minimal symmetric factorizations of symmetric real and complex rational matrix functions abstract real and complex rational matrix functions w such that w w t where 1 and their minimal factorizations w l t d l are studied such factorizations are described geometrically in terms of invariant subspaces with certain isotropic properties with respect to a quadratic form using results partly known and partly proved in the paper concerning the dimensions of such subspaces upper bounds are given for the degrees of the rational matrix functions l in the above factorizations

semi parametric single index panel data models with interactive fixed effects theory and practice abstract in this paper we propose a single index panel data model with unobserved multiple interactive fixed effects this model has the advantages of being flexible and of being able to allow for common shocks and their heterogeneous impacts on cross sections thus making it suitable for the investigation of many economic issues the asymptotic theories are established accordingly our monte carlo simulations show that our methodology works well for large n and t cases in our empirical application we illustrate our model by analysing the returns to scale of large commercial banks in the u s

estimating and testing structural changes in multivariate regressions this paper considers issues related to estimation inference and computation with multiple structural changes that occur at unknown dates in a system of equations changes can occur in the regression coefficients and or the covariance matrix of the errors we also allow arbitrary restrictions on these parameters which permits the analysis of partial structural change models common breaks that occur in all equations breaks that occur in a subset of equations and so forth the method of estimation is quasi maximum likelihood based on normal errors the limiting distributions are obtained under more general assumptions than previous studies for testing we propose likelihood ratio type statistics to test the null hypothesis of no structural change and to select the number of changes structural change tests with restrictions on the parameters can be constructed to achieve higher power when prior information is present for computation an algorithm for an efficient procedure is proposed to construct the estimates and test statistics we also introduce a novel locally ordered breaks model which allows the breaks in different equations to be related yet not occurring at the same dates

determining the number of factors in the general dynamic factor model this article develops an information criterion for determining the number q of common shocks in the general dynamic factor model developed by forni et al as opposed to the restricted dynamic model considered by bai and ng and by amengual and watson our criterion is based on the fact that this number q is also the number of diverging eigenvalues of the spectral density matrix of the observations as the number n of series goes to infinity we provide sufficient conditions for consistency of the criterion for large n and t where t is the series length we show how the method can be implemented and provide simulations and empirics illustrating its very good finite sample performance application to real data adds a new empirical facet to an ongoing debate on the number of factors driving the u s economy

induced hopf galois structures for a nite galois extension k k and an intermediate eld f such that gal k f has a normal complement in gal k k we construct and characterize hopf galois structures on k k which are induced by a pair of hopf galois structures on k f and f k

counting hopf galois structures on cyclic field extensions of squarefree degree abstract we investigate hopf galois structures on a cyclic field extension l k of squarefree degree n by a result of greither and pareigis each such hopf galois structure corresponds to a group of order n whose isomorphism class we call the type of the hopf galois structure we show that every group of order n can occur and we determine the number of hopf galois structures of each type we then express the total number of hopf galois structures on l k as a sum over factorisations of n into three parts as examples we give closed expressions for the number of hopf galois structures on a cyclic extension whose degree is a product of three distinct primes there are several cases depending on congruence conditions between the primes we also consider one case where the degree is a product of four primes

hopf galois structures on extensions of degree p2q and skew braces of order p2q the cyclic sylow p subgroup case abstract let p q be distinct primes with p 2 we classify the hopf galois structures on galois extensions of degree p 2 q such that the sylow p subgroups of the galois group are cyclic this we do according to greither and pareigis and byott by classifying the regular subgroups of the holomorphs of the groups g of order p 2 q in the case when the sylow p subgroups of g are cyclic this is equivalent to classifying the skew braces g furthermore we prove that if g and are groups of order p 2 q with non isomorphic sylow p subgroups then there are no regular subgroups of the holomorph of g which are isomorphic to equivalently a galois extension with galois group has no hopf galois structures of type g our method relies on the alternate brace operation on g which we use mainly indirectly that is in terms of the functions g aut g defined by g x x g g 1 these functions are in one to one correspondence with the regular subgroups of the holomorph of g and are characterised by the functional equation g h h g h for g h g we develop methods to deal with these functions with the aim of making their enumeration easier and more conceptual

