aubin s lemma for the yamabe constants of infinite coverings and a positive mass theorem aubin s lemma says that if the yamabe constant of a closed conformal manifold m c is positive then it is strictly less than the yamabe constant of any of its non trivial finite conformal coverings we generalize this lemma to the one for the yamabe constant of any m c of its infinite conformal coverings provided that 1 m has a descending chain of finite index subgroups tending to 1 m moreover if the covering m is normal the limit of the yamabe constants of the finite conformal coverings associated to the descending chain is equal to that of m c for the proof of this we also establish a version of positive mass theorem for a specific class of asymptotically flat manifolds with singularities

joint mean covariance models with applications to longitudinal data unconstrained parameterisation summary we provide unconstrained parameterisation for and model a covariance using covariates the cholesky decomposition of the inverse of a covariance matrix is used to associate a unique unit lower triangular and a unique diagonal matrix with each covariance matrix the entries of the lower triangular and the log of the diagonal matrix are unconstrained and have meaning as regression coefficients and prediction variances when regressing a measurement on its predecessors an extended generalised linear model is introduced for joint modelling of the vectors of predictors for the mean and covariance subsuming the joint modelling strategy for mean and variance heterogeneity gabriel s antedependence models dempster s covariance selection models and the class of graphical models the likelihood function and maximum likelihood estimators of the covariance and the mean parameters are studied when the observations are normally distributed applications to modelling nonstationary dependence structures and multivariate data are discussed and illustrated using real data a graphical method similar to that based on the correlogram in time series is developed and used to identify parametric models for nonstationary covariances

positive scalar curvature with symmetry we show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action furthermore we develop a new codimension 2 surgery technique which removes singular strata from fixed point free s 1 manifolds while preserv ing equivariant positive scalar curvature these results are applied to derive the following theorem each closed fixed point free s 1 manifold of dimension at least 6 whose isotropy groups have odd order and whose union of maximal orbits is simply connected and not spin carries an s 1 invariant metric of positive scalar curvature

computations of the orbifold yamabe invariant we consider the yamabe invariant of a compact orbifold with finitely many singular points we prove a fundamental inequality for the estimate of the invariant from above which also includes a criterion for the non positivity of it moreover we give a sufficient condition for the equality in the inequality in order to prove it we also solve the orbifold yamabe problem under a certain condition we use these results to give some exact computations of the yamabe invariant of compact orbifolds

modelling multivariate volatilities via conditionally uncorrelated components summary we propose to model multivariate volatility processes on the basis of the newly defined conditionally uncorrelated components cucs this model represents a parsimonious representation for matrix valued processes it is flexible in the sense that each cuc may be fitted separately with any appropriate univariate volatility model computationally it splits one high dimensional optimization problem into several lower dimensional subproblems consistency for the estimated cucs has been established a bootstrap method is proposed for testing the existence of cucs the methodology proposed is illustrated with both simulated and real data sets

smooth yamabe invariant and surgery we prove a surgery formula for the smooth yamabe invariant sigma m of a compact manifold m assume that n is obtained from m by surgery of codimension at least 3 we prove the existence of a positive number lambda n depending only on the dimension n of m such that sigma n geq min sigma m lambda n

the yamabe invariant for non simply connected manifolds the yamabe invariant is an invariant of a closed smooth manifold defined using conformal geometry and the scalar curvature recently petean showed that the yamabe invariant is nonnegative for all closed simply connected manifolds of dimension 5 we extend this to show that yamabe invariant is nonnegative for all closed manifolds of dimension 5 with fundamental group of odd order having all sylow subgroups abelian the main new geometric input is a way of studying the yamabe invariant on toda brackets a similar method of proof shows that all closed oriented manifolds of dimension 5 with non spin universal cover with finite fundamental group having all sylow subgroups elementary abelian admit metrics of positive scalar curvature once one restricts to the complement of manifolds whose homology classes are toral the exceptional toral homology classes only exist in dimensions not exceeding the rank of the fundamental group so this proves important cases of the gromov lawson rosenberg conjecture once the dimension is sufficiently large

