long memory continuous time models this paper presents a new family of long memory models the continuous time moving average fractional process the continuous time framework allows to reconcile two competitive types of modelling fractional integration of arma processes and fractional brownian motion a comparison with usual discrete time arfima models is lead some well known empirical evidence on macroeconomic and financial time series such as variability of forward rates aggregation of responses across heterogeneous agents are well captured by this continuous time modelling moreover the usual statistical tools for long memory series and for stochastic differential equations can be jointly applied in this setting

connes moscovici characteristic map is a lie algebra morphism let h be a hopf algebra with a modular pair in involution character 1 let a be a module algebra over h equipped with a non degenerated character invariant 1 trace tau we show that connes moscovici characteristic map varphi tau hc character 1 h rightarrow hc lambda a is a morphism of graded lie algebras we also have a morphism phi of batalin vilkovisky algebras from the cotorsion product of h text cotor h bbbk bbbk to the hochschild cohomology of a hh a a let k be both a hopf algebra and a symmetric frobenius algebra suppose that the square of its antipode is an inner automorphism by a group like element then this morphism of batalin vilkovisky algebras phi text cotor k vee mathbb f mathbb f cong text ext k mathbb f mathbb f hookrightarrow hh k k is injective

eventual practical stability of impulsive differential equations with time delay in terms of two measurements in this paper we introduce a new stability eventual practical stability for impulsive differential equations with time delay by using lyapunov functions and comparison principle we will get some criteria of eventual practical stability eventual practical quasistability and strong eventual practical stability for impulsive differential equations with time delay in terms of two measurements

impulsive delay differential inequality and stability of neural networks in this article a generalized model of neural networks involving time varying delays and impulses is considered by establishing the delay differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive delay model are obtained the results extend and improve the earlier publications an example is given to illustrate the theory

inference theory for volatility functional dependencies we develop inference theory for models involving possibly nonlinear transforms of the elements of the spot covariance matrix of a multivariate continuous time process observed at high frequency the framework can be used to study the relationship among the elements of the latent spot covariance matrix and processes defined on the basis of it such as systematic and idiosyncratic variances factor betas and correlations on a fixed interval of time the estimation is based on matching model implied moment conditions under the occupation measure induced by the spot covariance process we prove consistency and asymptotic mixed normality of our estimator of the random coefficients in the volatility model and further develop model specification tests we apply our inference methods to study variance and correlation risks in nine sector portfolios comprising the s p 500 index we document sector specific variance risks in addition to that of the market and time varying heterogeneous correlation risk among the market neutral components of the sector portfolio returns

the generalized dynamic factor model consistency and rates abstract a factor model generalizing those proposed by geweke in d j aigner and a s goldberger latent variables in socio economic models north holland amsterdam 1977 sargent and sims new methods in business research federal reserve bank of minneapolis minneapolis 1977 engle and watson j amer statist assoc 76 1981 774 and stock and watson j business econom statist 20 2002 147 has been introduced in forni et al rev econ statist 80 2000 540 where consistent as the number n of series and the number t of observations both tend to infinity along appropriate paths n t n estimation methods for the common component are proposed rates of convergence associated with these methods are obtained here as functions of the paths n t n along which n and t go to infinity these results show that under suitable assumptions consistency requires t n to be at least of the same order as n whereas an optimal rate of n is reached for t n of the order of n2 if convergence to the space of common components is considered consistency holds irrespective of the path t n thus can be arbitrarily slow the optimal rate is still n but only requires t n to be of the order of n

on consistency and sparsity for principal components analysis in high dimensions principal components analysis pca is a classic method for the reduction of dimensionality of data in the form of n observations or cases of a vector with p variables contemporary datasets often have p comparable with or even much larger than n our main assertions in such settings are a that some initial reduction in dimensionality is desirable before applying any pca type search for principal modes and b the initial reduction in dimensionality is best achieved by working in a basis in which the signals have a sparse representation we describe a simple asymptotic model in which the estimate of the leading principal component vector via standard pca is consistent if and only if p n n 0 we provide a simple algorithm for selecting a subset of coordinates with largest sample variances and show that if pca is done on the selected subset then consistency is recovered even if p n n

on the geometric properties of vandermonde s mapping and on the problem of moments on demontre que le domaine d hyperbolicite du polynome x n 2 x n 2 3 x n 3 n i r coupe par le demi plan 2 1 a la propriete de whitney on montre que les valeurs x 1 x 2 x n d une variable aleatoire sont determinees de facon unique par les probabilites correspondantes et par les u premiers moments

