on quandle homology groups of alexander quandles of prime order in this paper we determine the integral quandle homology groups of alexander quandles of prime order as a special case this settles the delayed f ibonacci conjecture by m niebrzydowski and j h przytycki in 7 moreover we determine the cohomology group of the alexander quandle and obtain relatively simple presentations of all higher degree cocycles which generate the cohomology group furthermore we prove that the integral quandle homology of a finite connected alexander quandle is annihilated by the order of the quandle

yang baxter deformations and rack cohomology abstract in his study of quantum groups drinfeld suggested to consider set theoretic solutions of the yang baxter equation as a discrete analogon as a typical example every conjugacy class in a group or more generally every rack q provides such a yang baxter operator cq x y 7 y x y in this article we study deformations of cq within the space of yang baxter operators infinitesimally these deformations are classified by yang baxter cohomology we show that the yang baxter cochain complex of cq homotopyretracts to a much smaller subcomplex called quasi diagonal this greatly simplifies the deformation theory of cq including the modular case which had previously been left in suspense by establishing that every deformation of cq is gauge equivalent to a quasi diagonal one in a quasi diagonal deformation only behaviourally equivalent elements of q interact if all elements of q are behaviourally distinct then the yang baxter cohomology of cq collapses to its diagonal part which we identify with rack cohomology this establishes a strong relationship between the classical deformation theory following gerstenhaber and the more recent cohomology theory of racks both of which have numerous applications in knot theory

generalized partially linear single index models abstract the typical generalized linear model for a regression of a response y on predictors x z has conditional mean function based on a linear combination of x z we generalize these models to have a nonparametric component replacing the linear combination t 0x t 0z by 0 t 0x t 0z where 0 is an unknown function we call these generalized partially linear single index models gplsim the models include the single index models which have 0 0 using local linear methods we propose estimates of the unknown parameters 0 0 and the unknown function 0 and obtain their asymptotic distributions examples illustrate the models and the proposed estimation methodology

topological gauge theories and group cohomology we show that three dimensional chern simons gauge theories with a compact gauge groupg not necessarily connected or simply connected can be classified by the integer cohomology grouph4 bg z in a similar way possible wess zumino interactions of such a groupg are classified byh3 g z the relation between three dimensional chern simons gauge theory and two dimensional sigma models involves a certain natural map fromh4 bg z toh3 g z we generalize this correspondence to topological spin theories which are defined on three manifolds with spin structure and are related to what might be calledz2 graded chiral algebras or chiral superalgebras in two dimensions finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group establishing links with two dimensional holomorphic orbifold models

knot theory for self indexed graphs we introduce and study so called self indexed graphs these are oriented finite graphs endowed with a map from the set of edges to the set of vertices such graphs naturally arise from classical knot and link diagrams in fact the graphs resulting from link diagrams have an additional structure an integral flow we call a self indexed graph with integral flow a comte the analogy with links allows us to define transformations of comtes generalizing the reidemeister moves on link diagrams we show that many invariants of links can be generalized to comtes most notably the linking number the alexander polynomials the link group etc we also discuss finite type invariants and quandle cocycle invariants of comtes

a combinatorial description of knotted surfaces and their isotopies abstract we discuss the diagrammatic theory of knot isotopies in dimension 4 we project a knotted surface to a three dimensional space and arrange the surface to have generic singularities upon further projection to a plane we examine the singularities in this plane as an isotopy is performed and give a finite set of local moves to the singular set that can be used to connect any two isotopic knottings we show how the notion of projections of isotopies can be used to give a combinatoric description of knotted surfaces that is sufficient for categorical applications in this description knotted surfaces are presented as sequences of words in symbols and there is a complete list of moves among such sequences that relate the symbolic representations of isotopic knotted surfaces

an explicit description of the second cohomology group of a quandle we use the inflation restriction sequence and a result of etingof and grana on the rack cohomology to give a explicit description of 2 cocycles of finite indecomposable quandles with values in an abelian group several applications are given

schur multipliers and second quandle homology abstract we define a map from second quandle homology to the schur multiplier and examine its properties furthermore we express the second homology of alexander quandles in terms of exterior algebras additionally we present a self contained proof of its structure and provide some computational examples

