a new boundary element method for bending of plates on elastic foundations abstract the bending of plates on a winkler foundation according to kirchhoff s theory is solved by using an original boundary integral equation method involving the fundamental solution for plate flexure problems an integral representation for the second member pressure of the foundation of the equation is given by discretizing the integral equation it is possible to eliminate the boundary unknowns so that one is reduced to solving a linear system the solutions of which are deflections inside the domain to illustrate the potentialities of this method several problems with various boundary conditions loads and values of the modulus of the foundation are successfully solved

an adaptive boundary element method this paper explores the concept of moving singularities in the boundary element analysis the singularities are placed on an auxiliary boundary which is located outside the domain of the problem and are allowed to move as part of the solution process this results in a highly adaptive but non linear method examples involving the two and three dimensional laplace s equations are solved excellent agreement with exact solutions is obtained using a minimal number of singularities also the trajectories of the singularity motion are plotted the behaviour seen here is that as the solution approaches convergence the singularities exhibit a general trend of moving away from the domain of the problem

study of coating flow by the finite element method abstract silliman s analysis of slot coating is extended to accommodate film flows with highly bent menisci as in slide and curtain coating by combining polar and cartesian coordinate parametrizations of meniscus shape the nonlinear algebraic equations from the subdomain galerkin weighted residual method and finite element basis functions are solved by newton s method which is perfected for the free boundary problem convergence behavior is examined slot coating results reveal slow flow zones and show that at high capillary number and low metering rate the downstream meniscus can no longer attach to the slot comparison of coyne and elrod s approximate solutions with the finite element solutions shows that their assumption of a parabolic velocity profile leads to reasonable approximations of meniscus shapes

detecting non uniqueness of solutions to biharmonic integral equations through svd we consider the singular values of an integral operator and of a corresponding square matrix derived from the integral operator by means of a quadrature formula and a collocation the integral operator and also the matrix depend on a real parameter which may also enter the singular values of the operator and the matrix when a singular value drops to zero for a certain critical value of the parameter the corresponding homogeneous integral equation or matrix equation has a nontrivial solution based on several examples with biharmonic integral operators we conjecture that the order of approximation of the critical value for the matrix is at least equal to the order of the quadrature formula used it is therefore possible with a reasonable accuracy to detect such critical values for the integral operator simply through a singular value decomposition of the matrix derived by a quadrature and collocation

linear tail biting trellises the square root bound and applications for reed muller codes linear tail biting trellises for block codes are considered by introducing the notions of subtrellis merging interval and sub tail biting trellis some structural properties of linear tail biting trellises are proved it is shown that a linear tail biting trellis always has a certain simple structure the parallel merged cosets structure a necessary condition required from a linear code in order to have a linear tail biting trellis representation that achieves the square root bound is presented finally the above condition is used to show that for r spl ges 2 and m spl ges 4r 1 or r spl ges 4 and r 3 spl les m spl les 4r 5 3 the reed muller code rm r m under any bit order cannot be represented by a linear tail biting trellis whose state complexity is half of that of the minimal conventional trellis for the code under the standard bit order

an asymptotic property of degenerate scales for multiple holes in plane elasticity the solution of an exterior dirichlet boundary value problem of plane isotropic elasticity by the boundary integral equation of the first kind obtained from the somigliana identity is considered the logarithmic function appearing in the integral kernel may cause that the operator is non invertible such a situation occurs if the size of the boundary coincides with a degenerate scale for a certain form of the fundamental solution used a technique for the evaluation of the degenerate scales for an asymptotic case of an exterior domain with holes placed far one from another is discussed and analyzed the examples provide results of particular cases and assess suitability of the proposed technique in relation to numerical calculation of degenerate scales by the boundary element method

boundary integration and interpolation procedures for plate bending in the direct boundary element method dbem for thin plate bending analysis the integration of the kernel shape function products can lead to complications due to a combination of factors the first is the existence of a singularity at the source point leading to the singular kernel which increases in strength as the integral equation is differentiated once for rotation again for moment and yet again for shear the second factor arises from the use of piecewise interpolation polynomials in the first part of the dbem analysis where the unspecified boundary values are computed the numerical procedures are fairly straightforward it is found in this paper that special care must be taken in calculating internal actions at domain points the problems which can be encountered are demonstrated and a modified boundary interpolation procedure is described examples are given which show the superiority of the recommended approach

