an approximate theory for geometrically nonlinear thin plates an approximate theory of thin plates is developed that is based on an assumed displacement field the strains described by a taylor series in the normal distance from the middle surface the exact strains of the middle surface and the equations of equilibrium governing the exact configuration of the deformed middle surface in this theory the exact geometry of the deformed middle surface is used to derive the strains and equilibrium of plates this theory reduces to some existing nonlinear theories through imposition of constraints application of this theory does not depend on the constitutive law because the physical deformation measure is used it can also be applied when the response loading and geometry of the plate are asymmetric and when the vibration mode number is not small predictions of membrane forces in a rectangular plate and of the equilibrium solution in a rotating disk are sample problems

second order linear plate theories partial differential equations stress resultants and displacements abstract by combining the uniform approximation technique with the pseudo reduction approach a consistent second order plate theory is developed with recourse to neither kinematical assumptions nor to shear correction factors by truncation of the elastic energy the governing partial differential equations and the expressions for the stress resultants are compared with those of other authors free coefficients of the resulting displacement ansatz are determined a posteriori in order to satisfy three dimensional boundary conditions and local equilibrium equations

correct asymptotic theories for the axisymmetric deformation of thin and moderately thick cylindrical shells abstract a refined shell theory is formulated for the elastostatics of long moderately thick cylindrical shells in axisymmetric deformation this theory corresponds to a two term outer asymptotic expansion of the exact solution for small values of the dimensionless shell thickness parameter the complexity of the known exact solution for the three dimensional elasticity problem has stimulated an interest in thin and thick shell theories to provide accurate approximate solutions in the shell interior without any reference or matching to the inner asymptotic solution the principal difficulty in developing a shell theory lies in the determination of an appropriate set of twodimensional boundary conditions for the shell solution from the prescribed edge data of the threedimensional theory the derivations of boundary conditions for the thin shell theory and the refined shell theory constitute a main contribution of this paper correct boundary conditions obtained for the first time include i displacement edge conditions for thin shell theory and ii stress and two types of mixed edge conditions for the refined shell theory several applications of the refined theory are given to show that corrections to the thin shell solution can be important

an asymptotic analysis of initial value problems for thin elastic plates an asymptotic technique is developed to analyse initial value problems in application to the three dimensional theory of thin elastic plates various sets of long wave initial data are considered with arbitrary distribution along the plate thickness to account for the initial data composite asymptotic expansions are employed utilizing both two dimensional low frequency and high frequency models the former correspond to the classical theories of plate bending and extension and their refinements whereas the latter are associated with the long wave motions occurring in the vicinities of thickness stretch and shear resonance frequencies six cases of iteration process are revealed depending on the symmetry of the initial data and their thickness variation for each case approximate two dimensional initial conditions are derived including higher order corrections for the two dimensional low frequency refined plate theories the validity of the proposed approach is justified by comparison with the exact solution of the model plane problem for initial data with uniform distribution along the thickness and sinusoidal distribution along the mid plane the methodology of the paper has potential for more general initial value problems specified over a narrow domain including many of those commonly met in physical applied mathematics

machine based methods in parameterized complexity theory we give machine characterizations of most parameterized complexity classes in particular of w p of the classes of the w hierarchy and of the a hierarchy for example we characterize w p as the class of all parameterized problems decidable by a nondeterministic fixed parameter tractable algorithm whose number of nondeterministic steps is bounded in terms of the parameter the machine characterizations suggest the introduction of a hierarchy wfunc between the w and the a hierarchy we study the basic properties of this hierarchy

a new simple third order shear deformation theory of plates an improved simple third order shear deformation theory for the analysis of shear flexible plates is presented in this paper this new plate theory is composed of three parts the simple third order kinematics of displacements reduced from the higher order displacement field derived previously by the author a system of 10th order differential equilibrium equations in terms of the three generalized displacements of bending plates five boundary conditions at each edge of plate boundaries although the resulting displacement field is the same as that proposed by murthy the variational consistent governing equations and the associated proper boundary conditions are derived and identified in this work for the first time in the literature the applications and accuracy of the present shear deformation theory of plates are demonstrated by analytically solving the differential governing equations of a twisting plate a bending beam and two bending plates to which the 3 d elasticity solutions are available and excellent agreements are achieved even for the torsion of a plate with square cross section as well the local effects of stresses at plate boundaries can be characterized accurately these analytical solutions clearly show that the simple third order shear deformation theory developed in this work indeed gives better results than the first order shear deformation theories and other simple higher order shear deformation theories since the present third order shear flexible theory is based on a more rigorous kinematics of displacements and consists of not only a system of variational consistent differential equations but also a group of consistent boundary conditions associated with the differential equations the present simple third order shear deformation theory can easily be applied to the static and dynamic finite element analysis of laminated plates just like the applications of other popular shear flexible plate theories and improved results could be obtained from the present simple third order shear deformable theories of plates

exact theory for a linearly elastic interior beam abstract in this paper an elasticity solution for a two dimensional 2d plane beam is derived and it is shown that the solution provides a complete framework for exact one dimensional 1d presentations of plane beams first an interior solution representing a general state of any 2d linearly elastic isotropic plane beam under a uniform distributed load is obtained by employing a stress function approach the solution excludes the end effects of the beam and is valid sufficiently far away from the beam boundaries then three kinematic variables defined at the central axis of the plane beam are formed from the 2d displacement field using these central axis variables the 2d interior elasticity solution is presented in a novel manner in the form of a 1d beam theory by applying the clapeyron s theorem it is shown that the stresses acting as surface tractions on the lateral end surfaces of the interior beam need to be taken into account in all energy based considerations related to the interior beam finally exact 1d rod and beam finite elements are developed by the aid of the axis variables from the 2d solution

