complexity of multi head finite automata origins and directions multi head finite automata were introduced and first investigated by rabin and scott in 1964 and rosenberg in 1966 since that time a vast literature on computational and descriptional complexity issues on multi head finite automata documenting the importance of these devices has been developed although multi head finite automata are a simple concept their computational behavior can be already very complex and leads to undecidable or even non semi decidable problems on these devices such as for example emptiness finiteness universality equivalence etc additionally the conversions between different types of multi head finite automata induce in most cases size bounds that cannot be bounded by any recursive function so called non recursive trade offs these strong negative results trigger the study of subclasses and alternative characterizations of multi head finite automata for a better understanding of the nature of non recursive trade offs and thus the borderline between decidable and undecidable problems in the present paper we tour a fragment of this literature

on new symplectic approach for exact bending solutions of moderately thick rectangular plates with two opposite edges simply supported the symplectic geometry method is introduced for exact bending solutions of moderately thick rectangular plates with two opposite edges simply supported the basic equations for the plates are first transferred into hamilton canonical equations the whole state variables are then separated using the method of eigenfunction expansion in the symplectic geometry typical examples for plates with selected boundary conditions are solved and exact bending solutions obtained since only the basic elasticity equations of the plates are used this method eliminates the need to pre determine the deformation function and is hence more reasonable than conventional methods numerical results were presented to demonstrate the validity and accuracy of this approach as compared to those reported in other literatures

lower bound technique for length reducing automata the class of growing context sensitive languages gcsl was proposed as a naturally defined subclass of context sensitive languages whose membership problem is solvable in polynomial time growing context sensitive languages and their deterministic counterpart called church rosser languages crl complement the chomsky hierarchy in a natural way as the classes filling the gap between context free languages and context sensitive languages they possess characterizations by a natural machine model length reducing two pushdown automata lrtpda we introduce a lower bound technique for lrtpdas using this technique we prove the conjecture of mcnaughton narendran and otto that the set of palindromes is not in crl as a consequence we obtain that cfl cocfl as well as ucfl coucfl are not included in crl where ucfl denotes the class of unambiguous context free languages this solves an open problem posed by beaudry holzer niemann and otto another corollary is that crl is a strict subset of gcsl cogcsl

regular languages are church rosser congruential this article shows a general result about finite monoids and weight reducing string rewriting systems as a consequence it proves a long standing conjecture in formal language theory all regular languages are church rosser congruential the class of church rosser congruential languages was introduced by mcnaughton narendran and otto in 1988 a language l is church rosser congruential if there exists a finite confluent and length reducing semi thue system s such that l is a finite union of congruence classes modulo s it was known that there are deterministic linear context free languages which are not church rosser congruential but the conjecture was that all regular languages are of this form the article offers a stronger statement a language is regular if and only if it is strongly church rosser congruential it is the journal version of the conference abstract which was presented at icalp 2012

the word and geodesic problems in free solvable groups we study the computational complexity of the word problem wp in free solvable groups s r d where r 2 is the rank and d 2 is the solvability class of the group it is known that the magnus embedding of s r d into matrices provides a polynomial time decision algorithm for wp in a fixed group s r d unfortunately the degree of the polynomial grows together with d so the uniform algorithm is not polynomial in d in this paper we show that wp has time complexity o rn log 2 n in s r 2 and o n 3 rd in s r d for d 3 however it turns out that a seemingly close problem of computing the geodesic length of elements in s r 2 is np complete we prove also that one can compute fox derivatives of elements from s r d in time o n 3 rd in particular one can use efficiently the magnus embedding in computations with free solvable groups our approach is based on such classical tools as the magnus embedding and fox calculus as well as on relatively new geometric ideas in particular we establish a direct link between fox derivatives and geometric flows on cayley graphs

buckling of a conical thin shell with variable thickness under a dynamic loading this study considers the buckling of an elastic truncated conical shell having a meridional thickness expressed by an arbitrary function subject to a uniform external pressure which is a power function of time at first the fundamental relations and donnell type dynamic buckling equation of an elastic conical shell with variable thickness have been obtained then employing galerkin s method those equations have been reduced to a time dependent differential equation with variable coefficients finally applying the ritz type variational method the critical static and dynamic loads the corresponding wave numbers dynamic factor and critical stress impulse have been found analytically using the results thus obtained the effects of the thickness variations with a power or an exponential function the variation of the semi vertex angle and the variation of the power of time in the external pressure expression are studied through pertinent computations it is observed that these factors have appreciable effects on the critical parameters of the problem in the heading

natural vibration of pre twisted shear deformable beam systems subject to multiple kinds of initial stresses free vibration and buckling of pre twisted beams exhibit interesting coupling phenomena between compression moments and torque and have been the subject of extensive research due to their importance as models of wind turbines and helicopter rotor blades the paper investigates the influence of multiple kinds of initial stresses due to compression shears moments and torque on the natural vibration of pre twisted straight beam based on the timoshenko theory the derivation begins with the three dimensional green strain tensor the nonlinear part of the strain tensor is expressed as a product of displacement gradient to derive the strain energy due to initial stresses the frenet formulae in differential geometry are employed to treat the pre twist the strain energy due to elasticity and the linear kinetic energy are obtained in classical sense from the variational principle the governing equations and the associated natural boundary conditions are derived it is noted that the first mode increases together with the pre twisted angle but the second decreases seeming to close the first two modes together for natural frequencies and compressions the gaps close monotonically as the angle of twist increases for natural frequencies and buckling compressions however unlike natural frequencies and compressions the closeness is not monotonic for buckling shears moments and torques

