abel lemma based finite sum inequality and its application to stability analysis for linear discrete time delay systems this paper is concerned with stability of linear discrete time delay systems note that a tighter estimation on a finite sum term appearing in the forward difference of some lyapunov functional leads to a less conservative delay dependent stability criterion by using abel lemma a novel finite sum inequality is established which can provide a tighter estimation than the ones in the literature for the finite sum term applying this abel lemma based finite sum inequality a stability criterion for linear discrete time delay systems is derived it is shown through numerical examples that the stability criterion can provide a larger admissible maximum upper bound than stability criteria using a jensen type inequality approach and a free weighting matrix approach

cartan decomposition subgroups of 2 for g sl 3 r and g so 2 n we give explicit practical conditions that determine whether or not a closed connected subgroup h of g has the property that there exists a compact subset c of g with chc g to do this we fix a cartan decomposition g ka k of g and then carry out an approximate calculation of khk n a for each closed connected subgroup h of g

discrete series representations for the orbit spaces arising from two involutions of real reductive lie groups leth gbe real reductive lie groups a discrete series representation for a homogeneous spaceg his an irreducible representation ofgrealized as a closedg invariant subspace ofl2 g h the condition for the existence of discrete series representations forg hwas not known in general except for reductive symmetric spaces this paper offers a sufficient condition for the existence of discrete series representations forg hin the setting thatg his a homogeneous submanifold of a symmetric space g hwhereg g h we prove that discrete series representations are non empty for a number of non symmetric homogeneous spaces such assp 2n r sp n0 c gl n1 c gl nk c nj n ando 4m n u 2m j 0 2j n

integral closedness of complete intersection ideals the aim of this paper is to give some structure theorem of certain integrally closed ideals in noetherian rings let a be a noetherian ring and i an ideal of a then an element x of a is said to be integral over z if x satisfies an equation x c x c 0 in a with ci e i the integral closure i of z is by definition the set of elements in a which are integral over z and the ideal z is called integrally closed if f i let ua z resp ht i denote the smallest number of elements in systems of generators for z resp the height of i let min a z be the set of minimal prime divisors of i in this paper we shall study the problem when the ideals z of a such that ua z ht z are integrally closed and our result is stated as follows

asymptotic expansions and boundary values of eigenfunctions on riemannian symmetric spaces soit x g k un espace de riemann symetrique de type non compacte a bord b k m et soit d x l algebre de tous les operateurs differentiels g invariants sur x on obtient des developpements asymptotiques pour une grande classe de fonctions jointives f sur x

new results on stability analysis for systems with discrete distributed delay the integral inequality technique is widely used to derive delay dependent conditions and various integral inequalities have been developed to reduce the conservatism of the conditions derived in this study a new integral inequality was devised that is tighter than existing ones it was used to investigate the stability of linear systems with a discrete distributed delay and a new stability condition was established the results can be applied to systems with a delay belonging to an interval which may be unstable when the delay is small or nonexistent three numerical examples demonstrate the effectiveness and the smaller conservatism of the method

poincare series for non riemannian locally symmetric spaces abstract we initiate the spectral analysis of pseudo riemannian locally symmetric spaces g h beyond the classical cases where h is compact automorphic forms or is trivial analysis on symmetric spaces for any non riemannian reductive symmetric space x g h on which the discrete spectrum of the laplacian is nonempty and for any discrete group of isometries whose action on x is sufficiently proper we construct l 2 eigenfunctions of the laplacian on x x for an infinite set of eigenvalues these eigenfunctions are obtained as generalized poincare series i e as projections to x of sums over the orbits of eigenfunctions of the laplacian on x we prove that the poincare series we construct still converge and define nonzero l 2 functions after any small deformation of inside g for a large class of groups thus the infinite set of eigenvalues we construct is stable under small deformations this contrasts with the classical setting where the nonzero discrete spectrum varies on the teichmuller space of a compact riemann surface we actually construct joint l 2 eigenfunctions for the whole commutative algebra of invariant differential operators on x

on closed anti de sitter spacetimes this article deals with the structure of the fundamental group of compact anti de sitter spacetimes i e lorentz manifolds with constant negative curvature algebraically such a manifold is the quotient of the universal cover of the homogeneous space so 2 n so 1 n by a discrete group gamma acting properly and co compactly on it this exists if and only if n is even indeed as this was observed by kulkarni u 1 d is contained in so 2 2d and acts properly transitively on so 2 2d so 1 2d it then suffices to take gamma as a co compact lattice in u 1 d the results of the present article give evidence to the question in dimension 3 are all compact anti de sitter spacetimes constructed in this way