preservation under extensions on well behaved finite structures a class of relational structures is said to have the extension preservation property if every first order sentence that is preserved under extensions on the class is equivalent to an existential sentence the class of all finite structures does not have the extension preservation property we study the property on classes of finite structures that are better behaved we show that the property holds for classes of acyclic structures structures of bounded degree and more generally structures that are wide in a sense that we will make precise we also show that the preservation property holds for the class of structures of treewidth at most k for any k in contrast we show that the property fails for the class of planar graphs

state space realizations and monomial equivalence for convolutional codes we will study convolutional codes with the help of state space realizations it will be shown that two such minimal realizations belong to the same code if and only if they are equivalent under the full state feedback group this result will be used in order to prove that two codes with positive forney indices are monomially equivalent if and only if they share the same adjacency matrix the adjacency matrix is an invariant of the code obtained via a minimal state space realization and counts in a detailed way the weights of all possible outputs it contains full information about the weights of the codewords in the given code

describing parameterized complexity classes we describe parameterized complexity classes by means of classical complexity theory and descriptive complexity theory for every classical complexity class we introduce a parameterized analogue in a natural way in particular the analogue of polynomial time is the class of all fixed parameter tractable problems we develop a basic complexity theory for the parameterized analogues of classical complexity classes and give among other things complete problems and logical descriptions we then show that most of the well known intractable parameterized complexity classes are not analogues of classical classes nevertheless for all these classes we can provide natural logical descriptions

radiation conditions for a semi infinite elastic strip high frequency vibrations of a semi infinite elastic strip with traction free faces are considered the conditions on end data that are derived do not allow non radiating in sommerfeld s sense of polynomial modes at thickness resonance frequencies these represent a high frequency analogue of the well known decay conditions in statics that agree with the classical saint venant principle the proposed radiation conditions are applied to the construction of boundary conditions in the theories of high frequency long wave vibrations describing slow varying motions in the vicinity of thickness resonance frequencies the derivation is based on the laplace transform technique along with the asymptotic methodology that is typical for thin plates and shells

cylindrical bending of thick plates abstract sixth and twelfth order plate theory solutions for cylindrical bending plate problems efficiently obtained by a preliminary reduction of the twelfth order theory for general cylindrical bending to a boundary value problem for a fourth order ode demonstrate the adequacy of these theories for the interior of thick plates with a thickness to span ratio up to at least in contrast kirchhoff s classical thin plate theory is not adequate for values of the same ratio greater than 1 10 comparison with the corresponding interior solutions of 3 d elastostatics shows that the twelfth order theory captures the numerically small first order correction term in the thicknessto span parameter e not possible by lower order plate theories while it is a qualitatively important feature this additional term associated with the effect of transverse normal stress does not significantly improve the plate theory approximation quantitatively for isotropic plates

thick levy plates re visited abstract this paper is concerned with the bending problem of levy plates which are simply supported on two opposite edges with any combination of simply supported clamped or free conditions at the remaining two edges this study attempts to solve thick levy plate problems in a novel way by establishing bending relationships that allow the prediction of mindlin plate results using the corresponding kirchhoff solutions based on the concept of load equivalence these relationships obviate the need for complicated thick plate analyses that involve significant computation time and effort numerical plate solutions are then determined from these relationships and the validity of these results is verified using other known results and those generated using the abaqus software it is through this study that the only analytical mindlin plate solutions by cooke and levinson int j mech sci 25 1983 207 are found to contain errors in this study it is found that there are important distinctions between the mindlin and reissner plate theories these differences will also be substantiated by numerical comparison

quasi cyclic unit memory convolutional codes unit memory convolutional codes with generator matrices which are composed of circulant submatrices are introduced this structure facilitates the analysis of efficient search for good codes equivalences among such codes and some of the basic structural properties are discussed in particular catastrophic encoders and minimal encoders are characterized and dual codes treated further various distance measures are discussed and a number of good codes some of which result from efficient computer search and some of which result from known block codes are presented

nonconcurrent error detection and correction in fault tolerant linear finite state machines in this paper we construct fault tolerant linear finite state machines lfsms in which error detection and correction can be performed nonconcurrently e g periodically more specifically by jointly choosing the state encoding constraints and the redundant dynamics of the fault tolerant lfsm we enable an external checker to detect and identify errors due to past faults based on the current possibly corrupted state of the lfsm the paper presents systematic constructions of fault tolerant lfsms based on a characterization of nonconcurrent error detection correction in terms of state encoding constraints and redundant dynamics in particular we develop a scheme that uses bose chaudhuri hocquenghem bch coding and obtains fault tolerant lfsms that require 2d additional state variables and have the ability to correct up to d errors in any state variable at any time step in the time interval consisting of the latest n time steps of operation the construction uses the minimum possible number of additional state variables and requires an error detecting correcting mechanism with computational complexity that is only linear in n

