restricted one dimensional central extensions of restricted simple lie algebras abstract we study the restricted one dimensional central extensions of an arbitrary finite dimensional restricted simple lie algebra for p 5 for h 2 g 0 we explicitly describe the cocycles spanning h 2 g and in the case h 2 g 0 we give a procedure to describe a basis for h 2 g

fixed point iterations for asymptotically nonexpansive mappings in banach spaces in this paper we suggest and analyze a three step iterative scheme for asymptotically nonexpansive mappings in banach spaces the new iterative scheme includes ishikawa type and mann type interations as special cases the results obtained in this paper represent an extension as well as refinement of previous known results

new approximation schemes for general variational inequalities in this paper we suggest and consider a class of new three step approximation schemes for general variational inequalities our results include ishikawa and mann iterations as special cases we also study the convergence criteria of these schemes

three step iterations for nonlinear accretive operator equations abstract in this paper we suggest and analyze a three step iterative scheme for solving nonlinear strongly accretive operator equation tx f without continuous condition in a uniformly smooth banach space our results include the ishikawa mann and noor iterations as special cases the results presented in this paper improve and extend almost all the current results in the more general setting

three steps iterative algorithms for mixed variational inequalities it is well known that the mixed variational inequalities are equivalent to the fixed point problems and the resolvent equations using this equivalence we suggest and consider a new three step iterative method for solving mixed variational inequalities the new iterative method is obtained by using three steps under suitable conditions we prove that the new method is globally convergent our results can be viewed as significant extensions of the previously known results for mixed variational inequalities since mixed variational inequalities include variational inequalities as special cases our method appears to be a new one for solving variational inequalities preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method

bayesian semiparametric median regression modeling median regression models become an attractive alternative to mean regression models when employing flexible families of distributions for the errors classical approaches are typically algorithmic with desirable properties emerging asymptotically however nonparametric error models may be most attractive in the case of smaller sample sizes where parametric specifications are difficult to justify hence a bayesian approach enabling exact inference given the observed data may be appealing in this context there is little bayesian work we develop two fully bayesian modeling approaches employing mixture models for the errors in a median regression model the associated families of error distributions allow for increased variability skewness and flexible tail behavior the first family is semiparametric with extra variability captured nonparametrically through mixing and skewness handled parametrically the second family a fully nonparametric one includes all unimodal densities on the real line with

approximating common fixed points of asymptotically nonexpansive maps in uniformly convex banach spaces we introduce three step iterative schemes with errors for two and three nonexpansive maps and establish weak and strong convergence theorems for these schemes mann type and ishikawa type convergence results are included in the analysis of these new iteration schemes the results presented in this paper substantially improve and extend the results due to s h khan h fukhar ud din weak and strong convergence of a scheme with errors for two nonexpansive mappings nonlinear anal 8 2005 1295 1301 n shahzad approximating fixed points of non self nonexpansive mappings in banach spaces nonlinear anal 61 2005 1031 1039 w takahashi t tamura convergence theorems for a pair of nonexpansive mappings j convex anal 5 1995 45 58 k k tan h k xu approximating fixed points of nonexpansive mappings by the ishikawa iteration process j math anal appl 178 1993 301 308 and h f senter w g dotson approximating fixed points of nonexpansive mappings proc amer math soc 44 1974 375 380

an empirical bayes approach to directional data and efficient computation on the sphere this paper proposes a consistent nonparametric empirical bayes estimator of the prior density for directional data the methodology is to use fourier analysis on s 2 to adapt euclidean techniques to this non euclidean environment general consistency results are obtained in addition a discussion of efficient numerical computation of fourier transforms on s 2 is given and their applications to the methods suggested in this paper are sketched

simple lie algebras of small characteristic vi completion of the classification let l be a finite dimensional simple lie algebra over an algebraically closed field of characteristic p 3 it is proved in this paper that if the p envelope of adl in derl contains a torus of maximal dimension whose centralizer in adl acts nontriangulably on l then p 5 and l is isomorphic to one of the melikian algebras m m n in conjunction with a premet h strade simple lie algebras of small characteristic v the non melikian case j algebra 314 2007 664 692 theorem 1 2 this implies that up to isomorphism any finite dimensional simple lie algebra over an algebraically closed field of characteristic p 3 is either classical or a filtered lie algebra of cartan type or a melikian algebra of characteristic 5 this result finally settles the classification problem for finite dimensional simple lie algebras over algebraically closed fields of characteristic 2 3

weak and strong convergence theorems for three step iterations with errors for asymptotically nonexpansive mappings abstract in the present paper several weak and strong convergence theorems are established for the three step iterative schemes with errors for asymptotically nonexpansive mappings our results extend and improve the recent ones announced by tan and xu xu and noor and many others