coupled tension torsion vibration of repetitive beam like structures equivalent continuum stiffness properties derived from the eigenanalysis of a single cell of a planar beam like repetitive structure have previously been employed within well known dynamic theories such as euler bernoulli and timoshenko for flexural vibration suitably modified to predict natural frequencies of vibration here the approach is applied to two structure types that exhibit tension torsion coupling the first is modelled on a nasa deployable structure with a cross section of equilateral triangular form but with asymmetric triangulation on the faces the second is a related more symmetric structure but with pre twist the simplest tension torsion dynamic theory due to di prima is employed and this is extended to more general end conditions this combined periodic structure substitute continuum approach provides excellent agreement with predictions from the finite element method especially for the lower modes of vibration typically agreement is within 1 for the lowest 8 10 natural frequencies for the longer 30 cell structures considered here the majority of these being torsional modes and within 1 for the lowest 4 5 modes for the shorter ten cell structures this level of accuracy is attainable so long as a single wavelength spans 2 3 cells of the repetitive structure

newton like method for nonlinear banded block diagonal system we present an efficient newton like method for solving systems of nonlinear equations with banded block diagonal structure such systems arise in economic models the main idea of this method is to exploit the special structure of the jacobian in a newton like method the proposed algorithm uses an iterative method for calculation of the approximation of diagonal blocks in the jacobian depending on dimensions of blocks significant reduction in computational cost is obtained and the algorithm can be easily parallelized local convergence of the proposed method is proved and some numerical results are presented

a complementary pivot algorithm for market equilibrium under separable piecewise linear concave utilities using lemke s scheme we give a complementary pivot algorithm for computing an equilibrium for arrow debreu markets under separable piecewise linear concave splc utilities despite the polynomial parity argument on directed graphs ppad completeness of this case experiments indicate that our algorithm is practical on randomly generated instances the number of iterations it needs is linear in the total number of segments i e pieces in all the utility functions specified in the input our paper settles a number of open problems 1 eaves 1976 gave an lcp formulation and a lemke type algorithm for the linear arrow debreu model we generalize both to the splc case hence settling the relevant part of his open problem 2 our path following algorithm for splc markets together with a result of todd 1976 gives a direct proof of membership of such markets in ppad and settles a question of vazirani and yannakakis 2011 3 we settle a question of devanur and kannan 2008 of obtaining a sy

weighted restarting automata and pushdown relations weighted restarting automata have been introduced to study quantitative aspects of computations of restarting automata here we study the special case that words over a given output alphabet are assigned as weights to the transitions of a restarting automaton in this way the automaton is extended to define a mapping from the words over its input alphabet into the semiring of formal languages over a given output alphabet generalizing the restarting transducers introduced by hundeshagen 2013 7 we establish that the monotone restarting transducers that are allowed to use auxiliary symbols characterize the class of almost realtime pushdown relations and we characterize the deterministic pushdown functions by a particular type of deterministic monotone restarting transducer further we show that already linearly bounded word weighted monotone restarting automata that use auxiliary symbols are more expressive than the corresponding restarting transducers both in the deterministic as well as in the nondeterministic case finally we prove that for word weighted monotone restarting automata with auxiliary symbols the variant that may keep on reading after performing a rewrite step the so called rrww automaton is strictly more expressive than the variant that must restart immediately after performing a rewrite step the so called rww automaton which again holds in the deterministic as well as in the nondeterministic case this is the first time that a version of the monotone rrww automaton is shown to differ in expressive power from the corresponding version of the monotone rww automaton

repetitive beam like structures distributed loading and intermediate support theory is developed for the elastostatic transfer matrix analysis of a repetitive beam like structure subject to point wise distributed loading with and without an intermediate support this complements previous work in which loading is applied at one end only and reacted at the other state vectors are expressed in terms of participation coefficients of the eigen and principal vectors leading to the simplest description of the evolution of nodal displacement and force components as one moves along the structure in terms of powers of the jordan canonical form inaccuracy due to ill conditioning is explained in terms of powers of greater than unity eigenvalues

the size of higman haines sets we show that for the family of church rosser languages the higman haines sets which are the sets of all scattered subwords of a given language and the sets of all words that contain some word of a given language as a scattered subword cannot be effectively constructed although both these sets are regular for any language this nicely contrasts the result on the effectiveness of the higman haines sets for the family of context free languages the non effectiveness is based on a non recursive trade off result between the language description mechanism of church rosser languages and the corresponding higman haines sets which in turn is also valid for all supersets of the language family under consideration and in particular for the family of recursively enumerable languages finally for the family of regular languages we prove an upper and a matching lower bound on the size of the higman haines sets in terms of nondeterministic finite automata

regulated variants of limited context restarting automata abstract in the literature various types of restarting automata have been studied that are based on contextual rewriting a word w is accepted by such an automaton if starting from the initial configuration that corresponds to input w the tape contents is reduced to a particular word within a finite number of applications of these contextual rewritings here we extend the limited context restarting automata by using additional global means to structure the reductions they execute in fact we study regulated lc r automata for which a regular control language is used to restrict the set of admissible reduction sequences and we propose random context conditions to restrict the place at which a transition of an lc r automaton can be applied