on the complexity of various parameterizations of common induced subgraph isomorphism abstract in the maximum common induced subgraph problem henceforth mcis given two graphs g 1 and g 2 one looks for a graph with the maximum number of vertices being both an induced subgraph of g 1 and g 2 mcis is among the most studied classical np hard problems it remains np hard on many graph classes including forests in this paper we study the parameterized complexity of mcis as a generalization of clique it is w 1 hard parameterized by the size of the solution being np hard even on forests most structural parameterizations are intractable one has to go as far as parameterizing by the size of the minimum vertex cover to get some tractability indeed when parameterized by k vc g 1 vc g 2 the sum of the vertex cover number of the two input graphs the problem was shown to be fixed parameter tractable with an algorithm running in time 2 o k log k we complement this result by showing that unless the eth fails it cannot be solved in time 2 o k log k this kind of tight lower bound has been shown for a few problems and parameters but to the best of our knowledge not for the vertex cover number we also show that mcis does not have a polynomial kernel when parameterized by k unless np conp poly finally we study mcis and its connected variant mccis on some special graph classes and with respect to other structural parameters

tight lower bounds for certain parameterized np hard problems based on the framework of parameterized complexity theory we derive tight lower bounds on the computational complexity for a number of well known np hard problems we start by proving a general result namely that the parameterized weighted satisfiability problem on depth t circuits cannot be solved in time n o k m o 1 where n is the circuit input length m is the circuit size and k is the parameter unless the t 1 st level w t 1 of the w hierarchy collapses to fpt by refining this technique we prove that a group of parameterized np hard problems including weighted sat hitting set set cover and feature set cannot be solved in time n o k m o 1 where n is the size of the universal set from which the k elements are to be selected and m is the instance size unless the first level w 1 of the w hierarchy collapses to fpt we also prove that another group of parameterized problems which includes weightedq sat for any fixed q 2 clique independent set and dominating set cannot be solved in time n o k unless all search problems in the syntactic class snp introduced by papadimitriou and yannakakis are solvable in subexponential time note that all these parameterized problems have trivial algorithms of running time either n km o 1 or o n k

parameterized and subexponential time complexity of satisfiability problems and applications we study the parameterized and the subexponential time complexity of the weighted and the unweighted satisfiability problems on bounded depth normalized boolean circuits we establish relations between the subexponential time complexity of the weighted and the unweighted satisfiability problems and use them to derive relations among the subexponential time complexity of several np hard problem we then study the role of certain natural structural parameters of the circuit in characterizing the parameterized and the subexponential time complexity of the circuit satisfiability problems under consideration we obtain threshold functions on some circuit structural parameters including the depth the number of gates the fan in and the maximum number of variable occurrences that lead to tight characterizations of the parameterized and the subexponential time complexity of the circuit satisfiability problems under consideration

application of the boundary integral equation method to reissner s plate model numerical solution of reissner s model for the bending of elastic plates by an advanced boundary integral equation method is outlined construction of fundamental solutions and computational strategy is fully described implementation of the resulting one dimensional model is illustrated by two test problems including comparison to analytical solutions

dominating set is fixed parameter tractable in claw free graphs we show that the dominating set problem parameterized by solution size is fixed parameter tractable fpt in graphs that do not contain the claw k 1 3 the complete bipartite graph on four vertices where the two parts have one and three vertices respectively as an induced subgraph we present an algorithm that uses 2 o k 2 n o 1 time and polynomial space to decide whether a claw free graph on n vertices has a dominating set of size at most k note that this parameterization of dominating set is w 2 hard on the set of all graphs and thus is unlikely to have an fpt algorithm for graphs in general the most general class of graphs for which an fpt algorithm was previously known for this parameterization of dominating set is the class of k i j free graphs which exclude for some fixed i j n the complete bipartite graph k i j as a subgraph for i j 2 the class of claw free graphs and any class of k i j free graphs are not comparable with respect to set inclusion we thus extend the range of graphs over which this parameterization of dominating set is known to be fixed parameter tractable we also show that in some sense it is the presence of the claw that makes this parameterization of the dominating set problem hard more precisely we show that for any t 4 the dominating set problem parameterized by the solution size is w 2 hard in graphs that exclude the t claw k 1 t as an induced subgraph our arguments also imply that the related connected dominating set and dominating clique problems are w 2 hard in these graph classes finally we show that for any t n the clique problem parameterized by solution size which is w 1 hard on general graphs is fpt in t claw free graphs our results add to the small and growing collection of fpt results for graph classes defined by excluded subgraphs rather than by excluded minors

state space approach for stress decay in laminates abstract stress decay in laminates due to edge boundary effects are studied through a state space formulation a self equilibrium eigenstress field accounting for the multilayer construction of the laminate is derived using the state variables and the transfer matrix method the eigenvalue determination requires only the solution of 6 6 determinants irrespective of the number of laminae through combinations of the eigenstress field and the interior stress field a complete solution valid in the boundary layer as well as in the interior region of the laminate can be obtained for verification the formulation is first applied to determining the eigenstress in a homogeneous anisotropic layer and then the free edge stress decay in laminates under uniform extension is examined

three dimensional asymptotic finite element method for anisotropic inhomogeneous and laminated plates abstract an asymptotic finite element model for anisotropic inhomogeneous and laminated plates is developed within the framework of three dimensional elasticity the formulation begins with a hellinger reissner functional in which the displacements and transverse stresses are taken to be the functions subject to variation by means of asymptotic expansion the h r functional for the problem is decomposed into functionals of various orders from which the asymptotic finite element equations are derived in the multilevel computations the transverse stresses and displacements may be interpolated independently and the midplane displacements are the only unknown nodal degree of freedoms dof in the system equations thus the total dof at each level is less than that of a homogeneous kirchhoff plate the stiffness matrix remains unchanged the one generated at the leading order level is always used at subsequent levels the formulation is three dimensional yet requires only two dimensional finite element discretization with no need of interpolation in the thickness direction the through thickness effect can be accounted for in a consistent and hierarchical manner numerical comparisons with the benchmark solutions show that the method is effective in modeling of multilayered composite plates

