separating k separated ence graph languages an ence graph grammar is k separated k 1 if the distance between any two nonterminal nodes in any of its sentential forms is at least k let sepk denote the class of graph languages generated by k separated grammars then sep1 sep2 is the class of ence boundary ence graph languages and so sep2 sep1 recently engelfriet 1991 showed that sep3 sep2 and conjectured that in fact sepk 1 sepk for each k 1 we prove this conjecture affirmatively

graph grammars with neighbourhood controlled embedding abstract a central feature that distinguishes graph grammars we consider grammars generating sets of node labelled undirected graphs only from string grammars is that in the former one has to provide a mechanism by which a daughter graph the right hand side of a production can be embedded in the rest of the mother graph while in the latter this embedding is provided automatically by the structure that all strings possess left to right orientation in this paper we consider a possible classification of embedding mechanisms for node rewriting graph grammars this classification originates from the basic ideas of 9 on the one hand it allows one to fit a number of existing notions of a graph grammar into a common framework and on the other hand it points out new natural possibilities for defining the embedding mechanism in a graph grammar the relationship between the graph language generating power of graph grammars using various embedding mechanisms is established

degree and birationality of multi graded rational maps we give formulas and effective sharp bounds for the degree of multi graded rational maps and provide some effective and computable criteria for birationality in terms of their algebraic and geometric properties we also extend the jacobian dual criterion to the multi graded setting our approach is based on the study of blow up algebras including syzygies of the ideal generated by the defining polynomials of the rational map a key ingredient is a new algebra that we call thesaturated special fiber ring which turns out to be a fundamental tool to analyze the degree of a rational map we also provide a very effective birationality criterion and a complete description of the equations of the associated rees algebra of a particular class of plane rational maps

plane cremona maps saturation and regularity of the base ideal abstract one studies plane cremona maps by focusing on the ideal theoretic and homological properties of its homogeneous base ideal indeterminacy locus the leitmotiv driving a good deal of the work is the relation between the base ideal and its saturation as a preliminary one deals with the homological features of arbitrary codimension 2 homogeneous ideals in a polynomial ring in three variables over a field which are generated by three forms of the same degree the results become sharp when the saturation is not generated in low degrees a condition to be given a precise meaning an implicit goal illustrated in low degrees is a homological classification of plane cremona maps according to the respective homaloidal types an additional piece of this work relates the base ideal of a rational map to a few additional homogeneous companion ideals such as the integral closure the fat ideal and a seemingly novel ideal defined in terms of valuations

on the bezoutian matrix for chebyshev polynomials abstract in the present paper a bezoutian type matrix relative to chebyshev polynomials of the second kind is introduced by the form of generating function a barnett type factorization formula and a triangular type formula are obtained for this generalized bezout matrix which generalize the corresponding results for classical bezout matrix two numerical examples are given to illustrate the correctness of our results

a hierarchy of ence families of graph languages abstract even though ence and its subclasses have been studied intensively their inclusion relations are not completely known this paper proves some unknown relations among ence families of graph languages which yield together with other known relations a solid hierarchy of graph languages that completely determines equivalence proper inclusion and incomparability among nlc nce enlc ence and their boundary linear and apex subclasses the bottom level of this hierarchy i e lin a nlc contains an np complete graph language

nondeterministic space is closed under complementation in this paper we show that nondeterministic space s n is closed under complementation for s n greater than or equal to log n it immediately follows that the context sensitive languages are closed under complementation thus settling a question raised by kuroda inform and control 7 1964 pp 207 233

on the bezoutian for polynomial matrices abstract the bezoutian b of two polynomial matrices can be described as a solution of a linear matrix equation this fact yields a new proof of the barnett factorization of b

sequences of linear type let a be a commutative ring 91 an ideal of a s 2l the symmetric algebra of 8 and r vl the recs algebra of vi there is a canonical surjection x s k which is homogeneous of degree zro and therefore gives canonical surjcctions r f 91 for every integer t 3 0 many recent papers 1 2 4 5 7 cc have investigated the problem of determining which ideals 91 have the property that a is an isomorphism such ideals have been dubbed ideals of lineur type s for example huneke showed that every ideal generated by a d sequence is of linear type 71 if ii is generated by n elements a a then for t 3 i there is an exact scquencc

confluent polynomial vandermonde like matrices displacement structures inversion formulas and fast algorithm in the present paper we use the displacement structure approach to introduce a new class of what are called confluent polynomial vandermonde like matrices which generalize the ordinary simple nodes polynomial vandermonde matrices studied earlier by different authors the displacement structure approach leads to the explicit inversion formulas for confluent polynomial vandermonde like matrices and fast algorithms for inversion and for solving the associated linear systems