transfer matrix analysis of the elastostatics of one dimensional repetitive structures transfer matrices are used widely for the dynamic analysis of engineering structures increasingly so for static analysis and are particularly useful in the treatment of repetitive structures for which in general the behaviour of a complete structure can be determined through the analysis of a single repeating cell together with boundary conditions if the structure is not of infinite extent for elastostatic analyses non unity eigenvalues of the transfer matrix of a repeating cell are the rates of decay of selfequilibrated loading as anticipated by saint venant s principle multiple unity eigenvalues pertain to the transmission of load e g tension or bending moment and equivalent homogenized continuum properties such as cross sectional area second moment of area and poisson s ratio can be determined from the associated eigen and principal vectors various disparate results the majority new others drawn from diverse sources are presented these include calculation of principal vectors using the moore penrose inverse bi and symplectic orthogonality and relationship with the reciprocal theorem restrictions on complex unity eigenvalues effect of cell left to right symmetry on both the stiffness and transfer matrices eigenvalue veering in the absence of translational symmetry and limitations on possible jordan canonical forms it is shown that only a repeating unity eigenvalue can lead to a non trivial jordan block form so degenerate decay modes cannot exist the present elastostatic analysis complements langley s langley 1996 proc r soc a 452 1631 1648 transfer matrix analysis of wave motion energetics

renormalisation group theory for two problems in linear continuum mechanics abstract we consider the problems of 1 the stress field in an infinite wedge when a moment is applied at the tip and 2 the flow of an inviscid incompressible fluid past an infinite wedge both problems are linear but nevertheless exhibit anomalous dimensions for wedge angles larger than a critical value c in 1 it is the stress field and in 2 it is the velocity potential which can have anomalous power law behaviour in distance from the tip we use these problems as simple examples to illustrate how partial differential equations can be solved using the renormalisation group

a polynomial time algorithm for breaking the basic merkle hellman cryptosystem the merkle hellman cryptosystem is one of the two major public key cryptosystems proposed so far it is shown that the basic variant of this cryptosystem in which the elements of the public key are modular multiples of a superincreasing sequence is breakable in polynomial time

irreducible affine varieties over a free group i irreducibility of quadratic equations and nullstellensatz the object of this paper which consists of two parts is to describe irreducible varieties over free groups and to characterize finitely generated fully residually free groups we prove that any variety over a free group f can be defined by a finite number of systems of equations s 1 in triangular form where quadratic words play the role of leading terms algebraically irreducible varieties are exactly the varieties whose coordinate groups are fully residually f the crucial point of the classification of fully residually free groups is to prove that the coordinate groups of irreducible varieties are embeddable into lyndon s free z x group f since every finitely generated fully residually free group is a free factor of the coordinate group of an irreducible variety and the group f is fully residually f we obtain a characterization of finitely generated fully residually free groups as subgroups of f the group f and its subgroups have been studied extensively during the last several years in particular every finitely generated subgroup of f hence every finitely generated fully residually free group can be obtained from free abelian groups of finite rank by finitely many free products with amalgamation and hnn extensions of the type where amalgamated and associated subgroups are free abelian of finite rank in particular this implies that every finitely generated fully residually free group is finitely presented there are three parts to this paper algebraic geometry over free groups the theory of free exponential groups and makanin razborov s machinery to deal with equations over free groups 11 14 13 the algebraic geometry approach has been shown to be very usefull in dealing with equations over groups it provides necessary topological means and a method to transcribe geometric notions into pure group theoretic language following baumslag myasnikov remeslennikov 1 we use the standard algebraic geometry notions such as variety zariski topology irreducibility of varieties radicals and coordinate groups some of the ideas of the algebraic geometry approach go back to r lyndon 9 e rips j stallings 16

a decomposition algorithm for general equilibrium computation with application to international trade models in this paper we outline the computation of general equilibrium in a pure exchange economy via a fixed point decomposition procedure for general equilibrium models of the required structure a full equilibrium may be computed through the solution of a sequence of smaller scale sub equilibrium problems the text contains a presentation of the methods involved along with a discussion of initial computational experience for some numerical examples in this paper we describe the computation of general equilibrium in a pure exchange economy via a fixed point decomposition procedure similar in spirit to the dantzig wolfe decomposition algorithm for the solution of linear programming problems dantzig and wolfe 2 the method involves the generation of labels for vertices on a master simplex through the separate solution of subequilibrium problems whose parameters are determined by the coordinates of the vertex on the master simplex for general equilibrium models of the required structure it is possible to compute a full equilibrium through the solution of a sequence of smaller scale sub equilibrium problems the analogues to the common constraints in the dantzig wolfe procedure are common commodities with common prices and the block diagonal structure on non common constraints in dantzig wolfe is replaced by an analogous block diagonal pattern of demands and endowments of agents over non common goods a natural application of the method is to international trade models with traded and non traded goods traded goods are common to all countries non traded goods are traded only within the country involved we report execution times for numerical examples using merrill s 5 algorithm for solution of both full dimensional problems and the same problems by the decomposition procedure we do not discuss the application of these procedures to economies with production although it seems likely to us that a similar procedure can be applied if a comparable block diagonal structure characterizes the production set the economic interpretation we offer for our procedure draws on the partition of the full list of commodities in a general equilibrium model into common goods traded among all agents and non common goods traded among a subset of agents the assignment of non common goods to agents is represented in a block diagonal pattern of demands and asset ownership by agent agents have