strict stability of impulsive functional differential equations strict stability is the kind of stability that can give us some information about the rate of decay of the solutions there are some results about strict stability of differential equations in the present paper we shall extend the strict stability to impulsive functional differential equations by using lyapunov functions and razumikhin technique we shall get some criteria for the strict stability of impulsive functional differential equations and we can see that impulses do contribute to the system s strict stability behavior

the fu yau equation with negative slope parameter the fu yau equation is an equation introduced by fu and yau as a generalization to arbitrary dimensions of an ansatz for the strominger system as in the strominger system it depends on a slope parameter alpha prime the equation was solved in dimension 2 by fu and yau in two successive papers for alpha prime 0 and for alpha prime 0 in the present paper we solve the fu yau equation in arbitrary dimension for alpha prime 0 to our knowledge these are the first non trivial solutions of the fu yau equation in any dimension strictly greater than 2

positive finite rank elementary operators and characterizing entanglement of states in this paper some indecomposable positive finite rank elementary operators of order n n are constructed this allows us to give a simple necessary and sufficient criterion for the separability of pure states in bipartite systems of any dimension in terms of positive elementary operators of order 2 2 and obtain some new mixed entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion

forecasting using principal components from a large number of predictors this article considers forecasting a single time series when there are many predictors n and time series observations t when the data follow an approximate factor model the predictors can be summarized by a small number of indexes which we estimate using principal components feasible forecasts are shown to be asymptotically efficient in the sense that the difference between the feasible forecasts and the infeasible forecasts constructed using the actual values of the factors converges in probability to 0 as both n and t grow large the estimated factors are shown to be consistent even in the presence of time variation in the factor model

an exact sequence interpretation of the lie bracket in hochschild cohomology we give an interpretation of the lie bracket and the divided squaring operations in the hochschild cohomology of an associative algebra in terms of exact sequences of bimodules we construct natural loops in the category of extensions whose homotopy classes represent the lie bracket and squaring operations 1991 ams math subj class 16e40

monotonicity of rotationally invariant convex and rank 1 convex functions let f m n n r be a function on the space m n n of n by n matrices that is invariant with respect to the left and right multiplication by proper orthogonal tensors it is shown that f a f if f is convex and the partial sums of the singular values of a m n n satisfy certain ordering inequalities the same holds if f is rank 1 convex and the partial products of the singular values satisfy analogous inequalities the proofs emphasize the roles of the ordered forces inequalities and the baker ericksen inequalities for invariant convex and rank 1 convex functions as an application the evaluation of the convex and lamination convex hulls of fully rotationally invariant sets by dacorogna and tanteri is simplified and similar results are given for sets invariant only with respect to the proper orthogonal group

stability for time varying linear dynamic systems on time scales we study conditions under which the solutions of a time varying linear dynamic system of the form x t a t x t are stable on certain time scales we give sufficient conditions for various types of stability including lyapunov type stability criteria and eigenvalue conditions on slowly varying systems that ensure exponential stability finally perturbations of the unforced system are investigated and an instability criterion is also developed

on wielandt s inequality and its application to the asymptotic distribution of the eigenvalues of a random symmetric matrix a relatively obscure eigenvalue inequality due to wielandt is used to give a simple derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix the asymptotic distributions are obtained under a fairly general setting an application of the general theory to the bootstrap distribution of the eigenvalues of the sample covariance matrix is given 1 introduction and summary the derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix arises in many papers in multivariate analysis although the main idea behind most of the derivations is quite basic i e the expansion of the sample roots about the population roots the derivations themselves are often quite involved these complications are primarily due to the mathematical rather than statistical nature of the eigenvalue problem one of the main objectives of this paper is to introduce a simple method for obtaining the asymptotic distribution of the eigenvalue of random symmetric matrices the method is based upon a relatively obscure eigenvalue inequality

derivatives of spectral functions a spectral function of a hermitian matrix x is a function which depends only on the eigenvalues of x 1x 2x nx and hence may be written f 1x 2x nx for some symmetric function f such functions appear in a wide variety of matrix optimization problems we give a simple proof that this spectral function is differentiable at x if and only if the function f is differentiable at the vector x and we give a concise formula for the derivative we then apply this formula to deduce an analogous expression for the clarke generalized gradient of the spectral function a similar result holds for real symmetric matrices