an exact theory of elastic plates abstract an extension of recent analyses for the transverse motion of an elastic plate under a transverse load is given which shows that the problem of the loading of a thin plate is a singular perturbation one expressions are obtained for all the displacements and stress components in terms of the mid plane transverse displacement w and its derivatives it is shown that in some cases w is the solution of a standard biharmonic problem additionally it is shown how to derive other approximations such as those of kirchhoff mindlin and reissner avoiding internal inconsistencies and how they are related to the exact theory

a perturbation solution for the flexible rotating disk non linear equilibrium and stability under transverse loading abstract a singular perturbation solution is developed for the transversely loaded flexible rotating disk using the von karman large deflection theory of thin plates no solution exists for these equations in the limit of vanishing dimensionless bending stiffness this fact along with the desire to have the terms describing non linear membrane stretching appear in the leading order equations motivates a perturbation expansion for displacement of the form 1 2 0 1 the dimensionless transverse loading term is retained in the leading order equations only if it is rescaled by 1 2 this rescaling of transverse load magnitude constitutes a similitude prediction for unifying the equilibrium and stability measurements of different flexible rotating disks experimental measurements of the stability of flexible rotating disks under transverse point loading support this prediction in addition the numerically computed stability of the perturbation solution agrees quantitatively with the experimental measurements

convolutional codes with maximum distance profile abstract maximum distance profile codes are characterized by the property that two trajectories which start at the same state and proceed to a different state will have the maximum possible minimum distance from each other relative to any other convolutional code of the same rate and degree in this paper we use methods from systems theory to characterize maximum distance profile codes algebraically the main result shows that maximum distance profile codes form a generic set inside the variety which parametrizes the set of convolutional codes of a fixed rate and a fixed degree

fixed parameter tractability and completeness i basic results for many fixed parameter problems that are trivially soluable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as k feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is soluable in time bounded by a polynomial of degree c where c is a constant independent of k we establish the main results of a completeness program which addresses the apparent fixed parameter intractability of many parameterized problems in particular we define a hierarchy of classes of parameterized problems fpt subseteq w 1 subseteq w 2 subseteq cdots subseteq w sat subseteq w p and identify natural complete problems for w t for t geq 2 in other papers we have shown many problems complete for w 1 dominating set is shown to be complete for w 2 and thus is not fixed parameter tractable unless independent set clique irredundant set and many other natural problems in w 2 are also fixed parameter tractable we also give a compendium of currently known hardness results as an appendix

an isomorphism between subexponential and parameterized complexity theory we establish a close connection between sub exponential time complexity and parameterized complexity by proving that the so called miniaturization mapping is a reduction preserving isomorphism between the two theories

enhanced first order theory based on mixed formulation and transverse normal effect abstract an accurate prediction of displacements and stresses for laminated and sandwich plates is presented using an enhanced first order plate theory based on the mixed variational theorem efsdtm developed in this paper in the mixed formulation transverse shear stresses based on an efficient higher order plate theory ehopt developed by cho and parmerter cho m parmerter r r 1993 efficient higher order composite plate theory for general lamination configurations aiaa journal 31 1299 1306 are utilized and modified to satisfy prescribed lateral conditions and displacements are assumed to be those of a first order shear deformation theory fsdt relationships between the modified ehopt and the fsdt are systematically derived via both the mixed variational theorem and the least square approximation of difference between in plane stresses including the transverse normal stress effect it is shown that the transverse normal stress effect should be considered in predicting the in plane stresses when the poisson effect is dominant the developed efsdtm preserves the computational advantage of the classical fsdt while allowing for important local through the thickness variations of displacements and stresses through the recovery procedure the accuracy and efficiency of the present theory are assessed by comparing its results with various plate models as well as the three dimensional exact solutions for thick laminated and sandwich plates

bridging plate theories and elasticity solutions abstract in this work we present an exact 3d plate solution in the conventional form of 2d plate theories without invoking any of the assumptions inherent to 2d plate formulations we start by formulating a rectangular plate problem by employing saint venant s principle so that edge effects do not appear in the plate then the exact general 3d elasticity solution to the formulated interior problem is examined by expressing the solution in terms of mid surface variables exact 2d equations are obtained for the rectangular interior plate it is found that the 2d presentation includes the kirchhoff mindlin and levinson plate theories and their general solutions as special cases the key feature of the formulated interior plate problem is that the interior stresses of the plate act as surface tractions on the lateral plate edges and contribute to the total potential energy of the plate we carry out a variational interior formulation of the levinson plate theory and take into account as a novel contribution the virtual work due to the interior stresses along the plate edges remarkably this way the resulting equilibrium equations become the same as in the case of a vectorial formulation a gap in the conventional energy based derivations of 2d engineering plate theories founded on interior kinematics is that the edge work due to the interior stresses is not properly accounted for this leads to artificial edge effects through higher order stress resultants finally a variety of numerical examples are presented using the 3d elasticity solution