technical communique improved stability criterion and its applications in delayed controller design for discrete time systems this paper is concerned with the problem of delay dependent stability analysis for discrete time systems with interval like time varying delays and the problem of stabilization for discrete time linear systems via time delayed controllers the first problem is solved by applying a novel lyapunov functional and an improved delay dependent stability criterion is obtained in terms of a linear matrix inequality based on this a sufficient condition for the solvability of the second problem is presented the reduced conservatism of the proposed stability result is shown through a numerical example while the applicability of the time delayed controller design method is demonstrated by an inverted pendulum system

stochastic finite time h state estimation for discrete time semi markovian jump neural networks with time varying delays in this article the finite time h infty state estimation problem is addressed for a class of discrete time neural networks with semi markovian jump parameters and time varying delays the focus is mainly on the design of a state estimator such that the constructed error system is stochastically finite time bounded with a prescribed h infty performance level via finite time lyapunov stability theory by constructing a delay product type lyapunov functional in which the information of time varying delays and characteristics of activation functions are fully taken into account and using the jensen summation inequality the free weighting matrix approach and the extended reciprocally convex matrix inequality some sufficient conditions are established in terms of linear matrix inequalities to ensure the existence of the state estimator finally numerical examples with simulation results are provided to illustrate the effectiveness of our proposed results

actions propres sur les espaces homogenes reductifs let g be a linear semisimple real lie group and h be a re ductive subgroup of g we give a necessary and sufficient condition for the existence of a nonabelian free discrete subgroup r of g acting properly on g h for instance such a group r does exist for sl 2n ir sl 2n 1 ir but does not for sl 2n 1 r sl 2n r with n 1

proper action on a homogeneous space of reductive type an action of l on a homogeneous space g h is investigated where l h g are reductive lie groups a criterion of the properness of this action is obtained in terms of the little weyl group of g in particular r rankg r rankh iff calabi markus phenomenon occurs i e only finite subgroups of g can act properly discontinuously on g h then by using cohomological dimension theory of a discrete group l g h is proved compact iff d g d l d h where d g denotes the dimension of a riemannian symmetric space associated with g etc these results apply to the existence problem of lattice in g h several series of classical pseudo riemannian homogeneous spaces are found to admit non uniform lattice as well as uniform lattice while some necessary condition for the existence of uniform lattice is obtained when rankg rankh partially supported by grant in aid for scientific research no 63740074

rees algebras of modules we study rees algebras of modules within a fairly general framework we introduce an approach through the notion of bourbaki ideals that allows the use of deformation theory one can talk about the essentially unique generic bourbaki ideal i e of a module e which in many situations allows one to reduce the nature of the rees algebra of e to that of its bourbaki ideal i e properties such as cohen macaulayness normality and being of linear type are viewed from this perspective the known numerical invariants such as the analytic spread the reduction number and the analytic deviation of an ideal and its associated algebras are considered in the case of modules corresponding notions of complete intersection almost complete intersection and equimultiple modules are examined in some detail special consideration is given to certain modules which are fairly ubiquitous because interesting vector bundles appear in this way for these modules one is able to estimate the reduction number and other invariants in terms of the buchsbaum rim multiplicity

almost gorenstein rings abstract barucci and froberg 1997 2 introduced the notion of an almost gorenstein ring in the case of an analytically unramified local ring r m in this work we provide a framework that allows us to generalize this notion to include the analytically ramified case as a consequence for any cohen macaulay local ring r m of dimension one we solve in full generality the problem of determining when the endomorphism algebra m m is gorenstein we also provide characterizations for rings to be almost gorenstein in connection with the principle of idealization several examples are explored as well

an extended reciprocally convex matrix inequality for stability analysis of systems with time varying delay abstract the reciprocally convex combination lemma rccl is an important technique to develop stability criteria for the systems with a time varying delay this note develops an extended reciprocally convex matrix inequality which reduces the estimation gap of the rccl based matrix inequality and reduces the number of decision variables of the recently proposed delay dependent rccl a stability criterion of a linear time delay system is established through the proposed matrix inequality finally a numerical example is given to demonstrate the advantage of the proposed method