four applications of majorization to convexity in the calculus of variations abstract the resemblance between the horn thompson theorem and a recent theorem by dacorogna marcellini tanteri indicates that schur convexity and the majorization relation are relevant for applications in the calculus of variations and its related notions of convexity such as rank one convexity or quasiconvexity in theorem 6 6 we give simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant majorization is used in order to give a very short proof of a theorem of thompson and freede r c thompson l j freede eigenvalues of sums of hermitian matrices iii j res nat bur standards b 75b 1971 115 120 ball j m ball constitutive inequalities and existence theorems in nonlinear elastostatics in r j knops ed nonlinear analysis and mechanics heriot watt symposium vol 1 res notes math 17 pitman 1977 pp 187 241 or le dret h le dret sur les fonctions de matrices convexes et isotropes cr acad sci paris serie i 310 1990 617 620 concerning the convexity of a class of isotropic functions which appear in nonlinear elasticity next we prove theorem 7 3 a lower semicontinuity result for functionals with the form w d x d x with w f h ln v f here f r f u f v f r f is the usual polar decomposition of f gl n r and ln v f is hencky s logarithmic strain we close this paper with a compact proof of dacorogna marcellini tanteri theorem based only on classical results about majorization the mentioned resemblance of this theorem with the horn thompson theorem is thus explained

a new criterion and a special class of k positive maps abstract we study k positive maps on operators we obtain a new criterion on k positivity in terms of the k numerical range and use it to improve and refine some earlier results on k positive maps related to the study of quantum information science we also consider a special class of positive maps extending the construction of choi on positive maps that are not completely positive some open questions on the decomposability of such maps are answered

dynamic factor models with infinite dimensional factor space asymptotic analysis abstract factor models all particular cases of the generalized dynamic factor model gdfm introduced in forni et al 2000 have become extremely popular in the theory and practice of large panels of time series data the asymptotic properties consistency and rates of the corresponding estimators have been studied in forni et al 2004 those estimators however rely on brillinger s concept of dynamic principal components and thus involve two sided filters which leads to rather poor forecasting performances no such problem arises with estimators based on standard static principal components which have been dominant in this literature on the other hand the consistency of those static estimators requires the assumption that the space spanned by the factors has finite dimension which severely restricts their generality prohibiting for instance autoregressive factor loadings this paper derives the asymptotic properties of a semiparametric estimator of the loadings and common shocks based on one sided filters recently proposed by forni et al 2015 consistency and exact rates of convergence are obtained for this estimator under a general class of gdfms that does not require a finite dimensional factor space a monte carlo experiment and an empirical exercise on us macroeconomic data corroborate those theoretical results and demonstrate the excellent performance of those estimators in out of sample forecasting

constitutive theory for some constrained elastic crystals abstract some of the observations of a 15 superconductors near cubic tetragonal phase transformations suggest treating them as thermoelastic bodies subject to certain material constraints here we begin to develop a theory of this kind

on the distribution of the largest eigenvalue in principal components analysis let x 1 denote the square of the largest singular value of an n p matrix x all of whose entries are independent standard gaussian variates equivalently x 1 is the largest principal component variance of the covariance matrix x x or the largest eigenvalue of a p variate wishart distribution on n degrees of freedom with identity covariance consider the limit of large p and n with n p gamma ge 1 when centered by mu p sqrt n 1 sqrt p 2 and scaled by sigma p sqrt n 1 sqrt p 1 sqrt n 1 1 sqrt p 1 3 the distribution of x 1 approaches the tracey widom law of order 1 which is defined in terms of the painleve ii differential equation and can be numerically evaluated and tabulated in software simulations show the approximation to be informative for n and p as small as 5 the limit is derived via a corresponding result for complex wishart matrices using methods from random matrix theory the result suggests that some aspects of large p multivariate distribution theory may be easier to apply in practice than their fixed p counterparts

convex analysis on the hermitian matrices there is growing interest in optimization problems with real symmetric matrices as variables generally the matrix functions involved are spectral they depend only on the eigenvalues of the matrix it is known that convex spectral functions can be characterized exactly as symmetric convex functions of the eigenvalues a new approach to this characterization is given via a simple fenchel conjugacy formula we then apply this formula to derive expressions for subdifferentials and to study duality relationships for convex optimization problems with positive semidefinite matrices as variables analogous results hold for hermitian matrices

stability and instability for dynamic equations on time scales in this paper we examine the stability and instability of the equilibrium solution x 0 to the first order system of dynamic equations x d f t x t t 0 x d r n where t is from a so called time scale t with t 0 tand d is a compact set our methods involve the existence of a positive definite liapunov function v such that its delta derivative v d satisfies certain integral definite or semidefinite sign properties finally we use liapunov functions to develop an invariance principle regarding solutions to the above dynamic equation