augmented levy michell equations for flexural plates abstract a new sixth order isotropic elastic and flexural plate theory is presented based on the fourth order equations of levy 1877 and michell 1900 the lack of surface loading in these levy michell equations is overcome by including the dominant flexural component of dougall s 1904 solution for a point load on the surface of a three dimensional isotropic elastic layer the augmented plate equations are arranged to fit the form of a consistent sixth order system of isotropic plate equations which include the well known work of reissner and static equations of mindlin numerical applications to two three dimensional problems with analytical solutions show good comparative results

two dimensional theories deduced from three dimensional theory for a transversely isotropic body ii plane problems abstract the problem of deducing two dimensional theories from the three dimensional theory for a transversely isotropic body is investigated it is shown that the spatial displacements of a three dimensional body can be represented by the mid plane displacements and their derivatives and that the general deformation can be decomposed to two independent parts the asymmetric deformation plate problems and the symmetric part plane problems the exact equations for the homogeneous transversely isotropic plates and the approximate equations for the transversely isotropic plates under transverse loads are derived directly from the three dimensional theory torsion of a rectangular plate and bending of an infinitely large plate with a circular hole are examined to illustrate the application of the plate theory developed

on timoshenko reissner type theories of plates and shells abstract linear tr theories timoshenko reissner theories of isotropic plates and shells are discussed these theories take into account the transversal shear deformation and rotation inertia the main subject under consideration is the construction of these theories by the asymptotic method and the related error estimates for static and dynamic problems in the dynamic case a method is suggested for the extension of the range of applicability of the tr theory

low frequency decay conditions for a semi infinite elastic strip in this paper we investigate in plane harmonic vibrations of a semi infinite elastic strip with prescribed edge stresses low frequency decay conditions are established demonstrating the deviation from the classical saint venant principle in quadratic terms in frequency in the case of the symmetric motion strip extension the proposed correction is expressed explicitly in terms of given end data whereas for the antisymmetric motion strip bending this also involves unknown edge displacements further applications are defined including those related to dynamic analysis of plates and shells excited by statically self equilibrated edge loads the derivation is based on a perturbation approach using the laplace transform technique we also address methodological aspects dealing with a continuous eigenspectrum and the two parametric nature of the problem

simplifying the weft hierarchy we give simple self contained proofs of the basic hardness results for the classes w t of the weft hierarchy we extend these proofs to higher levels of the hierarchy and illuminate the distinctions among its classes the anti monotone collapse at w 1 s and the normalization of weft t formulas arise as by products of the proofs

the general fundamental solution of the sixth order reissner and mindlin plate bending models revisited abstract the sixth order differential equation system of the reissner and mindlin plate bending models describe mathematically the plate problem where lines normal to the mid plane before deformation remain straight and inextensible in the deformed configuration but not necessarily normal to the reference plane anymore the non normality condition is due to the consideration of transverse shearing strains disregarded in the classical bi harmonic kirchhoff plate model as the plate thickness is reduced and or the transverse shear modulus is increased the deformed configuration is less dependent of the transverse shear strains and in the limit as the plate thickness approaches zero and or the transverse shear modulus approaches the transverse shear strain effects vanish and the problem is exactly that described by the classical plate model in this paper we investigate the fundamental solutions of both the fourth order kirchhoff and the sixth order reissner and mindlin plate models we consider a transversely isotropic material and show that the fundamental solution of the bi harmonic problem can be obtained directly from the general fundamental solution of the sixth order plate problem in the limit as the plate thickness approaches zero and or the transverse shear modulus approaches this solution is in agreement with the analytical solution of an infinite thin clamped circular plate submitted to a unitary concentrated load acting at its center

a novel three variable shear deformation plate formulation theory and isogeometric implementation abstract this study brings to readers the generalized formulation of three variable plate theory and an efficient computational approach for analyzing plates the theory not only has three degree of freedoms dofs per node which complies with three dimensional space of full plate model as classical plate theory cpt but also accounts for the effect of shear deformation without any requirement of shear correction factors scf a complete set of strong forms weak form as well as classical and non classical boundary conditions bcs for linear and geometrically nonlinear analysis are consistently derived in this paper through a variational approach the strong forms are sixth order differential equations resulting in the symmetrical fourth order differential weak form it is known that isogeometric analysis iga arguably outweighs classical finite element method in terms of high continuity and high order differentiability thanks to its advantage an iga framework for the generalized three variable plate theory is formulated with completely locking free and only three dofs per node the classical bcs are strongly enforced to system equations as usual whilst the non classical bcs are weakly imposed by a penalty approach the new plate theory with only three variable is thereafter used for static linear and nonlinear analysis of isotropic and functionally graded material fgm plates to demonstrate its ability the reliability and accuracy of the present approach are ascertained by comparing the obtained results with other existing ones based on a robust formulation devoted in the paper the proposed approach can be further extended for numerous problems related to the shear deformable effect in the literature

a perturbation approach for evaluating natural frequencies of moderately thick elliptic plates natural frequencies for moderately thick elliptic plates are calculated by perturbing initial values corresponding to the kirchhoff classical theory of plate bending the proposed approach utilizes a universal algebraic equation for perturbed eigenvalues previously derived by the authors for elliptic plates of a small eccentricity a dual procedure is developed to evaluate the sought for natural frequencies starting from those for a circular thin plate a comparison with finite element computations is presented an importance of the perturbation techniques in question for interpreting of finite element data is emphasized

refined engineering beam theory based on the asymptotic expansion approach a systematic derivation of a refined engineering theory governing the response of elastic beams is presented the method employed to accomplish this is that of asymptotic expansion that combines dimensional analysis with the expansion in powers of a small parameter of the solution of the three dimensional linear elasticity theory the present beam theory contains more information than the classical timoshenko theory a new shear coefficient is defined and compared with existing ones