dynamic buckling of cylindrical shells subject to an axial impact in a symplectic system this paper discusses the dynamic pre buckling of finite cylindrical shells in the propagation and reflection of axial stress waves by introducing the hamiltonian system into dynamic buckling of structures the problem can be described mathematically in a symplectic space the solutions of hamiltonian dual equations shown in canonical variables are obtained the problem is reduced to the determination of eigenvalues and eigensolutions with the former indicating critical buckling loads and the latter buckling modes numerical example presented shows phenomena of axisymmetric and non axisymmetric dynamic buckling subject to impacts of axial load

a new simplicial variable dimension algorithm to find equilibria on the product space of unit simplices a new simplicial variable dimension restart algorithm is introduced to solve the nonlinear complementarity problem on the product spaces of unit simplices the triangulation which underlies the algorithm differs from the triangulations ofs used thus far moreover the number of rays along which the algorithm can leave the arbitrarily chosen starting point is much larger more precisely there is a ray leading from the starting point to each vertex ofs in cases is the product ofn one dimensional unit simplices the alogrithm is similar to the octahedral algorithm onrn having 2n rays also the accuracy of an approximate solution in the terminal simplex of the algorithm is in general better than for the other algorithms ons computational results will show that the number of iterations for the new algorithm is much less the examples concern the computation of equilibria in noncooperative games exchange economies and trade models

eigenanalysis and continuum modelling of pre twisted repetitive beam like structures a repetitive pin jointed pre twisted structure is analysed using a state variable transfer matrix technique within a global coordinate system the transfer matrix is periodic but introduction of a local coordinate system rotating with nodal cross sections results in an autonomous transfer matrix for this floquet system eigenanalysis reveals four real unity eigenvalues indicating tension torsion coupling and equivalent continuum properties such as poisson s ratio cross sectional area torsion constant and the tension torsion coupling coefficient are determined a variety of real and complex near diagonal jordan decompositions are possible for the multiple eight complex unity eigenvalues and these are discussed in some detail analysis of the associated principal vectors shows that a bending moment produces curvature in the plane of the moment together with shear deformation in the perpendicular plane but no bending bending coupling the choice of a structure having an equilateral triangular cross section is thought responsible for this unexpected behaviour as the equivalent continuum second moments of area are equal about all cross sectional axes in addition an asymmetric stiffness matrix is obtained for bending moment and shearing force coupling and possible causes are discussed

church rosser thue systems and formal languages since about 1971 much research has been done on thue systems that have properties that ensure viable and efficient computation the strongest of these is the church rosser property which states that two equivalent strings can each be brought to a unique canonical form by a sequence of length reducing rules in this paper three ways in which formal languages can be defined by thue systems with this property are studied and some general results about the three families of languages so determined are studied

fourier series for polygonal plate bending a very large plate element abstract in this study we developed an edge function approach using the fourier series for boundary value problems on polygonal domains the method was then applied to classical plate bending problems in subsequent work this method has been extended to the moderate rotation equations for a shallow shell preliminary results indicate that the stability of a curved surface plays an important role in the morphogenesis of plants for a polygonal plate with a convex domain the levy type solutions for each edge serve as a set of fundamental functions the set is complete and each member satisfies the equation exactly the problem is solved by superimposing the solution functions and matching the fourier harmonics of the prescribed boundary conditions the process is much like the boundary element method bem except that the unknowns are the amplitudes of fourier harmonics rather than the weightings of individual point sources an extra harmonic is added so that corner boundary conditions can be treated more efficiently by this approach a convex polygon is one element nonconvex domains however are divided into convex subdomains with appropriate continuity conditions at the interfaces in this method similar to the boundary integral method no mesh generation is involved the number of elements and the degrees of freedom is significantly smaller than in the finite element or finite difference methods the advantage over boundary elements is that the matrices are generally well conditioned and the approach is readily extended to the shallow shells

irreducible affine varieties over a free group ii systems in triangular quasi quadratic form and description of residually free groups abstract we shall prove the conjecture of myasnikov and remeslennikov 4 which states that a finitely generated group is fully residually free every finite set of nontrivial elements has nontrivial images under some homomorphism into a free group if and only if it is embeddable in the lyndon s exponential groupfz x which is thez x completion of the free group herez x is the ring of polynomials of one variable with integer coefficients historically lyndon s attempts to solve tarski s famous problem concerning the elementary equivalence of free groups of different ranks led him to introducefz x an free group is a groupgsuch that the class of formulas true ing is the same as the class of formulas true in a nonabelian free group a finitely generated group is free if and only if it is fully residually free 22 our result gives an algebraic description of free groups we shall give an algorithm to represent a solution set of an arbitrary system of equations overfas a union of finite number of irreducible components in the zariski topology onfn the solution set for every system is contained in the solution set of a finite number of systems in triangular form with quadratic words as leading terms the possibility of such a decomposition for a solution set was conjectured by razborov in 20 and also by rips we shall give a description of systems of equations determining irreducible components using methods developed in 13 19 it is possible to find some of these methods in 18 we are thankful to e rips for attracting our attention to these techniques

