algebra finally an outer probabilistic measure is induced by a class of probabilistic decomposable measures and the t norm based on this kind of measure a menger probabilistic pseudometric space can be obtained for a non strict continuous archimedean t norm

fuzzy t conorm integral with respect to fuzzy measures generalization of sugeno integral and choquet integral abstract this article discusses integrals with respect to sugeno s fuzzy measures sugeno integrals and choquet integrals with respect to general fuzzy measures are generalized in the setting of a t conorm algebraic system first t conorm integrals with respect to decomposable measures based on t conorm algebraic system are defined they are a modification of the weber integral secondly they are extended to fuzzy t conorm integrals with respect to general fuzzy measures the extension is made in the same way as the extension of the lebesgue integral to the choquet integral the class of fuzzy t conorm integrals includes choquet integrals and sugeno integrals properties of the integrals especially their representation are discussed

notes on stability of time delay systems bounding inequalities and augmented lyapunov krasovskii functionals the bounding inequalities and the lyapunov krasovskii functionals lkfs are important for the stability analysis of time delay systems much attention has been paid to develop tighter inequalities for improving stability criteria while the contribution of the lkfs has not been considered when discussing the relationship between the tightness of inequalities and the conservatism of criteria this note is concerned with this issue firstly it is proved that when a simple lkf is applied the stability criteria obtained by the wirtinger based inequality and the jensen inequality are equivalent although the wirtinger based inequality is tighter it means that the tighter inequality does not always lead to a less conservative criterion secondly it is found that a suitable augmented lkf with necessary integral vectors in its derivative is required to achieve the advantage of the wirtinger based inequality based on this observation two delay product type terms are introduced into the lkf to establish new stability criteria finally a numerical example is given to verify the equivalence statements and to show the benefit of the proposed criteria

event triggered h_ infty state estimation for delayed stochastic memristive neural networks with missing measurements the discrete time case in this paper the event triggered h infty state estimation problem is investigated for a class of discrete time stochastic memristive neural networks dsmnns with time varying delays and missing measurements the dsmnn is subject to both the additive deterministic disturbances and the multiplicative stochastic noises the missing measurements are governed by a sequence of random variables obeying the bernoulli distribution for the purpose of energy saving an event triggered communication scheme is used for dsmnns to determine whether the measurement output is transmitted to the estimator or not the problem addressed is to design an event triggered h infty estimator such that the dynamics of the estimation error is exponentially mean square stable and the prespecified h infty disturbance rejection attenuation level is also guaranteed by utilizing a lyapunov krasovskii functional and stochastic analysis techniques sufficient conditions are derived to guarantee the existence of the desired estimator and then the estimator gains are characterized in terms of the solution to certain matrix inequalities finally a numerical example is used to demonstrate the usefulness of the proposed event triggered state estimation scheme

h state estimation for neural networks with general activation function and mixed time varying delays this article deals with h state estimation of neural networks with mixed delays in order to make full use of delay information novel delay product lyapunov krasovskii functional lkf by using parameterized delay interval is first constructed then generalized free weighting matrix integral inequality is used to estimate the derivative of lkf to reduce the conservatism also a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model finally sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed h performance numerical examples are simulated to show the benefits of our proposed method