imperfection sensitivity in the nonlinear vibration oscillations of initially stressed plates abstract in this paper nonlinear partial differential equations for the vibrating motion of an initially stressed imperfect isotropic plate are presented the derived equations include the effects for imperfections transverse shear deformation rotary inertia and non uniform initial stresses using these derived governing equations the nonlinear vibration of initially stressed plates with initial imperfection is studied present approach employs perturbation technique galerkin method and runge kutta method the perturbation technique was used to derive the nonlinear governing equations the motion of imperfect plates is obtained by performing the galerkin method and then solved by runge kutta method numerical solutions are presented that relate to the performances of perfect and imperfect plates a combination of pure bending stress plus an extensional stress is taken to be the initial stress in the plane of the plate it is found that the existence of initial stresses and geometric imperfection may result in a drastic change on the nonlinear vibration behavior the effects of various parameters on the nonlinear free vibrations of imperfect plates are presented

on the computation of weight enumerators for convolutional codes performance bounds for maximum likelihood decoding of convolutional codes over memoryless channels are commonly measured using the distance weight enumerator t x y also referred to as the transfer function of the code this paper presents an efficient iterative method to obtain t x y called the state reduction algorithm the algorithm is a systematic technique to simplify signal flow graphs that algebraically manipulate the symbolic adjacency matrix associated with the convolutional code next the algorithm is modified to compute the first few terms of the series expansion of t 1 y and spl part t x y spl part x sub x 1 the distance spectra without first computing the complete t x y

the complexity of homomorphism and constraint satisfaction problems seen from the other side we give a complexity theoretic classification of homomorphism problems for graphs and more generally relational structures obtained by restricting the left hand side structure in a homomorphism for every class c of structures let hom c be the problem of deciding whether a given structure a c has a homomorphism to a given arbitrary structure s we prove that under some complexity theoretic assumption from parameterized complexity theory hom c is in polynomial time if and only if c has bounded tree width modulo homomorphic equivalence translated into the language of constraint satisfaction problems our result yields a characterization of the tractable structural restrictions of constraint satisfaction problems translated into the language of database theory it implies a characterization of the tractable instances of the evaluation problem for conjunctive queries over relational databases

on minimality of convolutional ring encoders convolutional codes are considered with code sequences modeled as semi infinite laurent series it is well known that a convolutional code c over a finite group g has a minimal trellis representation that can be derived from code sequences it is also well known that for the case that g is a finite field any polynomial encoder of c can be algebraically manipulated to yield a minimal polynomial encoder whose controller canonical realization is a minimal trellis in this paper we seek to extend this result to the finite ring case g bbzpr by introducing a so called ldquo p encoderrdquo we show how to manipulate a polynomial encoding scheme of a noncatastrophic convolutional code over bbzpr to produce a particular type of p encoder ldquominimal p encoderrdquo whose controller canonical realization is a minimal trellis with nonlinear features the minimum number of trellis states is then expressed as p gamma where gamma is the sum of the row degrees of the minimal p encoder in particular we show that any convolutional code over bbzpr admits a delay free p encoder which implies the novel result that delay freeness is not a property of the code but of the encoder just as in the field case we conjecture that a similar result holds with respect to catastrophicity i e any catastrophic convolutional code over bbzpr admits a noncatastrophic p encoder

an improved deterministic local search algorithm for 3 sat we slightly improve the pruning technique presented in dantsin et al theoret comput sci 289 2002 69 to obtain an o 1 473n deterministic algorithm for 3 sat

constructions of mds convolutional codes maximum distance separable mds convolutional codes are characterized through the property that the free distance attains the generalized singleton bound the existence of mds convolutional codes was established by two of the authors by using methods from algebraic geometry this correspondence provides an elementary construction of mds convolutional codes for each rate k n and each degree spl delta the construction is based on a well known connection between quasi cyclic codes and convolutional codes

on a generalization of some formulas of the theory of moderately thick elastic plates abstract we first restate formulas for stresses and stress couples of a theory of isotropic modcrately thick plates in the classical texts of love and of timoshcnko in simplified form we then use recent results for a two dimensional twelfth order plate theory to derive a generalization of the classical formulas such that the results for the isotropic case appear as special cases of the corresponding results for transversely isotropic plates in addition we transform the general equations of our twodimensional twelfth order theory so as to be left with one fourth order equation for an interior solution contribution and one fourth order equation for transverse normal stress edge zone effects in addition to the previously known two simultaneous second order equations for transverse shear stress edge zone effects

on miniaturized problems in parameterized complexity theory we introduce a general notion of miniaturization of a problem that comprises the different miniaturizations of concrete problems considered so far we develop parts of the basic theory of miniaturizations using the appropriate logical formalism we show that the miniaturization of a definable problem in w t lies in w t too in particular the miniaturization of the dominating set problem is in w 2 furthermore we investigate the relation between f k no k time and subexponential time algorithms for the dominating set problem and for the clique problem

on behaviors and convolutional codes it is well known that a convolutional code is essentially a linear system defined over a finite field in this paper we elaborate on this connection we define a convolutional code as the dual of a complete linear behavior in the sense of willems 1979 using ideas from systems theory we describe a set of generalized first order descriptions for convolutional codes as an application of these ideas we present a new algebraic construction for convolutional codes