bounds on degrees of birational maps with arithmetically cohen macaulay graphs abstract a rational map whose source and image are projectively embedded varieties is said to have an arithmetically cohen macaulay graph if the rees algebra of one hence any of its base ideals is a cohen macaulay ring the main objective of this paper is to obtain an upper bound for the degree of a representative of the map in case it is birational onto the image with an arithmetically cohen macaulay graph in the plane case a complete classification is given of the cremona maps with arithmetically cohen macaulay graph while in arbitrary dimension n it is shown that a cremona map with arithmetically cohen macaulay graph has degree at most n 2

tensored polynomial models the theme of the present paper is the study of two different versions of tensor products of functional models and present some applications to various problems related to system theory among those are stability of higher order systems tangent spaces spaces of intertwining maps invariant factors of tensor products of linear transformations and the solvability of sylvester equations

boundary nlc graph grammars basic definitions normal forms and complexity node label controlled nlc grammars are graph grammars operating on node labeled undirected graphs which rewrite single nodes only and establish connections between the embedded graph and the neighbors of the rewritten node on the basis of the labels of the involved nodes only they define possibly infinite languages of undirected node labeled graphs or if we just omit the labels languages of unlabeled graphs here we consider a restriction of nlc grammars so called boundary nlc bnlc grammars distinguished by the property that whenever in a graph already generated two nodes may be rewritten then these nodes are not adjacent the graph languages generated by this type of grammars are called bnlc languages although we show that this restriction leads to a smaller class of languages still enough generative power remains to define interesting graph languages for example trees complete bipartite graphs maximal outerplanar graphs k trees graphs of bandwidth k graphs of cyclic bandwidth k graphs of binary tree bandwidth k graphs of cutwidth k always for a fixed positive integer k turn out all to be bnlc languages we prove a number of normal forms for bnlc grammars and then we indicate their usefulness by various applications in particular we show that for connected graphs of bounded degree the membership problem for bnlc languages is solvable in deterministic polynomial time

the jacobian conjecture reduction of degree and formal expansion of the inverse introduction i the jacobian conjecture 1 statement of the jacobian problem first observations 2 some history of the jacobian conjecture 3 faulty proofs 4 the use of stabilization and of formal methods ii the reduction theorem 1 notation 2 statement of the reduction theorem 3 reduction to degree 3 4 proof of the reduction theorem 5 r linearization and unipotent reduction 6 nilpotent rank 1 jacobians iii the formal inverse 1 notation 2 abhyankar s inversion formula 3 the terms gj 4 the tree expansion g lt a t lfptf 5 calculations references

powers of ideals generated by quadratic sequences huneke s conjecture that weak d sequences generate ideals of quadratic type is proved the proof suggests the definition of quadratic sequences which are more general than weak d sequences yet simpler to define and handle in addition to being just as useful we extend the theory of d sequences and weak d sequences to quadratic sequences results of costa on sequences of linear type are generalized an example of a two dimensional local domain in which every system of parameters is a d sequence in some order but which nevertheless fails to be buchsbaum is given a criterion is established for when equality holds in burch s inequality for an ideal generated by a quadratic sequence

cremona transformations and some related algebras abstract one proves a general characteristic free criterion for a rational map between projective varieties to be birational in terms of ideal theoretic and modulo theoretic conditions this criterion is more inclusive than that of f russo a simis compositio math 126 2001 335 358 and moreover differs from previous criteria in its nature in that the syzygies of the base ideal of the map are not directly involved in its formulation however a great deal of the consequences are phrased by means of those very syzygies avoided in the formulation of the criterion in any case the criterion is stated in effective terms so it yields an efficient computable test of birationality one also introduces a so called linear obstruction principle for base ideals of linear type thus raising a basic question concerning the structure of a certain related bilinear algebra

displacement structures and fast inversion formulas for q adic vandermonde like matrices a new class of so called q adic vandermonde like matrices over an arbitrary nonalgebraically closed field is introduced this class generalizes the ordinary vandermonde like matrices over the complex field three kinds of displacement structures and fast inversion formulas for this class of matrices are presented by using displacement structure theory method which generalize some of the well known results for confluent vandermonde like matrices in the closed field case

on bezoutian reduction with the vandermonde matrix abstract the vandermonde matrix reduces by congruence the bezoutian matrix when the zeros of the highest degree associated polynomial are simple in this paper a generalization of this result to the case of multiple zeros is presented

on structured graph grammars ii abstract in paper i we introduced a framework of sequential graph rewriting and demonstrated how various existing approaches fit into it in this paper we take a closer look at various basic features of this framework

resultants companion matrices and jacobson chains the multiplicative property of triangular toeplitz matrices is used to derive a polyproduct rule for companion matrices this rule is then used to obtain some new identities involving resultants and companion matrices and to investigate the block structure of jacobson chains relating companion and hypercompanion matrices