central extensions and h1 l l of the graded lie algebras of cartan type let f be an algebraically closed field of characteristic p 0 l i rsl i a graded lie algebra of cartan type over f we give a description of the dual adjoint module l by means of the mixed product and the coinduced module such that the computation of h1 l l can be reduced to that of the first cohomology of l 0 then we determine the central extensions and h2 l f by computing h1 l l

restricted one dimensional central extensions of the restricted filiform lie algebras m0λ p abstract consider the filiform lie algebra m 0 with nonzero lie brackets e 1 e i e i 1 for 1 i p where the characteristic of the field f is p 0 we show that there is a family m 0 p of restricted lie algebra structures parameterized by elements f p we explicitly describe both the ordinary and restricted 1 cohomology spaces and show that for p 3 these spaces are equal we also describe the ordinary and restricted 2 cohomology spaces and interpret our results in the context of one dimensional central extensions

approximating common fixed points of asymptotically quasi nonexpansive mappings by a k 1 step iterative scheme with error terms in this paper a k 1 step iterative scheme with error terms involving k 1 asymptotically quasi nonexpansive mappings is studied in usual banach spaces some sufficient and necessary conditions are given for the iterative scheme to approximate a common fixed point in uniformly convex banach spaces power equicontinuity for a mapping is introduced and a series of new convergence theorems are established several known results in the current literature are extended and refined

data tracking and the understanding of bayesian consistency summary we deal with strong consistency for bayesian density estimation an awkward con sequence of inconsistency is described it is pointed out that consistency at some density fo depends on the prior mass assigned to the pathological set of those densities that are close to fo in a weak sense and far apart from fo in a hellinger sense an analysis of these sets leads to the identification of the notion of data tracking specific examples in which this phenomenon cannot occur are discussed when it can happen we show how and where things can go wrong thus providing more intuition about the sources of inconsistency

weak and strong convergence criteria of noor iterations for asymptotically nonexpansive mappings in this paper weak and strong convergence theorems are established for a three step iterative scheme for asymptotically nonexpansive mappings in banach spaces mann type and ishikawa type iterations are included by the new iterative scheme the results obtained in this paper extend and improve the recent ones announced by xu and noor glowinski and le tallec noor ishikawa and many others

zip bifurcation in a competition model on considere le systeme s s 1 s k m 1 x 1 s a 1 s m 2 x 2 s a 2 s x 1 m 1 x 1 s a 1 s d 1 w 1 x 2 m 2 x 2 s a 2 s d 2 x 2 soit i a i d i m i d i on etudie le cas 1 2

common fixed points noor iteration for a finite family of asymptotically quasi nonexpansive mappings in banach spaces in this paper we introduce a general iteration scheme for a finite family of asymptotically quasi nonexpansive mappings the new iterative scheme includes the modified mann and ishikawa iterations three step iterative scheme of xu and noor and khan and takahashi scheme as special cases our results are generalizations as well as refinement of several known results in the current literature

convergence of ishikawa iterates of quasi nonexpansive mappings abstract this paper deals with a necessary and sufficient condition for the convergence of ishikawa iterates of quasi nonexpansive mapping in a banach space the convergence of ishikawa iterates for nonexpansive mappings in a uniformly convex banach space is also discussed

strong convergence of an implicit iteration process for a finite family of asymptotically quasi nonexpansive mappings in the present paper we prove that the modified implicit iteration sequence for a finite family of asymptotically quasi nonexpansive mappings converges strongly to a common fixed point of the family in a uniformly convex banach space requiring one member t in the family to be semi compact our results extend and improve some recent results

isotropic probabilistic models for directions planes and referential systems although simple probabilistic models for directions in two dimensional 2d and three dimensional 3d spaces are well known respectively the von mises and fisher distributions probabilistic models for directions planes and referential systems in an n dimensional n d space are either not popular or not available the results for directions in 2d and 3d can be generalized for i arbitrary directions ii planes iii referential systems and iv symmetric random tensors and in turn all these results can be generalized to n d spaces in this paper we will focus on and build up isotropic probabilistic models for directions planes and referential systems in n d space

convergence theorems for common fixed points of asymptotically quasi nonexpansive mappings in convex metric spaces abstract in this paper we consider an implicit iteration process to approximate the common fixed points of two finite families of asymptotically quasi nonexpansive mappings in convex metric spaces as a consequence of our result we obtain some related convergence theorems our results generalize some recent results of khan and ahmed 4 khan et al 6 sun 12 wittmann 14 and xu and ori 15