inversion of integral transforms associated with a class of perturbed heat equations abstract let lx be the sturm liouville differential operator l x d 2 dx 2 q x x 0 we assume that lx has either a purely discrete spectrum that is bounded from below by zero or a continuous spectrum that fills up the interval 0 with possibly a finite number of negative eigenvalues the w transform of y l2 0 is defined by x 0 y g x y 1 dy where g x y t is a function associated with the fundamental solution of the perturbed equation l x u x t u x t t the main purpose of this paper is to derive an inversion formula for the w transform this inversion formula generalizes the known inversion formulae for the weierstrass weierstrass hankel convolution and weierstrass laguerre transforms the results of this paper are easily extended to the case where lx is considered over the entire line

a boundary element method for plate bending problems abstract an indirect boundary element formulation is constructed by using a fundamental solution of the biharmonic operator it is shown that the fundamental solution and its derivatives can be represented by four functions with two integers the new representation is not only a simpler representation but also reveals a structure that is exploited in the development of an algorithm based on the analytical integration of line and area integrals the analytical integral values are used to establish continuity requirements on the unknown fictitious densities numerical examples consider the consequences of satisfying and violating the continuity requirements by the unknown fictitious densities it is also shown that if the fictitious density distributions do not satisfy certain conditions then he solution can be affected by the choice of the non dimensionalizing variables numerical examples with a variety of boundary conditions demonstrate the effectiveness and limitations of the proposed algorithm

importance and use of rigid body mode in boundary element method the superposition of a rigid body mode on a body should result in a corresponding change in displacement values but should not affect the stresses however in the numerical solution by the boundary element method bem large errors may be obtained for displacements and stresses if a rigid body mode is present in the input data to eliminate the effects of the rigid body mode on the numerical accuracy of the solution the fundamental solutions for displacements must be correctly interpreted and used the rigid body mode may be unknowingly present in the boundary condition data it may be present because the boundary data are not known accurately or it may be present if the displacement values at the support have been computed from a separate analysis a rigid body mode may arise due to the collocation nature of satisfying the boundary conditions the point values of the applied load at the collocation point may not satisfy equilibrium or the point values of the specified displacements may not satisfy the condition of zero translation and rotation for bodies under pure traction we know that the analytical solution can contain an arbitrary amount of rigid body mode numerically however some unknown value is assigned to this rigid body mode it might be desirable for example in limit analysis to eliminate the rigid body mode from the displacements to obtain deformation of a point with respect to a point on the body in addition knowledge and elimination of the rigid body mode is necessary for the implementation of a scheme described by this author in an earlier work the importance of the earlier work is that it reduced the sensitivity of the bem to changes and errors in the input data in this paper the causes and the effects of the rigid body mode on the bem the correct interpretation of the fundamental solution for displacements and an algorithm for determining and accounting for the rigid body mode are discussed a numerical example validates the ideas in this paper for the indirect version the algorithm for the direct version is presented without a numerical example in the appendices

continuity and collocation effects in the boundary element method the presence of singularities in the integral operators of the boundary element methods requires that the density functions must satisfy certain continuity requirements if the displacements and stresses are to be bounded quite often the continuity conditions particularly on the derivatives of the density functions are relaxed at the element ends for the sake of simplicity in approximating the unknown density functions in this paper a numerical study on the effects of satisfying or violating the continuity requirements and the effect of the boundary condition collocating point on three different bem formulations is presented two are indirect formulations using force singularities and displacement discontinuity singularities and the third is rizzo s direct formulation the two integral operators in the direct bem appear individually in the two different formulations of the indirect bem this makes it possible to study the numerical error and other problems in each integral operator and the interaction of the two integral operators in the direct bem the impact of the study on numerical modelling for the three bem formulations is presented in the paper 1997 by john wiley sons ltd

on stability of approximation methods for the muskhelishvili equation we study approximation methods for the muskhelishvili integral equations on curves with comer points and establish necessary and sufficient conditions for their stability

minimal trellises for block codes basic concepts in the study of trellises of block codes are defined it is shown that minimal proper trellises exists for all block codes bounds on the size of such trellises are established these bounds are shown to be exact for maximum distance separable codes and nearly so for perfect codes