quandle homotopy invariants of knotted surfaces given a finite quandle we introduce a quandle homotopy invariant of knotted surfaces in the 4 sphere modifying that of classical links this invariant is valued in the third homotopy group of the quandle space and is universal among the generalized quandle cocycle invariants we compute the second and third homotopy groups with respect to regular alexander quandles as a corollary any quandle cocycle invariant using the dihedral quandle of prime order is a scalar multiple of mochizuki 3 cocycle invariant as another result we determine the third quandle homology group of the dihedral quandle of odd order

tail asymptotics for the busy period in the gi g 1 queue we characterise the tail behaviour of the busy period distribution in thegi g 1 queue under the assumption that the tail of the service time distribution is of intermediate regular variation this extends a result of de meyer and teugels de meyer and teugels 1980 who treated them g 1 queue with a regularly varying service time distribution our method of proof is opposed to the one in de meyer and teugels 1980 probabilistic and reveals an insightful relationship between the busy period and the cycle maximum

on quantum gauge theories in two dimensions two dimensional quantum yang mills theory is studied from three points of view i by standard physical methods ii by relating it to the largek limit of three dimensional chern simons theory and two dimensional conformal field theory iii by relating its weak coupling limit to the theory of reidemeister ray singer torsion the results obtained from the three points of view agree and give formulas for the volumes of the moduli spaces of representations of fundamental groups of two dimensional surfaces

local polynomial kernel regression for generalized linear models and quasi likelihood functions abstract we investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to generalized linear models and quasi likelihood contexts in the ordinary regression case local polynomial fitting has been seen to have several appealing features in terms of intuitive and mathematical simplicity one noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators these properties are shown to carry over to generalized linear model and quasi likelihood settings we also derive the asymptotic distributions of the proposed class of estimators that allow for straightforward interpretation and extensions of state of the art bandwidth selection methods

an asymptotic analysis of positive solutions of generalized thomas fermi differential equations the sub half linear case abstract the existence and the asymptotics behavior for the large value of the variable of the positive solutions of generalized thomas fermi equation presented in this article are proved it is assumed that coefficient q t belongs to the class of regularly varying functions in the sense of karamata properties of these functions and the schauder tychonoff fixed point theorem are the main tools for the proofs

topological models on the lattice and a remark on string theory cloning the addition of a topological model to the matter content of a conventional closed string theory leads to the appearance of many perturbatively decoupled spacetime worlds we illustrate this by classifying topological vertex models on a triangulated surface we comment on how such worlds could have been coupled in the planck era

homologies of algebraic structures via braidings and quantum shuffles abstract in this paper we construct structural pre braidings characterizing different algebraic structures a rack an associative algebra a leibniz algebra and their representations some of these pre braidings seem original on the other hand we propose a general homology theory for pre braided vector spaces and braided modules based on the quantum co shuffle comultiplication applied to the structural pre braidings above it gives a generalization and a unification of many known homology theories all the constructions are categorified resulting in particular in their super and co versions loday s hyper boundaries as well as certain homology operations are efficiently treated using the shuffle tools

on the asymptotic behavior of nonoscillatory solutions of second order quasilinear ordinary differential equations abstract in this paper second order quasilinear ordinary differential equations are considered and a necessary and sufficient condition for the existence of a slowly growing positive solution is established moreover the precise asymptotic forms as t of slowly growing positive solutions and slowly decaying positive solutions are obtained

lattice topological field theory in two dimensions the lattice definition of a two dimensional topological field theory tft is given generically and the exact solution is obtained explicitly in particular the set of all lattice topological field theories is shown to be in one to one correspondence with the set of all associative algebrasr and the physical hilbert space is identified with the centerz r of the associative algebrar perturbations of tft s are also considered in this approach showing that the form of topological perturbations is automatically determined and that all tft s are obtained from one tft by such perturbations several examples are presented including twistedn 2 minimal topological matter and the case wherer is a group ring

