a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

adjoint ideals and gorenstein blowups in two dimensional regular local rings in this article we investigate when a complete ideal in a two dimensional regular local ring is a multiplier ideal of some ideal with an integral multiplying parameter in particular we show that this question is closely connected to the gorenstein property of the blowup along the ideal

on reachability and stabilization of switched linear systems reachability and stabilization issues for switched linear control systems are addressed a necessary and a sufficient condition are presented for reachability under mild assumptions we prove that the switched linear control systems are stabilizable in addition we show that an element driven switching stabilization strategy can be explicitly constructed

blowing up finitely supported complete ideals in a regular local ring let i be a finitely supported complete m primary ideal of a regular local ring r m we consider singularities of the projective models projr it and projr it over spec r where r it denotes the integral closure of the rees algebra r it a theorem of lipman implies that the ideal i has a unique factorization as a product of special simple complete ideals with possibly negative exponents for some of the factors if projr it is regular we prove that projr it is the regular model obtained by blowing up the finite set of base points of i extending work of lipman and huneke sally in dimension 2 we prove that every local ring s on projr it that is a unique factorization domain is regular moreover if dim s 2 and s dominates r then s is an infinitely near point to r that is s is obtained from r by a finite sequence of local quadratic transforms

birational extensions in dimension two and integrally closed ideals the aim of this paper is to examine primarily from an algebraic point of view the structure of a 2 dimensional normal local domain s n which birationally dominates a 2 dimensinal regular local ring r m from the geometric point of view the sine qua non is lipman s paper lr on rational singularities for it follows from one of the early results in that paper that s has a rational singularity using elementary algebraic techniques we are able to recover much information concerning the structure of s we have particularly focused on the fact from lipman ll and artin ar that s must have minimal multiplicity we hope this approach will aid in understanding the algebra of rational singularities and in the exploration of many open questions in dimension two and in higher dimensions the framework of the paper is set up as follows in the first section we use basic algebraic techniques such as analytic independence and zariski s main theorem to prove for example that s has a regular height 1 prime if r m is infinite if s is not regular we may assume that r is maximally regular in s and when this is the case we show for instance that the

on controllability of switched linear systems in this paper the controllability of a switched linear system which is a collection of linear time invariant systems along with some maps for switching among them is addressed first a controllable state set is defined as a basic tool to discuss the controllability condition next it is proved that the controllability of a multi input system is equivalent to that of a single input system finally a sufficient and necessary condition for controllability of third order systems is presented according to the proof of this criterion we state a conjecture on the controllability condition of n dimensional systems a numeric example is given to illustrate the result

brief paper on partitioned controllability of switched linear systems when a switched linear system is not completely controllable the controllability subspace is not enough to describe the controllability of the system over whole state space in this case the state space can be divided into two or three control invariant sub manifolds which form a control related partition of the state space this paper investigates when each component is a controllable sub manifold first we consider when a sub manifold is controllable for no control input case then the results are used to produce a necessary and sufficient condition assuring the controllability of the partitioned control invariant sub manifolds of a class of switched linear systems an example is given to demonstrate the effectiveness of the results

poincare series of a toric variety abstract for an affine toric variety x we compute the poincare series of the multi index filtration defined by a finite number of monomial divisorial valuations on the ring o x 0 we give an alternative description of the poincare series as an integral with respect to the euler characteristic over the projectivization of the space of germs o x 0 in particular we study divisorial valuations on the ring o c d 0 that arise by considering toric constellations we give an explicit formula for the poincare series and a nice geometric description this generalizes an expression of the poincare series for curves and rational surface singularities

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

integral closedness of mi and the formula of hoskin and deligne for finitely supported complete ideals abstract we obtain necessary and sufficient conditions for a finitely supported monomial ideal i in a polynomial ring of dimension at least three for mi to be integrally closed this is obtained via the higher dimensional analogue of the formula of hoskin and deligne for the length of a finitely supported ideal in a regular local ring

integrally closed and componentwise linear ideals in a two dimensional regular local ring integrally closed ideals have a unique factorization property and their associated graded ring is cohen macaulay in higher dimension these properties do not hold and the goal of the paper is to identify a subclass of integrally closed ideals for which they do we restrict our attention to 0 dimensional homogeneous ideals in polynomial rings r of arbitrary dimension we identify a class of integrally closed ideals the goto class mathcal g which is closed under product and it has a suitable unique factorization property ideals in mathcal g have a cohen macaulay associated graded ring if either they are monomial or dim r 3 our approach is based on the study of the relationship between the notions of integrally closed contracted full and componentwise linear ideals

on the last hilbert samuel coefficient of isolated singularities abstract j lipman proved that the last hilbert samuel coefficient of normal ideals of a 2 dimensional complete local ring r are bounded by the geometric genus of x spec r in this paper we extend this result to ideals i of a d dimensional cohen macaulay local ring r such that the associated graded ring of r with respect to i n is cohen macaulay for n 0 we study the ideals such that their last hilbert samuel coefficients equal the geometric genus

on the computation of darboux first integrals of a class of planar polynomial vector fields abstract we study the class of planar polynomial vector fields admitting darboux first integrals of the type i 1 r f i i where the i s are positive real numbers and the f i s are polynomials defining curves with only one place at infinity we show that these vector fields have an extended reduction procedure and give an algorithm which from a part of the extended reduction of the vector field computes a darboux first integral for generic exponents

