on twisted q hurwitz zeta function and q two variable l function abstract in this study by applying the mellin transformation to the generating function of the h q bernoulli polynomials we construct integral representation of the twisted h q hurwitz function and twisted h q two variable l function these functions are interpolate the twisted h q bernoulli polynomials and generalized twisted h q bernoulli numbers at non positive integers respectively we also give the relation between twisted h q hurwitz zeta function and twisted h q two variable l function

on p adic interpolating function for q euler numbers and its derivatives abstract in this paper we study a two variable p adic q l function l p q s t for dirchlet s character with the property that l p q n t e n n q p t 2 q 2 q p n p p q n e n n q p t for positive integers n and t c p with t p 1 and e n n q x generalized euler polynomials finally we prove that l p q s t is analytic in s and t for s c p with s p p 1 1 p 1 and t c p with t p 1

an iterative method for linear discrete ill posed problems with box constraints many questions in science and engineering give rise to linear discrete ill posed problems often it is desirable that the computed approximate solution satisfies certain constraints e g that some or all elements of the computed solution be nonnegative this paper describes an iterative method of active set type for the solution of large scale problems of this kind the method employs conjugate gradient iteration with a stopping criterion based on the discrepancy principle and allows updates of the active set by more than one index at a time

polar decomposition in e rings an e ring is a generalization of the ring of bounded linear operators on a hilbert space together with the subset consisting of all effect operators on that space associated with an e ring is a partially ordered abelian group called its directed group that generalizes the additive group of bounded hermitian operators on the hilbert space we prove that every element of the directed group of an e ring has a polar decomposition if and only if every element has a carrier projection and is split by a projection into a positive and a negative part

a hierarchical neural model of matching abstract the issue of matching two fuzzy sets emerges as an essential design aspect in many algorithms of processing fuzzy information including fuzzy controllers pattern classifiers knowledge based systems etc this paper introduces a new model of matching the primordial features of the proposed model involve 1 i matching being carried out with respect to the grades of membership of the discussed fuzzy sets as well as some of their functionals like energy entropy transom 2 ii the concepts of hierarchies of matching in the model leading directly to a straightforward distinction between local and global levels of matching and 3 iii a distributed character of the model that is realized as a logic based neural network with enhanced learning capabilities

q dedekind type sums related to q zeta function and basic l series abstract the main purpose of this paper is to define new generating functions by applying the mellin transformation formula to these generating functions we define q analogue of riemann zeta function q analogue hurwitz zeta function q analogue dirichlet l function and two variable q l function in particular by using these generating functions we will construct new generating functions which produce q dedekind type sums and q dedekind type sums attached to dirichlet character we also give the relations between these sums and dedekind sums furthermore by using product which is given in this paper we will give the relation between dedekind sums and q l function as well

on p adic q l functions and sums of powers abstract in this paper we give an explicit p adic expansion of j 1 j p 1 n p 1 j q j j q r as a power series in n the coefficients are values of p adic q l function for q euler numbers

on the q extension of euler and genocchi numbers abstract carlitz has introduced an interesting q analogue of frobenius euler numbers in l carlitz q bernoulli numbers and polynomials duke math j 15 1948 987 1000 l carlitz q bernoulli and eulerian numbers trans amer math soc 76 1954 332 350 he has indicated a corresponding stadudt clausen theorem and also some interesting congruence properties of the q euler numbers a recent author s study of more general q euler and genocchi numbers can be found in previous publication t kim l c jang h k pak a note on q euler and genocchi numbers proc japan acad ser a math sci 77 2001 139 141 in this paper we give a new construction of q euler numbers which are different from carlitz s q extension and author s q extension in previous publication see t kim l c jang h k pak a note on q euler and genocchi numbers proc japan acad ser a math sci 77 2001 139 141 by using our q extension of euler numbers we can also consider a new q extension of genocchi numbers and obtain some interesting relations between q extension of euler numbers and q extension of genocchi numbers

twisted h q bernoulli numbers and polynomials related to twisted h q zeta function and l function abstract in this paper by using q volkenborn integral we construct new generating functions of the new twisted h q bernoulli polynomials and numbers by applying the mellin transformation to these generating functions we obtain integral representations of the new twisted h q zeta function and twisted h q l function which interpolate the twisted h q bernoulli numbers and generalized twisted h q bernoulli numbers at non positive integers respectively furthermore relation between twisted h q zeta function and twisted h q l function are proved some new relations related to twisted h q bernoulli polynomials and numbers are given

