on robust hurwitz polynomials in this note kharitonov s theorem on robust hurwitz polynomials is simplified for low order polynomials specifically for n 3 4 and 5 the number of polynomials required to check robust stability is one two and three respectively instead of four furthermore it is shown that for n geq 6 the number of polynomials for robust stability checking is necessarily four thus further simplification is not possible the same simplifications arise in robust schur polynomials by using the bilinear transformation applications of these simplifications to two dimensional polynomials as well as to robustness for single parameters are indicated

on finity countability cardinalities and cylindric extensions of type 2 fuzzy sets in linguistic summarization of databases the discussion in this paper is closely related to our idea of a type 2 linguistic summary of a database presented by niewiadomski a niewiadomski a type 2 fuzzy approach to linguistic summarization of data ieee trans fuzzy syst vol 16 no 1 pp 198 213 feb 2008 which is intended to be an efficient tool of knowledge discovery from large databases in that approach we put emphasis on algorithms and applications of type 2 fuzzy sets in summarizing databases hence we have implicitly assumed and considered linguistic expressions represented by sets in discrete or even finite universes of discourse now in this paper we discuss more thoroughly some of the properties and formal aspects of both discrete and continuous type 2 fuzzy sets that represent the elements of linguistic summaries i e quantifiers summarizers and or qualifiers we underline differences between type 2 fuzzy sets in finite and in infinite usually continuous universes of discourse and henceforth between their cardinalities and similar measures which are used in evaluating the goodness quality of type 2 linguistic summaries in addition we define new imprecision measures of linguistic expressions represented by type 2 fuzzy sets and propose a definition of the cylindric extension of a type 2 fuzzy set finally we apply these new concepts to generalize algorithms of type 2 linguistic summarization and propose some new features in comparison to our previous approach a niewiadomski a type 2 fuzzy approach to linguistic summarization of data ieee trans fuzzy syst vol 16 no 1 pp 198 213 feb 2008

stability of polynomials under coefficient perturbation let the real polynomial a 0 x n a 1 x n 1 a n 1 x a n be stable and let the real numbers b k c k geq 0 0 leq k leq n be given we present a simple determinant criterion for finding the largest t 0 geq 0 such that the polynomial alpha 0 x n alpha 1 x n 1 alpha n 1 x alpha n is stable for all alpha k in a k b k t 0 a k c k t 0 cup a k 0 leq k leq n several further observations allow us to reduce the computational cost considerably

stability of perturbed polynomials based on the argument principle and nyquist criterion the stability robustness of the characteristic polynomial with perturbed coefficients for linear time invariant systems is studied the schur strictly hurwitz and g stability properties of perturbed polynomials are all considered with a unified approach new upper bounds on the allowable coefficient perturbation of a polynomial for keeping one of the stability properties are obtained the proposed upper bounds are directly formulated in terms of the polynomial coefficients and can be computed easily we also provide a sufficient condition for the discrete stability of interval polynomials and an algorithm for testing the g stability of polynomials with constant coefficients illustrative examples are given to show the applicability of our results especially in determining measures of stability robustness for any schur polynomial subject to coefficient perturbation

ostrowski type inequalities on h type groups the main aim of this paper is to establish an ostrowski type inequality on h type groups using the l norm of the horizontal gradient the work has been motivated by the work of anastassiou and goldstein in g a anastassiou j a goldstein higher order ostrowski type inequalities over euclidean domains j math anal appl 337 2008 962 968

higher order ostrowski type inequalities over euclidean domains abstract the classical ostrowski inequality for functions on intervals estimates the value of the function minus its average in terms of the maximum of its first derivative this result is extended to functions on general domains using the l norm of its n th partial derivatives for radial functions on balls the inequality is sharp

fuzzy cardinality and the modeling of imprecise quantification abstract the concept of cardinality of a fuzzy set has received attention from several researchers and has been defined in several apparently independent manners a systematic investigation of this notion is performed which unifies and improves previous attempts the cardinality of a fuzzy set viewed as a fuzzy integer is related to scalar cardinality indices the closely related question of the probability of a fuzzy event is dealt with lastly the usefulness of fuzzy cardinality for meaning representation of statements or queries involving fuzzy linguistic quantifiers is emphasized

a generalization of the routh hurwitz stability criteria and an application to a problem in robust controller design the classical results of routh and hurwitz on the stability of polynomials are generalized from the open left half plane to certain other subregions g of the complex plane by our method arbitrary conic sections can be handled the results are interpreted as criteria for g stability of linear systems a numerical algorithm to compute the criteria is given an application to a problem in robust controller design is outlined