characteristic generators and dualization for tail biting trellises this paper focuses on dualizing tail biting trellises particularly kv trellises these trellises are based on characteristic generators as introduced by koetter vardy 2003 and may be regarded as a natural generalization of minimal conventional trellises even though they are not necessarily minimal two dualization techniques will be investigated the local dualization introduced by forney 2001 for general normal graphs and a linear algebra based dualization tailored to the specific class of tail biting bahl cocke jelinek raviv bcjr trellises introduced by nori shankar 2006 it turns out that in general the bcjr dual is a subtrellis of the local dual while for kv trellises these two coincide furthermore making use of both the bcjr construction and the local dualization it will be shown that for each complete set of characteristic generators of a code there exists a complete set of characteristic generators of the dual code such that their resulting kv trellises are dual to each other if paired suitably this proves a stronger version of a conjecture formulated by koetter vardy

natural convection in steady solidification finite element analysis of a two phase rayleigh benard problem abstract galerkin finite element approximations and newton s method for solving free boundary problems are combined with computer implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt the newton method gives rapid convergence to steady state velocity temperature and pressure fields and melt solid interface shapes and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability the power of this combination is demonstrated for a two phase rayleigh benard problem composed of melt and and solid in a vertical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt solid interface is always a solution multiple cellular flows bifurcating from the static state are detected and followed as rayleigh number is varied changing the boundary conditions to approach those appropriate for the vertical bridgman solidification system causes imperfections that eliminate the static state the flow structure in the bridgman system is related to those for the rayleigh benard system by a continuous evolution of the boundary conditions

making the boundary element method less sensitive to changes or errors in the input data to solve a problem by the boundary element method requires a solution of an integral equation by discretizing the boundary the integral equation is reduced to a set of linear algebraic equations if the matrix in algebraic equation is not diagonal dominant or more precisely poorly conditioned then the accuracy of the numerical solution becomes very sensitive to small changes in the input data small errors in the input data or changes in the mesh description can change the solution drastically in this paper a scheme is described which improves the condition of the matrix furthermore it also reduces the sensitivity of the condition of the matrix to changes in the mesh description the ideas described are applicable to any boundary element formulation however the numerical examples are from two dimensional elastostatics solved by the indirect version of the boundary element method

paley wiener type theorems for a class of integral transforms abstract a characterization of weighted l 2 i spaces in terms of their images under various integral transformations is derived where i is an interval finite or infinite this characterization is then used to derive paley wiener type theorems for these spaces unlike the classical paley wiener theorem our theorems use real variable techniques and do not require analytic continuation to the complex plane the class of integral transformations considered is related to singular sturm liouville boundary value problems on a half line and on the whole line

on viewing block codes as finite automata block codes are viewed from a formal language theoretic perspective it is shown that properties of trellises for subclasses of block codes called rectangular codes follow naturally from the myhill nerode theorem a technique termed subtrellis overlaying is introduced with the object of reducing decoder complexity necessary and sufficient conditions for trellis overlaying are derived from the representation of the block code as a group partitioned into a subgroup and its cosets the conditions turn out to be simple constraints on coset leaders it is seen that overlayed trellises are tail biting trellises for which decoding is generally more efficient than that for conventional trellises finally a decoding algorithm for tail biting trellises is described and the results of some simulations are presented

the direct boundary element method in plate bending the direct boundary element method based on the rayleigh green identity is employed for the static analysis of kirchhoff plates the starting point is a slightly modified version of stern s equations the focus is on the implementation of the method for linear elements and a hermitian interpolation for the deflection w the concept of element matrices is developed and the cauchy principal values of the singular integrals are given in detail the treatment of domain integrals the handling of internal supports the properties of the solution and the effect of singularities are discused numerical examples illustrate the various techniques in the appendix the influence functions for the second and third derivatives of the deflection w are given

analytical treatment of boundary integrals in direct boundary element analysis of plate bending problems a direct type boundary element method bem for the analysis of simply supported and built in plates is employed the integral equations due to a combined biharmonic and harmonic governing equations are first established the boundary integrals developed are then evaluated analytically the domain integrals due to external body forces are also transformed over the boundary and subsequently evaluated analytically thus it needs only the boundary to be discretized without loss of generality the exact expression for the integrals would enhance the solution accuracy of the bem this is due to the fact that at locations where the fundamental solutions approach their singular points the value determined by numerical quadrature may be inconsistent and inaccurate also another major advantage of the exact expressions for integrations is the insensitivity to the geometrical location of the source point on the boundary the distribution of boundary quantities is approximated either over linear or quadratic boundary elements general type of plate bending problems with plates of different geometrical shapes supported simply or fixed can be handled loading may be applied point concentrated uniformly distributed within the domain or over the boundary also hydrostatic pressure can be applied the results obtained by bem in comparison with those obtained by analytical or other approximate solutions are found to be very accurate and the solution method is efficient