on self adjoint matrix polynomials with constant signature abstract this paper mainly concerns the class of self adjoint matrix polynomials with constant signature we define the order of neutrality for a regular self adjoint matrix polynomial l suppose that the leading coefficient of l is nonsingular then it is proved that l is of constant signature if and only if nl is even and the order of neutrality of l is equal to nl 2 where n is the degree l is the size of the polynomial l a similar result is obtained for regular self adjoint matrix polynomials we give an answer to an open problem concerning symmetric factorizations of self adjoint matrix polynomials of constant signature let l be a self adjoint matrix polynomial of even degree and constant signature and with a nonsingular leading coefficient an if all the elementary divisors of l are linear then l m gl a n m with m a monic matrix polynomial in particular this shows that generically a self adjoint matrix polynomial of even degree and constant signature admits such a factorization the proof of this factorization result is based on a result concerning invariant maximal neutral subspaces for a matrix which is self adjoint in an indefinite inner product the latter result also applies to other situations e g to factorizations of rational matrix functions with constant signature and to the existence of hermitian solutions for a class of algebraic riccati equations

skew braces and hopf galois structures of heisenberg type abstract we classify all skew braces of heisenberg type for a prime number p 3 furthermore we determine the automorphism group of each one of these skew braces as well as their socle and annihilator hence by utilising a link between skew braces and hopf galois theory we can determine all hopf galois structures of heisenberg type on galois field extensions of fields of degree p 3

spectral factorization via hermitian pencils abstract the spectral factorization problem is solved for state space systems via results on the canonical forms and inertia of hermitian matrix pencils these algebraic results then give a deflation method for spectral factorization

canonical forms for symmetric skew symmetric real matrix pairs under strict equivalence and congruence a systematic development is made of the simultaneous reduction of pairs of quadratic forms over the reals one of which is skew symmetric and the other is either symmetric or skew symmetric these reductions are by strict equivalence and by congruence over the reals or over the complex numbers and essentially complete proofs are presented the proofs are based on canonical forms attributed to jordan and kronecker some closely related results which can be derived from the canonical forms of pairs of symmetric skew symmetric real forms are also included they concern simultaneously neutral subspaces hamiltonian and skew hamiltonian matrices and canonical structures of real matrices which are selfadjoint or skew adjoint in a regular skew symmetric indefinite inner product and real matrices which are skew adjoint in a regular symmetric indefinite inner product the paper is largely expository and continues the comprehensive account of the reduction of pairs of matrices started in p lancaster l rodman canonical forms for hermitian matrix pairs under strict equivalence and congruence siam rev in press

direct complements of invariant lagrangian subspaces and minimal factorizations of skew symmetric rational matrix functions abstract symmetric factorizations of skew symmetric real rational matrix functions are studied in particular it is proved that generically a proper skew symmetric real rational matrix mxm matrix function w w t with w invertible can be factorized minimally as w l tdl for a real rational mxm matrix function l applications are given concerning symmetric solutions of matrix quadratic equations

linear regression for panel with unknown number of factors as interactive fixed effects in this paper we study the least squares ls estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects assuming that the number of factors used in estimation is larger than the true number of factors in the data we establish the limiting distribution of the ls estimator for the regression coefficients as the number of time periods and the number of cross sectional units jointly go to infinity the main result of the paper is that under certain assumptions the limiting distribution of the ls estimator is independent of the number of factors used in the estimation as long as this number is not underestimated the important practical implication of this result is that for inference on the regression coefficients one does not necessarily need to estimate the number of interactive fixed effects consistently

hopf galois structures on separable field extensions of odd prime power degree abstract we study hopf galois structures on separable field extensions l k of degree p n p an odd prime and denote by g the galois group of the normal closure over k we prove that if l k has a hopf galois structure of cyclic type then it has no structure of noncyclic type for n 3 we characterize the transitive groups g such that l k has cyclic hopf galois structures we prove that if l k has a nonabelian hopf galois structure of type n then it has an abelian structure whose type has the same exponent as n we obtain that for p 3 the two abelian noncyclic hopf galois structures do not occur on the same extension finally we list all possible sets of hopf galois structure types on a separable extension of degree p 3 for p 3 a prime