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

on analyticity of functions involving eigenvalues abstract let a z be an n n complex matrix whose elements depend analytically on z c m it is well known that any individual eigenvalue of a z may be nondifferentiable when it coalesces with others in this paper we investigate the analycity property of functions on the eigenvalues z 1 z n z of a z we first introduce the notion of functions that are symmetric with respect to partitions it is then shown that if a function c n c is analytic at a where a c m and is symmetric with respect to a certain partition induced by a then the composite function g z 1 z n z is analytic at a when z is real a z is symmetric or hermitian and the aforementioned assumptions hold so that g z is analytic at a we also derive formulae for its first and second order partial derivatives we apply the results to several problems involving eigenvalues

asymptotic behavior of solutions of a third order nonlinear dynamic equation on time scales in this paper we will establish some sufficient conditions which guarantee that every solution of the third order nonlinear dynamic equation c t a t x t q t f x t 0 t t0 oscillates or converges to zero

determining the number of factors in approximate factor models in this paper we develop some econometric theory for factor models of large dimensions the focus is the determination of the number of factors r which is an unresolved issue in the rapidly growing literature on multifactor models we first establish the convergence rate for the factor estimates that will allow for consistent estimation of r we then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria the theory is developed under the framework of large cross sections n and large time dimensions t no restriction is imposed on the relation between n and t simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice

a unified approach to operator monotone functions abstract the notion of operator monotonicity dates back to a work by lowner in 1934 a map f s n s m is called operator monotone if a b implies f a f b here s n is the space of symmetric matrices with the semidefinite partial order often the function f is defined in terms of an underlying simpler function f of main interest is to find the properties of f that characterize operator monotonicity of f in that case it is said that f is also operator monotone classical examples are the lowner operators and the spectral scalar valued isotropic functions operator monotonicity for these two classes of functions is characterized in seemingly very different ways this work extends the notion of operator monotonicity to symmetric functions f on k arguments the latter is used to define generated k isotropic maps f s n s n k for any n k necessary and sufficient conditions are given for f to generate an operator monotone k isotropic map f when k 1 the k isotropic map becomes a lowner operator and when k n it becomes a spectral function this allows us to reconcile and explain the differences between the conditions for monotonicity for the lowner operators and the spectral functions

lagrangian mean curvature flow for entire lipschitz graphs ii we prove longtime existence and estimates for smooth solutions to a fully nonlinear lagrangian parabolic equation with locally c 1 1 initial data u 0 satisfying either 1 1 eta i n le d 2u 0 le 1 eta i n for some positive dimensional constant eta 2 u 0 is weakly convex everywhere or 3 u 0 verifies a large supercritical lagrangian phase condition

extremal solutions of second order impulsive dynamic equations on time scales in this paper we give an existence theorem for the extremal solutions for second order impulsive dynamic equations on time scales

curvature contraction of convex hypersurfaces by nonsmooth speeds the research of the second author was supported by an australian postgraduate award the research of the first third fourth and fifth authors was supported by discovery project grant dp120100097 of the australian research council

a return map algorithm for general isotropic elasto visco plastic materials in principal space we describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto visco plastic models whose yield function incorporates the third stress invariant the developments presented are based upon original results proved in the paper concerning the derivatives of eigenvalues and eigenprojectors of symmetric second order tensors with respect to the tensor itself and upon an original algebra of fourth order tensors obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument the analysis initially referred to the small strain case is then extended to a formulation for the large deformation regime for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the lagrangian description of large strain elastoplasticity copyright 2004 john wiley sons ltd

quasiconvexity at the boundary positivity of the second variation and elastic stability for one dimensional problems of the calculus of variations there is a well developed theory relating the positivity of the second variation at a critical point i e linearized stability to strong relative minima these results largely due to weierstrass are usually proved by the method of fields of extremals as is described in bolza 1904 and morrey 1966 or by an argument involving a careful use of taylor series as in hestenes 1966 chapter 3 14

on the development of explicit robust schemes for implementation of a class of hyperelastic models in large strain analysis of rubbers the issue of developing effective and robust schemes to implement a class of the ogden type hypereiastic constitutive models for large strain analysis of rubber like materials is addressed to this end explicit forms for the corresponding material tangent stiffness tensors are developed and these are valid for the entire deformation range i e with both distinct as well as repeated principal stretch values throughout the analysis the various implications of the underlying property of separability of the strain energy functions are exploited thus leading to compact final forms of the tensor expressions in particular this facilitated the treatment of the complex cases of uncoupled volumetric deviatoric formulations for incompressible materials which are becoming increasingly popular in recent years the forms derived are also amenable for use with symbolic manipulation packages for systematic code generation