an improved summation inequality to discrete time systems with time varying delay the summation inequality plays an important role in developing delay dependent criteria for discrete time systems with time varying delay this note proposes an improved summation inequality to estimate the summation terms appearing in the forward difference of lyapunov krasovskii functional compared with the inequality recently developed by the wirtinger based summation inequality and the reciprocally convex lemma the proposed one reduces the estimation gap while requires the same number of decision variables a relaxed stability criterion of a linear discrete time system with a time varying delay is established by using such novel inequality two numerical examples are given to demonstrate the advantages of the proposed method

new results on stability of discrete time systems with time varying state delay this note is concerned with the stability analysis of discrete time systems with time varying state delay by defining new lyapunov functions and by making use of novel techniques to achieve delay dependence several new conditions are obtained for the asymptotic stability of these systems the merit of the proposed conditions lies in their less conservativeness which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms sigmam k dk k 1 middot and sigma m k dm k 1 middot which is largely ignored in the existing literature these conditions are shown via several examples to be much less conservative than some existing result

completeness of compact lorentzian manifolds with abelian holonomy we address the problem of finding conditions under which a compact lorentzian manifold is geodesically complete a property which always holds for compact riemannian manifolds it is known that a compact lorentzian manifold is geodesically complete if it is homogeneous or has constant curvature or admits a time like conformal vector field we consider certain lorentzian manifolds with abelian holonomy which are locally modelled by the so called pp waves and which in general do not satisfy any of the above conditions we show that compact pp waves are universally covered by a vector space determine the metric on the universal cover and prove that they are geodesically complete using this we show that every ricci flat compact pp wave is a plane wave

further results on stability analysis of discrete time systems with time varying delays via the use of novel convex combination coefficients this paper focuses on deriving an improved stability criterion for discrete time delay systems via a lyapunov krasovskii functional approach that takes advantage of triple summation terms to this end novel convex combination coefficients coupled with second order time varying delay terms are introduced and the corresponding reciprocally convex approach is established with the use of the minimal number of slack matrix variables finally three numerical examples are provided to illustrate the effectiveness of the proposed method with particular regard to robustness and h performance

structure of lorentzian tori with a killing vector field all lorentzian tori with a non discrete group of isometries are characterized and explicitly obtained they can lie into three cases a flat b conformally flat but non flat and c geodesically incomplete a detailed study of many of their properties including results on the logical dependence of the three kinds of causal completeness on geodesic connectedness and on prescribed curvature is carried out the incomplete case is specially analyzed and several known examples and results in the literature are generalized from a unified point of view

deformation of proper actions on reductive homogeneous spaces let g be a real reductive lie group and h a closed reductive subgroup of g we investigate the deformation of standard compact quotients of g h that is of quotients of g h by discrete groups that are uniform lattices in some closed reductive subgroup l of g acting properly and cocompactly on g h for l of real rank 1 we prove that after a small deformation in g such a group keeps acting properly discontinuously and cocompactly on g h more generally we prove that the properness of the action of any convex cocompact subgroup of l on g h is preserved under small deformations and we extend this result to reductive homogeneous spaces g h over any local field as an application we obtain compact quotients of so 2n 2 u n 1 by zariski dense discrete subgroups of so 2n 2 acting properly discontinuously

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

stability analysis of systems with time varying delay via novel augmented lyapunov krasovskii functionals and an improved integral inequality abstract delay dependent stability analysis of linear systems with a time varying delay is investigated in this paper firstly instead of developing a lyapunov krasovskii functional lkf including augmented non integral quadratic terms as usual this paper proposes two augmented integral function based lkfs which can reflect closer relationships among system states secondly to bound the derivative of lkf more accurately a new integral inequality with several free matrices is developed compared with the free matrix based integral inequality this inequality can provide additional freedom due to the free matrices introduced then by employing those lkfs and the improved integral inequality several delay dependent stability criteria are established for two types of delays finally two numerical examples are given to demonstrate the superiority of the proposed method

