fuzzy subfields of finite fields abstract basic structure theorems are given for fuzzy subfieldsof finite fields in particular the result that a finite field f is generated over its prime subfield z p by any generator of the multiplicative group f 0 is carried over to fuzzy subfields for f it is also shown that every fuzzy subfield of f is a direct sum of fuzzy subgroups whose supportsare cyclic and of order p of the additive group f

fuzzy vector spaces abstract this paper defines a basis for a fuzzy vector space and its dimension a class of fuzzy vector spaces having dimension is introduced and two standard results from crisp theory are proved for this case namely d i m e1 e2 d i m e1 d i m e2 d i m e1 e2 and rmd i m i m f d i m k e r f the product of two fuzzy vector spaces under certain conditions is also characterised

a fuzzy subgroupoid which is not a fuzzy group abstract we give an example to show that the proposition a fuzzy subgroupoid of a group must be a fuzzy group which appeared in fuzzy sets and systems 51 1992 105 109 structure and constructing of fuzzy subgroups of a group by l filep is wrong we also point out that the proof of theorem 6 in the same article is not true we give a valid proof of it

prime fuzzy ideals in rings abstract in this paper give a characterization of prime fuzzy ideals we introduce weakly completely prime fuzzy ideals and establish a relation between completely prime fuzzy ideals and weakly completely prime fuzzy ideals

a contribution to the theory of fuzzy subgroups abstract in this paper we continue our study in order to give a partial answer to the question suggested by asaad in 1991 what can be said about the structure of a group g when the information are known about the structure of a fuzzy subgroup a of g and viceversa

fuzzy e subgroups the aim of the paper is to investigate the known classical problem of a partition of a semigroup into a family of groups in the lattice valued fuzzy framework for that purpose a fuzzy subgroup of a fuzzy subsemigroup is introduced and characterized by cuts using the cutworthy approach as a main result it is proved that a fuzzy subsemigroup can be partitioned using special type of fuzzy partitions into a family of fuzzy e subgroups if and only if it is fuzzy completely regular

on fuzzy ideals and fuzzy quotient rings of a ring abstract in this paper we define fuzzy quotient rings induced by fuzzy ideals and give the notion of fuzzy nilpotent ideals we give also a characterization of semiprime rings in terms of fuzzy ideals

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

a sieve estimator for the covariance of a gaussian process on considere l estimation du maximum de vraisemblance de la covariance r d un processus gaussien de moyenne nulle avec aucune hypothese sur la covariance ou sur l ensemble des parametres temps on montre que la fonction de vraisemblance est presque surement non bornee en general et on construit un estimateur r

a note on an equivalence relation of fuzzy subgroups the purpose of this paper is to discuss the following three problems 1 the number of equivalent classes of fuzzy subgroups of a group g 2 the relationship between the number of equivalent classes of fuzzy subgroups and the order of a cyclic group g 3 the relationship between the order of fuzzy subgroups and the order of a cyclic group g 4 a classification of a group using membership values of fuzzy subgroups is given

fuzzy maximal radical and primary ideals of a ring we introduce the concepts of fuzzy maximal ideal the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring we show that a fuzzy left right ideal a of a ring r is a fuzzy maximal ideal if and only a 0 1 and a x r a x a 0 is a maximal left right ideal of r we also show that a fuzzy ideal a of a commutative ring r with unity is a fuzzy primary ideal of r if and only a 0 1 a is two valued and a is a primary ideal of r

fuzzy groups and collections of subgroups abstract the aim of the paper is to investigate fuzzy subgroups of a group from a general point of view using collections of ordinary subgroups fuzzy subgroups are taken to be special mappings from a group to a partially ordered set which can also be a lattice and particularly the unit interval 0 1 as it is known every fuzzy subgroup uniquely determines a poset of level subgroups of the same group properties of that poset are investigated on the other hand it is proved that every collection of subgroups can be used for the construction of a suitable fuzzy subgroup of a group for that purpose particular fuzzy completions of collections of subsets are introduced it turns out that fuzzy subgroup is an intrinsic notion expressible in terms of collections of subgroups under set theoretic relations and operations