connectives and fuzziness for classical effects abstract this article investigates various constructs on a set of classical effects measurable fuzzy sets or fuzzy events we begin by studying the properties of a connective and its dual connective which seem to have been neglected in the literature the importance of these connectives for fuzzy probability theory is pointed out we then introduce and investigate the properties of a commutator which can be employed to define a degree of relative fuzziness a special case of this commutator defines a degree of fuzziness the expectation of the commutator provides a relative entropy whose properties are delineated and the expectation of the special case gives an entropy function that has been previously studied as a measure of fuzziness

an iterative image space reconstruction algorthm suitable for volume ect the trend in the design of scanners for positron emission computed tomography has traditionally been to improve the transverse spatial resolution to several millimeters while maintaining relatively coarse axial resolution 1 2 cm several scanners are being built with fine sampling in the axial as well as transverse directions leading to the possibility of the true volume imaging the number of possible coincidence pairs in these scanners is quite large the usual methods of image reconstruction cannot handle these data without making approximations it is computationally most efficient to reduce the size of this large sparsely populated array by back projecting the coincidence data prior to reconstruction while analytic reconstruction techniques exist for back projected data an iterative algorithm may be necessary for those cases where the point spread function is spatially variant a modification of the maximum likelihood algorithm is proposed to reconstruct these back projected data the method the iterative image space reconstruction algorithm isra is able to reconstruct data from a scanner with a spatially variant point spread function in less time than other proposed algorithms results are presented for single slice data simulated and actual from the penn pet scanner

on the combinatorics of normal ordering bosonic operators and deformations of it recently some combinatorial aspects for the normal ordering of powers of arbitrary monomials of boson operators were discussed in particular it was shown that the resulting formulae lead to generalizations of the usual bell and stirling numbers in this paper these considerations are generalized to the q deformed case in particular it is shown that the simplest example of this generalization leads to q deformed lah numbers the connection between generalized stirling and bell numbers and matrix elements of the above mentioned operators with respect to the usual fock space basis and coherent states is discussed

stirling number identities interconsistency of q analogues q analogues of stirling number identities are formulated and the interconsistency among the q analogues of the stirling numbers and of the binomial coefficients is investigated the close relation with the normal ordering problem for arik coon type q bosons plays a central role in the derivations presented

on the degree of fuzziness of a fuzzy set abstract the purpose of this paper is to study the notion of transom fuzzy indefinite integral on the algebra m x of fuzzy measurable subsets of a given space x this integral is defined with respect to a usual measure the probability of a fuzzy event a defined by a lebesgue stieltjes integral introduced by zadeh 10 is obtained as a particular case this measure is used to distinguish fuzzy sets which have the same fuzzy degree thus we introduce two parameters for characterizing the fuzziness of a fuzzy set

generalized cross validation applied to conjugate gradient for discrete ill posed problems in this paper we propose a new method to apply the generalized cross validation gcv as a stopping rule for the conjugate gradient cg in general to apply gcv to an iterative method one must estimate the trace of the so called influence matrix which appears in the denominator of the gcv function in the case of cg unlike what happens with stationary iterative methods the regularized solution has a nonlinear dependence on the noise which affects the data of the problem this fact is often pointed out as a cause of poor performance of gcv to overcome this drawback our proposal linearizes the dependence by computing the derivatives through iterative formulas we compare the proposed method with other methods suggested in the literature by an extensive numerical experimentation on both 1d and 2d test problems

image regularization by nonnegatively constrained conjugate gradient abstract in the image reconstruction context the nonnegativity of the computed solution is often required conjugate gradient cg used as a reliable regularization tool may give solutions with negative entries particularly when large nearly zero plateaus are present the active constraints set detected by projection onto the nonnegative orthant turns out to be largely incomplete leading to poor effects on the accuracy of the reconstructed image in this paper an inner outer method based on cg is proposed to compute nonnegative reconstructed images with a strategy which enlarges subsequently the active constraints set this method appears to be especially suitable for the reconstruction of images having large nearly zero backgrounds the numerical experimentation validates the effectiveness of the proposed method when compared to other strategies for nonnegative reconstruction

direct and inverse problem in comparison of fuzzy data abstract discussed is the direct and inverse problem of comparison of two linguistic quantities specified as fuzzy sets relations in the same universe of discourse the proposed way of comparison makes use of some logical properties of connectives and implication operators stemming from the foundations of fuzzy sets a list of plausible equality indices is provided the inverse problem is formulated a set of its solutions is provided direct impacts of the discussed approach on development of fuzzy modelling are clearly indicated also it is pointed out how fuzzy sets of higher type or interval valued sets can be generated as a result of analysis of performance of any fuzzy model