the degree of word expansion of lexicalized rrww automata a new measure for the degree of nondeterminism of context free languages restarting automata can be seen as analytical variants of classical automata as well as of regulated rewriting systems we study a measure for the degree of nondeterminism of context free languages in terms of deterministic restarting automata that are strongly lexicalized this measure is based on the number of occurrences of auxiliary symbols categories used for recognizing a language as the projection of its characteristic language onto its input alphabet this type of recognition is typical for analysis by reduction a method used in linguistics for the creation and verification of formal descriptions of natural languages our main results establish a hierarchy of classes of context free languages and two hierarchies of classes of non context free languages that are based on the expansion factor of a language

on new symplectic elasticity approach for exact bending solutions of rectangular thin plates with two opposite sides simply supported abstract this paper presents a bridging research between a modeling methodology in quantum mechanics relativity and elasticity using the symplectic method commonly applied in quantum mechanics and relativity a new symplectic elasticity approach is developed for deriving exact analytical solutions to some basic problems in solid mechanics and elasticity which have long been bottlenecks in the history of elasticity in specific it is applied to bending of rectangular thin plates where exact solutions are hitherto unavailable it employs the hamiltonian principle with legendre s transformation analytical bending solutions could be obtained by eigenvalue analysis and expansion of eigenfunctions here bending analysis requires the solving of an eigenvalue equation unlike in classical mechanics where eigenvalue analysis is only required in vibration and buckling problems furthermore unlike the semi inverse approaches in classical plate analysis employed by timoshenko and others such as navier s solution levy s solution rayleigh ritz method etc where a trial deflection function is pre determined this new symplectic plate analysis is completely rational without any guess functions and yet it renders exact solutions beyond the scope of applicability of the semi inverse approaches in short the symplectic plate analysis developed in this paper presents a breakthrough in analytical mechanics in which an area previously unaccountable by timoshenko s plate theory and the likes has been trespassed here examples for plates with selected boundary conditions are solved and the exact solutions discussed comparison with the classical solutions shows excellent agreement as the derivation of this new approach is fundamental further research can be conducted not only on other types of boundary conditions but also for thick plates as well as vibration buckling wave propagation etc

knapsack in hyperbolic groups abstract recently knapsack problems have been generalized from the integers to arbitrary finitely generated groups the knapsack problem for a finitely generated group g is the following decision problem given a tuple g g 1 g k of elements of g are there natural numbers n 1 n k n such that g g 1 n 1 g k n k holds in g myasnikov nikolaev and ushakov proved that for every gromov hyperbolic group the knapsack problem can be solved in polynomial time in this paper the precise complexity of the knapsack problem for hyperbolic group is determined for every hyperbolic group g the knapsack problem belongs to the complexity class logcfl and it is logcfl complete if g contains a free group of rank two moreover it is shown that for every hyperbolic group g and every tuple g g 1 g k of elements of g the set of all n 1 n k n k such that g g 1 n 1 g k n k in g is semilinear and a semilinear representation where all integers are of size polynomial in the total geodesic length of the g g 1 g k can be computed groups with this property are also called knapsack tame this enables us to show that knapsack can be solved in logcfl for every group that belongs to the closure of hyperbolic groups under free products and direct products with z

natural frequencies of a pre twisted blade in a centrifugal force field abstract in this paper starting with the thin shell theory the governing partial differential equation of motion for the transverse deflection of a rotating pre twisted plate is derived strain displacement relationships include the effect of warping of the cross section due to twist bend coupling effect introduced as a result of pre twist in the plate of non circular rectangular cross section then the equation of motion thus derived is used to formulate the free vibration of a typical turbo machinery cantilevered airfoil blade by considering it as a plate of an equivalent rectangular cross section subjected to a quasi static load due to centrifugal force field the analytical derivation considers both the stress stiffening as well as stress softening effects of the centrifugal forces on the spinning airfoil the partial differential equation governing the flexural motion of the plate is transformed into a matrix eigenvalue form using a rayleigh ritz technique the plate deformations are represented by a set of admissible sinusoidal trial functions which fully satisfy all the clamped end constrains as well as the free edge boundary conditions the results of the analytical model exhibit an excellent agreement with the previously published test data both for thin and thick plate geometries and even in highly twisted configurations the results of the eigenvalue solution are presented in a non dimensional form for plates of varying aspect ratios and different amounts of pre twist in the plate the numerical results are directly applicable in determining the static and running frequencies of typical blades used in turbo machinery

higher order effective modeling of periodic heterogeneous beams ii derivation of the proper boundary conditions for the interior asymptotic solution abstract this paper constitutes the second part of a study devoted to the 1d modeling of beam like structures of arbitrary cross section with periodic properties along the axis in the first part the asymptotic expansion method has been described and the equations involving the successive terms of the outer solution have been given in particular it has been shown that neither the leading term nor the full outer solution are able to satisfy arbitrary prescribed edge data a specific study is thus necessary and it is presented in this paper the method used is the decay analysis initially proposed for homogeneous plates by gregory and wan j elast 14 1984 27 this approach consists in deriving the appropriate set of boundary conditions for the outer expansion solution for any arbitrary edge data stress displacement or mixed data these boundary conditions are obtained from the solution of canonical beam problems without computing any inner solution the method is illustrated through numerical examples on a lattice structure the results obtained prove the importance of a correct treatment of the edge effects in order that the inclusion of higher order terms in the beam model serves actually to increase the accuracy of the outer expansion solution