bending solutions of levinson beams and plates in terms of the classical theories using the mathematical similarity of the governing equations of the classical beam and plate theories and the levinson beam and plate theories and the basis of load equivalence exact relationships between the bending solutions of the two theories for beams and plates are derived these relationships enable the conversion of the well known classical euler bernoulli beam and kirchhoff plate solutions to their shear deformable counterparts using the levinson beam and plate theories examples are given to illustrate the use of these relationships

deciding first order properties of locally tree decomposable structures we introduce the concept of a class of graphs or more generally relational structures being locally tree decomposable there are numerous examples of locally tree decomposable classes among them the class of planar graphs and all classes of bounded valence or of bounded tree width we also consider a slightly more general concept of a class of structures having bounded local tree width we show that for each property of structures that is definable in first order logic and for each locally tree decomposable class c of structures there is a linear time algorithm deciding whether a given structure a c has property for classes c of bounded local tree width we show that for every k 1 there is an algorithm solving the same problem in time o n1 1 k where n is the cardinality of the input structure

on parameterized exponential time complexity in this paper we study the notion of parameterized exponential time complexity we show that a parameterized problem can be solved in parameterized 2 o f k p n time if and only if it is solvable in time o 2 d f k q n for any constant d 0 where p and q are polynomials we then illustrate how this equivalence can be used to show that special instances of parameterized np hard problems are as difficult as the general instances for example we show that the planar dominating set problem on degree 3 graphs can be solved in 2 o k p n parameterized time if and only if the general planar dominating set problem can apart from their complexity theoretic implications our results have some interesting algorithmic implications as well

the appropriate edge conditions for two dimensional quasicrystal semi infinite strips with mixed edge data abstract for two dimensional quasicrystal semi infinite strips with mixed edge data the betti rayleigh reciprocal theorem and the general solution of plane elasticity of quasicrystals are applied in a novel way to obtain the appropriate edge conditions accurate to all order by introducing two definitions for the decaying and regular states the necessary conditions deduced form the reciprocal theorem for the edge data to induce only a decaying elastostatic are directly translated into the appropriate edge conditions for the existence of a rapidly decaying solution of the strips once a suitable regular state which fulfills load free boundary conditions is constructed for the relevant edge data the translation is immediate however this is not the situation for general edge data for the case of transverse bending and in plane extension of the strips these decaying state conditions are obtained explicitly for the first time when the mixed edge data are imposed on the strip edge besides for a degenerated form an analytical solution of the decaying state is formulated to verify validity of these edge conditions

on the weight distribution of convolutional codes detailed information about the weight distribution of a convolutional code is given by the adjacency matrix of the state diagram associated with a minimal realization of the code we will show that this matrix is an invariant of the code moreover it will be proven that codes with the same adjacency matrix have the same dimension and the same forney indices and finally that for one dimensional binary convolutional codes the adjacency matrix determines the code uniquely up to monomial equivalence

woven convolutional codes i encoder properties encoders for convolutional codes with large free distances can be constructed by combining several less powerful convolutional encoders this paper is devoted to constructions in which the constituent convolutional codes are woven together in a manner that resembles the structure of a fabric the general construction is called twill and it is described together with two special cases viz woven convolutional encoders with outer warp and with inner warp the woven convolutional encoders inherit many of their structural properties such as minimality and catastrophicity from their constituent encoders for all three types of woven convolutional codes upper and lower bounds on their free distances as well as lower bounds on the active distances of their encoders are derived

minimal grobner bases and the predictable leading monomial property abstract we focus on grobner bases for modules of univariate polynomial vectors over a ring we identify a useful property the predictable leading monomial plm property that is shared by minimal grobner bases of modules in f x q no matter what positional term order is used the plm property is useful in a range of applications and can be seen as a strengthening of the wellknown predictable degree property row reducedness a terminology introduced by forney in the 70 s because of the presence of zero divisors minimal grobner bases over a finite ring of the type z p r where p is a prime integer and r is an integer 1 do not necessarily have the plm property in this paper we show how to derive from an ordered minimal grobner basis a so called minimal grobner p basis that does have a plm property we demonstrate that minimal grobner p bases lend themselves particularly well to derive minimal realization parametrizations over z p r applications are in coding and sequences over z p r

stress boundary conditions for plate bending abstract the determination of the appropriate boundary conditions for a two dimensional theory of elastic flat plates and shells consistent with the expected order of accuracy of the theory is both critical and challenging the reciprocal theorem of elasticity will be applied in a novel way to obtain the appropriate stress boundary conditions for plate bending accurate to all order with respect to the usual dimensionless thickness parameter for plates of general edge geometry and loading kirchhoff s two contracted stress boundary conditions are shown to be consistent with a leading term thin plate approximation theory but the more general results obtained herein are needed for higher order theories

on recursiveness and related topics in linear systems a decomposition of matrix formal power series linear systems is developed the interconnections between formal power series realization pade approximation recursiveness berlekamp massey algorithm feedback interconnections matrix linear fractional representations matrix continued fractions and the matrix euclidean algorithm are thereby revealed

query evaluation via tree decompositions a number of efficient methods for evaluating first order and monadic second order queries on finite relational structures are based on tree decompositions of structures or queries we systematically study these methods in the first part of the article we consider arbitrary formulas on tree like structures we generalize a theorem of courcelle 1990 by showing that on structures of bounded tree width a monadic second order formula with free first and second order variables can be evaluated in time linear in the structure size plus the size of the output in the second part we study tree like formulas on arbitrary structures we generalize the notions of acyclicity and bounded tree width from conjunctive queries to arbitrary first order formulas in a straightforward way and analyze the complexity of evaluating formulas of these fragments moreover we show that the acyclic and bounded tree width fragments have the same expressive power as the well known guarded fragment and the finite variable fragments of first order logic respectively