geometric realization of discrete series for semisimple symmetric spaces let g be a connected semisimple lie group a an involution of g and h the connected component of the fixed point set of a containing the identity then g h is a semisimple symmetric space we assume g is a real form of a complex lie group and rank g h rank k k c h where k is a a stable maximal compact subgroup of g flensted jensen using his duality principle and poisson transform constructed countably many discrete series in u g h f j i then using deep results of hyperfunction theory and microlocal analysis oshima and matsuki gave a detailed characterization of these discrete series including a proof of flensted jensen s conjecture c 0 om based on these results we give the discrete series a geometric interpretation in locally symmetric spaces f c where g k and f cg is a cocompact discrete group such that f c h c h is cocompact our geometric interpretation is the following first of all to a flensted jensen function which is the generating function of a discrete series v we associate a harmonic form cb z on g with values in a finite dimensional g module v right g translates of coefficients of 5z realizes the contragredient t of r and tba is left invariant under h and under right k action it transforms according to the minimal k type with highest weight of 3 is the pull back of a v valued from coz on and v determines a locally constant bundle e on f so that if convergence holds

new stability criteria for linear discrete time systems with interval like time varying delays this technical note is concerned with stability of linear discrete time systems with interval like time varying delays two new stability criteria are derived by constructing a new lyapunov functional and utilizing two novel techniques for estimating the forward difference of the lyapunov functional the relationship between these stability criteria and some existing ones is established through the relationship it is clear that these stability criteria are less conservative than some existing ones which is confirmed by a numerical example

the almost gorenstein rees algebras of parameters abstract there is given a characterization for the rees algebras of parameters in a gorenstein local ring to be almost gorenstein graded rings a characterization is also given for the rees algebras of socle ideals of parameters the latter one shows almost gorenstein rees algebras rather rarely exist for socle ideals if the dimension of the base local ring is greater than two

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

discrete groups and non riemannian homogeneous spaces a basic question in geometry is to understand compact locally homogeneous manifolds i e those compact manifolds that can be locally modelled on a homogeneous space j h of a finite dimensional lie group h this means that there is an atlas on a manifold m consisting of local diffeomorphisms with open sets in j h where the transition functions between these open sets are given by translations by elements of h a basic example is the case of m j h f where f c h is a discrete subgroup acting freely and properly discontinuously on j h with a compact quotient these examples can be abstractly characterized as the complete case see g we then call f a cocompact lattice on j h when j is compact j h has an h invariant riemannian metric so that m itself becomes a riemannian manifold in a natural way thus the class of locally homogeneous riemannian manifolds includes but is not exhausted by the locally symmetric spaces for h aff rn and j gl n r the spaces j h f are the complete affinely flat manifolds a non riemannian example which has been extensively studied when h is simple and j is not compact the situation is far from being well understood some special series of such homogeneous spaces admitting a cocompact lattice have been constructed by kulkarni ku and by t kobayashi k for example kulkarni shows the existence of such a discrete group f for the homogeneous spaces so 1 2n so 2 2n and kobayshi does the same for u 1 n so 2 2n on the other hand the constructions they give for these and other similar series are quite special and there has been the general suspicion that most homogeneous spaces j h with h simple and j not compact do not admit a cocompact lattice we recall that when j is compact i e the riemannian case such f always exist by a result of borel b one general situation in which it is known that no such f exists is the case in which j h is noncompact and of reductive type and r rank h r rank j this situation was studied by calabi markus cm wolf w and kobayashi k and the nonexistence of f in this situation is a special case of a more general result known as the calabi markus phenomenon kobayashi and ono ko use the hirzebruch proportionality principle to show that some other special series do

deformation of compact clifford klein forms of indefinite riemannian homogeneous manifolds 1 1 let g be a lie group and h a closed subgroup of g if a discrete subgroup of g acts properly discontinuously and freely on g h then the double coset space g h carries naturally a manifold structure such that the quotient map g h g h is locally diffeomorphic the manifold g h is said to be a clifford klein form of g h if it is compact then is said to be a uniform lattice for g h a typical example is a compact riemann surface mg with genus g 2 which is biholomorphic to a compact clifford klein form of the poincare disk g h sl 2 r so 2 by the uniformization theorem it is important from geometric view point that a clifford klein form g h inherits any g invariant local geometric structure on g h such as indefinite riemannian metric complex structure symplectic structure causal structure and so on

pseudo frobenius numbers versus defining ideals in numerical semigroup rings abstract the structure of the defining ideal of the semigroup ring k h of a numerical semigroup h over a field k is described when the pseudo frobenius numbers of h are multiples of a fixed integer