shrinkage estimation of dynamic panel data models with interactive fixed effects abstract we consider the problem of determining the number of factors and selecting the proper regressors in linear dynamic panel data models with interactive fixed effects based on the preliminary estimates of the slope parameters and factors a la bai 2009 and moon and weidner 2015 we propose a method for simultaneous selection of regressors and factors and estimation through the method of adaptive group lasso least absolute shrinkage and selection operator we show that with probability approaching one our method can correctly select all relevant regressors and factors and shrink the coefficients of irrelevant regressors and redundant factors to zero further we demonstrate that our shrinkage estimators of the nonzero slope parameters exhibit some oracle property we conduct monte carlo simulations to demonstrate the superb finite sample performance of the proposed method we apply our method to study the determinants of economic growth and find that in addition to three common unobserved factors selected by our method government consumption share has negative effects whereas investment share and lagged economic growth have positive effects on economic growth

panel data models with interactive fixed effects and multiple structural breaks abstractin this article we consider estimation of common structural breaks in panel data models with unobservable interactive fixed effects we introduce a penalized principal component ppc estimation procedure with an adaptive group fused lasso to detect the multiple structural breaks in the models under some mild conditions we show that with probability approaching one the proposed method can correctly determine the unknown number of breaks and consistently estimate the common break dates furthermore we estimate the regression coefficients through the post lasso method and establish the asymptotic distribution theory for the resulting estimators the developed methodology and theory are applicable to the case of dynamic panel data models simulation results demonstrate that the proposed method works well in finite samples with low false detection probability when there is no structural break and high probability of correctly estimating the break numbers when the structural breaks exist we finall

bi skew braces and regular subgroups of the holomorph abstract l childs has defined a skew brace g to be a bi skew brace if g is also a skew brace and has given applications of this concept to the equivalent theory of hopf galois structures the goal of this paper is to deal with bi skew braces g from the yet equivalent point of view of regular subgroups of the holomorph of g in particular we find that certain groups studied by t kohl f dalla volta and the author and c tsang all yield examples of bi skew braces building on a construction of childs we also give various methods for exhibiting further examples of bi skew braces

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

hopf galois structures on field extensions of degree twice an odd prime square and their associated skew left braces abstract we determine the hopf galois structures on a galois field extension of degree twice an odd prime square and classify the corresponding skew left braces besides we determine the separable field extensions of degree twice an odd prime square allowing a cyclic hopf galois structure and the number of these structures

elementary abelian hopf galois structures and polynomial formal groups abstract we find a relationship between regular embeddings of g an elementary abelian p group of order p n into unipotent upper triangular matrices with entries in f p and commutative dimension n degree 2 polynomial formal groups with nilpotent upper triangular structure matrices we classify the latter when n 3 up to linear isomorphism and use that classification to determine the number of hopf galois structures on a galois extension l k of fields with galois group g elementary abelian of order p 3 we also obtain a lower bound on the number of hopf galois structures on a galois extension l k when the galois group is elementary abelian of order p n

normal forms of elements of classical real and complex lie and jordan algebras elements of the classical complex and real lie and jordan algebras with involutions are classified into conjugacy classes under the action of the corresponding classical lie group normal forms of representatives of each conjugacy class are chosen so as to resemble the jordan normal forms of n n complex matrices for completeness similar results are given for gl n c gl n r and gl n h

multiple holomorphs of finite p groups of class two abstract let g be a group and s g be the group of permutations on the set g the abstract holomorph of g is the natural semidirect product aut g g we will write hol g for the normalizer of the image in s g of the right regular representation of g hol g n s g g aut g g aut g g and also refer to it as the holomorph of g more generally if n is any regular subgroup of s g then n s g n is isomorphic to the holomorph of n g a miller has shown that the group t g n s g hol g hol g acts regularly on the set of the regular subgroups n of s g which are isomorphic to g and have the same holomorph as g in the sense that n s g n hol g if g is non abelian inversion on g yields an involution in t g other non abelian regular subgroups n of s g having the same holomorph as g yield other involutions in t g in the cases studied in the literature t g turns out to be a finite 2 group which is often elementary abelian in this paper we exhibit an example of a finite p group g p of class 2 for p 2 a prime which is the smallest p group such that t g p is non abelian and not a 2 group moreover t g p is not generated by involutions when p 3 more generally we develop some aspects of a theory of t g for g a finite p group of class 2 for p 2 in particular we show that for such a group g there is an element of order p 1 in t g and exhibit examples where t g p 1 and others where t g contains a large elementary abelian p subgroup