integrability aspects with optical solitons of a generalized variable coefficient n coupled higher order nonlinear schrodinger system from inhomogeneous optical fibers for describing the long distance communication and manufacturing problems of n fields propagation in inhomogeneous optical fibers we consider a generalized variable coefficient n coupled nonlinear schrodinger system with higher order effects such as the third order dispersion self steepening and self frequency shift using the painleve singularity structure analysis we obtain two cases for this system to admit the painleve property then for case 1 we derive the optical dark solitons via solving the hirota bilinear equations and based on the obtained 2n 1 2n 1 lax pair we construct the darboux transformation to obtain the optical bright solitons including the multisoliton profiles for case 2 finally the features of optical solitons both dark and bright ones in inhomogeneous optical fibers are analyzed and graphically discussed

the model confidence set this paper introduces the model confidence set mcs and applies it to the selection of models a mcs is a set of models that is constructed such that it will contain the best model with a given level of confidence the mcs is in this sense analogous to a confidence interval for a parameter the mcs acknowledges the limitations of the data such that uninformative data yield a mcs with many models whereas informative data yield a mcs with only a few models the mcs procedure does not assume that a particular model is the true model in fact the mcs procedure can be used to compare more general objects beyond the comparison of models we apply the mcs procedure to two empirical problems first we revisit the inflation forecasting problem posed by stock and watson 1999 and compute the mcs for their set of inflation forecasts second we compare a number of taylor rule regressions and determine the mcs of the best regression in terms of in sample likelihood criteria

a spinorial analogue of aubin s inequality let m g be a compact riemannian spin manifold of dimension 2 for any metric tilde g conformal to g we denote by tilde lambda the first positive eigenvalue of the dirac operator on m tilde g sigma we show that rm inf tilde g in g tilde lambda rm vol m tilde g 1 n leq n 2 rm vol s n 1 n this inequality is a spinorial analogue of aubin s inequality an important inequality in the solution of the yamabe problem the inequality is already known in the case n 3 and in the case n 2 ker d 0 our proof also works in the remaining case n 2 ker d 0 with the same method we also prove that any conformal class on a riemann surface contains a metric with 2 tilde lambda 2 leq tilde mu where tilde mu denotes the first positive eigenvalue of the laplace operator

classification of prime 3 manifolds with σ invariant greater than rp 3 in this paper we compute the invariants sometimes also called the smooth yamabe invariants of rp 3 and rp 2 s 1 which are equal and show that the only prime 3 manifolds with larger invariants are s 3 s 2 s 1 and s 2 s 1 the nonorientable s 2 bundle over s 1 more generally we show that any 3 manifold with invariant greater than rp 3 is either s 3 a connect sum with an s 2 bundle over s 1 or has more than one nonorientable prime compo

gauge transformation of the third kind for u 1 invariant coupled schrodinger equations we consider a large class of canonical coupled nonlinear schrodinger equations invariant over the action of the u 1 group the most general nonlinearity is taken into account through a matrix that without loss of generality can be separated into the sum of a hermitian matrix and an anti hermitian matrix the u 1 symmetry implies the existence of a set of continuity equations for the conserved densities where the corresponding currents have in general a nonlinear structure for this class of coupled schrodinger equations we introduce a nonlinear gauge transformation which changes the nonlinear matrix into another one purely hermitian consequently the currents are transformed in the standard bilinear form generalization to noncanonical systems is also discussed some examples are presented to illustrate the applicability of the method

consistency and limiting distribution of the least squares estimator of a threshold autoregressive model it is shown that under some regularity conditions the least squares estimator of a stationary ergodic threshold autoregressive model is strongly consistent the limiting distribution of the least squares estimator is derived it is shown that the estimator of the threshold parameter is n consistent and its limiting distribution is related to a compound poisson process

initial data engineering we present a local gluing construction for general relativistic initial data sets the method applies to generic initial data in a sense which is made precise in particular the trace of the extrinsic curvature is not assumed to be constant near the gluing points which was the case for previous such constructions no global conditions on the initial data sets such as compactness completeness or asymptotic conditions are imposed as an application we prove existence of spatially compact maximal globally hyperbolic vacuum space times without any closed constant mean curvature spacelike hypersurface

about the mass of certain second order elliptic operators abstract let m g be a closed riemannian manifold of dimension n 3 and let f c m such that the operator p f g f is positive if g is flat near some point p and f vanishes around p we can define the mass of p f as the constant term in the expansion of the green function of p f at p in this paper we establish many results on the mass of such operators in particular if f n 2 4 n 1 s g i e if p f is the yamabe operator we show the following result assume that there exists a closed simply connected non spin manifold m such that the mass is non negative for every metric g as above on m then the mass is non negative for every such metric on every closed manifold of the same dimension as m

