interaction equations for short and long dispersive waves abstract we show the time local well posedness for a system of nonlinear dispersive equations for the water wave interaction formula it is shown that for any initial data u0 v0 hs r hs 1 2 r s 0 the solution for the above equation uniquely exists in a subset ofc t t hs c t t hs 1 2 and depends continuously on the data by virtue of a special structure of the nonlinear coupling the solution is stable under a singular limiting process

testing linearity against smooth transition autoregressive models summary we study a general univariate smooth transition autoregressive star model it contains as a special case the self exciting threshold autoregressive setar model we present three tests for testing linearity against star models and discuss their properties the power of the tests in small samples is investigated by simulation when the alternative is the logistic star model one of the tests is identical to tsay s 1986 test statistic and is recommended only in a special case of the two remaining tests with wider applicability one seems superior to the other in small samples it is also more powerful than the cusum test recently proposed for testing linearity against setar models

orbits and invariants associated with a pair of commuting involutions let be commuting involutions of the connected reductive algebraic group g where and g are defined over a usually algebraically closed field k char k 2 we have fixed point groups h g and k g and an action h k g g where h k g hgk 1 h h k k g g let g h k denote spec o g h k the categorical quotient let a be maximal among subtori s of g such that s s s 1 for all s s there is the associated weyl group w wh k a we show the inclusion a g induces an isomorphism a w g h k in particular the closed h k orbits are precisely those which intersect a the fibers of g g h k are the same as those occurring in certain associated symmetric varieties in particular the fibers consist of finitely many orbits we investigate the structure of w and its relation to other naturally occurring weyl groups and to the action of on the a weight spaces of the relation of the orbit type stratifications of a w and g h k along the way we simplify some of richardson s proofs for the symmetric case and at the end we quickly recover results of berger flensted jensen hoogenboom and matsuki ber57 fj78 hoo84 mat97 for the case k

singularity analysis and localized coherent structures in 2 1 dimensional generalized korteweg de vries equations in this article a singularity structure analysis of a 2 1 dimensional generalized korteweg de vries equation studied originally by boiti et al admitting a weak lax pair is carried out and it is proven that the system satisfies the painleve property its bilinear form is constructed in a natural way from the p analysis and then it is used to generate multidromion solutions exponentially decaying solutions in all directions the same analysis can be extended to construct the multidromion solutions of the generalized nizhnik novikov veselov nnv equation from which the nnv equation follows as a special case

on the classification of k involutions let g be a connected reductive algebraic group defined over a field k of characteristic not 2 an involution of g defined over k h a k open subgroup of the fixed point group of and gk resp hk the set of k rational points of g resp h the variety gk hk is called a symmetric k variety these varieties occur in many problems in representation theory geometry and singularity theory over the last few decades the representation theory of these varieties has been extensively studied for k r and c as most of the work in these two cases was completed the study of the representation theory over other fields like local fields and finite fields began the representations of a homogeneous space usually depend heavily on the fine structure of the homogeneous space like the restricted root systems with weyl groups etc thus it is essential to study first this structure and the related geometry in this paper we give a characterization of the isomorphy classes of these symmetric k varieties together with their fine structure of restricted root systems and also a classification of this fine structure for the real numbers p adic numbers finite fields and number fields

testing for a unit root in the nonlinear star framework in this paper we propose a simple testingprocedure to detect the presence of nonstationarity against nonlinear but globally stationary exponential smooth transition autoregressive processes we provide an advance over the existingliterature in three senses first we derive the limiting nonstandard distribution of the proposed tests second we 0nd via monte carlo simulation exercises that under the alternative of a globally stationary estar process our proposed test has better power than the standard dickey fuller test in the region of the null where the processes are highly persistent third we provide an application to ex post real interest rates and bilateral real exchange rates with the us dollar from the 11 major oecd countries and 0nd our test is able to reject a unit root in many cases whereas the linear df tests fail providing some evidence of nonlinear mean reversion in both real interest and exchange rates c 2002 elsevier science b v all rights reserved jel classi cation c12 c32 e43 f31