groups that have the same holomorph as a finite perfect group abstract we describe the groups that have the same holomorph as a finite perfect group our results are complete for centerless groups when the center is non trivial some questions remain open the peculiarities of the general case are illustrated by a couple of examples that might be of independent interest

pencils of complex and real symmetric and skew matrices abstract this expository paper establishes the canonical forms under congruence for pairs of complex or real symmetric or skew matrices the treatment is in the spirit of the well known book of gantmacher on matrix theory and may be regarded as a supplement to gantmacher s chapters on pencils of matrices

skew symmetric matrix polynomials and their smith forms we characterize the smith form of skew symmetric matrix polynomials over an arbitrary field f showing that all elementary divisors occur with even multiplicity restricting the class of equivalence transformations to unimodular congruences a smith like skew symmetric canonical form for skew symmetric matrix polynomials is also obtained these results are used to analyze the eigenvalue and elementary divisor structure of matrices expressible as products of two skew symmetric matrices as well as the existence of structured linearizations for skew symmetric matrix polynomials by contrast with other classes of structured matrix polynomials e g alternating or palindromic polynomials every regular skew symmetric matrix polynomial is shown to have a structured strong linearization while there are singular skew symmetric polynomials of even degree for which a structured linearization is impossible for each odd degree we develop a skew symmetric companion form that uniformly provides a structured linearization for every regular and singular skew symmetric polynomial of that degree finally the results are applied to the construction of minimal symmetric factorizations of skew symmetric rational matrices

estimation and inference in large heterogeneous panels with a multifactor error structure this paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure the unobserved factors and the individual specific errors are allowed to follow arbitrary stationary processes and the number of unobserved factors need not be estimated the basic idea is to filter the individual specific regressors by means of cross section averages such that asymptotically as the cross section dimension n tends to infinity the differential effects of unobserved common factors are eliminated the estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross sectional averages of the dependent variable and the individual specific regressors a number of estimators referred to as common correlated effects cce estimators are proposed and their asymptotic distributions are derived the small sample properties of mean group and pooled cce estimators are investigated by monte carlo experiments showing that the cce estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics and for relatively small values of n and t

estimating and testing linear models with multiple structural changes this paper develops the statistical theory for testing and estimating multiple change points in regression models the rate of convergence and limiting distribution for the estimated parameters are obtained several test statistics are proposed to determine the existence as well as the number of change points a partial structural change model is considered the authors study both fixed and shrinking magnitudes of shifts in addition the models allow for serially correlated disturbances mixingales an estimation strategy for which the location of the breaks need not be simultaneously determined is discussed instead the authors method successively estimates each break point

efficient estimation of heterogeneous coefficients in panel data models with common shocks this paper investigates efficient estimation of heterogeneous coefficients in panel data models with common shocks which have been a particular focus of recent theoretical and empirical literature we propose a new two step method to estimate the heterogeneous coefficients in the first step the maximum likelihood ml method is first conducted to estimate the loadings and idiosyncratic variances the second step estimates the heterogeneous coefficients by using the structural relations implied by the model and replacing the unknown parameters with their ml estimates we establish the asymptotic theory of our estimator including consistency asymptotic representation and limiting distribution the two step estimator is asymptotically efficient in the sense that it has the same limiting distribution as the infeasible generalized least squares gls estimator intensive monte carlo simulations show that the proposed estimator performs robustly in a variety of data setups

panel threshold models with interactive fixed effects abstract this paper studies estimation and inference in a panel threshold model in the presence of interactive fixed effects we study the asymptotic properties of the least squares estimators of the regression parameters in the shrinking threshold effect framework we find that under some regularity conditions the threshold parameter estimator possesses super consistency in the sense that its estimation error has an asymptotically negligible effect on the asymptotic properties of the slope coefficients the inference on the threshold parameter can be conducted based on a likelihood ratio test statistic as in the cross sectional or time series setup we also propose a test for the presence of the threshold effect monte carlo simulations suggest that our estimators and test statistics perform well in finite samples we apply our method to study the effect of financial development on economic growth and find that there is indeed a turning point in the effect for all three measures of financial development when the cross sectional dependence is properly accounted for