relational queries computable in polynomial time we characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe we also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation this proves that the fixed point query hierarchy suggested by chandra and harel collapses at the first fixed point level it is also a general result showing that in finite model theory one application of fixed point suffices

fixed parameter tractability and completeness ii on completeness for w 1 abstract for many fixed parameter problems that are trivially solvable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is solvable in time bounded by a polynomial of degree c where c is a constant independent of k in a previous paper the w hierarchy of parameterized problems was defined and complete problems were identified for the classes w t for t 2 our main result shows that independent set is complete for w 1

a refined nonlinear theory of plates with transverse shear deformation abstract a higher order shear deformation theory of plates accounting for the von karman strains is presented the theory contains the same dependent unknowns as in the hencky mindlin type first order shear deformation theory and accounts for parabolic distribution of the transverse shear strains through the thickness of the plate exact solutions of simply supported plates are obtained using the linear theory and the results are compared with the exact solutions of 3 d elasticity theory the first order shear deformation theory and the classical plate theory the present theory predicts the deflections stresses and frequencies more accurately when compared to the first order theory and the classical plate theory

deciding first order properties of nowhere dense graphs nowhere dense graph classes introduced by neset il and ossona de mendez 2010 2011 form a large variety of classes of sparse graphs including the class of planar graphs actually all classes with excluded minors and also bounded degree graphs and graph classes of bounded expansion we show that deciding properties of graphs definable in first order logic is fixed parameter tractable on nowhere dense graph classes parameterized by the length of the input formula at least for graph classes closed under taking subgraphs this result is optimal it was known before that for all classes c of graphs closed under taking subgraphs if deciding first order properties of graphs in c is fixed parameter tractable then c must be nowhere dense under a reasonable complexity theoretic assumption as a by product we give an algorithmic construction of sparse neighborhood covers for nowhere dense graphs this extends and improves previous constructions of neighborhood covers for graph classes with excluded minors at the same time our construction is considerably simpler than those our proofs are based on a new game theoretic characterization of nowhere dense graphs that allows for a recursive version of locality based algorithms on these classes on the logical side we prove a rank preserving version of gaifman s locality theorem

fixed parameter tractability definability and model checking in this article we study parameterized complexity theory from the perspective of logic or more specifically descriptive complexity theory we propose to consider parameterized model checking problems for various fragments of first order logic as generic parameterized problems and show how this approach can be useful in studying both fixed parameter tractability and intractability for example we establish the equivalence between the model checking for existential first order logic the homomorphism problem for relational structures and the substructure isomorphism problem our main tractability result shows that model checking for first order formulas is fixed parameter tractable when restricted to a class of input structures with an excluded minor on the intractability side for every t ge 0 we prove an equivalence between model checking for first order formulas with t quantifier alternations and the parameterized halting problem for alternating turing machines with t alternations we discuss the close connection between this alternation hierarchy and downey and fellows w hierarchy on a more abstract level we consider two forms of definability called fagin definability and slicewise definability that are appropriate for describing parameterized problems we give a characterization of the class fpt of all fixed parameter tractable problems in terms of slicewise definability in finite variable least fixed point logic which is reminiscent of the immerman vardi theorem characterizing the class ptime in terms of definability in least fixed point logic

on plate theories and saint venant s principle abstract it is generally known hat the classical germain kirchhoff plate theory is the leading term of the outer asymptotic expansion or interior solution in a small thickness parameter for the linear elastostatics of thin flat isotropic bodies this leading term or the actual outer solution alone cannot satisfy arbitrarily prescribed admissible edge data on the other hand the complementary inner asymptotic expansion or boundary layer solution is determined by a sequence of boundary value problems which are nearly as difficult to solve as the original problem for stress edge data saint venant s principle has been invoked to generate a set of stress boundary conditions for the classical plate theory as well as for higher order terms in the outer expansion giving various thick plate theories without any reference to the inner solution attempts to derive the corresponding boundary conditions for displacement and other types of edge data in the literature for general shape plates have not been successful the present study applies a general method developed by the authors to derive the correct set of boundary conditions for arbitrarily prescribed admissible edge data without an explicit solution of the inner or boundary layer solution for a number of special cases of general interest including cases with displacement edge data our general results also show that to be strictly correct saint venant s principle should be applied only to the leading term outer solution i e the classical plate theory

nonlinear model reduction of von karman plates under quasi steady fluid flow a reduced order model for von karman plates using a method of quadratic components is presented in this paper the method of quadratic components postulates the full kinematics of the plate as consisting of a combination of linear and quadratic components this reduced model is then discretized in space with a galerkin approximation and in time with an implicit integration scheme the plate is coupled with a fluid flowing over it at a supersonic speed using a quasi steady pressure model commonly referred to as piston theory a static loading example is used to validate the model reduction of the plate with respect to other numerical and approximate solutions the limit cycles of the plate coupled with piston theory are calculated via a cyclic method and the results from parameter studies are compared to classical results a previously unexplored regime of the limit cycle amplitudes is investigated a second coexisting limit cycle is found that yields a discontinuity in the limit cycle amplitudes at a critical dynamic pressure