unit root tests in arma models with data dependent methods for the selection of the truncation lag abstract we analyze the choice of the truncation lag in the context of the said dickey test for the presence of a unit root in a general autoregressive moving average model it is shown that a deterministic relationship between the truncation lag and the sample size is dominated by data dependent rules that take sample information into account in particular we study data dependent rules that are not constrained to satisfy the lower bound condition imposed by said dickey akaike s information criterion falls into this category the analytical properties of the truncation lag selected according to a class of information criteria are compared to those based on sequential testing for the significance of coefficients on additional lags the asymptotic properties of the unit root test under various methods for selecting the truncation lag are analyzed and simulations are used to show their distinctive behavior in finite samples our results favor methods based on sequential tests over those based on informat

real double coset spaces and their invariants abstract let g be a real form of a complex reductive group suppose that we are given involutions and of g let h g denote the fixed group of and let k g denote the fixed group of we are interested in calculating the double coset space h g k we use moment map and invariant theoretic techniques to calculate the double cosets especially the ones that are closed one salient point of our results is a stratification of a quotient of a compact torus over which the closed double cosets fiber as a collection of trivial bundles

periodic and localized solutions of the long wave short wave resonance interaction equation in this paper we investigate the 2 1 dimensional long wave short wave resonance interaction lsri equation and show that it possess the painleve property we then solve the lsri equation using painleve truncation approach through which we are able to construct solution in terms of three arbitrary functions utilizing the arbitrary functions present in the solution we have generated a wide class of elliptic function periodic wave solutions and exponentially localized solutions such as dromions multidromions instantons multi instantons and bounded solitary wave solutions

extended multilinear variable separation approach and multivalued localized excitations for some 2 1 dimensional integrable systems the multilinear variable separation approach and the related universal formula have been applied to many 2 1 dimensional nonlinear systems starting from the universal formula abundant 2 1 dimensional localized excitations have been found in this paper the universal formula is extended in two different ways one is obtained for the modified nizhnik novikov veselov equation such that two universal terms can be combined linearly and this type of extension is also valid for the 2 1 dimensional symmetric sine gordon system the other is for the dispersive long wave equation the broer kaup kupershmidt system the higher order broer kaup kupershmidt system and the burgers system where arbitrary number of variable separated functions can be involved because of the existence of the arbitrary functions in both the original universal formula and its extended forms the multivalued functions can be used to construct a new type of localized excitations folded solitary waves fsws and foldons the fsws

the existence of a global attractor for the 2 1 dimensional long wave short wave resonance interaction equation abstract in this paper we prove the existence of a global attractor and an asymptotic smoothing effect of the solution for the 2 1 dimensional long wave short wave resonance interaction equation

the global solution of the 2 1 dimensional long wave short wave resonance interaction equation in this paper we prove the existence and uniqueness of the global smooth solution to the 2 1 dimensional long wave short wave resonance interaction equation

revisitation of the localized excitations of the 2 1 dimensional kdv equation in a previous paper lou s y 1995 j phys a math gen 28 7227 a generalized dromion structure was revealed for the 2 1 dimensional kdv equation which was first derived by boiti et al boiti m leon j j p manna m and pempinelli f 1986 inverse problems 2 271 using the idea of the weak lax pair in this paper using a backlund transformation and the variable separation approach we find there exist much more abundant localized structures for the 2 1 dimensional kdv equation the abundance of the localized structures of the model is introduced by the entrance of an arbitrary function of the seed solution some special types of dromion solution lumps breathers instantons and the ring type of soliton are discussed by selecting the arbitrary functions appropriately the dromion solutions can be driven by sets of straight line and curved line ghost solitons the dromion solutions may be located not only at the cross points of the lines but also at the closed points of the curves the breathers may breathe both in amplitude and in shape