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

interpolation function of the h q extension of twisted euler numbers in h ozden y simsek i n cangul generating functions of the h q extension of euler polynomials and numbers acta math hungarica in press doi 10 1007 510474 008 7139 1 by using p adic q invariant integral on z p in the fermionic sense ozden et al constructed generating functions of the h q extension of euler polynomials and numbers they defined h q euler zeta functions and h q euler l functions they also raised the following problem find ap adic twisted interpolation function of the generalized twisted h q euler numbers e n g w h q the aim of this paper is to give a partial answer to this problem therefore we constructed twisted h q partial zeta function and twisted p adic h q euler l functions l e p x q h s g 2 m 1 m p 1 g m 1 m x mq h mm s which interpolate h q extension of euler numbers at negative integers l e p x q h n g e n x g n h q p n g n p e n x p g n h q p by using this interpolation function and twisted h q partial zeta function we proved distribution relations of the h q extension of generalized euler polynomials consequently we find a partial answer to the above question

p adic distribution of the unification of the bernoulli euler and genocchi polynomials abstract the aim of this paper is to construct p adic distribution on x c p of the unification of the bernoulli euler and genocchi polynomials y n x k a b which is given by n k a b j dp n z p a b dp n p dp n n k a jb y n dp n j dp n k a dp n b where y n x k a b are defined by 1 1 we give some applications related to these functions and distribution

q hardy berndt type sums associated with q genocchi type zeta and q l functions abstract the aim of this paper is to define new generating functions by applying a derivative operator and the mellin transformation to these generating functions we define q analogue of the genocchi zeta function q analogue hurwitz type genocchi zeta function and q genocchi type l function we define partial zeta function by using this function we construct p adic interpolation functions which interpolate generalized q genocchi numbers at negative integers we also define p adic meromorphic functions on c p furthermore we construct new generating functions of q hardy berndt type sums and q hardy berndt type sums attached to dirichlet character we also give some new relations related to these sums

some new identities for the apostol bernoulli polynomials and the apostol genocchi polynomials in this paper we present a further investigation for the apostol bernoulli polynomials and the apostol genocchi polynomials by making use of the generating function methods and summation transform techniques we establish some new identities involving the products of the apostol bernoulli polynomials and the apostol genocchi polynomials many of the results presented here are the corresponding generalizations of some known formulas on the classical bernoulli polynomials and the classical genocchi polynomials

some relationships between the apostol bernoulli and apostol euler polynomials recently srivastava and pinter 1 investigated several interesting properties and relationships involving the classical as well as the generalized or higher order bernoulli and euler polynomials they also showed among other things that the main relationship proven earlier by cheon 2 can easily be put in a much more general setting the main object of the present sequel to these earlier works is to derive several general properties and relationships involving the apostol bernoulli and apostol euler polynomials some of these general results can indeed be suitably specialized in order to deduce the corresponding properties and relationships involving the generalized bernoulli and generalized euler polynomials other relationships associated with the stirling numbers of the second kind are also considered

brouwer zadeh posets and three valued ł ukasiewicz posets abstract this paper is a study of the structure of brouwer zadeh or bz poset i e a poset endowed with two non usual orthocomplementations these two orthocomplementations allow definition of two unary operators which can be considered as algebraic counterparts of the necessity and possibility operators of modal logic a construction of how to induce a three valued bz poset from a bz poset is given the examples of the bz lattice of all generalized characteristic functionals on a reference space and of the bz poset of all generalized orthogonal projections on a hilbert space are dealt with

construction a new generating function of bernstein type polynomials abstract main purpose of this paper is to reconstruct generating function of the bernstein type polynomials some properties of this generating functions are given by applying this generating function not only derivative of these polynomials but also recurrence relations of these polynomials are found interpolation function of these polynomials is also constructed by mellin transformation this function interpolates these polynomials at negative integers which are given explicitly moreover relations between these polynomials the stirling numbers of the second kind and bernoulli polynomials of higher order are given furthermore some remarks associated with the bezier curves are given