biharmonic analysis of rectilinear plates by the boundary element method an improved boundary element formulation bem for two dimensional non homogeneous biharmonic analysis of rectilinear plates is presented a boundary element formulation is developed from a coupled set of poisson type boundary integral equations derived from the governing non homogeneous biharmonic equation emphasis is given to the development of exact expressions for the piecewise rectilinear boundary integration of the fundamental solution and its derivatives over several types of isoparametric elements incorporation of the explicit form of the integrations into the boundary element formulation improves the computational accuracy of the solution by substantially eliminating the error introduced by numerical quadrature particularly those errors encountered near singularities in addition the single iterative nature of the exact calculations reduces the time necessary to compile the boundary system matrices and also provides a more rapid evaluation of internal point values than do formulations using regular numerical quadrature techniques the evaluation of the domain integrations associated with biharmonic forms of the non homogeneous terms of the governing equation are transformed to an equivalent set of boundary integrals transformations of this type are introduced to avoid the difficulties of domain integration the resulting set of boundary integrals describing the domain contribution is generally evaluated numerically however some exact expressions for several commonly encountered non homogeneous terms are used several numerical solutions of the deflection of rectilinear plates using the boundary element method bem are presented and compared to existing numerical or exact solutions

derivation and analytical investigation of three direct boundary integral equations for the fundamental biharmonic problem we derive and investigate three families of direct boundary integral equations for the solution of the plane fundamental biharmonic boundary value problem these three families are fairly general so that they as special cases encompass various known and applied equations as demonstrated by giving many references to the literature we investigate the families by analytical means for a circular boundary curve where the radius is a parameter we find for all three combinations of equations i that the solution of the equations is non unique for one or more critical radius radii and ii that this lack of uniqueness can always be removed by combining the integral equations with a suitable combination of one or more supplementary condition s we conjecture how the results obtained can or cannot be generalized to other boundary curves through the concept logarithmic capacity a few published general results about uniqueness are compared with our findings

local irreducibility of tail biting trellises this paper investigates tail biting trellis realizations for linear block codes intrinsic trellis properties are used to characterize irreducibility on given intervals of the time axis it proves beneficial to always consider the trellis and its dual simultaneously a major role is played by trellis properties that amount to observability and controllability of trellis fragments of various lengths for fragments of length less than the minimum span length of the code it is shown that fragment observability and fragment controllability are equivalent to irreducibility for reducible trellises a constructive reduction procedure is presented the considerations also lead to a characterization for when the dual of a trellis allows a product factorization into elementary atomic trellises

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

evaluation of boundary integrals for plate bending the alternative to quadrature as a procedure for dealing with the integrations required in the direct boundary element method dbem is to carry out the integration analytically and code the results directly the potential benefits are efficient computer programs the avoidance of numerical instability and generally better accuracy the technique is developed in this paper serious problems arise when gauss quadrature is employed for the integration of functions which contain or are close to singularities a numerical integration approach may fail at the first stage of the analysis that is during the assembly of the discrete equations or it may fail at the subsequent stage of computing domain points near the boundary the severity of the problem is dependent both on the strength of the singularity and on geometry these points are illustrated with examples

a new differential quadrature methodology for beam analysis and the associated differential quadrature element method this paper presents a computationally efficient and an accurate new methodology in differential quadrature analysis of beam elements the methodology would overcome the difficulties in boundary conditions implementations of fourth order differential equations encountered in such problems the methodology benefited from defining the second order derivatives along the boundaries as independent degrees of freedom would enable the differential quadrature method to exactly satisfy some types of boundary conditions where by most other conventional algorithms have to be satisfied approximately the weighting coefficients employed are not exclusive and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the methods weighting coefficients by solving some typical stability deflection and frequency analysis beam problems and by comparing the results with those of exact solutions and or those of other methodologies accuracy convergency and efficiency of the methodology is asserted in order to generalize its application to large scale beam structures and to the cases with the discontinuity in loading conditions and geometry a new one dimensional differential quadrature element method formulation is presented and implemented