nonparametric censored and truncated regression we propose new estimators of the latent regression function in nonparametric cen sored and truncated regression models our estimators are computationally convenient consisting only of two nonparametric regressions and a univariate integral we establish consistency and asymptotic normality for an implementation based on local linear ker nel estimators an extension permits estimation in the presence of a general form of heteroscedasticity both the function m and the distribution f of the error e are unknown the errors are not assumed to be symmetric this paper provides a simple consistent estimator of m x k for some constant k under an additional tail condition we provide a consistent estimator of m x when m is the conditional mean function of the uncensored population also we show that f can be estimated given m x the proposed estimator is extended to deal with the truncated regression model where yi is only observed when it is not censored we also describe extensions to deal with a general form of heteroskedasticity in which the distribution of e could depend in unknown ways on a subset of elements of x for any continuously distributed element xk of x let mk x am x axk we also provide direct estimators of the derivatives mk x in both the censored and truncated regression models these derivatives are interpretable as the marginal effect of a change in x on the underlying uncensored population they can also be used to test or estimate parametric or semiparametric specifications of m x for example mk x is constant if m x is linear in xk and mk x depends only on xk if m x is additive in a function of xk

local likelihood estimation of truncated regression and its partial derivatives theory and application in this paper we propose a very flexible estimator in the context of truncated regression that does not require parametric assumptions to do this we adapt the theory of local maximum likelihood estimation we provide the asymptotic results and illustrate the performance of our estimator on simulated and real data sets our estimator performs as good as the fully parametric estimator when the assumptions for the latter hold but as expected much better when they do not provided that the curse of dimensionality problem is not the issue overall our estimator exhibits a fair degree of robustness to various deviations from linearity in the regression equation and also to deviations from the specification of the error term so the approach shall prove to be very useful in practical applications where the parametric form of the regression or of the distribution is rarely known

the lower bound of the w indices of surface links via quandle cocycle invariants the w index of a surface link f is the minimal number of the triple points of surface braids representing f in this paper for a given 3 cocycle we consider the minimal number of the w indices of surface links whose quandle cocycle invariants associated with f are non trivial and denote it f in particular we show that 3 6 and p 7 where n is mochizuki s 3 cocycle of the dihedral quandle of order n and p is an odd prime integer 3 as a consequence for a given non negative integer g there are surface knots with genus g with the w index 6

the 2 twist spun trefoil has the triple point number four the triple point number of an embedded surface in 4 space is the minimal number of the triple points on all the projection images into 3 space we show that the 2 twist spun trefoil has the triple point number four

o regularly varying functions and strong asymptotic equivalence in this paper we prove that in the class of all measurable positive functions defined on the interval a a 0 the class of functions which preserve the strong asymptotic equivalence on the set of functions x a r x t t is a class of o regularly varying functions with continuous index function we also prove a representation theorem for functions from this class

precise large deviations for compound random sums in the presence of dependence structures in this paper we deal with the compound random sums of dependent real valued random variables with heavy tailed distributions we establish a precise large deviation result for a nonstandard renewal risk model in which innovations are extended negatively dependent real valued random variables with a common dominatedly varying distribution function their interarrival times are extended negatively dependent nonnegative random variables and the numbers of innovations caused by individual events are also extended negatively dependent positive random variables as an illustration of the obtained result we give two applications related to some insurance risk models

asymptotic properties of kneser solutions to nonlinear second order odes with regularly varying coefficients in this work we investigate properties of a class of solutions to the second order ode p t u t q t f u t 0 on the interval a a 0 where p and q are functions regularly varying at infinity and f satisfies f l 0 f 0 f l 0 with l0 0

sample function behavior of increasing processes of class l we consider increasing processes x t t 0 of classl that is increasing self similar processes with inswpendent increments leth t be an increasing positive function on 0 withh 0 0 andh by virtue of the zero one laws there existsc resp c 0 such that lim inf resp lim sup x t h t c resp c a s both ast tends to 0 and ast tends to we decide a necessary and sufficient condition for the existence ofh t withc orc 1 and explicitly constructh t in caseh t exists withc orc 1 moreover we give a criterion to classify functionsh t withc orc 0 andh t withc orc in caseh t does not exist withc orc 1