asymptotics of cholesky garch models and time varying conditional betas this paper proposes a new model with time varying slope coefficients our model called char is a cholesky garch model based on the cholesky decomposition of the conditional variance matrix introduced by pourahmadi 1999 in the context of longitudinal data we derive stationarity and invertibility conditions and prove consistency and asymptotic normality of the full and equation by equation qml estimators of this model we then show that this class of models is useful to estimate conditional betas and compare it to the approach proposed by engle 2016 finally we use real data in a portfolio and risk management exercise we find that the char model outperforms a model with constant betas as well as the dynamic conditional beta model of engle 2016

equivariant yamabe problem and hebey vaugon conjecture abstract in their study of the yamabe problem in the presence of isometry groups e hebey and m vaugon announced a conjecture this conjecture generalizes t aubin s conjecture which has already been proven and is sufficient to solve the yamabe problem in this paper we generalize aubin s theorem and we prove the hebey vaugon conjecture in dimensions less or equal to 37

n fold darboux transformation and solitonic interactions of a variable coefficient generalized boussinesq system in shallow water abstract under consideration in this paper is a variable coefficient generalized boussinesq system for the long weakly nonlinear and weakly dispersive surface waves in shallow water with the aid of symbolic computation n fold darboux transformation n dt is constructed for that system analytic solutions of the system are obtained via the n dt elastic interactions of three bell shaped and periodic bell shaped solitons are obtained fusion interactions and periodic fusion fission interactions of the solitary waves are graphically analyzed which are inelastic

multisoliton solutions and integrability aspects of coupled higher order nonlinear schrodinger equations using painleve singularity structure analysis we show that coupled higher order nonlinear schrodinger chnls equations admit the painleve property using the results of the painleve analysis we succeed in hirota bilinearizing the chnls equations for the integrable cases solving the hirota bilinear equations one soliton and two soliton solutions are explicitly obtained lax pairs are explicitly constructed

generalized cylinders in semi riemannian and spin geometry we use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory it has the advantage of being very simple and the result directly extends to semi riemannian manifolds and to embeddings into spaces of constant curvature we also give a new way to identify spinors for different metrics and to derive the variation formula for the dirac operator moreover we show that generalized killing spinors for codazzi tensors are restrictions of parallel spinors finally we study the space of lorentzian metrics and give a criterion when two lorentzian metrics on a manifold can be joined in a natural manner by a 1 parameter family of such metrics

new types of exact solutions for the fourth order dispersive cubic quintic nonlinear schrodinger equation abstract in this study we use two direct algebraic methods to solve a fourth order dispersive cubic quintic nonlinear schrodinger equation which is used to describe the propagation of optical pulse in a medium exhibiting a parabolic nonlinearity law by using complex envelope ansatz method we first obtain a new dark soliton and bright soliton which may approach nonzero when the time variable approaches infinity then a series of analytical exact solutions are constructed by means of f expansion method these solutions include solitary wave solutions of the bell shape solitary wave solutions of the kink shape and periodic wave solutions of jacobian elliptic function

method of moments estimation of go garch models we propose a new estimation method for the factor loading matrix in generalized orthogonal garch go garch models the method is based on the eigenvectors of a suitably defined sample autocorrelation matrix of squares and cross products of the process the method can therefore be easily applied to high dimensional systems where likelihood based estimation will run into computational problems we provide conditions for consistency of the estimator and study its efficiency relative to maximum likelihood estimation using monte carlo simulations the method is applied to european sector returns and to the correlation between oil and kerosene returns and airline stock returns

strict stationarity of generalized autoregressive processes in this paper we consider the multivariate equation x n 1 a n 1 x n b n 1 with i i d coefficients which have only a logarithmic moment we give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future as an application we characterize the multivariate arma equations with general noise which have such a solution

stationarity of garch processes and of some nonnegative time series abstract two time series models are considered garch processes and generalized multivariate autoregressive equations x n 1 a n 1 x n b n 1 with nonnegative i i d coefficients in each case a necessary and sufficient condition ensuring the existence of a strictly stationary solution is given