polynomial bezoutian matrix with respect to a general basis we introduce a class of so called polynomial bezoutian matrices the operator representation relative to a pair of dual bases and the generalized barnett factorization formula for this kind of matrix are derived an intertwining relation and generalized bezoutian reduction via polynomial vandermonde matrix are presented

on the structure of linear apex nlc graph grammars it is known that linear apex nlc lin a nlc grammars can generate np complete graph languages the present paper examines the source of this expressive power by analyzing complexity and decidability of the so called k connecting lin a nlc k lin a nlc grammars in which the right hand side of each production contains at most k nodes that can be connected to outside nodes the number of connecting nodes is indeed one source of the expressive power of graph grammars in that k lin a nlc k 1 lin a nlc for every k 0 there exists a 2 lin a nlc language which is np complete but every 1 lin a nlc language is in nlog the equivalence problem is undecidable for 1 lin a nlc languages but is decidable for 0 lin a nlc languages even when one of two input languages is an arbitrary b nlc language

on bezoutians van der monde matrices and the lienard chipart stability criterion we show how the bezoutian can be reduced by congruence to diagonal form with the congruence given by a van der monde matrix this result is applied to obtain new proofs of some classical stability criteria and in particular of the lienardchipart theorem

node replacement graph languages squeezed with chains trees and forests we present results on language theoretic properties such as closure membership and other decision properties of node replacement graph languages such as nlc b nlc and lin nlc languages squeezed with chains trees and forests

a comparison of boundary graph grammars and context free hypergraph grammars context free hypergraph grammars and boundary graph grammars of bounded nonterminal degree have the same power both for generating sets of graphs and for generating sets of hypergraphs arbitrary boundary graph grammars have more graph generating power than context free hypergraph grammars but they have the same hypergraph generating power to obtain these results several normal forms for boundary graph grammars are given it is also shown that the class of boundary graph languages is closed under the operation of edge contraction where the label of the edge indicates whether or not the edge should be contracted

bezoutian representation via vandermonde matrices abstract the result on benoutian representation via vandermonde matrices is provided with a proof which is based on polynomial models

an axiomatic definition of context free rewriting and its application to nlc graph grammars abstract an abstract notion of context free grammar is introduced it deals with abstract objects that can be words trees graphs or other combinatorial objects it is applied to nlc graph grammars introduced by rozenberg and janssens the monadic second order theory of a context free nlc set of graphs is decidable

displacement structure approach to q adic chebyshev vandermonde like matrices abstract in this paper a new class of so called q adic chebyshev vandermonde like matrices over an arbitrary non algebraically closed field is introduced this class generalizes both the ordinary chebyshev vandermonde like matrices over the complex field studied earlier by kailath and olshevsky t kailath v olshevsky displacement structure approach to chebyshev vandermonde and related matrices integral equations operator theory 22 1995 65 92 and the classical q adic vandermonde like matrices with respect to power basis by yang and hu z h yang y j hu displacement structure and fast inversion formulas for q adic vandermonde like matrices j comput appl math 176 2005 1 14 three kinds of displacement structures and consequently three kinds of fast inversion formulas are presented for this class of matrices by using displacement structure theory method which generalize the corresponding results for chebyshev vandermonde like and q adic vandermonde like matrices

displacement structure approach to q adic polynomial vandermonde and related matrices abstract in the present paper a new class of the so called q adic polynomial vandermonde like matrices over an arbitrary non algebraically closed field is introduced this class generalizes both the simple and the confluent polynomial vandermonde like matrices over the complex field and the q adic vandermonde and the q adic chebyshev vandermonde like matrices studied earlier by different authors three kinds of displacement structures and two kinds of fast inversion formulas are obtained for this class of matrices by using displacement structure matrix method which generalize the corresponding results of the polynomial vandermonde like and the q adic vandermonde like matrices

cohen macaulay graded rings associated to ideals let g i be the associated graded ring of an ideal i in a cohen macaulay local ring a we give a sufficient condition for g i to be a cohen macaulay ring it is described in terms of the depths of a i n for finitely many n the reduction numbers of i q for certain prime ideals q and the artin nagata property of i in the sense of ulrich contemp math vol 159 pp 373 400 the main theorem unifies several results which are already known in this aspect of the theory although the statement of the main theorem is rather complicated we restate the conditions under special situations so that they are practical and simple

a generalized bezoutian matrix with respect to a polynomial sequence of interpolatory type in this note a generalized bezoutian matrix with respect to a polynomial sequence of interpolatory type is introduced the operator representation relative to a pair of dual bases and the generalized barnett type factorization formula are derived an intertwining relation and a bezoutian reduction to a block diagonal form by congruence via a generalized vandermonde matrix are presented fujiwara hermite and routh hurwitz criteria in terms of this generalized bezout matrix are obtained