theory and methods of panel data models with interactive effects this paper considers the maximum likelihood estimation of the panel data models with interactive effects motivated in economics and other social sciences a notable feature of the model is that the explanatory variables are correlated with the unobserved effects the usual within group estimator is inconsistent existing methods for consistent estimation are either designed for panel data with short time periods or are less efficient the maximum likelihood estimator has desirable properties and is easy to implement as illustrated by the monte carlo simulations this paper develops the inferential theory for the maximum likelihood estimator including consistency rate of convergence and the limiting distributions we further extend the model to include time invariant regressors and common regressors cross section invariant the regression coefficients for the time invariant regressors are time varying and the coefficients for the common regressors are cross sectionally varying

common breaks in means and variances for panel data this paper establishes the consistency of the estimated common break point in panel data consistency is obtainable even when a regime contains a single observation making it possible to quickly identify the onset of a new regime we also propose a new framework for developing the limiting distribution for the estimated break point and show how to construct confidence intervals the least squares method is used for estimating breaks in means and the quasi maximum likelihood qml method is used to estimate breaks in means and in variances qml is shown to be more efficient than the least squares even if there is no change in the variances

properties and refinements of the fused lasso we consider estimating an unknown signal both blocky and sparse which is corrupted by additive noise we study three interrelated least squares procedures and their asymptotic properties the first procedure is the fused lasso put forward by friedman et al ann appl statist 1 2007 302 332 which we modify into a different estimator called the fused adaptive lasso with better properties the other two estimators we discuss solve least squares problems on sieves one constrains the maximal l 1 norm and the maximal total variation seminorm and the other restricts the number of blocks and the number of nonzero coordinates of the signal we derive conditions for the recovery of the true block partition and the true sparsity patterns by the fused lasso and the fused adaptive lasso and we derive convergence rates for the sieve estimators explicitly in terms of the constraining parameters

estimating and accounting for unobserved covariates in high dimensional correlated data many high dimensional and high throughput biological datasets have complex sample correlation structures which include longitudinal and multiple tissue data as well as data with multiple treatmen

the multiple holomorph of a finitely generated abelian group w h mills has determined for a finitely generated abelian group g the regular subgroups n gn g of s g s g the group of permutations on the set g which have the same holomorph as g that is such that ns g n ns g g ns g n ns g g where is the right regular representation we give an alternative approach to mills result which relies on a characterization of the regular subgroups of ns g g ns g g in terms of commutative ring structures on g we are led to solve for the case of a finitely generated abelian group g the following problem given an abelian group g g what are the commutative ring structures g g such that all automorphisms of g as a group are also automorphisms of g as a ring

classification of the hopf galois structures on prime power radical extensions abstract let p be an odd prime and n a positive integer and let k be a field of characteristic zero let k k w with w p n a k where a is such that k k p n and let r denote the largest integer between 0 and n such that k k p r k p r where p r denotes a primitive p r th root of unity the extension k k is separable but not necessarily normal and by greither and pareigis is h galois with h a k hopf algebra form of a group ring kn where k is the normal closure of k k h is said to be almost classical if n k k the result is that if r n then there are p r hopf galois structures on k k for which the associated group n is cyclic of order p n of these p min r n r are almost classical and the rest are non almost classical when r n there are p n 1 h galois structures for which n c p n of which only one is almost classical finally we show that these are the only structures possible that is for this class of extensions n must be cyclic

estimation of large dimensional factor models with an unknown number of breaks abstract in this paper we study the estimation of a large dimensional factor model when the factor loadings exhibit an unknown number of changes over time we propose a novel three step procedure to detect the breaks if any and then identify their locations in the first step we divide the whole time span into subintervals and fit a conventional factor model on each interval in the second step we apply the adaptive fused group lasso to identify intervals containing a break in the third step we devise a grid search method to estimate the location of the break on each identified interval we show that with probability approaching one our method can identify the correct number of changes and estimate the break locations simulation studies indicate superb finite sample performance of our method we apply our method to investigate stock and watson s 2009 u s monthly macroeconomic dataset and identify five breaks in the factor loadings spanning 1959 2006

counterexample to a conjecture about braces abstract we find an example of a finite solvable group in fact a finite p group in which is not possible to define a left brace structure or equivalently which is not an iyb group this answers a question posed by cedo jespers and del rio related to the yang baxter equation our argument is an improvement of an argument of rump using results about hopf galois extensions and lsa structures we explain explicitly the relation between these two areas of mathematics and brace theory hoping that it will be useful in the future