invariance of a strict hurwitz property for uncertain polynomials with dependent coefficients this note is concerned with the invariance of strict hurwitz property for uncertain polynomials having dependent coefficients a feasible test criterion is provided which reduces the conservatism of the kharitonov theorem

linear system stability under parameter uncertainties a sufficient condition for linear system stability under parameter variations is presented it yields parameter bounds which are not conservative and the test is easily implemented on a digital computer

strictly hurwitz property invariance of quartics under coefficient perturbation in this note it is shown how the maximum interval centered around each of the coefficients of a prescribed fourth degree strictly hurwitz polynomial may be determined so that the strictly hurwitz property remains invariant when each coefficient might be perturbed to any arbitrary value within its permissible interval

ostrowski type inequalities for functions whose higher order derivatives have a single point of non differentiability ostrowski type inequalities for the class of functions whose n 1 th order derivatives are continuous of bounded variation and have a single point of non differentiability are derived special attention is given to functions whose first derivative has a single point of non differentiability improvements of some previously obtained results are provided

hardy type inequalities and pohozaev type identities for a class of p degenerate subelliptic operators and applications abstract the purpose of this paper is to consider a class of p degenerate subelliptic operators l p constructed by generalizing greiner s vector fields their fundamental solutions at the origin are established with the aid of the properties of radial functions a picone type identity and a hardy type inequality with respect to vector fields are proved some pohozaev type identities and applications to nonlinear equations are given finally a carleman type estimate and uniqueness of the operator l 2 are discussed

a note on the location of the roots of a polynomial two new theorems and two corollaries are presented which give sufficient conditions for a polynomial to have all its roots inside the unit circle these results unify and extend certain earlier stability tests for discrete time systems the significance of the new results is illustrated by a couple of examples

fuzzy cardinals based on the generalized equality of fuzzy subsets the purpose of this paper is to present a new concept of the cardinality of finite fuzzy subsets which is based on the notion of the generalized equality the proposed idea will be compared with several approaches which were earlier offered in fuzzy literature using the new definition of the fuzzy cardinality we next introduce a notion of fuzzy semicardinals i e we construct fuzzy natural numbers defining degrees to which a finite fuzzy subset has respectively at most least and less than more than k elements various properties of different fuzzy cardinals and semicardinals as well as some interdependences between them are also given

general euler ostrowski formulae and applications to quadratures the aim of this paper is to generalize inequality f x 1 b a ab f s1 ds1 f b f a b a x a b 2 f b f a 2 b a x2 a b x a2 b2 4ab 6 f b a 3 6i x a b a obtained in a aglic aljinovic m matic j pecaric improvements of some ostrowski type inequalities j comput anal appl in press and therefore obtain a generalization and improvement of inequality f x 1 b a ab f s1 ds1 f b f a b a x a b 2 f b f a 2 b a x2 a b x a2 b2 4ab 6 f a x b a 3 obtained in g a anastassiou univariate ostrowski inequalities revisited monatsh math 135 2002 175 189 to do this first we derive general euler ostrowski formulae which generalize extended euler formulae obtained in lj dedic m matic j pecaric on generalizations of ostrowski inequality via some euler type identities math inequal appl 3 3 2000 337 353 the main novelty is that a remainder is expressed in terms of bn x mt which enables us to obtain a vide variety of quadrature formulae such as trapezoid midpoint bitrapezoid twopoint formulae and their multipoint generalizations

allowable coefficient perturbations with preserved stability of a hurwitz polynomial given a polynomial p s ansn an 11sn 1 a1s a0 which satisfies the routh hurwitz criterion a procedure is given for finding non conservative upper bounds on the allowable variations of the coefficients such that the perturbed polynomial maintains the stability property

cardinality quantifiers and the aggregation of fuzzy criteria abstract in this paper we are interested in counting the number of elements of a fuzzy set we study two concepts of fuzzy cardinality one which gives the answer as a fuzzy set or fuzzy number and the other which gives an ordinary integer relationships between these concepts and others which have been studied in the literature e g sigma count are also investigated some properties of the new concepts are studied such as fuzzy convexity monotonicity and additivity the concepts of fuzzy cardinality are important for a better understanding of fuzzy quantified rules of the form qx s are a or qa s are b where q is a fuzzy quantifier and a b are fuzzy sets we study such rules as well as aggregation rules of the form q of a1 ap contain x