a continuous deformation algorithm on the product space of unit simplices a continuous deformation algorithm is introduced on s 1 where s denotes the product space of unit simplices with arbitrary grid refinement between two subsequent levels the set s 1 is triangulated in such a way that for each m m 1 2 s m is triangulated by the so called v triangulation the algorithm starts by applying a variable dimension algorithm on s until an approximating simplex has been found on level 1 then the algorithm follows a path of approximating simplices in s 1 starting on level 1 until a certain level or a certain accuracy of a solution of the underlying problem has been reached if the algorithm returns to level 1 then we again apply the variable dimension algorithm until a new approximating simplex is found on level 1 etc we allow solutions to lie on the boundary of s 1 in which case the algorithm in general will follow a path on the boundary of s 1

solving non linear portfolio optimization problems with the primal dual interior point method stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning the deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets time stages and scenarios per time stage so far models treated by mathematical programming approaches have been limited to simple linear or quadratic models due to the inability of currently available solvers to solve nlp problems of typical sizes however stochastic programming problems are highly structured the key to the efficient solution of such problems is therefore the ability to exploit their structure interior point methods are well suited to the solution of very large non linear optimization problems in this paper we exploit this feature and show how portfolio optimization problems with sizes measured in millions of constraints and decision variables featuring constraints on semi variance skewness or non linear utility functions in the objective can be solved with the state of the art solver

isoperimetric functions of groups and computational complexity of the word problem we prove that the word problem of a finitely generated group g is in np solvable in polynomial time by a nondeterministic turing machine if and only if this group is a subgroup of a finitely presented group h with polynomial isoperimetric function the embedding can be chosen in such a way that g has bounded distortion in h this completes the work started in 6 and 25

discrete time finite horizon approximation of infinite horizon optimization problems with steady state invariance the computation of large scale nonlinear intertemporal optimization problems requires time aggregation a procedure generally adopted is shown to introduce a dependency of the solution steady state to a specific choice of sequence of time intervals the authors establish necessary and sufficient conditions to avoid this dependency the result is a considerable improvement in the numerical accuracy of the time aggregated approximation the conditions apply to a broad class of models and prove useful in large scale applied general equilibrium modeling this conclusion is highlighted by a comparison with a spectral projection method using optimal orthogonal collocation as in k l judd 1992 copyright 1994 by the econometric society

small overlap monoids ii automatic structures and normal forms abstract we show that any finite monoid or semigroup presentation satisfying the small overlap condition c 4 has word problem which is a deterministic rational relation it follows that the set of lexicographically minimal words forms a regular language of normal forms and that these normal forms can be computed in linear time we also deduce that c 4 monoids and semigroups are rational in the sense of sakarovitch asynchronous automatic and word hyperbolic in the sense of duncan and gilman from this it follows that c 4 monoids satisfy analogues of kleene s theorem and admit decision algorithms for the rational subset and finitely generated submonoid membership problems we also prove some automata theoretic results which may be of independent interest

influence of localized imperfections on the buckling of cylindrical shells under axial compression the influence of localized imperfections on the buckling of a long cylindrical shell under axial compression is analysed by using a double scale analysis including interaction modes this leads to a system of coupled complex non linear differential equations with discontinuous derivatives we propose analytical formulas to predict the reduction of the critical buckling load

random vibration analysis of axially compressed cylindrical shells under turbulent boundary layer in a symplectic system a random vibration analysis of an axially compressed cylindrical shell under a turbulent boundary layer tbl is presented in the symplectic duality system by expressing the cross power spectral density psd of the tbl as a fourier series in the axial and circumferential directions the problem of structures excited by a random distributed pressure due to the tbl is reduced to solving the harmonic response function which is the response of structures to a spatial and temporal harmonic pressure of unit magnitude the governing differential equations of the axially compressed cylindrical shell are derived in the symplectic duality system and then a symplectic eigenproblem is formed by using the method of separation of variables expanding the excitation vector and unknown state vector in symplectic space decoupled governing equations are derived and then the analytical solution can be obtained in contrast to the modal decomposition method mdm the present method is formulated in the symplectic duality system and does not need modal truncation and hence the computations are of high precision and efficiency in numerical examples harmonic response functions for the axially compressed cylindrical shell are studied and a comparison is made with the mdm to verify the present method then the random responses of the shell to the tbl are obtained by the present method and the convergence problems induced by fourier series expansion are discussed finally influences of the axial compression on random responses are investigated