on the analogs of euler numbers and polynomials associated with p adic q integral on zp at q 1 abstract the purpose of this paper is to construct euler numbers and polynomials by using fermionic expression of p adic q integral at q 1 from these euler polynomials we derive the harmonic sums of higher order finally we investigate several interesting properties and relationships involving the classical as well as the generalized euler numbers and polynomials as an application we will treat p adic invariant integrals on z p involving trigonometric functions

new changhee q euler numbers and polynomials associated with p adic q integrals using non archimedean q integrals on z p defined in t kim on a q analogue of the p adic log gamma functions and related integrals j number theory 76 1999 320 329 t kim q volkenborn integration russ j math phys 9 2002 288 299 we define new changhee q euler polynomials and numbers which are different from those of kim t kim p adic q integrals associated with the changhee barnes q bernoulli polynomials integral transforms spec funct 15 2004 415 420 and carlitz l carlitz q bernoulli and eulerian numbers trans amer math soc 76 1954 332 350 we define generating functions of multiple q euler numbers and polynomials furthermore we construct a multivariate hurwitz type zeta function which interpolates the multivariate q euler numbers or polynomials at negative integers

modification and unification of the apostol type numbers and polynomials and their applications abstract in this paper we construct generating functions for modification and unification of the apostol type polynomials y n v x k a b of order v by using these generating functions we derive many new identities related to the generalized stirling type numbers of the second kind array type polynomials eulerian polynomials and the modification and unification of the apostol type polynomials and numbers we give many applications related to these numbers and polynomials and pdes

a family of p adic twisted interpolation functions associated with the modified bernoulli numbers the main purpose of this paper is to construct a family of modified p adic twisted functions which interpolate the modified twisted q bernoulli polynomials and the generalized twisted q bernoulli numbers at negative integers we also give some applications and examples related to these functions and numbers

towards the theory of fuzzy differential equations comparative analysis of two ideologically distinct approaches in the theory of fuzzy differential equations is given domains of applications advantages and shortcomings of those approaches are described new definitions of solutions to fuzzy differential equations are proposed

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

the instability of some gradient methods for ill posed problems for the solution of linear ill posed problems some gradient methods like conjugate gradients and steepest descent have been examined previously in the literature it is shown that even though these methods converge in the case of exact data their instability makes it impossible to base a priori parameter choice regularization methods upon them

fuzzy neural networks with reference neurons as pattern classifiers a heterogeneous neural network consisting of logic neurons and realizing mappings in 0 1 hypercubes is presented the two kinds of neurons studied are utilized to perform matching functions equality or reference neurons and aggregation operations aggregation neurons all computations are driven by logic operations widely used in fuzzy set theory the network is heterogeneous in its nature and includes two types of neurons organized into a structure detecting individual regions of patterns using reference neurons and combining them to yield a final classification decision

fuzzy sets and statistical data abstract specific features of probability and possibility theories are discussed with emphasis on semantical aspects instead of putting forward the acknowledged usefulness of possibility theory for the non statistical modelling of subjective categories we try to figure out how statistical data and possibility theory could be matched as a result procedures for constructing weak possibilistic substitutes of probability measures and for processing imprecise statistical data are outlined they provide new insights on relationship between fuzzy sets and probability theories

on the behavior of two variable twisted p adic euler q l functions abstract in this paper we study on h q euler zeta and l functions we give relations between twisted h q partial zeta function twisted h q euler zeta and twisted two variable h q euler l functions we also give the value of twisted two variable h q euler l function at s 0 the main purpose of this paper is to construct two variable twisted p adic euler h q l function which interpolates twisted h q euler polynomials at negative integers we give p adic fermionic integral representation of this functions

some generalizations of the apostol bernoulli and apostol euler polynomials abstract the main object of this paper is to give analogous definitions of apostol type see t m apostol on the lerch zeta function pacific j math 1 1951 161 167 and h m srivastava some formulas for the bernoulli and euler polynomials at rational arguments math proc cambridge philos soc 129 2000 77 84 for the so called apostol bernoulli numbers and polynomials of higher order we establish their elementary properties derive several explicit representations for them in terms of the gaussian hypergeometric function and the hurwitz or generalized zeta function and deduce their special cases and applications which are shown here to lead to the corresponding results for the classical bernoulli numbers and polynomials of higher order