simply supported plates by the boundary integral equation method plates governed by kirchhoff s equation have been analysed by the boundary integral equation method using the fundamental solution of the biharmonic equation in the case of supported plates the boundary conditions permit the uncoupling of the field equation into two harmonic equations that originate due to the nature of the fundamental solution easier integration kernels and a simpler system of equations the calculation of bending and twisting moments and transverse shear force can be formed combining derivatives of the integral equation which defines the expression of the deflection on any point of the plate the uncoupling of the biharmonic equation into two poisson s equations involves the discretization of the domain of the studied problems nevertheless the unknown quantity of the problem does not appear in the domain integrations for which a refined discretization is unnecessary in the paper however a numerical alternative is considered to express the domain integral by means of boundary integrals in this way we need only discretize the boundary of the plate making it necessary to solve a supplementary system of equations in order to calculate the coefficients of the approximation carried out

on the bcjr trellis for linear block codes in this semi tutorial paper we will investigate the computational complexity of an abstract version of the viterbi algorithm on a trellis and show that if the trellis has e edges the complexity of the viterbi algorithm is spl theta e this result suggests that the best trellis representation for a given linear block code is the one with the fewest edges we will then show that among all trellises that represent a given code the original trellis introduced by bahl cocke jelinek and raviv in 1974 and later rediscovered by wolf 1978 massey 1978 and forney 1988 uniquely minimizes the edge count as well as several other figures of merit following forney and kschischang and sorokine 1995 we will also discuss trellis oriented or minimal span generator matrices which facilitate the calculation of the size of the bcjr trellis as well as the actual construction of it

application of a new differential quadrature methodology for free vibration analysis of plates a new methodology is introduced in the differential quadrature dq analysis of plate problems the proposed approach is distinct from other dq methods by employing the multiple boundary conditions in a different manner for structural and plate problems the methodology employs the displacement within the domain as the only degree of freedom whereas along the boundaries the displacements as well as the second derivatives of the displacements with respect to the co ordinate variable normal to the boundary in the computational domain are considered as the degrees of freedom for the problem employing such a procedure would facilitate the boundary conditions to be implemented exactly and conveniently in order to demonstrate the capability of the new methodology all cases of free vibration analysis of rectangular isotropic plates in which the conventional dq methods have had some sort of difficulty to arrive at a converged or accurate solution are carried out excellent convergence behaviour and accuracy in comparison with exact results and or results obtained by other approximate methods were obtained the analogous dq formulation for a general rectangular plate is derived and for each individual boundary condition the general format for imposing the given conditions is devised it must be emphasized that the computational efforts of this new methodology are not more than for the conventional differential quadrature methods copyright 2002 john wiley sons ltd

on integral transforms whose kernels are solutions of singular sturm liouville problems on etudie des transformees integrales du type f x 0 f s x s d ou x s est la solution du probleme de sturm liouville y s 2 q x y 0 0 x avec y 0 cos y 0 sin 0 y x est bornee a l infini et d est la mesure spectrale

unifying views of tail biting trellis constructions for linear block codes in this paper we present new ways of describing and constructing linear tail biting trellises for block codes we extend the well known bahl cocke jelinek raviv bcjr construction for conventional trellises to tail biting trellises the bcjr like labeling scheme yields a simple specification for the tail biting trellis for the dual code with the dual trellis having the same state complexity profile as that of the primal code finally we show that the algebraic specification of forney for state spaces of conventional trellises has a natural extension to tail biting trellises

degenerate scales for boundary value problems in anisotropic elasticity abstract degenerate scales usually refer to a size effect which causes non unique solutions of boundary integral equations for certain type of boundary value problems with a unique solution they are closely connected to the presence of a logarithmic function in the integral kernel of the single layer potential operator the equations of the elasticity theory provide one of the known application fields where degenerate scales appear the paper discusses conditions and formula for controlling and detection of the degenerate scales in the case of fully anisotropic analysis no restrictions are considered for the material only the loading should cause two dimensional deformation of the anisotropic body a technique for the evaluation of the degenerate scales is discussed and tested the examples provide results of special simple cases and demonstrate suitability of the proposed technique in relation to calculation of degenerate scales by numerical solution of pertinent boundary integral equation by the boundary element method

a new numerical method for the analysis of anisotropic thin plate bending problems abstract a new method is presented for the analysis of anisotropic thin plate bending problems this method appears to enjoy several advantages over other numerical methods for linear problems in concept the present method is quite simple using the influence function for an infinite plate of the same material the solution to the problem of interest is expressed as the superposition of the effect of the actual lateral load plus 2n unknown point loads located outside the region occupied by the plate these 2n loads are then determined through imposition of the boundary conditions at n selected locations an interesting numerical question arises regarding the selection of the 2n external points it is shown that proper distribution of these points leads to excellent results with minimal computer effort several example problems are presented demonstrating the ability of the method to deal with difficult geometries and boundary conditions and with material anisotropy