quasi rocking real time pushdown automata a pushdown automaton pda is quasi rocking if it preserves the stack height for no more than a bounded number of consecutive moves every pda can be transformed into an equivalent one that is quasi rocking and real time and every finite turn one turn pda can be transformed into an equivalent one that is quasi rocking or real time the quasi rocking quasi rocking in the increasing mode and quasi rocking in the decreasing mode real time restriction in finite turn one turn pdas coincides with the double greibach reverse greibach and greibach form in nonterminal bounded linear context free grammars this provides complete grammatical characterizations of quasi rocking and or real time finite turn and one turn pdas and together with known relations and other relations proved in the present paper yields an extended hierarchy of pda languages basic decision properties for pdas can be stated in stronger forms by using the quasi rocking and real time restrictions and their undecidability decidability status rests on the way pdas quasi rock

generalized polynomial bezoutian with respect to a jacobson chain basis over an arbitrary field abstract we introduce a so called generalized polynomial bezoutian with respect to a jacobson chain basis over an arbitrary field some characterization of this kind of matrix such as the barnett type factorization and the intertwining relation with generalized hypercompanion matrix are obtained the diagonal reduction formula via the generalized confluent vandermonde matrix similar to that of classical bezoutian is presented the method used is based on polynomial module and operator representation

double greibach operator grammars every context free grammar can be transformed into one in double greibach operator form that satisfies both double greibach form and operator form examination of the expressive power of various well known subclasses of context free grammars in double greibach and or operator form yields an extended hierarchy of language classes basic decision properties such as equivalence can be stated in stronger forms via new classes of languages in this hierarchy

on a invariant formulas abstract let g i be the form ring of an ideal i of positive height in a local ring a in this work we will provide formulas for the a invariant of g i our main result will only need the assumption that a is cohen macaulay and that g i fulfills serre s condition sl where l is the analytic spread of i as a consequence of our formula we will prove upper bounds for the reduction exponent of i in the case that a is a regular local ring if g i fulfills serre s condition sl then this upper bound is l 1 and in the case that g i is even gorenstein it is l 2

duality in polynomial models with some applications to geometric control theory duality is studied in the context of polynomial models for linear systems the output injection group the dual of the feedback group is studied and a polynomial characterization of c a invariant subspaces as well as of the maximal reachability subspaces contained in ker c is given

nonterminal bounded nlc graph grammars il est montre que ces grammaires ne peuvent pas etre simulees par une grammaire graphe lineaire

linear graph grammars power and complexity abstract a graph grammar is linear if it generates graphs with at most one nonterminal node linear graph grammars can simulate nonterminal bounded graph grammars which generate graphs with a bounded number of nonterminal nodes and derivation bounded graph grammars if a linear graph language contains connected graphs of bounded degree only then it is in nspace log n these results are shown for graph grammars with neighbourhood controlled embedding and with dynamic edge relabeling ence grammars

generalized polynomial bases and the bezoutian abstract a foundation polynomial is used to induce polynomial bases for fn 1 x the vector space of polynomials of degree less than n over an arbitrary field f the associated bases are then used to block diagonalize the bezout matrix of two polynomials under congruence

powers of ideals generated by weak d sequences this paper is concerned with establishing a general method to answer questions concerning the analytic behavior of an ideal z in a commutative noetherian ring r by analytic we mean the analysis of r z for n 1 two specific questions are the most important if z p is prime when is p p here p is the nth symbolic power of p secondly if r is local what are depth r z for arbitrary n if i has finite projective dimension then of course this is the same question as that of computing the projective dimension of r r even in specific cases which have been extensively studied these questions are extremely hard to answer the literature concerning symbolic powers is fairly extensive see for example 11 s 141 171 or 23 if k is a field and x xu is a generic r x s matrix r 2 and robbiano 21 has conjectured that the depths are independent on n if n 2 we are able to show

nonterminal separation in graph grammars abstract the notion of nonterminal separation in ence graph grammars is introduced such a graph grammar is k separated with k 1 if the distance between any two nonterminal nodes in any of its sentential forms is at least k 2 separated ence grammars are known as boundary ence graph grammars there exists a 2 separated ence graph language that is not 3 separated apex ence graph grammars can be arbitrarily separated every apex ence graph language can be generated by a k separated apex ence grammar for every k

a characteristic free criterion of birationality abstract one develops ab initio the theory of rational birational maps over reduced but not necessarily irreducible projective varieties in arbitrary characteristic a virtual numerical invariant of a rational map is introduced called the jacobian dual rank it is proved that a rational map in this general setup is birational if and only if the jacobian dual rank is well defined and attains its maximal possible value even in the classical case where the source variety is irreducible there is some gain for this invariant over the degree of the map because on one hand it relates naturally to constructs in commutative algebra and on the other hand is effectively computable applications are given to results only known so far in characteristic zero one curious byproduct is an alternative approach to deal with the result of dolgachev concerning the degree of a plane polar cremona map