estimation and inference in two stage semi parametric models of production processes many papers have regressed non parametric estimates of productive efficiency on environmental variables in two stage procedures to account for exogenous factors that might affect firms performance none of these have described a coherent data generating process dgp moreover conventional approaches to inference employed in these papers are invalid due to complicated unknown serial correlation among the estimated efficiencies we first describe a sensible dgp for such models we propose single and double bootstrap procedures both permit valid inference and the double bootstrap procedure improves statistical efficiency in the second stage regression we examine the statistical performance of our estimators using monte carlo experiments

intermediate solutions of second order quasilinear ordinary differential equations in the framework of regular variation intermediate solutions of emden fowler type differential equationp t x t a 1x t q t x t b 1x t 0 a b 0 are studied in the framework of regular variation under the assumptions that p t q t are generalized regularly varying functions necessary and sufficient conditions are established for the existence of three possible types of intermediate solutions witch are generalized regularly varying functions and it is shown that the asymptotic behavior of all such solutions of each type is governed by a unique explicit decay law

virtual yang baxter cocycle invariants we extend the yang baxter cocycle invariants for virtual knots by augmenting yang baxter 2 cocycles with cocycles from a cohomology theory associated to a virtual biquandle structure these invariants coincide with the classical yang baxter cocycle invariants for classical knots but provide extra information about virtual knots and links in particular they provide a method for detecting non classicality of virtual knots and links

nonparametric stochastic frontiers a local maximum likelihood approach this paper proposes a new approach to handle nonparametric stochastic frontier sf models it is based on local maximum likelihood techniques the model is presented as encompassing some anchorage parametric model in a nonparametric way first we derive asymptotic properties of the estimator for the general case local linear approximations then the results are tailored to a sf model where the convoluted error term efficiency plus noise is the sum of a half normal and a normal random variable the parametric anchorage model is a linear production function with a homoscedastic error term the local approximation is linear for both the production function and the parameters of the error terms the performance of our estimator is then established in finite samples using simulated data sets as well as with a cross sectional data on us commercial banks the methods appear to be robust numerically stable and particularly useful for investigating a production process and the derived efficiency scores

lattice topological field theory on nonorientable surfaces the lattice definition of the two dimensional topological quantum field theory fukuma et al commun math phys 161 157 1994 is generalized to arbitrary not necessarily orientable compact surfaces it is shown that there is a one to one correspondence between real associative algebras and the topological state sum invariants defined on such surfaces the partition and n point functions on all two dimensional surfaces connected sums of the klein bottle or projective plane and g tori are defined and computed for arbitrary algebras in general and for the group ring a r g of discrete groups g in particular

the interplay between k graphs and the yang baxter equation in this paper we initiate the study of the interplay between k graphs and the yang baxter equation for this we provide two very different perspectives on one hand we show that the set of all set theoretic solutions of the yang baxter equation is a special class of single vertex k graphs as a consequence we construct an infinite family of large solutions of the yang baxter equation from an arbitrarily given one on the other hand we prove that all single vertex k graphs are yb semigroups of square free involutive solutions of the yang baxter equation other various connections are also investigated

the rack space the main result of this paper is a new classification theorem for links smooth embeddings in codimension 2 the classifying space is the rack space and the classifying bundle is the first james bundle we investigate the algebraic topology of this classifying space and report on calculations given elsewhere apart from de ning many new knot and link invariants including generalised james hopf invariants the classification theorem has some unexpected applications we give a combinatorial interpretation for pi 2 of a complex which can be used for calculations and some new interpretations of the higher homotopy groups of the 3 sphere we also give a cobordism classification of virtual links

large deviations for random walks under subexponentiality the big jump domain for a given one dimensional random walk sn with a subexponential step size distribution we present a unifying theory to study the sequences xn for which as n uniformly for x xn we also investigate the stronger local analogue our theory is self contained and fits well within classical results on domains of partial attraction and local limit theory when specialized to the most important subclasses of subexponential distributions that have been studied in the literature we reproduce known theorems and we supplement them with new results

intermediate solutions of fourth order quasilinear differential equations in the framework of regular variation intermediate solutions of fourth order quasilinear differential equation p t x t 1 x t q t x t 1 x t 0 0 are studied in the framework of regular variation under the assumptions that p t q t are regularly varying functions satisfying conditions a t p t 1 dt a t p t 1 dt and a dt p t 1 necessary and sufficient conditions are established for the existence of regularly varying intermediate solutions and it is shown that the asymptotic behavior of all such solutions is governed by a unique explicit law