double coset decompositions of reductive lie groups arising from two involutions g 0 h g and g 0 l g here g g g g g for an automorphism of g and f0 denote the connected component of f containing the identity e for a lie group f in 8 we gave standard representatives of double coset decompositions h g l for some typical triples g h l by only using algebraic method as the most elementary example we studied the case g h l gl n if gl p if gl n p if gl r if gl n r if for an arbitrary field if we also studied in 8 other examples related to quadratic forms on vector spaces over the fields ir c and ih in this paper we assume that g is a reductive lie group and we will describe the structure of the double coset decomposition h g l for an arbitrary g h l first we study the compact case section 3 and next the noncompact case section 4 in section 3 we assume that the semisimple part gs of g is compact gs is the analytic subgroup of g for gs g g when g gs and

testing for unit roots in heterogeneous panels abstract this paper proposes unit root tests for dynamic heterogeneous panels based on the mean of individual unit root statistics in particular it proposes a standardized t bar test statistic based on the augmented dickey fuller statistics averaged across the groups under a general setting this statistic is shown to converge in probability to a standard normal variate sequentially with t the time series dimension followed by n the cross sectional dimension a diagonal convergence result with t and n while n t k k being a finite non negative constant is also conjectured in the special case where errors in individual dickey fuller df regressions are serially uncorrelated a modified version of the standardized t bar statistic is shown to be distributed as standard normal as n for a fixed t so long as t 5 in the case of df regressions with intercepts and t 6 in the case of df regressions with intercepts and linear time trends an exact fixed n and t test is also developed using the simple average of the df statistics monte carlo results show that if a large enough lag order is selected for the underlying adf regressions then the small sample performances of the t bar test is reasonably satisfactory and generally better than the test proposed by levin and lin unpublished manuscript university of california san diego 1993

specification estimation and evaluation of smooth transition autoregressive models abstract this article considers the application of two families of nonlinear autoregressive models the logistic lstar and exponential estar autoregressive models this includes the specification of the model based on simple statistical tests linearity testing against smooth transition autoregression determining the delay parameter and choosing between lstar and estar models are discussed estimation by nonlinear least squares is considered as well as evaluating the properties of the estimated model the proposed techniques are illustrated by examples using both simulated and real time series

localized excitations in 2 1 dimensional systems by means of a special variable separation approach a common formula with some arbitrary functions has been obtained for some suitable physical quantities of various 2 1 dimensional models such as the davey stewartson ds model the nizhnik novikov veselov nnv system asymmetric nnv equation asymmetric ds equation dispersive long wave equation broer kaup kupershmidt system long wave short wave interaction model maccari system and a general n m component ablowitz kaup newell segur akns system selecting the arbitrary functions appropriately one may obtain abundant stable localized interesting excitations such as the multidromions lumps ring soliton solutions breathers instantons etc it is shown that some types of lower dimensional chaotic patterns such as the chaotic chaotic patterns periodic chaotic patterns chaotic line soliton patterns chaotic dromion patterns fractal lump patterns and fractal dromion patterns may be found in higher dimensional soliton systems the interactions between the traveling ring type soliton solutions are completely elastic the traveling ring solitons pass through each other and preserve their shapes velocities and phases some types of localized weak solutions peakons are also discussed especially the interactions between two peakons are not completely elastic after the interactions the traveling peakons also pass through each other and preserve their velocities and phases however they completely exchange their shapes

vecteurs distributions h invariants pour les series principales generalisees d espaces symetriques reductifs et prolongement meromorphe d integrales d eisenstein