some generalizations of the apostol genocchi polynomials and the stirling numbers of the second kind abstract recently the authors introduced some generalizations of the apostol bernoulli polynomials and the apostol euler polynomials see q m luo h m srivastava j math anal appl 308 2005 290 302 and q m luo taiwanese j math 10 2006 917 925 the main object of this paper is to investigate an analogous generalization of the genocchi polynomials of higher order that is the so called apostol genocchi polynomials of higher order for these generalized apostol genocchi polynomials we establish several elementary properties provide some explicit relationships with the apostol bernoulli polynomials and the apostol euler polynomials and derive various explicit series representations in terms of the gaussian hypergeometric function and the hurwitz or generalized zeta function we also deduce their special cases and applications which are shown here to lead to the corresponding results for the genocchi and euler polynomials of higher order by introducing an analogue of the stirling numbers of the second kind that is the so called stirling numbers of the second kind we derive some basic properties and formulas and consider some interesting applications to the family of the apostol type polynomials furthermore we also correct an error in a previous paper q m luo h m srivastava comput math appl 51 2006 631 642 and pose two open problems on the subject of our investigation

on the twisted q euler numbers and polynomials associated with basic q l functions one of the purposes of this paper is to construct the twisted q euler numbers by using p adic invariant integral on zp in the fermionic sense moreover we consider the twisted euler q zeta functions and q l functions which interpolate the twisted q euler numbers and polynomials at a negative integer

a unified presentation of the generating functions of the generalized bernoulli euler and genocchi polynomials the goal of this paper is to unify and extend the generating functions of the generalized bernoulli polynomials the generalized euler polynomials and the generalized genocchi polynomials associated with the positive real parameters a and b and the complex parameter b by using this generating function we derive recurrence relations and other properties for these polynomials by applying the mellin transformation to the generating function of the unification of bernoulli euler and genocchi polynomials we construct a unification of the zeta functions furthermore we give many properties and applications involving the functions and polynomials investigated in this paper

a unified presentation of certain meromorphic functions related to the families of the partial zeta type functions and the l functions abstract the aim of this paper is to construct a unified family of meromorphic functions which is related to many known functions such as a unified family of partial zeta type functions a unified family of l functions and so on we investigate and derive many properties of this family of meromorphic functions moreover we compute the residues of this family of meromorphic functions at their poles we also give some applications and remarks involving this family of meromorphic functions

bernoulli numbers in p adic analysis in this paper we consider new representations of the analogue higher order bernoulli numbers in p adic analysis also we prove kummer type congruence for these numbers using ota s method j number theory 92 2002 1 which is a solution to a part of the question 2 in the paper by jang and kim appl math comput 137 2 3 2003 387

identities of symmetry for q bernoulli polynomials in this paper we derive eight basic identities of symmetry in three variables related to q bernoulli polynomials and the q analogue of power sums these and most of their corollaries are new since there have been results only concerning identities of symmetry in two variables these abundant symmetries shed new light even on the existing identities so as to yield some further interesting ones the derivations of the identities are based on the p adic integral expression of the generating function for the q bernoulli polynomials and the quotient of integrals that can be expressed as the exponential generating function for the q analogue of power sums

a new approach to q genocchi numbers and their interpolation functions abstract the aim of this paper is to define generating functions of higher order q genocchi numbers by using a p adic q deformed fermionic integral on z p we give witt s type integral of these numbers furthermore we give the interpolation functions of these numbers

some series identities involving the generalized apostol type and related polynomials a unification and generalization of various apostol type polynomials was introduced and investigated recently by luo and srivastava q m luo h m srivastava some generalizations of the apostol genocchi polynomials and the stirling numbers of the second kind appl math comput 217 2011 5702 5728 in this paper we prove several symmetry identities for these generalized apostol type polynomials by using their generating functions as special cases and consequences of our results we obtain the corresponding symmetry identities for the apostol euler polynomials of higher order the apostol bernoulli polynomials of higher order and the apostol genocchi polynomials of higher order and also for another family of generalized apostol type polynomials which were investigated systematically by ozden et al h ozden y simsek h m srivastava a unified presentation of the generating functions of the generalized bernoulli euler and genocchi polynomials comput math appl 60 2010 2779 2787 we also derive several relations between the apostol type polynomials the generalized sum of integer powers and the generalized alternating sum it is shown how each of these results would extend the corresponding known identities