stochastic vibration of axially loaded monosymmetric timoshenko thin walled beam abstract an analytical method is presented to perform the flexure torsion coupled stochastic response analysis of monosymmetric axially loaded timoshenko thin walled beam subjected to various kinds of concentrated and distributed stochastic excitations with stationary and ergodic properties the effects of warping stiffness axial force shear deformation and rotary inertia are included in the present formulations first the damped general governing differential equations of motion of axially loaded timoshenko thin walled beam are developed and the free vibration analysis is performed once the natural frequencies and mode shapes are obtained mode superposition method in conjunction with receptance method is used to compute the mean square displacement response of the axially loaded thin walled beam finally the method is illustrated by its application to two test examples to investigate the effects of warping stiffness axial force shear deformation and rotary inertia on the stochastic response of the thin walled beams

on saint venant s principle in pin jointed frameworks numerical experiments performed by hoff 50 years ago on the application of saint venant s principle to frameworks are extended and his conclusions qualified guided by these results a general treatment is formulated employing a state variable approach this leads directly to an eigenvalue problem in which the decay rates are the eigenvalues of the cell transfer matrix unity eigenvalues correspond to the transmitting modes of rigid body displacement and the stress resultants of tension bending moment shearing force and twisting moment consideration of the associated eigenvectors and principal vectors gives exact values for the equivalent continuum beam properties of the framework such as equivalent cross sectional area poisson s ratio second moment of area shear coefficient and torsion constant

the torsion extension coupling in pretwisted elastic beams abstract an explicit asymptotic formula is derived for the untwist of a pretwisted elastic beam subjected to homogeneous extension or equivalently for the longitudinal contraction produced by a torsional moment it is based on an asymptotic expansion of the three dimensional equations of linear elasticity the general result consists of two terms one due to lengthwise variation of the warping of the cross sections and another due to local rotations from bending when the elastic center is not on the axis of pretwist the result supports some recent approximate theories for pretwisted elastic beams

on state space elastostatics within a plane stress sectorial domain the wedge and the curved beam the plane stress sectorial domain is analysed according to a state space formulation of the linear theory of elasticity when loading is applied to the straight radial edges flanks with the circular arcs free of traction one has the curved beam when loading is applied to the circular arcs with the flanks free of traction one has the elastic wedge a complete treatment of just one problem the elastic wedge say requires two state space formulations the first describes radial evolution for the transmission of the stress resultants force and moment while the second describes circumferential evolution for determination of the rates of decay of self equilibrated loading on the circular arcs as anticipated by saint venant s principle these two formulations can be employed subsequently for the curved beam where now radial evolution is employed for the saint venant decay problem and circumferential evolution for the transmission modes power law radial dependence is employed for the wedge and is quite adequate except for treatment of the so called wedge paradox for this and the curved beam the formulations are modified so that ln r takes the place of the radial coordinate r the analysis is characterised by a preponderance of repeating eigenvalues for the transmission modes and the state space formulation allows a systematic approach for determination of the eigen and principal vectors the so called wedge paradox is related to accidental eigenvalue degeneracy for a particular angle and its resolution involves a principal vector describing the bending moment coupled to a decay eigenvector restrictions on repeating eigenvalues and possible jordan canonical forms are developed finally symplectic orthogonality relationships are derived from the reciprocal theorem

hamiltonian system based saint venant solutions for multi layered composite plane anisotropic plates this paper presents hamiltonian system based saint venant solutions for the problem of multi layered composite plane anisotropic plates a mixed energy variational principle is proposed and dual equations are derived in the symplectic space the schemes of separation of variables and eigenfunction expansion instead of the traditional semi inverse method are implemented and compatibility conditions at interfaces are formulated by dual variables by expending eigenfunctions in the subspace with zero eigenvalue an analytical solution of a cantilever composite plate is presented to illustrate the proposed approach

a shorter proof that palindromes are not a church rosser language with extensions to almost confluent and preperfect thue systems in 2002 jurdzinski and lorys settled a long standing conjecture that palindromes are not a church rosser language their proof involved a difficult analysis of computation graphs associated with 2 pushdown stack automata we present a shorter and easier proof in terms of 1 tape turing machines we also discuss how the proof generalises to almost confluent thue systems and the differing powers of church rosser almost confluent and preperfect thue systems in relation to palindromes

a semi analytical buckling analysis of imperfect cylindrical shells under axial compression abstract in the framework of the cellular bifurcation theory we investigate the effect of distributed and or localized imperfections on the buckling of long cylindrical shells under axial compression using a double scale perturbative approach including modes interaction we establish that the evolution of amplitudes of instability patterns is governed by a non homogeneous second order system of three non linear complex equations the localized imperfections are included by employing jump conditions for their amplitude and permitting discontinuous derivatives by solving these amplitude equations we show the influence of distributed and or localized imperfections on the reduction of the critical load to assess the validity of the present method our results are compared to those given by two finite element codes

the saint venant problem and principle in elasticity abstract the traditional semi inverse solution method of the saint venant problem and the saint venant principle which were described in the euclidian space under the lagrange system formulation are updated to be solved in the symplectic space under the conservative hamiltonian system thus the saint venant problem and the saint venant principle have been unified by the direct method it is proved in the present paper that all the saint venant solutions can be obtained directly via the zero eigenvalue solutions and all their jordan normal forms of the corresponding hamiltonian operator matrix and the saint venant principle corresponds to neglect of all the non zero eigenvalue solutions in which the non zero eigenvalue gives the decay rate