sally modules of canonical ideals in dimension one and 2 agl rings abstract the notion of 2 agl ring in dimension one which is a natural generalization of almost gorenstein local ring is posed in terms of the rank of sally modules of canonical ideals the basic theory is developed investigating also the case where the rings considered are numerical semigroup rings over fields examples are explored

output feedback stabilization for a discrete time system with a time varying delay this study employs the free weighting matrix approach to investigate the output feedback control of a linear discrete time system with an interval time varying delay first the delay dependent stability is analyzed using a new method of estimating the upper bound on the difference of a lyapunov function without ignoring any terms and based on the results a design criterion for a static output feedback sof controller is derived since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility sof control problem furthermore the problem of designing a dynamic output feedback controller is formulated as one of designing an sof controller numerical examples demonstrate the effectiveness of the method and its advantage over existing methods

delay variation dependent stability of delayed discrete time systems this note is concerned with the stability analysis of linear discrete time system with a time varying delay a generalized free weighting matrix gfwm approach is proposed to estimate summation terms in the forward difference of lyapunov functional and theoretical study shows that the gfwm approach encompasses several frequently used estimation approaches as special cases moreover an augmented lyapunov functional with a delay product type term is constructed to take into account delay changing information as a result the proposed gfwm approach together with the augmented lyapunov functional leads to a less conservative delay variation dependent stability criterion finally numerical examples are given to illustrate the advantages of the proposed criterion

classification of semisimple symmetric spaces with proper actions we give a complete classification of irreducible symmetric spaces for which there exist proper sl 2 mathbb r actions as isometries using the criterion for proper actions by t kobayashi and combinatorial techniques of nilpotent orbits in particular we classify irreducible symmetric spaces that admit surface groups as discontinuous groups combining this with benoist s theorem

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

ideals having the expected reduction number 1 introduction let r be a noetherian local ring with infinite residue field k and let be an r ideal when studying algebraic properties of the blow up of spec along v l it is often important to have good upper bounds for the reduction number of the ideal recall that an ideal c is a reduction of if the extension of rees algebras r jt c r it is module finite or equivalently if ir l j r for some r 0 32 the least such r is denoted by rj i a reduction is minimal if it is minimal with respect to inclusion and the reduction number r l of is defined as min o j a minimal reduction of finally the analytic spread i of is the krull dimension of the fiber ring r lt r k or equivalently the minimal number of generators jbi j of any minimal reduction j of 1 32 philosophically speaking j is a simplification of with the reduction number r l measuring how closely the two ideals are related of the numerous recent results about rees algebras and associated graded rings of ideals having small reduction number 18 19 38 35 12 13 14 4 3

stability of discrete time systems with time varying delays via a novel summation inequality this technical note is concerned with the stability analysis of discrete linear systems with time varying delays the novelty of the technical note comes from the consideration of a new inequality which is less conservative than the celebrated jensen inequality employed in the context of discrete time delay systems this inequality is a discrete time counterpart of the wirtinger based integral inequality that was recently employed for the improved analysis of continuous tine systems with delays however differently from the continuous time case the proof of the new inequality is not based on the wirtinger inequality the method is also combined with an efficient representation of the improved reciprocally convex combination inequality in order to reduce the conservatism induced by the lmis optimization setup the effectiveness of the proposed result is illustrated by some classical examples from the literature

stability and passivity analysis of discrete time linear systems with time varying delay abstract this paper focuses on the stability and passivity analysis for a class of discrete time linear systems a novel general free matrix based summation inequality is proposed and two improved stability criteria in terms of linear matrix inequalities lmis are derived by employing the new summation inequality furthermore when an external disturbance appears a sufficient condition is established to ensure the considered linear system to be passive three numerical examples are provided to demonstrate the improvement of the proposed method

compact lorentz manifolds with local symmetry we prove a structure theorem for compact aspherical lorentz manifolds with abundant local symmetry if m is a compact aspherical real analytic complete lorentz manifold such that the isometry group of the universal cover has semisimple identity component then the local isometry orbits in m are roughly fibers of a fiber bundle a corollary is that if m has an open dense locally homogeneous subset then m is locally homogeneous acknowledgements i thank my dissertation advisor benson farb for his guidance and encouragement i also thank abdelghani zeghib with whom i had helpful conversations while working on this project in loving memory of laura sue jung kang