on preserving the limit points of corresponding objects abstract suppose that for two given sequences a n and b n lim inf n b n a n 1 and let a function f be given what can then be said about the limit behavior of the corresponding ratio f b n f a n as n in general no definite answer can be given to this question we study a case where a definite answer is possible namely the case of a regularly varying function f of nonzero order

asymptotic behavior of increasing solutions to a system of n nonlinear differential equations abstract we consider the system x i a i t x i 1 i sgn x i 1 i 1 n n 2 where a i i 1 n are positive continuous functions on a i 0 i 1 n with 1 n 1 and x n 1 means x 1 we analyze the asymptotic behavior of the solutions to this system whose components are eventually positive increasing in particular we derive exact asymptotic formulas for the extreme case where all the solution components tend to infinity the so called strongly increasing solutions we offer two approaches one is based on the asymptotic equivalence theorem and the other utilizes the theory of regular variation the above mentioned system includes as special cases two term nonlinear scalar differential equations of arbitrary order n and systems of n 2 second order nonlinear equations provided n is even which are related to elliptic partial differential systems applications to these objects are presented and a comparison with existing results is made it turns out that some of our results yield new information even in the simplest case a second order emden fowler differential equation

asymptotic behavior of positive solutions of sublinear differential equations of emden fowler type this paper is concerned with asymptotic analysis of positive solutions of the second order nonlinear differential equation a x t q t f x t 0 where q a 0 is a continuous function which is regularly varying and f 0 0 is a continuous increasing function which is regularly varying of index c 0 1 an application of the theory of regular variation gives the possibility of determining precise information about the asymptotic behavior at infinity of intermediate solutions of eq a

quandle cocycles from invariant theory abstract let g be a group any g module m has an algebraic structure called a g family of alexander quandles given a 2 cocycle of a cohomology associated with this g family topological invariants of handlebody knots in the 3 sphere are defined we develop a simple algorithm to algebraically construct n cocycles of this g family from g invariant group n cocycles of the abelian group m we present many examples of 2 cocycles of these g families using facts from modular invariant theory

towards invariants of surfaces in 4 space via classical link invariants in this paper we introduce a method to construct ambient isotopy invariants for smooth imbeddings of closed surfaces into 4 space by using hyperbolic splittings of the imbedded surfaces and an arbitrary given isotopy or regular isotopy invariant of classical knots and links in 3 space using this construction adopting the kauffman bracket polynomial as an example we produce some invariants

strong asymptotic equivalence and inversion of functions in the class kc abstract in this paper we consider the class of functions kc introduced by w matuszewska 1964 studia math 24 271 279 and w matuszewska and w orlicz 1965 studia math 26 11 24 as a main result we describe in terms of the class kc when two strictly increasing functions as well as their inverse functions are asymptoticaly equivalent in the strong sense this result also gives a proper characterization of the class kc

quandle cohomology and state sum invariants of knotted curves and surfaces the 2 twist spun trefoil is an example of a sphere that is knotted in 4 dimensional space a proof is given in this paper that this sphere is distinct from the same sphere with its orientation reversed our proof is based on a state sum invariant for knotted surfaces developed via a cohomology theory of racks and quandles also known as distributive groupoids a quandle is a set with a binary operation the axioms of which model the reidemeister moves in classical knot theory colorings of diagrams of knotted curves and surfaces by quandle elements together with cocycles of quandles are used to define state sum invariants for knotted circles in 3 space and knotted surfaces in 4 space cohomology groups of various quandles are computed herein and applied to the study of the state sum invariants non triviality of the invariants is proved for a variety of knots and links and conversely knot invariants are used to prove non triviality of cohomology for a variety of quandles

tauberian theorems for power series methods applied to double sequences abstract we discuss the relations between power series methods weighted mean methods and ordinary convergence for double sequences in particular we study tauberian theorems for methods being products of the related one dimensional summability methods

doubly slice knots and the casson gordon invariants we find knots in all dimensions which are algebraically but not geometri cally doubly slice our new obstructions involve the casson gordon invariants of the finite cyclic covers in odd dimensions and of the infinite cyclic cover in even dimensions these same invariants provide new criteria for amphicheirality and invertibility of even dimensional knots