mcnaughton families of languages in 1988 the church rosser languages were introduced by mcnaughton et al as those languages that are recognized by finite length reducing and confluent string rewriting systems using extra non terminal symbols here we generalize this concept by considering classes of languages that are obtained by other types of string rewriting systems to honour robert mcnaughton s original contribution we call the resulting families of languages mcnaughton families here it is shown that the concept of mcnaughton families is as powerful as the notion of turing machine or the notion of phrase structure grammar we investigate the relationships between the various mcnaughton families obtaining an extensive hierarchy of classes that includes many well known language and complexity classes as well as some new classes further we consider some closure and non closure properties for those mcnaughton families that are contained in the class of context free languages and we address the complexity of the fixed and the general membership problems for these families

isoperimetric and isodiametric functions of groups this is the first of two papers devoted to connections between asymptotic functions of groups and computational complexity in particular we show how to construct a finitely presented group with np complete word problem one of the main results of this paper states that if a real number cx 4 is computable in time 0 then na is equivalent big o to the dehn function of a finitely presented group the smallest isodiametric function of this group is n3 8 4 on the other hand if na is equivalent to the dehn function of a finitely presented group then oe is computable in time 4 are equivalent to dehn functions of some finitely presented groups and that n1r and na for all rational numbers oe 3 are equivalent to the smallest isodiametric functions of finitely presented groups moreover we describe all dehn functions of finitely presented groups f n4 as time functions of turing machines modulo two conjectures

algebraic geometry over groups i algebraic sets and ideal theory abstract the object of this paper which is the first in a series of three is to lay the foundations of the theory of ideals and algebraic sets over groups

asymptotic numerical method for buckling analysis of shell structures with large rotations in this paper the buckling and post buckling of elastic structures taking into account large rotations are investigated using an asymptotic numerical method the critical points are detected by two different ways first by a bifurcation indicator second by analysing the poles of a pade approximant the first step of the post buckling branch is computed starting from the bifurcation point and using an extended system the remaining bifurcating branch is followed by the same algorithm as for the fundamental path several examples are tested to show the effectiveness of the proposed method

on wave propagation in repetitive structures two forms of transfer matrix abstract two forms of dynamic transfer matrix are derived for a one dimensional beam like repetitive pin jointed structure with point masses located at nodal cross sections the displacement force transfer matrix g and the displacement displacement transfer matrix h similarity matrices are introduced to relate g and h together with their respective metrics symplectic orthogonality relationships for the eigenvectors of both g and h are derived together with relationships between their respective sets of eigenvectors new expressions for the group velocity are derived for repetitive structures of finite length natural frequency equations are derived employing both g and h including phase closure and the direct application of boundary end conditions besides an exposition of the theory some familiar but much new the focus of the present paper is on the relationships between the two forms of transfer matrix including their respective dis advantages numerical results together with further theory necessary for interpretation are presented in companion papers

the axial torsional vibration of pretwisted beams we investigate the coupled axial torsional vibration of pretwisted beams the equations of motion governing the extension torsion and cross sectional warping of pretwisted beams are derived from hamiltons principle and the common assumptions used to simplify the equations are carefully examined through scaling analysis inconsistencies in previous works such as the neglect of spatial and time derivatives of torsion in the lagrangian functional are remedied giving rise to fourth order terms in the equations of motion that are significant for higher harmonics furthermore scaling analysis of the governing equations yields a set of objective criteria for checking the validity of the frequently misused assumption that the warping function under pretwist is locally identical to that of a prismatic beam we show that this simplification is responsible for the common poor prediction of axial resonance frequencies for pretwisted beams

a symplectic method for approximating all the eigenvalues of a hamiltonian matrix a fast method for computing all the eigenvalues of a hamiltonian matrix m is given the method relies on orthogonal symplectic similarity transformations which preserve structure and have desirable numerical properties the algorithm is about four times faster than the standard q r algorithm the computed eigenvalues are shown to be the exact eigenvalues of a matrix m e where vert e vert depends on the square root of the machine precision the accuracy of a computed eigenvalue depends on its condition and its magnitude larger eigenvalues typically being more accurate

growing context sensitive languages and church rosser languages the growing context sensitive languages gcsl are characterized by a nondeterministic machine model the so called shrinking two pushdown automaton stpda then the deterministic version of this automaton sdtpda is shown to characterize the class of generalized church rosser languages gcrl finally we prove that each growing context sensitive language is accepted in polynomial time by some one way auxiliary pushdown automaton with a logarithmic space bound ow auxpda log poly as a consequence the class of generalized church rosser languages and the class of context free languages are incomparable under set inclusion which verifies a conjecture of mc naughton et al mno88

the chop of languages abstract we investigate chop operations which can be seen as generalized concatenation for several language families of the chomsky hierarchy we prove non closure properties under chop operations and incomparability to the family of languages that are the chop of two regular languages we also prove non closure of that language family under boolean operations and closure under reversal further the representation of a regular language as the chop of two regular expressions can be exponentially more succinct than its regular expression by considering the chop of two linear context free languages we already obtain language families that have non semi decidable problems such as emptiness or finiteness

efficient algorithms for solving systems of nonlinear equations with a block diagonal structure the purpose of this paper is to present efficient algorithms for computing solutions to systems of nonlinear equations with a block diagonal structure the special structure of the systems which arises in economic models allows us to use the decomposition of the problems