invariance of the strict hurwitz property for polynomials with perturbed coefficients given a strictly hurwitz polynomial f lambda lambda n a n 1 lambda n 1 a n 2 lambda n 2 a 1 lambda a 0 it is of interest to know how much the coefficients a i can be perturbed while simultaneously preserving the strict hurwitz property for systems with n leq 4 maximal intervals of the a i are given in a recent paper by guiver and bose 1 in this note a theorem of kharitonov is exploited to obtain a general result for polynomials of any degree

cardinality concepts for type two fuzzy sets in this paper we define generalized concepts of cardinality of a fuzzy valued function and obtained some properties of these new concepts also we investigate examples for the calculation of two generalized cardinality of fuzzy valued functions and compared with concepts of cardinality of a fuzzy set and a fuzzy valued function

on possibilities of the extension of kharitonov s stability test for interval polynomials to the discrete time case it is shown that the kharitonov test for hurwitz stability of an interval polynomial does not extend in general to the discrete time case unless the degree n of the polynomial is not greater than two for n leq 3 a given monic interval polynomial has all roots inside the unit disk if all 2 3 8 extreme polynomials have that property instead of only four polynomials in kharitonov s test for n 4 it is shown by a counterexample that discrete time stability of all extreme polynomials does not guarantee the stability of the interval polynomial

correlation of fuzzy numbers abstract in this paper we introduce the concepts of correlation and correlation coefficient of fuzzy numbers which could be used to measure the interrelation of fuzzy numbers we also give a brief discussion about the so called information energy of fuzzy numbers

some discrete time counterparts to kharitonov s stability criterion for uncertain systems in 1 kharitonov gave an elegant and simple stability criterion for continuous time systems this note reports on similar results for discrete time systems

extensions of fuzzy aggregation abstract we discuss the equivalence between aggregation of fuzzy sets and integration with respect to a special class of non additive set functions both fuzzy integral and choquet integral are considered first we study aggregation of a finite family of fuzzy sets and then we extend our results to aggregation of an infinite family the concepts of comonotonic maxitivity and additivity play a central role we argue that for the purpose of aggregating fuzzy sets comonotonic maxitivity is a more desirable requirement than comonotonic additivity in the absence of any such requirement we explore a wider class of aggregation procedures another important subject that we study is a comparison between two aggregation functions and we obtain a simple characterization in both the finite and infinite case our results are related to concepts that were studied in the three areas where non additive set functions and integrals were found particularly useful fuzzy sets theory mathematical economics and mathematical statistics

on the stability properties of polynomials with perturbed coefficients given a polynomial p c s s n t 1 s n 1 t n 0 which is hurwitz or p d z z n t 1 z n 1 t n 0 which has zeros only within or on the unit circle it is of interest to know how much the coefficients t j can be perturbed while preserving the stability properties in this note a method is presented for obtaining the largest hypersphere centered at t t t 1 t n containing only polynomials which are stable

ostrowski type inequalities and hardy inequalities with boundary terms related to the generalized greiner operator in this paper we first show a representation formula related to the generalized greiner operator by an improved method then using the representation formula and l norm of the horizontal gradient we establish ostrowski type inequalities in the ball and general bounded domain related to the generalized greiner operator moreover in the same spirit we show the hardy inequalities with boundary terms keywords generalized greiner operator representation formula ostrowski type inequal ity hardy inequality mr 2010 subject classification 35r45 26d10 35j70 clc number o178 document code a article id 1000 0917 2015 01 0091 11

gruss and ostrowski type inequalities abstract in this paper we use a method originated in s s dragomir some gruss type inequalities in inner product spaces j inequal pure appl math 4 2 2003 article 42 to establish some gruss and ostrowski type inequalities

a type 2 fuzzy approach to linguistic summarization of data this paper introduces an application of type 2 fuzzy sets in data linguistic summarization the original approach by yager 1982 based on representing natural language statements via type 1 i e the zadeh fuzzy sets is generalized with type 2 fuzzy sets applied as models of linguistically expressed quantities and or properties of objects type 2 sets extend the known summarization procedures by handling fuzzy values stored in databases and allow to represent a linguistic term via a few different membership functions e g provided by different experts which makes the method more general and human consistent furthermore quality measures for type 2 summaries are discussed in order to evaluate the informativeness of the messages generated finally two prototype applications are presented and the success of the new method is discussed