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

laguerre moments and generalized functions here we explore the link between the moments of the laguerre polynomials or laguerre moments and the generalized functions as the dirac delta function and its derivatives presenting several interesting relations a useful application is related to a procedure for calculating mean values in quantum optics that makes use of the so called quasi probabilities one of them the p distribution can be represented by a sum over laguerre moments when the electromagnetic field is in a photon number state consequently the p distribution can be expressed in terms of dirac delta function and derivatives more specifically we found a direct relation between p distributions and the laguerre factorial moments

subspace based discrete transform encoded local binary patterns representations for robust periocular matching on nist s face recognition grand challenge in this paper we employ several subspace representations principal component analysis unsupervised discriminant projection kernel class dependence feature analysis and kernel discriminant analysis on our proposd discrete transform encoded local binary patterns dt lbp to match periocular region on a large data set such as nist s face recognition grand challenge frgc ver2 database we strictly follow frgc experiment 4 protocol which involves 1 to 1 matching of 8014 uncontrolled probe periocular images to 16 028 controlled target periocular images 128 million pairwise face match comparisons the performance of the periocular region is compared with that of full face with different illumination preprocessing schemes the verification results on periocular region show that subspace representation on dt lbp outperforms lbp significantly and gains a giant leap from traditional subspace representation on raw pixel intensity additionally our proposed approach using only the periocular region is almost as good as full face with only 2 5 reduction in verification rate at 0 1 false accept rate yet we gain tolerance to expression occlusion and capability of matching partial faces in crowds in addition we have compared the best standalone dt lbp descriptor with eight other state of the art descriptors for facial recognition and achieved the best performance the two general frameworks are our major contribution 1 a general framework that employs various generative and discriminative subspace modeling techniques for dt lbp representation and 2 a general framework that encodes discrete transforms with local binary patterns for the creation of robust descriptors

o n symmetries sum rules for generalized hermite polynomials and squeezed states quantum optics has been dealing with coherent states squeezed states and many other non classical states the associated mathematical framework makes use of special functions as hermite polynomials laguerre polynomials and others in this connection we here present some formal results that follow directly from the group o n of complex transformations motivated by the squeezed states structure we introduce the generalized hermite polynomials which include as particular cases the hermite polynomials as well as the heat polynomials using generalized raising operators we derive new sum rules for the which are covariant under o n transformations the and the associated sum rules become useful for evaluating wigner functions in a straightforward manner as a byproduct we use one of these sum rules on the operator level to obtain raising and lowering operators for the laguerre polynomials and show that they generate an sl 2 r su 1 1 algebra

continuous time stochastic model simplification approximation of high order and time varying linear continuous time gaussian models by low order and time invariant models is considered the recent work of baram and be eri pertaining to the discrete time systems is extended to continuous time system models the model simplification is carried out by maximizing the probabilistic ambiguity between the actual system and the approximate model differences between the continuous time and the discrete time model simplification problems are examined the case when the observation noise covariance of the approximate model differs from that of the actual system presents technical difficulties not present in the discrete time version

galois theory for fuzzy fields abstract the aim of this paper is to present a generalized form of the galois connection between the intermediate fields of a field extension and the subgroups of the corresponding galois group we prove that the fundamental theorem of galois theory accepts a generalization in the fuzzy framework

global identification of continuous time systems with unknown noise covariance corresp global convergence pf the maximum likelihood estimates of unknown parameters of a continuous time stochastic linear dynamical system is investigated when the observation noise covariance is unknown the unknown parameter set is assumed to be finite the situation where the true parameter does not belong to the unknown parameter set is considered as well as the situation where the true model is included in the unknown parameter set convergence is proved under a certain sufficient condition called the identifiability condition

structure and construction of fuzzy subgroups of a group abstract we define the order of a fuzzy set and give conditions for different order fuzzy sets to be fuzzy subgroups through their level subgroups finally we give a list of fuzzy subgroups of order 1 6