estimating a common deterministic time trend break in large panels with cross sectional dependence abstract this paper develops an estimation procedure for a common deterministic time trend break in large panels the dependent variable in each equation consists of a deterministic trend and an error term the deterministic trend is subject to a change in the intercept slope or both and the break date is common for all equations the estimation method is simply minimizing the sum of squared residuals for all possible break dates both serial and cross sectional correlations are important factors that decide the rate of convergence and the limiting distribution of the break date estimate the rate of convergence is faster when the errors are stationary than when they have a unit root when there is no cross sectional dependence among the errors the rate of convergence depends on the number of equations and thus is faster than the univariate case when the errors have a common factor structure with factor loadings correlated with the intercept and slope change parameters the rate of convergence does not depend on the number of equations and thus reduces to the univariate case the limiting distribution of the break date estimate is also provided some monte carlo experiments are performed to assess the adequacy of the asymptotic results a brief empirical example using the us gdp price index is offered

panel data models with interactive fixed effects this paper considers large n and large t panel data models with unobservable multiple interactive eects these models are useful for both micro and macro econometric modelings in earnings studies for example workers motivation persistence and diligence combined to influence the earnings in addition to the usual argument of innate ability in macroeconomics the interactive eects represent unobservable common shocks and their heterogeneous responses over cross sections since the interactive eects are allowed to be correlated with the regressors they are treated as fixed eects parameters to be estimated along with the common slope coecients the model is estimated by the least squares method which provides the interactive eect s counterpart of the within estimator we first consider model identification and then derive the rate of convergence and the limiting distribution of the interactive eect s estimator of the common slope coecients the estimator is shown to be p nt consistent this rate is valid even in the presence of correlations and heteroskedasticities in both dimensions a striking contrast with fixed t framework in which serial correlation and heteroskedasticity imply unidentification the asymptotic distribution is not necessarily centered at zero biased corrected estimators are derived we also derive the constrained estimator and its limiting distribution imposing additivity coupled with interactive eects the problem of testing additive versus interactive eects is also studied we also derive identification conditions for models with grand mean time invariant regressors and common regressors it is shown that there exists a set of necessary and sucient identification conditions for those models given identification the rate of convergence and limiting results continue to hold

shrinkage estimation of common breaks in panel data models via adaptive group fused lasso abstract in this paper we consider estimation and inference of common breaks in panel data models via adaptive group fused lasso we consider two approaches penalized least squares pls for first differenced models without endogenous regressors and penalized gmm pgmm for first differenced models with endogeneity we show that with probability tending to one both methods can correctly determine the unknown number of breaks and estimate the common break dates consistently we establish the asymptotic distributions of the lasso estimators of the regression coefficients and their post lasso versions we also propose and validate a data driven method to determine the tuning parameter used in the lasso procedure monte carlo simulations demonstrate that both the pls and pgmm estimation methods work well in finite samples we apply our pgmm method to study the effect of foreign direct investment fdi on economic growth using a panel of 88 countries and regions from 1973 to 2012 and find multiple breaks in the model

nilpotent and abelian hopf galois structures on field extensions abstract let l k be a finite galois extension of fields with group when is nilpotent we show that the problem of enumerating all nilpotent hopf galois structures on l k can be reduced to the corresponding problem for the sylow subgroups of we use this to enumerate all nilpotent resp abelian hopf galois structures on a cyclic extension of arbitrary finite degree when is abelian we give conditions under which every abelian hopf galois structure on l k has type we also give a criterion on n such that every hopf galois structure on a cyclic extension of degree n has cyclic type

estimation and inference of change points in high dimensional factor models abstract in this paper we consider the estimation of break points in high dimensional factor models where the unobserved factors are estimated by principal component analysis pca the factor loading matrix is assumed to have a structural break at an unknown time we establish the conditions under which the least squares ls estimator is consistent for the break date our consistency result holds for both large and small breaks we also find the ls estimator s asymptotic distribution simulation results confirm that the break date can be accurately estimated by the ls even if the magnitudes of breaks are small in two empirical applications we implement the method to estimate break points in the u s stock market and u s macroeconomy respectively

braces radical rings and the quantum yang baxter equation abstract non degenerate cycle sets are equivalent to non degenerate unitary set theoretical solutions of the quantum yang baxter equation we embed such cycle sets into generalized radical rings braces and study their interaction in this context we establish a galois theory between ideals of braces and quotient cycle sets our main result determines the relationship between two square free cycle sets operating transitively on each other