unified apostol bernoulli euler and genocchi polynomials in this paper we present a unified family of polynomials including not only the apostol bernoulli euler and genocchi polynomials but also a general family of polynomials suggested by ozden et al h ozden y simsek h m srivastava a unified presentation of the generating functions of the generalized bernoulli euler and genocchi polynomials comput math appl 60 10 2010 2779 2787 we obtain the explicit representation of this unified family in terms of a gaussian hypergeometric function some symmetry identities and multiplication formula are also given

non usual orthocomplementations on partially ordered sets and fuzziness abstract in this paper we are interested in partially ordered sets for which non usual orthocomplementations can be introduced in particular we consider orthocomplementation mappings which associate with any element a its non usual orthocomplement or negation a with the properties of being weak i e a a a and degenerate i e it may happen that for certain elements a a holds as examples of this we discuss the distributive complete lattice of all generalized characteristic functions or fuzzy sets and the analogous structure of a suitable class of self adjoint bounded operators in hilbert space also called fuzzy projections

twisted p adic h q l functions by using the q volkenborn integral on z p in simsek 2006 33 and simsek 2007 34 generating functions for the h q bernoulli polynomials and numbers were defined by using these functions we define a new twisted h q partial zeta function which interpolates the twisted h q bernoulli polynomials and generalized twisted h q bernoulli numbers at negative integers we give a relation between twisted h q partial zeta functions and the twisted h q two variable l function we find the value of this function at s 0 we also find the residue of this function at s 1 we construct a p adic twisted h q l function which interpolates the twisted h q bernoulli polynomials l x p q h 1 n t g b n g n x h p t q email protected n p p n 1b n g n 1 h p 1p t q p n furthermore we construct an integral representation of the twisted h q two variable l function we give some applications related to the p adic twisted h q l function and the twisted h q bernoulli polynomials

weighted fuzzy pattern matching the fuzzy pattern matching technique has been developed in the framework of fuzzy set and possibility theory in order to take into account the imprecision and the uncertainty pervading values which have to be compared in a matching process this technique has proved very useful for implementing patterns of approximate reasoning in expert system inference engines and for designing retrieval systems capable of managing incomplete and fuzzy information data bases and vague queries in this paper the fuzzy pattern matching procedure is improved by introducing weights assessing the relative importance of atoms in the pattern matching indices are obtained using weighted versions of the minimum and maximum operations of fuzzy set theory this approach is extended to the case of variable weights and is related to aggregation schemes proposed by yager when modeling soft quantified statements such as most of the criteria must be met a notion of soft partial matching is thus modelled

notes on generalization of the bernoulli type polynomials abstract recently srivastava et al introduced a new generalization of the bernoulli euler and genocchi polynomials see h m srivastava m garg s choudhary russian j math phys 17 2010 251 261 and h m srivastava m garg s choudhary taiwanese j math 15 2011 283 305 they established several interesting properties of these general polynomials the generalized hurwitz lerch zeta functions and also in series involving the familiar gaussian hypergeometric function by the same motivation of srivastava s et al 11 12 we introduce and derive multiplication formula and some identities related to the generalized bernoulli type polynomials of higher order associated with positive real parameters a b and c we also establish multiple alternating sums in terms of these polynomials moreover by differentiating the generating function of these polynomials we give a interpolation function of these polynomials

a fast monte carlo cross validation procedure for large least squares problems with noisy data we propose a fast monte carlo algorithm for calculating reliable estimates of the trace of the influence matrixa involved in regularization of linear equations or data smoothing problems where is the regularization or smoothing parameter this general algorithm is simply as follows i generaten pseudo random valuesw 1 w n from the standard normal distribution wheren is the number of data points and letw w 1 w n t ii compute the residual vectorw a w iii take the normalized inner product w t w a w w t w as an approximation to 1 n tr i a we show both by theoretical bounds and by numerical simulations on some typical problems that the expected relative precision of these estimates is very good whenn is large enough and that they can be used in practice for the minimization with respect to of the well known generalized cross validation gcv function this permits the use of the gcv method for choosing in any particular large scale application with only a similar amount of work as the standard residual method numerical applications of this procedure to optimal spline smoothing in one or two dimensions show its efficiency