global c2 estimates for convex solutions of curvature equations we establish a c2 a priori estimate for convex hypersurfaces whose principal curvatures 1 n satisfy k x f x x the weingarten curvature equation we also obtain such an estimate for admissible 2 convex hypersurfaces in the case k 2 our estimates resolve a longstanding problem in geometric fully nonlinear elliptic equations 2015 wiley periodicals inc

the higher order derivatives of spectral functions in this paper we are interested in the higher order derivatives of functions of the eigenvalues of symmetric matrices with respect to the matrix argument we describe the formula for the k th derivative of such functions in two general cases the flrst case concerns the derivatives of the composition of an arbitrary not necessarily symmetric k times difierentiable function with the eigenvalues of symmetric matrices at a symmetric matrix with distinct eigenvalues the second case describes the derivatives of the composition of a k times difierentiable separable symmetric function with the eigenvalues of symmetric matrices at an arbitrary symmetric matrix we show that the formula signiflcantly simplifles when the separable symmetric function is k times continuously difierentiable as an application of the developed techniques we re derive the formula for the hessian of a general spectral function at an arbitrary symmetric matrix the new tools lead to a shorter cleaner derivation than the original one in 16 to make the exposition as self contained as possible we have included the necessary background results and deflnitions the proofs of the intermediate technical results are collected in the appendices

poincare like approach to landau theory i general theory we discuss a procedure to simplify the landau potential based on michel s reduction to orbit space and poincare normalization procedure and illustrate it by concrete examples the method makes use as in poincare theory of a chain of near identity coordinate transformations with homogeneous generating functions using michel s insight one can work in orbit space it is shown that it is possible to control the choice of generating functions so to obtain a in many cases substantial simplification of the landau polynomial including a reduction of the parameters it depends on several examples are considered in detail

a uniqueness theorem in kahler geometry we consider compact kahler manifolds with their kahler ricci tensor satisfying f ric constant under the nonnegative bisectional curvature assumption and certain conditions on f we prove that such metrics are in fact kahler einstein

a characterization of positive linear maps and criteria of entanglement for quantum states let h and k be finite or infinite dimensional complex hilbert spaces a characterization of positive completely bounded normal linear maps from into is given which particularly gives a characterization of positive elementary operators including all positive linear maps between matrix algebras this characterization is then applied to give a representation of quantum channels operations between infinite dimensional systems a necessary and sufficient criterion of separability is given which shows that a state on h k is separable if and only if i 0 for all positive finite rank elementary operators examples of ncp and indecomposable positive linear maps are given and are used to recognize some entangled states that cannot be recognized by the ppt criterion and the realignment criterion

a family of metric strains and conjugate stresses prolonging usual material laws from small to large transformations abstract a new family of simple generalized strains and conjugate stresses based on the material metric right cauchy green tensor is proposed it includes an interesting quasilinear pair it is a close approximation of the seth hill family with the advantage of being easier to calculate it extends the realm of application of the classical theories of linear elasticity and perfect plasticity from small to large transformations for isotropic and anisotropic materials without any modification

inference for continuous semimartingales observed at high frequency the econometric literature of high frequency data often relies on moment estimators which are derived from assuming local constancy of volatility and related quantities we here study this local constancy approximation as a general approach to estimation in such data we show that the technique yields asymptotic properties consistency normality that are correct subject to an ex post adjustment involving asymptotic likelihood ratios these adjustments are derived and documented several examples of estimation are provided powers of volatility leverage effect and integrated betas the first order approximations based on local constancy can be over the period of one observation or over blocks of successive observations it has the advantage of gaining in transparency in defining and analyzing estimators the theory relies heavily on the interplay between stable convergence and measure change and on asymptotic expansions for martingales

cartesian currents weak diffeomorphisms and existence theorems in nonlinear elasticity in this paper we introduce some new classes of functions among these a class of weak diffeomorphisms in these classes we prove by direct methods the existence of minimizers for several kinds of variational integrals in particular we prove the existence of one to one orientation preserving maps that minimize suitable energies associated with hyperelastic materials the minimizers are also proved to satisfy equilibrium equations finally radial deformations are discussed in connection with cavitation

an interior estimate for convex solutions and a rigidity theorem abstract we establish an interior c 2 estimate for k 1 convex solutions to dirichlet problems of k hessian equations we also use such estimate to obtain a rigidity theorem for k 1 convex entire solutions of k hessian equations in euclidean space