algebraic groups with a commuting pair of involutions and semisimple symmetric spaces let g be a connected reductive algebraic group defined over an algebraically closed field f of characteristic not 2 denote the lie algebra of g by 9 in this paper we shall classify the isomorphism classes of ordered pairs of commuting involutorial automorphisms of g this is shown to be independent of the characteristic of f and can be applied to describe all semisimple locally symmetric spaces together with their line structure involutorial automorphisms of g occur in several places in the literature cartan has already shown that for f c the isomorphism classes of involutorial automorphisms of g correspond bijectively to the isomorphism classes of real semisimple lie algebras which correspond in their turn to the isomorphism classes of riemannian symmetric spaces see helgason 111 if one lifts this involution to the group g then the present work gives a characteristic free description of these isomorphism classes in a similar manner we can show that semisimple locally symmetric spaces correspond to pairs of commuting involutorial automorphisms of g namely let go a be a semisimple locally symmetric pair i e go is a real semisimple lie algebra and rr e aut g an involution then by a result of berger 2 there exists a cartan involution 8 of go such that 00 ea if we denote the complexilication of go by g then o and 8 induce a pair of commuting involutions of g conversely if c 8 e aut g are commuting involutions then c and 8 determine two locally semisimple symmetric pairs for if u is a o and o stable compact real form with conjugation r then ger 1 ge and g f3 i ger are semisimple locally symmetric pairs where

tori invariant under an involutorial automorphism i abstract the geometry of the orbits of a minimal parabolick subgroup acting on a symmetrick variety is essential in several areas but its main importance is in the study of the representations associated with these symmetrick varieties see for example 5 6 20 and 31 up to an action of the restricted weyl group ofg these orbits can be characterized by thehk conjugacy classes of maximalk split tori which are stable underk involution associated with the symmetrick variety herehis a openk subgroup of the fixed point group of this is the second in a series of papers in which we characterize and classify thehk conjugacy classes of maximalk split tori the first paper in this series dealt with the case of algebraically closed fields in this paper we lay the foundation for a characterization and classification for the case of nonalgebraically closed fields this includes a partial classification in the cases where the base field is the real numbers p adic numbers finite fields and number fields

long time behavior for the weakly damped driven long wave short wave resonance equations abstract in this paper we consider the cauchy problem of the long wave short wave resonance equations by making use of a strichartz type inequality for the solutions decomposing suitably the solution semigroup into a decay parts and a more regular parts and ruling out the vanishing and dichotomy of the solutions we prove the existence of the global attractor and the asymptotic smoothing effect of the solutions

decompositions related to symmetric varieties abstract let g be a connected reductive group over an algebraically closed field of characteristic 2 and let be an automorphism of g of order 2 whose fixed point group is k the paper establishes for certain g varieties x a decomposition of x in finitely many k stable locally closed pieces namely a if x g p where p is a parabolic subgroup of g and b g adjoint if x is the wonderful compactification of the symmetric variety g k

orbits invariants and representations associated to involutions of reductive groups by an involution of an algebraic group or lie algebra we mean an automorphism 0 such that 0 2 is the identity automorphism let 0 be an involution of a complex reductive lie algebra q and let p denote the 1 eigenspace of 0 on q get g be the adjoint group of q and let k g glog go kostant and rallis 10 have made a detailed study of the action of k on p in particular they obtain very precise information concerning the orbits of k on p and the representation of k on c p the algebra of polynomial functions on p in this paper we consider a global analogue of the problem studied by kostant and rallis let g be a reductive affine algebraic group over an algebraically closed field k of characteristic 2 let 0 be an involution of g and let k gegi0 g g if g is semisimple and the base field is c then g k is the complexification of a riemannian symmetric space we study the action of k and of groups closely related to k by left translation on the coset space g k for technical reasons it is convenient to study a slightly different but equivalent problem let r g g be defined by r g g0 g i then z g p is a closed subvariety of g furthermore z is constant on left cosets of g modulo k and induces an isomorphism o g k p we have o k g k k o g k for k e k and geg thus p is stable under conjugation by k and a is a k isomorphism of affine k varieties we consider the action of k on p by conjugation let x e g have jordan decomposition x x x then we show that x e p if and only if both x and x are in p thus we have a jordan decomposition for elements of p this will play a key role in our results a torus s of g is o anisotropic if o s s 1 for every ses it is known that any two maximal 0 anisotropic tori of g are k let a be a maximal 0 anisotropic torus of g the following result characterizes semisimple elements of p