dirichlet process mixed generalized linear models abstract although generalized linear models glm s are an attractive and widely used class of models they are limited in the range of density shapes that they can provide for instance they are unimodal exponential families of densities in the response variable with tail behavior determined by the implicit mean variance relationship dirichlet process dp mixing adds considerable flexibility to these models using such mixing we develop models that we call dpmglm s which still retain the glm character with regard to the mean overdispersed glm s oglm s provide an alternative class of models to cope with extra variability in samples we show that how oglm s may be dp mixed leading to what we call dpmoglm s these models are extremely rich moreover recent computational advances enable them to be fitted straightforwardly we illustrate this with both simulated and real datasets we also address the question of choosing between the glm oglm dpmglm and dpmoglm finally we consider extensions by

bayesian nonparametric inference for random distributions and related functions in recent years bayesian nonparametric inference both theoretical and computational has witnessed considerable advances however these advances have not received a full critical and comparative analysis of their scope impact and limitations in statistical modelling many aspects of the theory and methods remain a mystery to practitioners and many open guestions remain in this paper we discuss and illustrate the rich modelling and analytic possibilities that are available to the statistician within the bayesian nonparametric and or semiparametric framework

a new approximation method for common fixed points of a finite family of asymptotically quasi nonexpansive mappings in banach spaces in this paper we consider a new iterative scheme to approximate a common fixed point for a finite family of asymptotically quasi nonexpansive mappings we prove several strong and weak convergence results of the proposed iteration in banach spaces these results generalize and refine many known results in the current literature

nonparametric estimation of convex models via mixtures we present a general approach to estimating probability measures constrained to lie in a convex set we represent constrained measures as mixtures of simple known extreme measures and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure convex constraints arise in many modeling situations such as estimation of the mean and estimation under stochastic ordering constraints we describe mixture representation techniques for these and other situations and discuss applications to maximum likelihood and bayesian estimation

three step iterative algorithms for multivalued quasi variational inclusions in this paper we suggest and analyze some new classes of three step iterative algorithms for solving multivalued quasi variational inclusions by using the resolvent equations technique new iterative algorithms include the ishikawa mann and noor iterations for solving variational inclusions inequalities and optimization problems as special cases the results obtained in this paper represent an improvement and a significant refinement of previously known results

convergence of a general iterative scheme for a finite family of asymptotically quasi nonexpansive mappings in convex metric spaces and applications in this paper we introduce the iterative scheme due to khan domlo and fukhar ud din 2008 8 in convex metric spaces and establish strong convergence of this scheme to a unique common fixed point of a finite family of asymptotically quasi nonexpansive mappings as a consequence of our result we obtain some related convergence theorems our results generalize some recent results obtained in 8

some developments in general variational inequalities general variational inequalities provide us with a unified natural novel and simple framework to study a wide class of equilibrium problems arising in pure and applied sciences in this paper we present a number of new and known numerical techniques for solving general variational inequalities using various techniques including projection wiener hopf equations updating the solution auxiliary principle inertial proximal penalty function dynamical system and well posedness we also consider the local and global uniqueness of the solution and sensitivity analysis of the general variational inequalities as well as the finite convergence of the projection type algorithms our proofs of convergence are very simple as compared with other methods our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems since the general variational inequalities include quasi variational inequalities and quasi implicit complementarity problems as special cases results presented here continue to hold for these problems several open problems have been suggested for further research in these areas

weak and strong convergence of a scheme with errors for two nonexpansive mappings abstract in this paper we are concerned with the study of an iterative scheme with errors involving two nonexpansive mappings we approximate the common fixed points of these two mappings by weak and strong convergence of the scheme in a uniformly convex banach space under a condition weaker than compactness

bayes methods for a symmetric unimodal density and its mode on donne des solutions de bayes pour un echantillonnage independant et identiquement distribue a partir d une densite decroissante sur la demi droite et pour un tel echantillonnage a partir d une densite unimodale symetrique avec un mode inconnu on obtient des quantites a posteriori comme sommes finies des methodes de monte carlo basees sur l echantillonnage de chaines de markov finies sont developpees pour leur evaluation

strong convergence theorems with a noor type iterative scheme in convex metric spaces the paper introduces some new mappings in convex metric spaces and then it considers a noor type iterative scheme to approximate common fixed points of an infinite family of uniformly quasi sup f n lipschitzian mappings and an infinite family of g n expansive mappings in convex metric spaces its results generalize improve and unify some results in chang et al 2010 13 fukhar ud din and khan 2007 14 liu et al 2010 17 tian 2005 7 wang and liu 2009 19 and wang et al 2009 20 under some appropriate conditions