uniform asymptotic stability of impulsive delay differential equations abstract in this paper criteria on uniform asymptotic stability are established for impulsive delay differential equations using lyapunov functions and razumikhin techniques it is shown that impulses do contribute to yield stability properties even when the underlying system does not enjoy any stability behavior some examples are also discussed to illustrate the theorems

hybrid systems on time scales in this paper we study hybrid dynamic systems on time scales using lyapunov like functions we obtain sufficient conditions for the practical stability of hybrid dynamic systems on time scales

injective hopf bimodules cohomologies of infinite dimensional hopf algebras and graded commutativity of the yoneda product abstract we prove that the category of hopf bimodules over any hopf algebra has enough injectives which enables us to extend some results on the unification of hopf bimodule cohomologies of r taillefer phd thesis 2001 arxiv preprint math qa 0005019 to the infinite dimensional case we also prove that the cup product defined on these cohomologies is graded commutative unlike the algebra case see s schwede j reine angew math 498 1998 153 172 these methods do not give a non trivial gerstenhaber algebra structure on the cohomology we consider we also comment that the other approach to finding such a structure that we know of see m farinati a solotar arxiv preprint math kt 0207243 also gives a trivial gerstenhaber algebra structure

a basis free formula for time rate of hill s strain tensors abstract in this paper we use the method to obtain a basis free formula for the time rate e of hill s strain tensor e u i i n ni here u is the right stretch tensor i are its eigenvalues and ni is a lagrangian triad of orthonormal eigenvectors subordinate to i is a smooth strictly increasing scalar function that satisfies 1 0 1 1 our formula is generally valid provided that u is a c1 function of time and is of class c3 until now all other basis free formulae for e in the literature have been burdened by one or other of the following deficiencies i valid only under various special circumstances ii a complete proof is wanting the formula derived herein is free of these difficulties

differential graded categories and deligne conjecture abstract we prove a version of the deligne conjecture for n fold monoidal abelian categories a over a field k of characteristic 0 assuming some compatibility and non degeneracy conditions for a the output of our construction is a weak leinster n 1 algebra over k a relaxed version of the concept of leinster n algebra in a lg k the difference between the leinster original definition and our relaxed one is apparent when n 1 for n 1 both concepts coincide we believe that there exists a functor from weak leinster n 1 algebras over k to c e n 1 k algebras well defined when k q and preserving weak equivalences for the case n 1 such a functor is constructed in 31 by elementary simplicial methods providing together with this paper a complete solution for 1 monoidal abelian categories our approach to deligne conjecture is divided into two parts the first part completed in the present paper provides a construction of a weak leinster n 1 algebra over k out of an n fold monoidal k linear abelian category provided the compatibility and non degeneracy condition are fulfilled the second part still open for n 1 is a passage from weak leinster n 1 algebras to c e n 1 k algebras as an application we prove in theorem 8 1 that the gerstenhaber schack complex of a hopf algebra over a field k of characteristic 0 admits a structure of a weak leinster 2 1 algebra over k extending the yoneda structure it relies on our earlier construction 30 of a 2 fold monoidal structure on the abelian category of tetramodules over a bialgebra

principal component analysis of high frequency data we develop the necessary methodology to conduct principal component analysis at high frequency we construct estimators of realized eigenvalues eigenvectors and principal components and provide

bialgebra cohomology deformations and quantum groups abstract we introduce cohomology and deformation theories for a bialgebra a over a commutative unital ring k such that the second cohomology group is the space of infinitesimal deformations our theory gives a natural identification between the underlying k modules of the original and the deformed bialgebra certain explicit deformation formulas are given for the construction of quantum groups i e hopf algebras that are neither commutative nor cocommutative whether or not they arise from quantum yang baxter operators these formulas yield in particular all glq n and slq n as deformations of gl n and sl n using a hodge decomposition of the underlying cochain complex we compute our cohomology for gl n with this we show that every deformation of gl n is equivalent to one in which the comultiplication is unchanged not merely on elements of degree one but on all elements settling in the strongest way a decade old conjecture and in which the quantum determinant as an element of the underlying k module is identical with the usual one