degenerate scale problem when solving laplace s equation by bem and its treatment in this paper laplace problems are solved by using the dual boundary element method bem it is found that a degenerate scale problem occurs if the conventional bem is used in this case the influence matrix is rank deficient and numerical results become unstable both the circular and elliptical bars are studied analytically in the continuous system in the discrete system the fredholm alternative theorem in conjunction with the svd singular value decomposition updating documents is employed to sort out the spurious mode which causes the numerical instability three regularization techniques method of adding a rigid body mode hypersingular formulation and cheef combined helmholtz exterior integral equation formulation concept are employed to deal with the rank deficiency problem the addition of a rigid body term c in the fundamental solution is proved to shift the original degenerate scale to a new degenerate scale by a factor e c the torsion rigidities are obtained and compared with analytical solutions numerical examples including elliptical square and triangular bars were demonstrated to show the failure of conventional bem in case of the degenerate scale after employing the three regularization techniques the accuracy of the proposed approaches is achieved copyright 2004 john wiley sons ltd

asymptotic expansions of some integral transforms by using generalized functions the technique devised by wong to derive the asymptotic expansions of multiple fourier transforms by using the theory of schwartz distributions is extended to a large class of integral transforms the extension requires establishing a general procedure to extend these integral transforms to generalized functions wong s technique is then applied to some of these integral transforms to obtain their asymptotic expansions this class of integral transforms encompasses among others the laplace the airy the k and the hankel transforms

an integral equation method for the solution of singular slow flow problems a biharmonic boundary integral equation bbie method is used to solve a two dimensional contained viscous flow problem in order to achieve a greater accuracy than is usually possible in this type of method analytic expressions are used for the piecewise integration of all the kernel functions rather than the more time consuming method of gaussian quadrature

proof of a conjecture of mceliece regarding the expansion index of the minimal trellis we prove a conjecture of mceliece establishing that for each fixed order of positions of a linear code c the minimal trellis minimizes the quantity e v 1 where e and v stand for the number of edges and vertices in the trellis respectively as a consequence it follows that the minimal trellis uniquely minimizes the total number of operations required for viterbi decoding of a given code moreover we show that these results extend to the general class of rectangular codes namely the class of codes that admit a biproper trellis presentation which includes all group codes and many other useful nonlinear codes

linear tail biting trellises characteristic generators and the bcjr construction this paper investigates the constructions of tail biting trellises for linear block codes as introduced by koetter and vardy 2003 and nori and shankar 2006 for a given code the sets of characteristic generators are defined slightly more generally than by koetter and vardy in particular they are not uniquely determined by the code the effect of the choice of characteristic generators on the resulting product trellises called kv trellises is discussed in detail it is shown that each kv trellis is a span based bcjr trellis and that the latter are always nonmergeable finally a duality conjecture posed by koetter and vardy is addressed by making use of a dualization technique of bcjr trellises the conjecture is proven for minimal trellises

boundary element analysis of cracks this paper presents a boundary element formulation that can be used for traction free or pressurized central edge or branch cracks the problems associated with the evaluation of integrals containing higher order singularities which have forced many researchers to modify the boundary integral equations are overcome in this paper this permits the use of traction boundary conditions with no modification or addition to the number of unknowns comparison of results for conforming and non conforming elements in modeling of cracks reveals that the oscillation in stresses near the crack tip for non conforming elements used in the past makes the stress intensity factor dependent on the points used in its calculation stress intensity factors are calculated using three different methods numerical results for central edge and branch cracks validate the ideas presented in this paper

an extension of the biharmonic boundary integral method to free surface flow in channels abstract the biharmonic boundary integral solution of two dimensional creeping flow of an incompressible newtonian fluid is extended to problems with free surfaces iterative construction of the free surface with the normal stress condition is achieved with a shooting method that is most appropriate for thin films and menisci of widely varying curvature a continuation scheme is also introduced to systematically construct the solution as a function of a given parameter these new techniques combined with the known storage and computational advantages of the biharmonic boundary integral method allow construction of difficult free surfaces we demonstrate this by solving the bretherton problem of a two dimensional air bubble traveling in a channel agreement with asymptotic theory and the finite difference method is shown other problems on formation and transport of bubbles in channels are also tackled