higher dimensional algebra iv 2 tangles just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions compact surfaces smoothly embedded in r4 can be described as certain 2 morphisms in the 2 category of 2 tangles in 4 dimensions using the work of carter rieger and saito we prove that this 2 category is the free semistrict braided monoidal 2 category with duals on one unframed self dual object by this universal property any unframed self dual object in a braided monoidal 2 category with duals determines an invariant of 2 tangles in 4 dimensions

automorphism groups of alexander quandles abstract an alexander quandle is a module m over z t t 1 whose quandle operation is defined by x y t x 1 t y x y m the automorphism group of a general alexander quandle previously unknown is determined in the present paper

local likelihood estimation abstract a scatterplot smoother is applied to data of the form x 1 y 1 x 2 y 2 xn yn and uses local fitting to estimate the dependence of y on x a simple example is the running lines smoother which fits a least squares line to the y values falling in a window around each x value the value of the estimated function at x is given by the value of the least squares line at x a smoother generalizes the least squares line which assumes that the dependence of y on x is linear in this article we extend the idea of local fitting to likelihood based regression models one such application is to the class of generalized linear models nelder and wedderburn 1972 we enlarge this class by replacing the covariate form 0 x 1 with an unspecified smooth function s x this function is estimated from the data by a technique we call local likelihood estimation the method consists of maximum likelihood estimation for 0 and 1 applied in a window around each x value multiple covariates are incor

the fixed points of the multivariate smoothing transform let mathbf t 1 mathbf t 2 ldots be a sequence of random d times d matrices with nonnegative entries and let q be a random vector with nonnegative entries consider random vectors x with nonnegative entries satisfying begin aligned x mathop limits mathcal l sum i ge 1 mathbf t i x i q end aligned where mathop limits mathcal l denotes equality of the corresponding laws x i i ge 1 are i i d copies of x and independent of q mathbf t 1 mathbf t 2 ldots for d 1 this equation known as fixed point equation of the smoothing transform has been intensively studied under assumptions similar to the one dimensional case we obtain a complete characterization of all solutions x to in the non critical case and existence results in the critical case

numerical accuracy of real inversion formulas for the laplace transform in this article we investigate and compare a number of real inversion formulas for the laplace transform the focus is on the accuracy and applicability of the formulas for numerical inversion in this contribution we study the performance of the formulas for measures concentrated on a positive half line to continue with measures on an arbitrary half line as our trial measure concentrated on a positive half line we take the broad gamma probability distribution family

large n expansion of q deformed two dimensional yang mills theory and hecke algebras we derive the q deformation of the chiral gross taylor holomorphic string large n expansion of two dimensional su n yang mills theory delta functions on symmetric group algebras are replaced by the corresponding objects canonical trace functions for hecke algebras the role of the schur weyl duality between unitary groups and symmetric groups is now played by q deformed schur weyl duality of quantum groups the appearance of euler characters of configuration spaces of riemann surfaces in the expansion persists we discuss the geometrical meaning of these formulae

homology groups of symmetric quandles and cocycle invariants of links and surface links we introduce the notion of a quandle with a good involution and its homology groups carter et al defined quandle cocycle invariants for oriented links and oriented surface links by use of good involutions quandle cocyle invariants can be defined for links and surface links which are not necessarily oriented or orientable the invariants can be used in order to estimate the minimal triple point numbers of non orientable surface links

structures and diagrammatics of four dimensional topological lattice field theories abstract crane and frenkel proposed a state sum invariant for triangulated 4 manifolds they sketched the definition of a hopf category that was to be used in their construction crane and yetter studied hopf categories and gave some examples using group cocycles that are associated to the drinfeld double of a finite group in this paper we define a state sum invariant of triangulated 4 manifolds using crane yetter cocycles as boltzmann weights our invariant is analogous to the 3 dimensional invariants defined by dijkgraaf and witten and the invariants that are defined via hopf algebras we present diagrammatic methods for the study of such invariants that illustrate connections between hopf categories and moves to triangulations