a fully nonlinear flow for two convex hypersurfaces in riemannian manifolds we consider a one parameter family of closed embedded hypersurfaces moving with normal velocity g kappa big sum i j frac 1 lambda i lambda j 2 kappa big 1 where lambda 1 le cdots le lambda n denote the curvature eigenvalues and kappa is a nonnegative constant this defines a fully nonlinear parabolic equation provided that lambda 1 lambda 2 2 kappa in contrast to mean curvature flow this flow preserves the condition lambda 1 lambda 2 2 kappa in a general ambient manifold our main goal in this paper is to extend the surgery algorithm of huisken sinestrari to this fully nonlinear flow this is the first construction of this kind for a fully nonlinear flow as a corollary we show that a compact riemannian manifold satisfying overline r 1313 overline r 2323 ge 2 kappa 2 with non empty boundary satisfying lambda 1 lambda 2 2 kappa is diffeomorphic to a 1 handlebody the main technical advance is the pointwise curvature derivative estimate the proof of this estimate requires a new argument as the existing techniques for mean curvature flow due to huisken sinestrari haslhofer kleiner and brian white cannot be generalized to the fully nonlinear setting to establish this estimate we employ an induction on scales argument this relies on a combination of several ingredients including the almost convexity estimate the inscribed radius estimate as well as a regularity result for radial graphs we expect that this technique will be useful in other situations as well

dynamic equations on time scales a survey the study of dynamic equations on time scales which goes back to its founder stefan hilger 1988 is an area of mathematics that has recently received a lot of attention it has been created in order to unify the study of differential and difference equations in this paper we give an introduction to the time scales calculus we also present various properties of the exponential function on an arbitrary time scale and use it to solve linear dynamic equations of first order several examples and applications among them an insect population model are considered we then use the exponential function to define hyperbolic and trigonometric functions and use those to solve linear dynamic equations of second order with constant coefficients finally we consider self adjoint equations and more generally so called symplectic systems and present several results on the positivity of quadratic functionals

asymptotic inference for eigenvectors abstract asymptotic procedures are given for testing certain hypotheses concerning eigenvectors and for constructing confidence regions for eigenvectors these asymptotic procedures are derived under fairly general conditions on the estimates of the matrix whose eigenvectors are of interest applications of the general results to principal components analysis and canonical variate analysis are given author

concrete examples of operator monotone functions obtained by an elementary method without appealing to lowner integral representation we study concrete examples of operator monotone functions obtained by an elementary method without appealing to lowner integral representation

existence results for second order boundary value problem of impulsive dynamic equations on time scales abstract in this paper schaefer s fixed point theorem and nonlinear alternative of leray schauder type are used to investigate the existence of solutions for second order boundary value problem for impulsive dynamic equations on time scales

invariants de classe c r des groupes finis engendres par des reflexions et theoreme de chevalley en classe c r

a closed form representation for the derivative of non symmetric tensor power series in the present paper a closed form representation for the derivative of non symmetric tensor power series is proposed particular attention is focused on the special case of repeated eigenvalues in this case a non symmetric tensor can possess no spectral decomposition in diagonal form such that the well known solutions in terms of eigenprojections as well as basis free representations for isotropic functions of symmetric tensor arguments cannot be used thus our representation seems to be the only possibility to calculate the derivative of non symmetric tensor power series in a closed form finally this closed formula is illustrated by an example being of special importance in large strain anisotropic elasto plasticity as such we consider the exponential function of the velocity gradient under simple shear right in this loading case the velocity gradient has a triple defective eigenvalue excluding the application of any other solutions based on the spectral decomposition

stability criteria of delay impulsive systems on time scales abstract in this paper we study stability of delay impulsive systems on time scales by using lyapunov functional and analysis method some stability and instability criteria for the delay system with impulses at fixed times on time scales are obtained two examples are presented to illustrate the efficiency of results proposed in this paper

stability for impulsive delay differential equations abstract in this paper the stability for the scalar impulsive delay differential equation y t a t y t f t y 0 t 0 t k y k y k i k y k k 1 2 lim k k where delay arguments may be bounded or unbounded is investigated some new stability theorems are established which improve and extend several known results in the literature

nonsmooth analysis of eigenvalues the eigenvalues of a symmetric matrix depend on the matrix nonsmoothly this paper describes the nonsmooth analysis of these eigenvalues in particular i present a simple formula for the approximate limiting frechet subdifferential of an arbitrary function of the eigenvalues subsuming earlier results on convex and clarke subgradients as an example i compute the subdifferential of the k th largest eigenvalue

uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity introduction 97 constitutive assumptions 99 0 the stored energy function and weak equilibrium solutions 101 1 properties of radial equilibrium solutions 105 2 uniqueness of solutions to boundary value problems for shells 111 3 uniqueness of cavitating solutions 117 4 existence of radial equilibria 121 5 asymptotic behaviour of equilibria for shells 128 6 concluding remarks 132 7 appendix 133 references 135