links of symbolic powers of prime ideals in this paper we prove the following let r frak m be a cohen macaulay local ring of dimension d 2 suppose that either r is not regular or if r is regular assume that d 3 let t 2 be a positive integer if alpha 1 dots alpha d is a regular sequence contained in frak m t then alpha 1 dots alpha d frak m t subseteq frak m t this result gives an affirmative answer to a conjecture raised by polini and ulrich

extended dissipativity analysis for discrete time delayed neural networks based on an extended reciprocally convex matrix inequality abstract in this paper the extended dissipativity analysis for discrete time neural networks with a time varying delay is investigated first a novel lyapunov krasovskii functional lkf is constructed with a delay product type term introduced then in the forward difference of the lkf the sum terms are bounded via an extended reciprocally convex matrix inequality as a result an extended dissipativity criterion is established in terms of linear matrix inequalities meanwhile this criterion is extended to the stability analysis of the counterpart system without disturbance finally two numerical examples are given to demonstrate the effectiveness and improvements of the presented criterion

discrete decomposability of the restriction of aq λ with respect to reductive subgroupsiii restriction of harish chandra modules and associated varieties let h g be real reductive lie groups and an irreducible unitary representation of g we introduce an algebraic formulation discretely decomposable restriction to single out the nice class of the branching problem breaking symmetry in physics in the sense that there is no continuous spectrum in the irreducible decomposition of the restriction h this paper offers basic algebraic properties of discretely decomposable restrictions especially for a reductive symmetric pair g h and for the zuckerman vogan derived functor module and proves that the sufficient condition invent math 94 is in fact necessary a finite multiplicity theorem is established for discretely decomposable modules which is in sharp contrast to known examples of the continuous spectrum an application to the restriction h of discrete series for a symmetric space g h is also given

ulrich ideals and 2 agl rings abstract the notion of 2 almost gorenstein local ring 2 agl ring for short is a generalization of the notion of almost gorenstein local ring from the point of view of sally modules of canonical ideals in this paper for further developments of the theory we discuss three different topics on 2 agl rings the first one is to clarify the structure of minimal presentations of canonical ideals and the second one is the study of the question of when certain fiber products so called amalgamated duplications are 2 agl rings we also explore ulrich ideals in 2 agl rings mainly two generated ones

discrete decomposability of the restriction of a q λ with respect to reductive subgroups and its applications letg g be real reductive lie groups and q a stable parabolic subalgebra of lie g this paper offers a sufficient condition on g g q that the irreducible unitary representation mathop a q limits ofg with non zero continuous cohomology splits into a discrete sum of irreducible unitary representations of a subgroupg each of finite multiplicity as an application to purely analytic problems new results on discrete series are also obtained for some pseudo riemannian non symmetric spherical homogeneous spaces which fit nicely into this framework some explicit examples of a decomposition formula are also found in the cases wherea q is not necessarily a highest weight module

stability analysis of lur e systems with additive delay components via a relaxed matrix inequality abstract this paper is concerned with the stability analysis of lur e systems with sector bounded nonlinearity and two additive time varying delay components in order to accurately understand the effect of time delays on the system stability the extended matrix inequality for estimating the derivative of the lyapunov krasovskii functionals lkfs is employed to achieve the conservatism reduction of stability criteria it reduces estimation gap of the popular reciprocally convex combination lemma rccl combining the extended matrix inequality and two types of lkfs lead to several stability criteria which are less conservative than the rccl based criteria under the same lkfs finally the advantages of the proposed criteria are demonstrated through two examples

classification and stability of relative equilibria for the two body problem in the hyperbolic space of dimension 2 we classify and analyze the stability of all relative equilibria for the two body problem in the hyperbolic space of dimension 2 and we formulate our results in terms of the intrinsic riemannian data of the problem

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

technical communique a delay partitioning approach to the stability analysis of discrete time systems this paper revisits the problem of stability analysis for linear discrete time systems with time varying delay in the state by utilizing the delay partitioning idea new stability criteria are proposed in terms of linear matrix inequalities lmis these conditions are developed based on a novel lyapunov functional in addition to delay dependence the obtained conditions are also dependent on the partitioning size we have also established that the conservatism of the conditions is a non increasing function of the number of partitions numerical examples are given to illustrate the effectiveness and advantage of the proposed methods