a few remarks on divergent sequences rates of divergence we continue investigation of certain classes of sequences of positive real numbers which are important in asymptotic analysis of divergent processes among others we define the notion of quotient speed give representation results for some kinds of sequences and improve several our earlier results concerning selection principles and games

positive solutions of fourth order emden fowler type differential equations in the framework of regular variation abstract the fourth order nonlinear differential equations a x 4 q t x sgn x 0 0 1 with regularly varying coefficient q t are studied in the framework of regular variation it is shown that thorough and complete information can be acquired about the existence of all possible regularly varying solutions of a and their accurate asymptotic behavior at infinity

on variations via statistical convergence abstract the paper introduces some notions of variation using the concept of statistical convergence in particular the ideas of variation such as regular translationally regular o regular and rapid are presented in statistical context first some results are established connecting some statistical variations with their non statistical counterparts then certain conditions are explored under which various statistical variations can occur finally the paper examined some conditions to connect two different statistical variations

some asymptotic relations for the generalized inverse abstract in this paper we investigate the connection between the asymptotic relations of subordination and the negligence with the generalized inverse function in the class of all nondecreasing and unbounded functions which are defined on a half axis a a 0 in the main theorems we prove a characterization of all nondecreasing unbounded slowly varying functions

optimal bandwidth selection for conditional efficiency measures a data driven approach in productivity analysis an important issue is to detect how external environmental factors exogenous to the production process and not under the control of the producer might in uence the production process and the resulting efficiency of the rms most of the traditional approaches proposed in the literature have serious drawbacks an alternative approach is to describe the production process as being conditioned by a given value of the environmental variables cazals florens and simar 2002 daraio and simar 2005 this de nes conditional efficiency measures where the production set in the input output space may depend on the value of the external variables the statistical properties of nonparametric estimators of these conditional measures are now established jeong park and simar 2008 these involve the estimation of a nonstandard conditional distribution function which requires the speci cation of a smoothing parameter a bandwidth so far only the asymptotic optimal order of this bandwidth has been established this is of little interest for the practitioner in this paper we ll this gap and we propose a data driven technique for selecting this parameter in practice the approach based on a least squares cross validation procedure lscv provides an optimal bandwidth that minimizes an appropriate weighted integrated squared error ise the method is carefully described and exempli ed with some simulated data with univariate and multivariate environmental factors an application on real data performances of mutual funds illustrates how this new optimal method of bandwidth selection works in practice

the yang baxter equation and invariants of links on considere le fait que l on peut construire des invariants d isotopie p et f pour des liens en utilisant certaines solutions des equations de yang baxter

homology of left non degenerate set theoretic solutions to the yang baxter equation abstract this paper deals with left non degenerate set theoretic solutions to the yang baxter equation lnd solutions a vast class of algebraic structures encompassing groups racks and cycle sets to each such solution there is associated a shelf i e a self distributive structure which captures its major properties we consider two co homology theories for lnd solutions one of which was previously known in a reduced form for biracks only an explicit isomorphism between these theories is described for groups and racks we recover their classical co homology whereas for cycle sets we get new constructions for a certain type of lnd solutions including quandles and non degenerate cycle sets the co homologies split into the degenerate and the normalized parts we express 2 cocycles of our theories in terms of group cohomology and in the case of cycle sets establish connexions with extensions this leads to a construction of cycle sets with interesting properties

on the order of functions at infinity abstract we define a new class of positive and measurable functions in terms of their asymptotic behavior at infinity this new class extends the class of regularly varying functions for broader applications we provide different characterizations of the new class and consider integrals convolutions and laplace transforms we give some applications in probability theory some natural extensions of the new class are also derived

nichols algebras of group type with many quadratic relations abstract we classify nichols algebras of irreducible yetter drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two all such nichols algebras are finite dimensional and all known finite dimensional nichols algebras of nonabelian group type appear in the result of our classification we find a new finite dimensional nichols algebra over fields of characteristic two

from 3 algebras to δ groups and symmetric cohomology we introduce groups and show how they fit in the context of lattice field theory to a topological space m we associate a group m we define the symmetric cohomology hsn g a of a group g with coefficients in a g module a the group m is determined by the action of 1 m on 2 m and an element of hs3 1 m 2 m