on isotropic rank 1 convex functions let f be a rotationally invariant function defined on the set lin of all tensors with positive determinant on a vector space of arbitrary dimension necessary and sufficient conditions are given for the rank 1 convexity of f in terms of its representation through the singular values for the global rank 1 convexity on lin the result is a generalization of a two dimensional result of aubert generally the inequality on contains products of singular values of the type encountered in the definition of polyconvexity but is weaker it is also shown that the rank 1 convexity is equivalent to a restricted ordinary convexity when f is expressed in terms of signed invariants of the deformation

variation of lyapunov s method for dynamic systems on time scales abstract a new comparison theorem that connects the solutions of perturbed and unperturbed dynamic systems in a manner useful to the theory of perturbations is given and this comparison theorem is employed as a stability criterion to compare the asymptotic behaviors of perturbed and unperturbed systems it is further shown by means of both theory and numerical computation that time scales do offer a unification in order to emphasize the better asymptotic behavior of perturbed systems in both continuous and discrete cases

high frequency covariance estimates with noisy and asynchronous financial data this article proposes a consistent and efficient estimator of the high frequency covariance quadratic covariation of two arbitrary assets observed asynchronously with market microstructure noise this estimator is built on the marriage of the quasi maximum likelihood estimator of the quadratic variation and the proposed generalized synchronization scheme and thus is not influenced by the epps effect moreover the estimation procedure is free of tuning parameters or bandwidths and is readily implementable monte carlo simulations show the advantage of this estimator by comparing it with a variety of estimators with specific synchronization methods the empirical studies of six foreign exchange future contracts illustrate the time varying correlations of the currencies during the 2008 global financial crisis demonstrating the similarities and differences in their roles as key currencies in the global market

the complex hessian equations with gradient terms on hermitian manifolds abstract in this paper we consider the complex hessian equation involving additional gradient terms on both left and right hand sides we derive the second order estimates for plurisubharmonic solutions to this equation on compact hermitian manifolds such an estimate may be helpful to study the existence and regularity for the solution of the equation

inferential theory for factor models of large dimensions this paper develops an inferential theory for factor models of large dimensions the principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator if normality is assumed we derive the rate of convergence and the limiting distributions of the estimated factors factor loadings and common components the theory is developed within the framework of large cross sections n and a large time dimension t to which classical factor analysis does not apply we show that the estimated common components are asymptotically normal with a convergence rate equal to the minimum of the square roots of n and t the estimated factors and their loadings are generally normal although not always so the convergence rate of the estimated factors and factor loadings can be faster than that of the estimated common components these results are obtained under general conditions that allow for correlations and heteroskedasticities in both dimensions stronger results are obtained when the idiosyncratic errors are serially uncorrelated and homoskedastic a necessary and sufficient condition for consistency is derived for large n but fixed t

dynamic factor models with infinite dimensional factor spaces one sided representations abstract factor model methods recently have become extremely popular in the theory and practice of large panels of time series data those methods rely on various factor models which all are particular cases of the generalized dynamic factor model gdfm introduced in forniet al 2000 that paper however rests on brillinger s dynamic principal components the corresponding estimators are two sided filters whose performance at the end of the observation period or for forecasting purposes is rather poor no such problem arises with estimators based on standard principal components which have been dominant in this literature on the other hand those estimators require the assumption that the space spanned by the factors has finite dimension in the present paper we argue that such an assumption is extremely restrictive and potentially quite harmful elaborating upon recent results by anderson and deistler 2008a b on singular stationary processes with rational spectrum we obtain one sided representations for the gdfm without assuming finite dimension of the factor space construction of the corresponding estimators is also briefly outlined in a companion paper we establish consistency and rates for such estimators and provide monte carlo results further motivating our approach

derivatives of compound matrix valued functions abstract primary matrix functions and spectral functions are two classes of orthogonally invariant functions on a symmetric matrix argument many of their properties have been investigated thoroughly and find numerous applications both theoretical and applied in areas ranging from engineering image processing optimization and physics we propose a family of maps that provide a natural connection and generalization of these two classes of functions the family of maps also contains the well known multiplicative and additive compound matrices we explain when each member of this family is a differentiable function and exhibit a formula for its derivative

basis free representations for the stress rate of isotopic materials in terms of the principal components of stress tensor and a scalar response function two kinds of basis free representation for the stress rate are obtained which only include the time rate of the strain tensor functions and invariants of the strain tensor the expressions for the stress rate valid in the cases that the eigenvalues of the strain are distinct doubly coalescent and triply coalescent respectively