brief paper periodic stabilizability of switched linear control systems stabilizability via direct observer based state feedback control for discrete time switched linear control systems slcss is investigated in this paper for an slcs the control factors are not only the control input but also the switching signal and they need to be designed in order to stabilize the system as a result stabilization design for slcss is more complicated than that for non switched ones differently from the existing approaches a periodic switching signal and piecewise constant linear state feedback control are adopted to achieve periodic stabilizability for such systems it is highlighted that multiple feedback controllers need to be designed for one subsystem for discrete time slcss it is proved that reachability implies periodic stabilizability via state feedback a necessary and sufficient criterion for periodic stabilizability is also established two stabilization design algorithms are presented for real application moreover it is proved that reachability and observability imply periodic stabilizability via observer based feedback for discrete time slcss periodic detectability as the dual concept of periodic stabilizability is discussed and the stabilization design algorithms via observer based feedback are presented as well

algebraic integrability of foliations of the plane we give an algorithm to decide whether an algebraic plane foliation f has a rational first integral and to compute it in the affirmative case the algorithm runs whenever we assume the polyhedrality of the cone of curves of the surface obtained after blowing up the set bf of infinitely near points needed to get the dicritical exceptional divisors of a minimal resolution of the singularities of f this condition can be detected in several ways one of them from the proximity relations in bf and as a particular case it holds when the cardinality of bf is less than 9

finitely supported simple complete ideals in a regular local ring abstract let i be a finitely supported complete m primary ideal of a regular local ring r m a theorem of lipman implies that i has a unique factorization as a product of special simple complete ideals with possibly negative exponents for some of the factors the existence of negative exponents occurs if dim r 3 because of the existence of finitely supported simple ideals that are not special we consider properties of special simple complete ideals such as their rees valuations and point basis let r m be a d dimensional equicharacteristic regular local ring with m x 1 x d r we define monomial quadratic transforms of r and consider transforms and inverse transforms of monomial ideals for a large class of monomial ideals i that includes complete inverse transforms we prove that the minimal number of generators of i is completely determined by the order of i we give necessary and sufficient conditions for the complete inverse transform of a product of monomial ideals to be the product of the complete inverse transforms of the factors this yields examples of finitely supported simple monomial ideals that are not special we prove that a finitely supported simple monomial ideal with linearly ordered base points is special simple

the reachable set of a linear endogenous switching system in this work switching systems are named endogenous when their switching pattern is controllable linear endogenous switching systems can be considered as a particular class of bilinear control systems the key idea is that both types of systems are equivalent to polysystems i e to systems whose flow is piecewise smooth the reachable set of a linear endogenous switching system can be studied consequently the main result is that in general it has the structure of a semigroup even when the lie algebra rank condition is satisfied since the logic inputs cannot reverse the direction of the flow the adaptation of existing controllability criteria for bilinear systems is straightforward

on asymptotic depth of integral closure filtration and an application abstract let a m be an analytically unramified formally equidimensional noetherian local ring with depth a 2 let i be an m primary ideal and set i to be the integral closure of i set g i n 0 i n i n 1 be the associated graded ring of the integral closure filtration of i we prove that depth g i n 2 for all n 0 as an application we prove that if a is also an excellent normal domain containing an algebraically closed field isomorphic to a m then there exists s 0 such that for all s s 0 and j is an integrally closed ideal strictly containing m s then we have a strict inequality j m s here j is the number of minimal generators of j

the plus closure of an ideal abstract if r is a local integral domain let r denote the integral closure of r in an algebraic closure of its quotient field if z r we would like to understand the conditions under which z ir where i is an ideal of r necessary and sufficient conditions on the coefficients of the minimal irreducible polynomial for z are known when i is generated by two elements of a regular system of parameters and when z is in a degree two extension of r in this article we obtain results for the case when z 3 r as well as a sufficient condition for z to be in ir when z a r for a 1 and i has a finite number of generators

a formula for jumping numbers in a two dimensional regular local ring abstract in this article we give an explicit formula for the jumping numbers of an ideal of finite colength in a two dimensional regular local ring with an algebraically closed residue field for this purpose we associate a certain numerical semigroup to each vertex of the dual graph of a log resolution of the ideal

accessibility of switched linear systems this note considers the controllability of switched linear systems the structure of accessibility lie algebra is revealed some accessibility properties are proved certain necessary and sufficient conditions for local or global weak or normal controllability of a large class of switched linear systems are obtained

controllability and observability of hybrid systems abstract a special class of hybrid systems is considered whose state space is a cross product space of a euclidean space and a finite state space such models may be used to represent systems subject to known abrupt parameter variations such as commu tated networks they may also be used to approximate some types of time varying systems controllability observability and stability of hybrid systems are inves tigated in particular a necessary and sufficient algebraic condition a simple algebraic criterion and a computationally simple algebraic sufficient test for controllability and observability are derived moreover a simple sufficient stability condition is provided

technical communique a new perspective on criteria and algorithms for reachability of discrete time switched linear systems the paper presents a unified perspective on geometric and algebraic criteria for reachability and controllability of controlled switched linear discrete time systems direct connections between geometric and algebraic criteria are established as well as that between the subspace based controllability reachability algorithm and kalman type algebraic rank criteria also the existing geometric criteria is simplified and new algebraic conditions on controllability and reachability are given